We should repeal Libnetz's law!
Seth Russell
Libnetz legislated that two symbols (A and B) point to the
same thing when one can be substituted for the other in a
statements without changing the truth of the statements.
These were not his exact words, I am currently attempting
to find the exact words of the law (uninterperted by
history) perhaps someone might provide me a www pointer.
Now let's assume we have a real something for A and B to
refer to, to symbolize, to point to and let us call that
thing *T* . Let's assume that we have three true
statements S, S', and P and that S contains the term A, S'
contains the term B, and that P contains the term B. Now
let us assume that within the system S S' we can prove
that A = B, and that the system S S' is very consistent.
Libnitz's law works nicely in the S S' system. We can
substitute A for B and visa versa between S and S' and
always know that S or S' are still talking about *T* and
that they will always be true. Now the statement P is
still talking about *T* because I told you that, it was
given: P contains the term B and B points to *T*. But
let me tell you something more about P, it is talking
about *T* from a totally different point of view. Now can
we apply Libnitz's law and substitute A for B in P just
because we have proven A = B ? I think not.
In short we cannot apply Libnetz's law wily nily, but must
apply it being sensitive to the context of the symbols and
their point of view on reality. I realize that in terms
of modern logic and mathematics I am saying nothing new.
But there are those among us who have not updated their
thinking since the original legislation was enacted, and
should be aware of this loophole.
Your comments and criticism of this "logic" would be
greatly appreciated.
--
Seth
See "Bozo's Conjecture" at
http://www.clickshop.com/ai/conjecture.htm
And then on to the AI Jump List ...
Neil Rickert
Seth Russell <seth...@clickshop.com> writes:
>Libnetz legislated that two symbols (A and B) point to the
>same thing when one can be substituted for the other in a
>statements without changing the truth of the statements.
>These were not his exact words,
I expect he use German.
In any case, the proper way to use logic is to first form a
mathematical model, use logic in the model, and then reinterpret the
model. It is generally a mistake to use logic with natural
language. And if you do it as I suggest, and if you do the
mathematical modelling properly, Leibniz's law never poses any
problems.
David Longley
In article <359D6DA6...@clickshop.com>
seth...@clickshop.com "Seth Russell" writes:
> Libnetz legislated that two symbols (A and B) point to the
> same thing when one can be substituted for the other in a
> statements without changing the truth of the statements.
> These were not his exact words, I am currently attempting
> to find the exact words of the law (uninterperted by
> history) perhaps someone might provide me a www pointer.
How about "Fragments" (rapidly becomming the source for most of
your posts)
"..the basic axiom of valid inference, namely Leibniz's Law: for any
objects x and y, if x is identical to y, then if x has a certain
property F, so does y. Symbolically: (x)(y)[(x=y) (Fx Fy)]. This is
the indiscernibility of identicals upon which all inference is
premised. ("Things are the same as each other, of which one can be
substituted for the other without loss of truth" - [Eadam sunt, quorum
unum potest substitui alteri salva veritate].
'...it is useless to suggest, as some logicians have done,
that the variable x may take as its values intensions of some
sort. For if we admit intensions as possible values of our
variables, we must abandon the principle of the
indiscernibility of identicals, and then, because we have no
clear criterion of identity, we shall be unable to say what
we want to say about extensions.'
Problems of Intensionality
W. Kneale and M Kneale (1962)
The Development of Logic p.617
Yes.... Leibniz's Law can not be relied on within intensional
contexts - the point is made very clearly within "Fragments"..
--
David Longley (check end reply line #)
Longley Consulting London, UK
Behaviour Assessment & Profiling Technology,
Research, Data Analysis and Training Services,
Small IT Systems http://www.longley.demon.co.uk
JRStern
On Fri, 03 Jul 1998 16:47:51 -0700, Seth Russell
<seth...@clickshop.com> wrote:
>In short we cannot apply Libnetz's law wily nily, but must
>apply it being sensitive to the context of the symbols and
>their point of view on reality.
Yes, this is known.
As to "Libnetz's law", you might start with the spelling of his name.
Blackwell's "A Companion to Metaphysics" identifies (!) "Leibniz's
Law" with the "identity of indiscernibles", which it differentiates
from "salve veritate", which is what it seems you have in mind. I'm
not enough of a Leibniz scholar to interpret the differences here.
Joshua Stern
JRS...@gte.net
David Longley
I've seen this too (and in other places too) ..., but it is moot.
David Longley
In article <6nk732$m...@ux.cs.niu.edu> ric...@cs.niu.edu "Neil Rickert" writes:
> Seth Russell <seth...@clickshop.com> writes:
>
> >Libnetz legislated that two symbols (A and B) point to the
> >same thing when one can be substituted for the other in a
> >statements without changing the truth of the statements.
> >These were not his exact words,
>
> I expect he use German.
>
> In any case, the proper way to use logic is to first form a
> mathematical model, use logic in the model, and then reinterpret the
> model. It is generally a mistake to use logic with natural
> language. And if you do it as I suggest, and if you do the
> mathematical modelling properly, Leibniz's law never poses any
> problems.
>
>
You miss the point.
The point is that substitution and quantification are a sine qua
non for deductive inference. But one can not substitute
identicals within contexts of propositional attitude (or other
intensional contexts), at least not reliably - this renders
inference in non extensional contexts unreliable.
To say "It is generally a mistake to use logic with natural
language. And if you do it as I suggest, and if you do the
mathematical modelling properly, Leibniz's law never poses any
problems." is just to ignore the problem and say that if you
stick to extensional contexts the problem doesn't arise - well of
course. But the empirical fact is that people *do* apply it in
non-extensional contexts, ie in the contexts of propositional
attitude such as belief and desire - ie within the context of
folk psychological language/judgement.
To do otherwise one has to, I have said, adopt the extensional
stance with respect to behaviour, eschewing intensional
heuristics. The work I have summarised in "Fragments" surveys the
relevant literature so that one can see the extent to which it
*is* an empirical matter.
One has to substitute the science of behaviour for folk
psychology, and to do that one has to train to use the technology
of the behavioural scientist, to speak his language - just as one
has to learn to speak the language of any other science if one is
to be able to practice it - one has to learn how to use the
predicates of the discipline, not just the language of logic, and
one has to learn to do this in place of natural folk
psychological idioms.
Jim Balter
Seth Russell wrote:
>
> Libnetz legislated that two symbols (A and B) point to the
> same thing when one can be substituted for the other in a
There seems to be a word missing here.
> statements without changing the truth of the statements.
I don't know about Libnetz, but Leibniz said something to the
effect that, if X and Y share all the same properties, then X = Y.
> These were not his exact words, I am currently attempting
> to find the exact words of the law (uninterperted by
> history) perhaps someone might provide me a www pointer.
Try http://setis.library.usyd.edu.au/stanford/archives/fall1997/entries/identity-indiscernible/
> Now let's assume we have a real something for A and B to
> refer to, to symbolize, to point to and let us call that
> thing *T* . Let's assume that we have three true
> statements S, S', and P and that S contains the term A, S'
> contains the term B, and that P contains the term B. Now
> let us assume that within the system S S' we can prove
> that A = B, and that the system S S' is very consistent.
As opposed to only somewhat consistent? In any case,
Since S and S' are both stipulated to be true, they can't be inconsistent (unless the system in which the stipulation is
made is inconsistent, but let's not get into that).
> Libnitz's law works nicely in the S S' system. We can
> substitute A for B and visa versa between S and S' and
> always know that S or S' are still talking about *T* and
> that they will always be true. Now the statement P is
> still talking about *T* because I told you that, it was
> given: P contains the term B and B points to *T*. But
> let me tell you something more about P, it is talking
> about *T* from a totally different point of view.
> Now can we apply Libnitz's law and substitute A for B in P just
> because we have proven A = B ? I think not.
You've mixed Leibniz' law with its converse. Leibniz' law, as you
stated it, is that,
*if* anything you can say about A you can also say about B, and v.v.,
*then* A = B.
Also, it would help to give an example or *some* reason to support
your "I think not"; "I think not" is not the most cogent form of
argument. An example of the failure of the converse of Leibniz'
law is "Oedipus knows that his wife is Jocasta. Jocasta is
Oedipus' mother. Oedipus knows that his wife is his mother."
> In short we cannot apply Libnetz's law wily nily,
As Longleybot has loopforever(said), you can't apply Leibniz'
law in intensional contexts.
> but must
> apply it being sensitive to the context of the symbols and
> their point of view on reality. I realize that in terms
> of modern logic and mathematics I am saying nothing new.
In those terms, I think saying "symbols and their point of view on
reality" is something new. Just what is the point of view of a symbol
on reality, in terms of modern logic and mathematics, or any other
terms?
> But there are those among us who have not updated their
> thinking since the original legislation was enacted, and
> should be aware of this loophole.
And who are they, and what makes you think so?
> Your comments and criticism of this "logic" would be
> greatly appreciated.
Until you can at least distinguish a statement from its converse,
you are going to have trouble with anything involving logic.
--
<J Q B>
David Longley
In article <359DFC21...@sandpiper.net>
j...@sandpiper.net "Jim Balter" writes:
>
> As Longleybot has loopforever(said), you can't apply Leibniz'
> law in intensional contexts.
Not quite all I've said though - for examople, the covers of "A
System Specification for Profiling Behaviour" have two equations
on them (aprt form the standard logical symbols) - one is
Leibniz's Law and the other the equation for (logistic)
regression.
It's the fact that the former fails in psychological
(intensional) contexts which makes the latter (and other (linear)
methods so useful - that I claim is worth paying attention to.
That, and the *further* implications I draw in "Fragments"...One
of which is the real status and nature of AI.
http://www.longley.demon.co.uk/Frag.htm
http://www.longley.demon.co.uk/Fragjn97.pdf
Ray Scanlon
David Longley wrote in message <899539...@longley.demon.co.uk>...
>
>One has to substitute the science of behaviour for folk
>psychology, and to do that one has to train to use the technology
>of the behavioural scientist, to speak his language - just as one
>has to learn to speak the language of any other science if one is
>to be able to practice it - one has to learn how to use the
>predicates of the discipline, not just the language of logic, and
>one has to learn to do this in place of natural folk
>psychological idioms.
There is no science of behavior except the science of molecular biology; all
psychology is folk psychology. Behaviorism is played out and the babblers
have gone on to cognitive "science".
Ray
If you are interested in the thinking brain look at
www.wsg.net/~rscanlon/brain.html
David Longley
>
> David Longley wrote in message <899539...@longley.demon.co.uk>...
> >
> >One has to substitute the science of behaviour for folk
> >psychology, and to do that one has to train to use the technology
> >of the behavioural scientist, to speak his language - just as one
> >has to learn to speak the language of any other science if one is
> >to be able to practice it - one has to learn how to use the
> >predicates of the discipline, not just the language of logic, and
> >one has to learn to do this in place of natural folk
> >psychological idioms.
>
>
> There is no science of behavior except the science of molecular biology; all
> psychology is folk psychology. Behaviorism is played out and the babblers
> have gone on to cognitive "science".
>
Not true - In the way you are talking, there are *sciences* of
behaviour in a number of contexts, it's a matter of
specialisation.
My post graduate training was in one of these - neuroscience, my
applied work another. All of it is an application of "Artificial
Intelligence", and bringing that point home is a matter of the
philosophy of Artificial Intelligence or, more generally, the
philosophy of science.
oho...@my-dejanews.com
In article <359D6DA6...@clickshop.com>,
Seth Russell <seth...@clickshop.com> wrote:
>
> Libnetz legislated that two symbols (A and B) point to the
> same thing when one can be substituted for the other in a
> to find the exact words of the law (uninterperted by
> history) perhaps someone might provide me a www pointer.
> refer to, to symbolize, to point to and let us call that
> thing *T* . Let's assume that we have three true
> statements S, S', and P and that S contains the term A, S'
> contains the term B, and that P contains the term B. Now
> let us assume that within the system S S' we can prove
> that A = B, and that the system S S' is very consistent.
> substitute A for B and visa versa between S and S' and
> always know that S or S' are still talking about *T* and
> that they will always be true. Now the statement P is
> still talking about *T* because I told you that, it was
> given: P contains the term B and B points to *T*. But
> let me tell you something more about P, it is talking
> about *T* from a totally different point of view. Now can
> we apply Libnitz's law and substitute A for B in P just
> because we have proven A = B ? I think not.
Leibnitz's law, IMHO, holds in any context. You have not
demonstrated a failue by your example. Quine claimed to have
found a failure in modal contexts. His argument was;
1. The number of planets is 9
2. It is necessary that (9>7).
Therefore
3. It is necessary that (the number of planets >7).
This argument is invalid (see: A. Smullyan 1948), the number
of planets is a descriptive term and as such according to Russell's
description theory; It's necessary that (the number of planets >7),
does not follow as an instance of Leibnitz's law but (The number
of planets is necessarily greater than 7) does follow and is an
instance.
(The number of planets = 9) and (Necessarily(9 is greater than7)) implies
(The number of planets is necessarily greater than 7). is valid.
(the x such that (x numbers the planets))=9, translates to
1a. EyAx(x=y<->(x numbers the planets).&(y=9)).
2a. [](9>7).
Therefore
3a. EyAx(x=y<->(x numbers the planets.&[](y>7)). is valid.
Leibnitz's law is not violated in modal or any other context.
For names (x ([]>) y) is the same as [](x>y) but not so for
descriptions. (The x such that Fx) []> y) is not the same as
[](the x such that Fx) > y).
Owen Holden
> In short we cannot apply Libnetz's law wily nily, but must
> apply it being sensitive to the context of the symbols and
> their point of view on reality. I realize that in terms
> of modern logic and mathematics I am saying nothing new.
> But there are those among us who have not updated their
> thinking since the original legislation was enacted, and
> should be aware of this loophole.
>
> Your comments and criticism of this "logic" would be
> greatly appreciated.
>
> --
> Seth
> See "Bozo's Conjecture" at
> http://www.clickshop.com/ai/conjecture.htm
> And then on to the AI Jump List ...
-----== Posted via Deja News, The Leader in Internet Discussion ==-----
http://www.dejanews.com/rg_mkgrp.xp Create Your Own Free Member Forum
Seth Russell
Jim Balter wrote:
> Seth Russell wrote:
> >
> > Jim Balter wrote:
> >
> > > Seth Russell wrote:
> > > >
> > > > Libnetz legislated that two symbols (A and B) point to the
> > > > same thing when one can be substituted for the other in a
> > >
> > > There seems to be a word missing here.
> > >
> > > > statements without changing the truth of the statements.
> >
> > Nothing missing, just a typo adding an extra "a", because I had originally
> wrote
>
> Well, something is missing, because it has to be true of *all*
> statements; if it isn't true of some statement, then there is a
> discernable difference between A and B.
If you are a mathematician playing in your mind or even on a piece of paper, you
can make statements like: "it has to be true of *all* statements" and have it
make a kind of sense. In other words you are allowed to take God's point of
view. Most mathematicians have been able to do that and get away with it,
because who can challenge them, so holding them to consistent reasoning is all
we can hope for. When we try to put those methods into the computer, we run
across the inability for us (or the computer algorithms) to take God's point of
view. We can start with a set of consistent statements with variables which can
be shuffled around, but then our robust ai must apply those statements and
variables in new situations (contexts) where we have not yet proven their
consistency. We may be testing the discernability of A from B, we may be
testing the validity of the statements, we may be testing the logical tools, we
may be testing the validity of using A and B in the new context, or (as you
pointed out) we may be testing the stupidity of the philosopher who designed the
system. From the point of view of this dialogue all of those are valid aspects
to question. All we ever really know in any given situation is the degree of
the match - we hit the point, or we missed it by just a little, or we missed it
by a mile.
> Um, so you believe it; so what? Liebniz' law *still* fails in intensional
> contexts. Intensional terms do not obey the rules of deductive logic, and
> there
> is no reason why they should.
"Tom" was from Chapter 6 of Quine's Word and Object, I thought that reference
would have been enough. But I like your example better and have now diagrammed
it and do not see where Liebniz' Law fails (see other post).
> > I define a symbol as an object of a mind which represents (refers to, points
> to,
> > links to, hyperlinks to) something that may not (or may) be included in that
>
> > mind. Such a symbol is like the reflection of your face in the mirror, it
> is
> > not your face, but represents you face to you when you look at it. I have
> no
> > idea how the human mind does this, but I believe it does do it.
>
> Why do you give your beliefs such authority?
I have no choice they are all I have.
> How committed are you to this belief?
I do not commit to beliefs. If they don't match reality, or if they project a
future that I do not choose, I change them if i can.
> Will you get upset if someone doubts this belief?
No. But I reserve the right to persuade them from their doubts.
> In any case, "a symbol's point of view" still seems nonsensical -- what's the
> point of view of the reflection of your face in the mirror?
Don't know ... never been there ... but when I blink my right eye, he blinks
his left eye ... so I know the guy has a weird point of view.
> If you talk about
> it as a reflection, then you are talking about it as a separate thing, not a
> symbol
> of your face. If you talk about the mirror, then likewise.
Bear in mind this was an analogy only ... to jar the old brain pan ... not to
argue from.
> > However, for an
> > artificial mind, such a symbol can be a mathematical object which is simply
> the
> > set of predicates about a singular subject (see
> > http://clickshop.com/ai/symknow.htm ).
>
> A set of predicates is not a symbol, it is a set of predicates. There may be
> a symbol in an artificial mind that represents a set of predicates, but that's
>
> a different thing.
You cannot talk or think about anything without using symbols as I have defined
them. If you can, then by all means provide a contra example. Bear in mind
that I have provided my definition of symbol. I suggest that if my definition
doesn't match the literature (and I'm not so sure it doesn't), then you could
consider these bozonian symbols, i don't care, but let's do talk about the same
thing. The advantage of this definition is that we can apply it to human minds
as well as artificial minds. When we apply it to artificial minds, then we add
a mathematical structure that still matches the definition. If I haven't done
that, then I am in error. If so, can you see the error?
> > Now since these symbols form a hairy maze,
>
> We've gone from symbols, sets, and predicates to "hairy maze". Is this
> "hairy maze" other than a set of relationships?
No. A set of relationships *is* a "hairy maze". Every object of one predicate
is a subject of other predicates. The "hairy maze" comes from seeing a set of
predicates as a network of nodes and arrows. Hopefully if you visited the page
you will see that I am on very firm ground here.
> > one can look at reality (or whatever on is actually seeing from this
> > particular mind point) from any point (or train of points) in that maze.
> That
> > is what I meant by "the point of view of a symbol on reality". Thanks for
> > asking :)
>
> So one can pick any symbol (representing a set of predicates), and pose a
> query
> ("look at reality") and get an answer?
Yes, if the answer can be inferred from that particular symbol.
> And these answers may differ (different
> points of view)?
Yes. We are in a real mind and real minds have that texture. We are not
allowed to be inside of God's mind, because we don't know how to do it.
> That sounds like the predicates are inconsistent,
> which may pose a problem.
Well yes it certainly does pose problems - even survival problems.
> It also doesn't sound like a particular problem for
> Leibniz' law.
The problem is when to apply Leibniz's law and when to punt.
> You seem to start out with somewhat formal terms like "set" and
> "predicate", but quickly switch to less formal terms like "hairy maze" and
> "point of view", and then try to apply something formal like Leibniz' Law to
> the result. if you are going to make convincing claims about logic, I think
> you
> are going to have to express them more formally.
Set, predicate, and point of view are all mathematically sound ideas. It all
could be written up formally, but I doubt that I will be doing that, it's not my
thing. The word "hairy" is just for people to be able to picture it.
> Confusing a statement with
> its converse appears to be the most common error in "folk logic", even among
> people who pride themselve on their reasoning
With all due respect, the site you pointed me at says very distinctly: "The
converse of the Principle, x=y (F)(Fx Fy), is called the Indiscernibility of
Identicals. Sometimes the conjunction of *both* principles, rather than the
Principle by itself, is known as Leibniz's Law." [emphasis mine]. I still do
not see the importance to *my* arguments as to whether we view the matter from
the standpoint of the "Identity of Indiscernibles" or the standpoint of
"Indiscernibility of Identicals".
> Mom: Marijuana leads to heroin.
What's the difference between having a pot head and having shit for brains ?
Vesa Monisto
"That every possible position is filled once
is the Law of Continuity: that it is filled
*only* ones is added by the Identity of Indiscernibles."
Bertrand Russell
The Philosophy of Leibniz, 1900
p.54
;-)
V.M.
Jim Balter
oho...@my-dejanews.com wrote:
> Leibnitz's law, IMHO, holds in any context. You have not
> demonstrated a failue by your example. Quine claimed to have
> found a failure in modal contexts. His argument was;
>
> 1. The number of planets is 9
> 2. It is necessary that (9>7).
> Therefore
> 3. It is necessary that (the number of planets >7).
Natural language does not follow rules of logic and no one,
certainly not Quine, should expect it to.
"A hamburger is better than nothing. Nothing is better than heaven.
A hamburger is better than heaven."
In order to make logic work with natural language, you have to
translate the natural language into the language of logic,
and then apply logic. Applying logic directly to natural language
can only be done when the natural language involved directly
corresponds to its logical form; otherwise it is folly, the folly
of Quine here, of such things as Sorites arguments, and of Penrose, Searle, Chalmers, Putnam, and many others. It is also folly to
think that natural language is necessarily translatable into the
language of logic, as with McCarthy's recent thread concerning the
logic of "but". The rules governing the use of natural language,
if it is to be viewed as having rules, are complex, shifting,
and governed by human social behavior, so an exact logical translation
might require first expressing the entirety of that behavior logically,
an effectively impossible task. Certainly one cannot treat "A but B"
as a logical form like "A and B" -- the semantics of "A and B" is
primarily a truth condition, determinable solely from the truth
conditions of A and B, but the semantics of "but" have to do with
contrast. Hopefully no one expects "A contrasted with B" to have
a logical translation, nor should one expect it of "he knows X"
or expect Leibniz' Law to be applicable to that phrase any more than
it is applicable to motorists.
--
<J Q B>
Jim Balter
Seth Russell wrote:
> If you are a mathematician playing in your mind or even on a piece of paper, you
> can make statements like: "it has to be true of *all* statements" and have it
> make a kind of sense.
That's the sort of thing Leibniz' Law is -- sorry.
> view. Most mathematicians have been able to do that and get away with it,
> because who can challenge them, so holding them to consistent
Ah, so both scientists *and* mathematicians have been "getting away"
with things. Have you considered therapy for this paranoia?
> > Um, so you believe it; so what? Liebniz' law *still* fails in intensional
> > contexts. Intensional terms do not obey the rules of deductive logic, and
> > there
> > is no reason why they should.
>
> "Tom" was from Chapter 6 of Quine's Word and Object, I thought that reference
> would have been enough. But I like your example better and have now diagrammed
> it and do not see where Liebniz' Law fails (see other post).
So Oedipus *did* know he was married to his mother?
> > Why do you give your beliefs such authority?
>
> I have no choice they are all I have.
How very sad.
> > Confusing a statement with
> > its converse appears to be the most common error in "folk logic", even among
> > people who pride themselve on their reasoning
>
> With all due respect, the site you pointed me at says very distinctly: "The
> converse of the Principle, x=y (F)(Fx Fy), is called the Indiscernibility of
> Identicals. Sometimes the conjunction of *both* principles, rather than the
> Principle by itself, is known as Leibniz's Law." [emphasis mine]. I still do
> not see the importance to *my* arguments as to whether we view the matter from
> the standpoint of the "Identity of Indiscernibles" or the standpoint of
> "Indiscernibility of Identicals".
You stated one and then used the other. I pointed out that you
had confused them, but went ahead and wrote about the one you had
actually used. The issue here isn't whether your argument goes
through -- that's another matter. The point is that, if one is
prone to such mistakes, one is bound to get into trouble.
If all you have are your beliefs, and your beliefs are derived from
this sort of confusion, then you are doomed to perpetual error.
> > Mom: Marijuana leads to heroin.
>
> What's the difference between having a pot head and having shit for brains ?
With pot, the condition is temporary.
--
<J Q B>
Seth Russell
Evidently of my posts got gobbled by the bit monster, here
is a summary of the dialogue, though sequenced slightly
differently to remove the chaff.
Jim Balter wrote:
Liebniz' law *still* fails in intensional contexts.
Intensional terms do not obey the rules of deductive
logic, and there is no reason why they should. An example
of the failure of the converse of Leibniz' law is
"Oedipus knows that his wife is Jocasta. Jocasta is
Oedipus' mother. Oedipus knows that his wife is his
mother."
Seth Russell:
I like your example better and have now diagrammed it and
do not see where Liebniz' Law fails.Jim Balter wrote:
So Oedipus *did* know he was married to his mother?
Seth Russell:
No he did not. The example is obviously dealing with
knowledge at the granularity where predicates themselves
have identity (can be pointed out). As can be seen from
the SVO diagram ( http://clickshop.com/ai/oedipus.jpg ),
Oedipus knows one predicate, but there is no implication
of knowledge of every existing predicate of the subject
which is the object of what he knew. So if Oedipus knows
he was married to his mother, it is not by virtue of the
first two sentences. Could someone point out the failure
of Leibniz's law in the diagram?
Anyone interested in representing symbolic knowledge with
SVO diagrams can find a short presentation at
http://clickshop.com/ai/symknow.htm .
Neil Rickert
Jim Balter <j...@sandpiper.net> writes:
> Applying logic directly to natural language
>can only be done when the natural language involved directly
>corresponds to its logical form; otherwise it is folly, the folly
>of Quine here, of such things as Sorites arguments, and of Penrose,
>Searle, Chalmers, Putnam, and many others. It is also folly to
>think that natural language is necessarily translatable into the
>language of logic, as with McCarthy's recent thread concerning the
>logic of "but".
Well said.
Jim Balter
Seth Russell wrote:
> Jim Balter wrote:
>
> Liebniz' law *still* fails in intensional contexts.
> Intensional terms do not obey the rules of deductive
> logic, and there is no reason why they should. An example
> of the failure of the converse of Leibniz' law is
> "Oedipus knows that his wife is Jocasta. Jocasta is
> Oedipus' mother. Oedipus knows that his wife is his
> mother."
>
> Seth Russell:
>
> I like your example better and have now diagrammed it and
> do not see where Liebniz' Law fails.Jim Balter wrote:
>
> So Oedipus *did* know he was married to his mother?
>
> Seth Russell:
>
> No he did not. The example is obviously dealing with
> knowledge at the granularity where predicates themselves
> have identity (can be pointed out). As can be seen from
> the SVO diagram ( http://clickshop.com/ai/oedipus.jpg ),
Your diagram seems to claim that Oedipus is Jocasta's wife.
Since Jocasta is both Oedipus' mother and his wife,
the two arrows between Jocasta and Oedipus should both point
the same way.
> Oedipus knows one predicate, but there is no implication
> of knowledge of every existing predicate of the subject
> which is the object of what he knew.
If the Indiscernability of Identicals holds, then there is the
implication that he knows the specific predicate mother_of(Oedipus).
You seem to be forgetting that the applicability of the Indiscernability
of Identicals is what's at issue.
> So if Oedipus knows
> he was married to his mother, it is not by virtue of the
> first two sentences.
No, it is (or would be, if it held) by virtue of the Indiscernability of
Identicals, which you seem to be forgetting is at issue.
> Could someone point out the failure
> of Leibniz's law in the diagram?
Assuming that the Indiscernability of Identicals applies to
my example, then
Oedipus_knows(wife_of_Oedipus = Jocasta) AND Jocasta = mother_of_Oedipus -> Oedipus_knows(wife_of_Oedipus = mother_of_Oedipus)
If Oedipus doesn't know that his wife was his mother then,
by modus tollens, the assumption that the Indiscernability of Identicals
applies is false.
If you want to claim that the Indiscernability
of Identicals applies to your diagram, then you need to show how
to apply it, then apply it, then we can look and see whether
the result contradicts our knowledge that Oedipus did not know that
his wife was his mother. Just drawing a diagram representing
what we do know and not bothering to apply the law is pointless;
of course the diagram looks fine.
This thread is more than a little strange. You started it with a
title that says Leibniz' Law should be repealed, and claimed
that it (it's converse, actually, which is not Leibniz' Law as that
term is normally understood, even if "Leibniz' Law" is sometimes
treated as including the converse) fails because of "point of view" of a
"symbol". Your justification was "I think not". I suggested that isn't
much of an argument, and provided an example of a common sort
involving knowledge (a similar example has been given in c.a.p
before, of a thief who is not known to be someone's uncle) where
Leibniz' Law clearly fails. You are now arguing that it doesn't.
How very odd.
Ohm's Law fails for superconductors, but that's no reason to repeal it.
One just needs to understand what contexts it applies in.
--
<J Q B>
Bill Taylor
|> "That every possible position is filled once
|> is the Law of Continuity: that it is filled
|> *only* ones is added by the Identity of Indiscernibles."
-------------------------------------------------------------------------------
Bill Taylor W.Ta...@math.canterbury.ac.nz
-------------------------------------------------------------------------------
Identity of indiscernibles: x = y <==> (P) Px <=> Py
Identity of indiscriminables: P = Q <==> (x) Px <=> Qx
-------------------------------------------------------------------------------
oho...@my-dejanews.com
In article <359FFED9...@sandpiper.net>,
Jim Balter <j...@sandpiper.net> wrote:
>
> oho...@my-dejanews.com wrote:
>
> > Leibnitz's law, IMHO, holds in any context. You have not
> > demonstrated a failue by your example. Quine claimed to have
> > found a failure in modal contexts. His argument was;
> >
> > 1. The number of planets is 9
> > 2. It is necessary that (9>7).
> > Therefore
> > 3. It is necessary that (the number of planets >7).
>
> Natural language does not follow rules of logic and no one,
> certainly not Quine, should expect it to.
>
> "A hamburger is better than nothing. Nothing is better than heaven.
> A hamburger is better than heaven."
I don't think anyone would consider the above (hamburger thing)
as a sensible argument. Ever since Aristotle, it has been clear
that language has to be more formal than natural language to deal
with logic. Quine's use of Leibnitz's law is not as trivial as
not formalizing language within his argument. He wants to say
that (the x such that Fx)=y->G(the x such that Fx)<->Gy, for
every G, fails in formalized modal context. Smullyan, and others
have pointed out that Quine is wrong....that was my point.
Owen
> In order to make logic work with natural language, you have to
> translate the natural language into the language of logic,
> and then apply logic. Applying logic directly to natural language
> can only be done when the natural language involved directly
> corresponds to its logical form; otherwise it is folly, the folly
> of Quine here, of such things as Sorites arguments, and of Penrose, Searle,
Chalmers, Putnam, and many others. It is also folly to
> think that natural language is necessarily translatable into the
> language of logic, as with McCarthy's recent thread concerning the
> logic of "but". The rules governing the use of natural language,
> if it is to be viewed as having rules, are complex, shifting,
> and governed by human social behavior, so an exact logical translation
> might require first expressing the entirety of that behavior logically,
> an effectively impossible task. Certainly one cannot treat "A but B"
> as a logical form like "A and B" -- the semantics of "A and B" is
> primarily a truth condition, determinable solely from the truth
> conditions of A and B, but the semantics of "but" have to do with
> contrast. Hopefully no one expects "A contrasted with B" to have
> a logical translation, nor should one expect it of "he knows X"
> or expect Leibniz' Law to be applicable to that phrase any more than
> it is applicable to motorists.
>
> --
> <J Q B>
>
Jim Balter
Neil Rickert wrote:
>
> Jim Balter <j...@sandpiper.net> writes:
>
> > Applying logic directly to natural language
> >can only be done when the natural language involved directly
> >corresponds to its logical form; otherwise it is folly, the folly
> >of Quine here, of such things as Sorites arguments, and of Penrose,
> >Searle, Chalmers, Putnam, and many others. It is also folly to
> >think that natural language is necessarily translatable into the
> >language of logic, as with McCarthy's recent thread concerning the
> >logic of "but".
>
Well, my views on the nature of natural language have been greatly
influenced by your posts on the subject. :-)
In fact, when I wrote "The rules governing the use of natural language,
if it is to be viewed as having rules", I added the conditional
particularly to avoid your objection that natural language
does not have a grammar.
--
<J Q B>
Jim Balter
Jim Balter wrote:
>
> Seth Russell wrote:
> > Could someone point out the failure
> > of Leibniz's law in the diagram?
> If you want to claim that the Indiscernability
> of Identicals applies to your diagram, then you need to show how
> to apply it, then apply it, then we can look and see whether
> the result contradicts our knowledge that Oedipus did not know that
> his wife was his mother. Just drawing a diagram representing
> what we do know and not bothering to apply the law is pointless;
> of course the diagram looks fine.
Here, let me save you the trouble of coming to grips with such a
difficult task, by applying the Indiscernability
of Identicals to your diagram by replacing "Jocasta" with the
identical "Oedipus' mother":
--------------------
------| Oedipus |
| --------------------
[knows that] ^ ^
| | |
-->[is wife of] [is mother of]
| |
---------------------
| Oedipus' mother |
---------------------
As you can see, the [is wife of] and [is mother of]
predicates are still just fine, but the [knows that]
predicate went from true to false upon the substitution.
If I need to explain this even further, be sure to let me know.
I'm hoping that, with enough demonstrations of simple difficulties with
logic, such as confusion between a statement and its converse,
and failure to see how to apply Leibniz' Law to your diagram
and how it fails upon doing so, you will begin to give up a bit of
your certainty about the evils of mathematicians, scientists,
empiricists, those who "doubt belief", etc., etc. since these conclusions of yours just may -- perish the thought -- be a result
of errors in very complex trains of logic.
--
<J Q B>
Vesa Monisto
Fine. I'll just correct my typo in the quote and direct the 'graphs'
to have the cases (with conventional names).
|> "That every possible position is filled once
|> is the Law of Continuity: that it is filled *only* once
|> is added by the Identity of Indiscernibles." (B. Russell)
>-------------------------------------------------------------------------------
> Bill Taylor W.Ta...@math.canterbury.ac.nz
>-------------------------------------------------------------------------------
> Identity of indiscernibles: x = y <==> (P) Px <=> Py
> Identity of indiscriminables: P = Q <==> (x) Px <=> Qx
>-------------------------------------------------------------------------------
Identity of indiscernibles: (P) Px <=> Py ==> x = y
Indiscernibility of identicals: x = y ==> (P) Px <=> Py
Identity of indiscriminables: (x) Px <=> Qx ==> P = Q
Indiscriminability of identicals: P = Q ==> (x) Px <=> Qx
Sat sapienti.
V.M.
Bloxy's
In article <359F356F...@sandpiper.net>, Jim Balter <j...@sandpiper.net> wrote:
>Seth Russell wrote:
>>
>> Jim Balter wrote:
>>
>
>> > An example of the failure of the converse of Leibniz'
>> > law is "Oedipus knows that his wife is Jocasta. Jocasta is
>> > Oedipus' mother. Oedipus knows that his wife is his mother."
First of all, when we attribute a name or a lable, such as wife, to a person
what we are doing is substituting the human being with one of its attributes.
When we say wife, did we completely describe that woman?
When we say Jocasta, did we describe that woman?
Now, we take a human being, substitute it first with wife, ignoring all
other aspects, then with an ASCII string of her name, then we say that
the same ASCII string happens to be a mother at the same time.
Don't you see the problem already?
That woman has many characteristics. We take one, reduce a woman to it
and then equate one falsity to another, expecting to get truthness out of it.
And we finally come to an absurd: the same entity happens to have 3 different
things equated to it, wife, mother and the name.
First of all, it is redundant, if that substitution is to be even considered.
The same thing can not have 3 different lables.
We are just fabricating a new prejudice, when we do that.
Now, is it valid to conclude that every woman that is a wife is a mother
to the same person?
Cause that is what we did on the first place.
"Oedipus knows that his wife is Jocasta.
[Incorrect. His wife has a NAME of Jocasta, as one of infinite number
of attributes]
Jocasta is Oedipus' mother.
[Incorrect. The ASCII string can not be mother.]
Oedipus knows that his wife is his mother."
[And, therefore, every wife that dude may have is his mother
at the same time, and all the wifes everybody has are all mothers
to the same individuals]
[...]
Jim Balter
Seth Russell wrote:
>
> Jim Balter wrote:
>
> > An example of the failure of the converse of Leibniz'
> > law is "Oedipus knows that his wife is Jocasta. Jocasta is
> > Oedipus' mother. Oedipus knows that his wife is his mother."
>
> http://clickshop.com/ai/oedipus.jpg . Could someone point out the
> failure of Leibniz's law in the diagram? The example is obviously
> dealing with knowledge at the granularity where predicates themselves
> Oedipus knows one predicate, but there is no implication of knowledge
> he know. So if Oedipus knows his wife is his mother, it is not by
> virtue of the first two sentences. What's the problem, have I missed
> something?
As you say, if Oedipus knows that his wife is his mother, it is not
by virtue of the first two sentences. Therefore, Leibniz' Law fails,
since it (actually, the Indiscernability of Identicals) says that, by
virtue of those two sentences, Oedipus knows that his wife is his
mother (since he knows that his wife is Jocasta and Jocasta is
identical with, and thus indiscernable from, Oedipus' mother).
--
<J Q B>
Leon Hoeneveld
Seth Russell :
>Libnetz legislated that two symbols (A and B) point to the
>same thing when one can be substituted for the other in a
>statements without changing the truth of the statements.
>
>In short we cannot apply Libnetz's law wily nily, but must
>apply it being sensitive to the context of the symbols and
>their point of view on reality. I realize that in terms
>of modern logic and mathematics I am saying nothing new.
>But there are those among us who have not updated their
>thinking since the original legislation was enacted, and
>should be aware of this loophole.
>
If A==B the symbols can be substituted for C, so that no
misunderstanding will take place.
So if P contains B and B points to *T* and if A=C and B=C in
the system SS' maybe P contains C or it might prove to be C'.
I think that a law of objects/symbols can never be a true representation.
When A->B occurs you might find the statement A+B==2*B to be true.
But is it the same as when B->A occurs? and when A+B==2*A?
You can't prove that A->B is the same proces or 'mirror'proces as B->A.
When you substitute A for B you should when A->B happens you should be aware
that it is also possible for B->A to happen again.
If you decide A=C and B=C you representate both A and B with a new
abstraction,
a symbol called C. Of course what really happens is that you decide to
process A->C
B->C at a given moment so that A->B and B->A won't happen again. That is why
the
law works within the system.
This is probably what you call a different perspective.
Regards,
Leon Hoeneveld
Anders N Weinstein
In article <359FFED9...@sandpiper.net>,
Jim Balter <j...@sandpiper.net> wrote:
>Natural language does not follow rules of logic and no one,
>certainly not Quine, should expect it to.
But all our reasoning and argumentation is done in natural
language. If there is no logic to natural language, then there
is no logic anywhere. Admittedly, FOPC may not capture everything
that is a matter of the logic in natural language.
>"A hamburger is better than nothing. Nothing is better than heaven.
>A hamburger is better than heaven."
This is a fallacy of equivocation, no matter what they language.
So what? It is true a logical language is usually rigged to
prevent ambiguity, but it does not seem to bear on the idea that
there is no logic in natural language.
>In order to make logic work with natural language, you have to
>translate the natural language into the language of logic,
>and then apply logic. Applying logic directly to natural language
But suppose T is the relation that holds between a sentence S of
natural language and a translation of it into "logic" L. Suppose |-L
expresses the relation between sentences L1 and L2 of "logic" when the
former deductively entails the latter. Then can define the relation
|-NL that holds between sentences S1, S2 of natural language when one
entails the other as holding just in case there exist translations L1
and L2 such that L1 T S1 and L2 T S2 and L1 |-L L2. This is something
akin to a change of basis -- if we simplified by considering T a
function, we could define |-NL as the composition of T, |-L, and T^-1.
But that would seem to be all you need for there to be logic in
the natural language after all. Translation into logical notation
gives expression to inference-relevant features of a proposition in,
it is hoped, a particularly perspicous way. But it does not create the
inferential relations, they are there in usage prior to formalization.
>and then apply logic. Applying logic directly to natural language
It is also folly to
>think that natural language is necessarily translatable into the
>language of logic, as with McCarthy's recent thread concerning the
If there is not translation of some piece of natural language into some
formal system of logic, that might shows the inadequacy of that system
of logic as a means of perspicously displaying the inference relevant
features of its significance. But as long as one can reason with it,
it would seem to have logical properties. At any rate, you would owe
us an explanation of what else it is doing (calling someone by name
is a use of language, but not one with logical properties, since it
does not play a role as premise or conclusion.)
>an effectively impossible task. Certainly one cannot treat "A but B"
>as a logical form like "A and B" -- the semantics of "A and B" is
>primarily a truth condition, determinable solely from the truth
>conditions of A and B, but the semantics of "but" have to do with
>contrast. Hopefully no one expects "A contrasted with B" to have
>a logical translation, nor should one expect it of "he knows X"
>or expect Leibniz' Law to be applicable to that phrase any more than
>it is applicable to motorists.
Many logicians do think that A and B captures the cognitive meaning or
truth conditions of A but B perfectly well; it is just that there are
other pragmatic dimensions to the use of words than cognitive meaning.
They must be dealt with somewhere in the account of lingustic usage,
but not necessarily with logic.
Jim Balter
Bloxy's wrote:
>
> In article <359F356F...@sandpiper.net>, Jim Balter <j...@sandpiper.net> wrote:
> >Seth Russell wrote:
> >>
> >> Jim Balter wrote:
> >>
> >
> >> > An example of the failure of the converse of Leibniz'
> >> > law is "Oedipus knows that his wife is Jocasta. Jocasta is
> >> > Oedipus' mother. Oedipus knows that his wife is his mother."
>
> what we are doing is substituting the human being with one of its attributes.
> When we say wife, did we completely describe that woman?
> When we say Jocasta, did we describe that woman?
Not at issue. "the" indicates that the attribute uniquely identifies
the person.
> Don't you see the problem already?
[confused ramblings snipped]
> Jocasta is Oedipus' mother.
>
> [Incorrect. The ASCII string can not be mother.]
Yes, I certainly see a problem when someone claims a truth to be
a falsehood.
BTW, ``"Jocasta" is Oedipus' mother'' is a claim about a "string"
(those latter are scare quotes, not string quotes).
--
<J Q B>
Jim Balter
Anders N Weinstein wrote:
>
> In article <359FFED9...@sandpiper.net>,
> Jim Balter <j...@sandpiper.net> wrote:
> >Natural language does not follow rules of logic and no one,
> >certainly not Quine, should expect it to.
>
> But all our reasoning and argumentation is done in natural
> language.
Who said otherwise? You have once again affirmed the consequent.
That logic must be expressible in natural language does not imply
that natural language must be expressible in logic.
> If there is no logic to natural language, then there
> is no logic anywhere.
See above.
> Admittedly, FOPC may not capture everything
> that is a matter of the logic in natural language.
Then nothing in natural language that is not captured by FOPC
need necessarily obey the rules of logic.
[further argumentation for the undenied consequent snipped]
--
<J Q B>
Anders N Weinstein
In article <35A12B56...@sandpiper.net>,
Jim Balter <j...@sandpiper.net> wrote:
>Anders N Weinstein wrote:
>>
>> In article <359FFED9...@sandpiper.net>,
>> Jim Balter <j...@sandpiper.net> wrote:
>> >Natural language does not follow rules of logic and no one,
>> >certainly not Quine, should expect it to.
>>
>> But all our reasoning and argumentation is done in natural
>> language.
>
>Who said otherwise? You have once again affirmed the consequent.
>That logic must be expressible in natural language does not imply
>that natural language must be expressible in logic.
Perhaps the problem is that you are taking "logic" to be synonymous
with FOPC. But I am using "logic" in the broader sense. In my sense
it may be an open question whether FOPC is the "right" logic, i.e.
whether it is an adequate formalism for codifying correct reasoning
in natural language. There are several people who claim it isn't for
various reasons.
But it is not really a sensible question for me whether there is such a
thing as logic in natural language. For there are arguments and
reasoning in natural language, and wherever one assertion follows from
or is incompatible with another, there you have logic, or so it seems
to me.
>> Admittedly, FOPC may not capture everything
>> that is a matter of the logic in natural language.
>
>Then nothing in natural language that is not captured by FOPC
>need necessarily obey the rules of logic.
As I said, in my terms that would only show that FOPC is not an
adequate formalization of the logic of natural language. But again,
I was not presupposing the identification of "logic" with FOPC.
Jim Balter
Anders N Weinstein wrote:
>
> In article <35A12B56...@sandpiper.net>,
> Jim Balter <j...@sandpiper.net> wrote:
> >Anders N Weinstein wrote:
> >>
> >> In article <359FFED9...@sandpiper.net>,
> >> Jim Balter <j...@sandpiper.net> wrote:
> >> >Natural language does not follow rules of logic and no one,
> >> >certainly not Quine, should expect it to.
> >>
> >> But all our reasoning and argumentation is done in natural
> >> language.
> >
> >Who said otherwise? You have once again affirmed the consequent.
> >That logic must be expressible in natural language does not imply
> >that natural language must be expressible in logic.
>
> Perhaps the problem is that you are taking "logic" to be synonymous
> with FOPC.
No, the problem is that you affirmed the consequent.
> But I am using "logic" in the broader sense. In my sense
> it may be an open question whether FOPC is the "right" logic, i.e.
> whether it is an adequate formalism for codifying correct reasoning
> in natural language. There are several people who claim it isn't for
> various reasons.
>
> But it is not really a sensible question for me whether there is such a
> thing as logic in natural language. For there are arguments and
> reasoning in natural language, and wherever one assertion follows from
> or is incompatible with another, there you have logic, or so it seems
> to me.
You are again affirming the consequent. That there are arguments
and reasoning and assertions following from and being or not
being incompatible with another in natural language does not imply
that all natural language is such.
>
> >> Admittedly, FOPC may not capture everything
> >> that is a matter of the logic in natural language.
> >
> >Then nothing in natural language that is not captured by FOPC
> >need necessarily obey the rules of logic.
>
> As I said, in my terms that would only show that FOPC is not an
> adequate formalization of the logic of natural language. But again,
> I was not presupposing the identification of "logic" with FOPC.
You *argued against* my statement that "natural language does not
follow rules of logic" by stating "But all our reasoning and argumentation is done in natural language". That is affirmation
of the consequent, and is not valid. You may have other reasons to
think that all natural language has some correct logical formalization,
but that won't do as one.
In addition, the context is regarding Leibniz' Law and Quine's
application of the Identity of Indiscernables to a piece of
natural language. When I said "Natural language does not follow rules
of logic and no one, certainly not Quine, should expect it to.",
this is clearly best interpreted as referring to the rules of the
logic in which Leibniz' Law is formulated for which it is believed
to hold. If natural language might just as well obey some logic
other than FOPC, Quine certainly should not expect it to obey FOPC.
But in fact Quine did not apply the Identity of Indiscernables
to "the logic of natural language" -- rather, he treated the
Identity of Indiscernables as a string replacement procedure on
strings of natural language, and it is hardly surprising that it
failed.
--
<J Q B>
========================================================================
========================================================================
========================================================================
========================================================================
Jim Balter
oho...@my-dejanews.com wrote:
>
> In article <359FFED9...@sandpiper.net>,
> Jim Balter <j...@sandpiper.net> wrote:
> >
> >
> > > Leibnitz's law, IMHO, holds in any context. You have not
> > > demonstrated a failue by your example. Quine claimed to have
> > > found a failure in modal contexts. His argument was;
> > >
> > > 1. The number of planets is 9
> > > 2. It is necessary that (9>7).
> > > Therefore
> > > 3. It is necessary that (the number of planets >7).
> >
> > certainly not Quine, should expect it to.
> >
> > A hamburger is better than heaven."
>
> as a sensible argument.
Of course not; such examples are intended to provide obvious,
unarguable instances of a class that contains less obvious,
arguable instances. For instance, application of rules of logic
to natural language as if they were string procedures defined on
any strings, rather than only on WFFs.
> Ever since Aristotle, it has been clear
> that language has to be more formal than natural language to deal
> with logic.
Which was my point.
> Quine's use of Leibnitz's law is not as trivial as
> not formalizing language within his argument.
Had he formalized the language, he would have had no argument.
> He wants to say
> that (the x such that Fx)=y->G(the x such that Fx)<->Gy, for
> every G, fails in formalized modal context.
He wants to say it because the natural language argument above
seems to lead to it, not because he has a formal argument.
> Smullyan, and others
> have pointed out that Quine is wrong....that was my point.
Quine applied the Identity of Indiscernables to natural language
by doing a string replacement of "the number of planets" for "9".
But IofI is only defined as a string replacement on logical forms,
not natural language. Since "the number of planets" is a descriptive
term, it is not preserved as a string when the language is
formalized. This really isn't that much more complicated than
the amphiboly of "nothing".
--
<J Q B>
Omar Haneef
Seth Russell (seth...@clickshop.com) wrote:
: Jim Balter wrote:
: > An example of the failure of the converse of Leibniz'
: > law is "Oedipus knows that his wife is Jocasta. Jocasta is
: > Oedipus' mother. Oedipus knows that his wife is his mother."
: I put up a SVO diagram of this example at
: http://clickshop.com/ai/oedipus.jpg . Could someone point out the
: failure of Leibniz's law in the diagram? The example is obviously
: dealing with knowledge at the granularity where predicates themselves
: have identity (can be pointed out). As can be seen from the diagram,
: Oedipus knows one predicate, but there is no implication of knowledge
: of every existing predicate on the subject which is the object of what
: he know. So if Oedipus knows his wife is his mother, it is not by
: virtue of the first two sentences. What's the problem, have I missed
: something?
Another way of putting what is missing -- other than the "it has to be true of all statements" -- is the following:
Oedipus "knows" an tremendous -- perhaps infinite -- number of
things about Jacosta: that she is his wife, that she is a woman, that
she believes the sky is blue, that she has never flown on wings, that
she was never a dolphin, that her parents are not ducks etc. How -- in
what principled manner -- do you include these beliefs about Jacosta
and rule out all the princples beliefs about Jacosta that follow from
what he does not know i.e. that she is his mother, that she bore him,
that she was fertilized by his father etc.
Surely you don't want to unclude a huge (possible infinity)
number of arrows to deal with the one case arbitrarily avoiding the
other.
-O
Neil Rickert
ande...@pitt.edu (Anders N Weinstein) writes:
>In article <359FFED9...@sandpiper.net>,
>Jim Balter <j...@sandpiper.net> wrote:
>>Natural language does not follow rules of logic and no one,
>>certainly not Quine, should expect it to.
>But all our reasoning and argumentation is done in natural
>language. If there is no logic to natural language, then there
>is no logic anywhere. Admittedly, FOPC may not capture everything
>that is a matter of the logic in natural language.
I disagree with this. Our argumentation may be done in natural
language, but our reasoning is done in brains. We may be able to
record the argumentation in books or computers, which might be said
to make the case that argumentation is done in language. We have
been unsuccessful in moving all of our reasoning to books or
computers, and this supports my claim that reasoning is done in
brains, with the language being used to describe what is happening in
the brains.
Jim Balter
Omar Haneef wrote:
> Another way of putting what is missing -- other than the "it has to be true of all statements" -- is the following:
>
> Oedipus "knows" an tremendous -- perhaps infinite -- number of
> things about Jacosta: that she is his wife, that she is a woman, that
> she believes the sky is blue, that she has never flown on wings, that
> she was never a dolphin, that her parents are not ducks etc. How -- in
> what principled manner -- do you include these beliefs about Jacosta
> and rule out all the princples beliefs about Jacosta that follow from
> what he does not know i.e. that she is his mother, that she bore him,
> that she was fertilized by his father etc.
> Surely you don't want to unclude a huge (possible infinity)
> number of arrows to deal with the one case arbitrarily avoiding the
> other.
Sure those are "missing", but they aren't relevant, so Seth had
no reason to add them. The *relevant* thing that is missing is
the application of Leibniz' Law, replacing "Jocasta" with the
identical (according to the accepted sentence "Jocasta is Oedipus'
mother") "Oedipus' mother". Such a substitution works just fine
when considering whether she is a woman, but not when considering
whether Oedipus knows that she bore him.
--
<J Q B>
Anders N Weinstein
In article <35A13FFA...@sandpiper.net>,
Jim Balter <j...@sandpiper.net> wrote:
>Anders N Weinstein wrote:
>You are again affirming the consequent. That there are arguments
>and reasoning and assertions following from and being or not
>being incompatible with another in natural language does not imply
>that all natural language is such.
Possibly I didn't understand what you were claiming. I agree that there
are many non-cognitive functions and uses of language to which logic is
irrelevant. There are the pleasantries that form most people's first
introduction to a foreign language, there are such things as calling
someone by name, these are not governed by laws of logic. Ditto for
exclamations and cooing and billing and baby talk and all the other
non-cognitive uses of language.
But pointing out the non-cognitive uses of language does not seem a
very interesting response to claims about the significance of Leibniz' law or
its inapplicability to intensional idioms. So I did not think that was
the point you were making.
Really I don't know what you are saying when you say there is no
reason to expect natural language to be governed by laws of logic.
If it's only non-cognitive uses, then it's true but not news. But if
it concerns statements that we can argue about, for which reasons can
be offered, which one person can second with "that's true", then it
is much more problematic. And I found your examples unpersuasive.
>You *argued against* my statement that "natural language does not
>follow rules of logic" by stating "But all our reasoning and argumentation is done in natural language". That is affirmation
>of the consequent, and is not valid. You may have other reasons to
I didn't see a conditional there with a consequent to affirm;
rather a broad slogan that I did not find persuasive. But it may well
be that I did not understand your point; take it as a request for
clarification then.
You seemed to me to say: there is no reason to be concerned about the
non-extensionality of psychological verbs, since there is no reason to
think logic applies to natural language. I think one has to be somewhat
concerned, since it is an issue about formulating the logic that is in
natural language.
>think that all natural language has some correct logical formalization,
>but that won't do as one.
I would never claim that *all* natural language is governed by logic.
There are plenty of non-cognitive uses and functions performed by language.
I didn't think you were just pointing to those.
>In addition, the context is regarding Leibniz' Law and Quine's
>application of the Identity of Indiscernables to a piece of
>natural language. When I said "Natural language does not follow rules
>of logic and no one, certainly not Quine, should expect it to.",
>this is clearly best interpreted as referring to the rules of the
>logic in which Leibniz' Law is formulated for which it is believed
>to hold. If natural language might just as well obey some logic
Indeed I am taking issue with your claim. I think there is excellent
reason to expect natural language, insofar as it is being used cognitively,
e.g. to argue for a claim, to follow rules of logic. Without logic,
there is no constraint on thought or cognition.
>other than FOPC, Quine certainly should not expect it to obey FOPC.
>But in fact Quine did not apply the Identity of Indiscernables
>to "the logic of natural language" -- rather, he treated the
>Identity of Indiscernables as a string replacement procedure on
>strings of natural language, and it is hardly surprising that it
>failed.
But it succeeds for large tracts of natural language; it is only
rather special subclasses of predicates (modal, psychological) that
create contexts recalcitrant to Quine's favored logical apparatus.
Anders N Weinstein
In article <6nrh9u$r...@ux.cs.niu.edu>, Neil Rickert <ric...@cs.niu.edu> wrote:
>I disagree with this. Our argumentation may be done in natural
>language, but our reasoning is done in brains. We may be able to
If it's done silently, call it reasoning, if it's done
out loud, call it argumentation. Now it appears there is no important
theoretical difference, for anything that could be done in reasoning
could be done in argumentation and vice versa. Since argumentation and
reasoning are identical in their logical properties -- for example,
it does not alter the validity of an inference whether it is part
of argumentation or reasoning -- it seems to make no theoretical
difference whether we consider one or the other. For the reasoning
can be articulated and so turned into argumentation; if not, then it
has no claim to be called *reasoning* at all.
>to make the case that argumentation is done in language. We have
>been unsuccessful in moving all of our reasoning to books or
>computers, and this supports my claim that reasoning is done in
>brains, with the language being used to describe what is happening in
>the brains.
I see no reason to think a computer could reason except in the most
attenuated of sense (one can speak of the proofs generated by an
automated theorem prover, say). That seems like a category mistake to
me. It is only in the context of a living organism that you find that
which gives content to reasoning. But that context is larger than the
brain.
Seth Russell
Relative to the example: 1) Oedipus knows that his wife is Jocasta. 2)
Jocasta is Oedipus's mother. Followed by the question: 3) Does Oedipus
know that his wife is his mother? I say no. Balter says yes. My
diagram is located at: http://clickshop.com/ai/oedipus.jpg , Balter's
is below.
Jim Balter wrote:
> Here, let me save you the trouble of coming to grips
> with such a difficult task, by applying the Indiscernability
> of Identicals to your diagram by replacing "Jocasta"
> with the identical "Oedipus' mother":
>
> --------------------
> ------| Oedipus |
> | --------------------
> [knows that] ^ ^
> | | |
> -->[is wife of] [is mother of]
> | |
> ---------------------
> | Oedipus' mother |
> ---------------------
>
> As you can see, the [is wife of] and [is mother of]
> predicates are still just fine, but the [knows that]
> predicate went from true to false upon the substitution.
> If I need to explain this even further, be sure to let me know.
The example stipulates only one predicate which Oedipus knows. The
other predicate he does not know. You substituted the predicate which
he does not know for the predicate he does know - thus transforming our
true representation of the example to a false one. You claim that
Liebnetz's law permits this. But the important thing to note is that we
are in a context where predicates themselves have identity - that's the
nature of the example. Clearly in this context "nameof (Jocasta)" is
not identical to "motherof (Oedipus)". Had we implemented our bot with
a relational db, then we would have filtered for "knownby(Oedipus)" and
the predicate "motherof(Oedipus)" would not have cropped up.
Yours and Quine's misuse of Liebniz's law is why we must repeal it for
across the board application.
Later to Weinstein you wrote: "But in fact Quine did not apply the
Identity of Indiscernables to 'the logic of natural language' -- rather,
he treated the Identity of Indiscernables as a string replacement
procedure on strings of natural language, and it is hardly surprising
that it failed."
Yes, it is hardly surprising. But everyone agrees that the meaning and
reasoning behind the words of natural language is sensitive to the
context. Then what purpose is served by ignoring that context and doing
string substitutions into the language string itself? Why would Quine
spend so much time doing something so patiently worthless? Again, what
have I missed?
Neil Rickert
>>I disagree with this. Our argumentation may be done in natural
>>language, but our reasoning is done in brains. We may be able to
>If it's done silently, call it reasoning, if it's done
>out loud, call it argumentation. Now it appears there is no important
>theoretical difference, for anything that could be done in reasoning
>could be done in argumentation and vice versa.
It may be correct that there is no important *theoretical* difference
between reasoning and argumentation. But if that is so, surely it is
because you are using an inept theory.
For me, the purpose of reasoning is to make a wise decision, while
the purpose of argumentation is to persuade somebody else. I see
these as very different. If philosophy cannot distinguish, then so
much the worse for philosophy.
> Since argumentation and
>reasoning are identical in their logical properties --
Well, that sounds about right. As we mathematicians would say, it is
vacuously true. In other words, argumentation has no logical
properties, and reasoning has no logical properties. Therefore these
are identical in their logical properties.
Now it may be that a particular argument uses logic. And it may be
that a particular instance of reasoning uses logic. But this would
not give logical properties to either argumentation or to reasoning.
> -- for example,
>it does not alter the validity of an inference whether it is part
>of argumentation or reasoning -- it seems to make no theoretical
>difference whether we consider one or the other.
That may well be correct. Is it relevant?
It seems to me that you are assuming what you are trying to prove --
namely, that reasoning and argumentation are both a matter of logic.
But that is part of what I have been challenging.
> For the reasoning
>can be articulated and so turned into argumentation; if not, then it
>has no claim to be called *reasoning* at all.
I must say, I really don't see this. It seems quite wrong. You seem
to be saying that no matter how excellent are my thought processes,
and how perfect is the judgement I make with those processes, it
doesn't count as reasoning unless I can persuade others. It almost
sounds like a claim that the validity of an inference is to be
determined by majority vote.
>I see no reason to think a computer could reason except in the most
>attenuated of sense (one can speak of the proofs generated by an
>automated theorem prover, say).
Fair enough. Yet it seems indisputable that computers could argue.
And you have said that there is no important theoretical difference
between reasoning and argumentation.
Jim Balter
Anders N Weinstein wrote:
> Really I don't know what you are saying when you say there is no
> reason to expect natural language to be governed by laws of logic.
> If it's only non-cognitive uses, then it's true but not news. But if
> it concerns statements that we can argue about, for which reasons can
> be offered, which one person can second with "that's true", then it
> is much more problematic. And I found your examples unpersuasive.
Of course it is "much more problematic", but it does not follow
from the fact that we express logic in natural language that
all cognitive uses of language "have a logic", but that's the
argument you gave. Feel free to give a better one.
As for the applicability of the laws of logic, as I've said,
these are laws that are defined within a particular domain.
The Identity of Indiscernables allows us to substitute B for A
given A=B, but the fact that we can do this substitution
in WFFs where ww can prove or at least give good reasons why
such substitutions should work does not give us license to
apply it in natural language, which has unstated combinatory rules,
and even to the degree that they are stated they do no match
"the rules of logic" or of algebra or of anything like them.
A similar problem applies to Sorites Paradoxes. We can
apply induction to the form
assume: not heap(1)
assume: not heap(i) -> not heap(i+1)
conclude: (n) not heap(n)
The logic is fine *as long as* heap() is a logical predicate
which yields a unique truth value for every value in its domain.
But the English word "heap" simply doesn't *have* that attribute.
There have been all sorts of attempts to solve the Sorites problem
using supervalued logics and such, but they are revealed as futile
because they have requirements such as vagueness being metaphysically
impossible. Whatever the "logic" of "heap" might be,
it seems that it is to be found in the complexities of ways we use the
term in practice, rather than following rules of logic. Perhaps it
would help to keep in mind what logic is. Here's the entry from
Peter Angeles' _Dictionary of Philosophy._ Certainly this source
is not the final word; feel free to provide other offerings that clarify
your statements about it.
1. The study of the rules of exact reasoning, of the forms of sound
and valid thought patterns. 2. The study and application of the
rules of inference to arguments or to systems of thought.
> Indeed I am taking issue with your claim. I think there is excellent
> reason to expect natural language, insofar as it is being used cognitively,
> e.g. to argue for a claim, to follow rules of logic. Without logic,
> there is no constraint on thought or cognition.
I find the above statements to be quite unconstrained and not
follow any rules of logic. Words can be strung together in all sorts
of ways, and often are. That a bunch of words concerning heaps
are strung together in a way that resembles a logical form does not
make the result logical. In fact, that it leads to paradox virtually
proves that it is not logical, unless you wish to entertain the
possibility that the rules of inference are inconsistent.
I gave an argument that hamburgers are better than heaven. It is
easy to recognize that that is not a logical argument -- the application of the rules of logic do not give the right result.
That's because it employs amphiboly, a phenomenon of linguistics, not
logic. There is no particular reason to think that Sorites problems
also fail to be logical because they employ a phenomenon of linguistics
or perhaps semantics, but not logic. Sorites arguments *don't work*
even though they follow the rules of logic precisely because the natural
language employed is nonlogical, just as hamburger arguments don't
work and Leibniz' Law arguments don't work in intensional contexts
or certain natural language modal expressions.
> >other than FOPC, Quine certainly should not expect it to obey FOPC.
> >But in fact Quine did not apply the Identity of Indiscernables
> >to "the logic of natural language" -- rather, he treated the
> >Identity of Indiscernables as a string replacement procedure on
> >strings of natural language, and it is hardly surprising that it
> >failed.
>
> But it succeeds for large tracts of natural language; it is only
> rather special subclasses of predicates (modal, psychological) that
> create contexts recalcitrant to Quine's favored logical apparatus.
It is trivial to invent natural language statements in which
substitution of equated phrases fails, from "better than nothing"
to "number of planets" to "Oedipus knows" to "what it's like" to
"my sense of red" to "a human is a collection of atoms"
to "A but B" and beyond. Noticing that "large tracts of natural
language" closely resemble the forms of FOPC and therefore can be
treated as those forms are treated is a bit like noticing that
many physical systems can be modeled linearly and then sweeping
away the rest as "special recalctrant subclasses".
--
<J Q B>
Jim Balter
Anders N Weinstein wrote:
>
> In article <6nrh9u$r...@ux.cs.niu.edu>, Neil Rickert <ric...@cs.niu.edu> wrote:
> >I disagree with this. Our argumentation may be done in natural
> >language, but our reasoning is done in brains. We may be able to
>
> If it's done silently, call it reasoning, if it's done
> out loud, call it argumentation. Now it appears there is no important
> theoretical difference, for anything that could be done in reasoning
> reasoning are identical in their logical properties -- for example,
> it does not alter the validity of an inference whether it is part
> of argumentation or reasoning -- it seems to make no theoretical
> can be articulated and so turned into argumentation; if not, then it
> has no claim to be called *reasoning* at all.
>
> >been unsuccessful in moving all of our reasoning to books or
> >computers, and this supports my claim that reasoning is done in
> >brains, with the language being used to describe what is happening in
> >the brains.
>
> attenuated of sense (one can speak of the proofs generated by an
> me. It is only in the context of a living organism that you find that
> which gives content to reasoning. But that context is larger than the
> brain.
A lovely contradiction. A computer that speaks Godel's argument
is doing something with "no important theoretical difference"
from reasoning, but it is a "category mistake" to say that it is
reasoning.
I agree that, in that case, it is a category mistake to call that
reasoning, just as it is a category mistake to equate reading
arguments out loud by humans with reasoning.
Better to give up the equation between argumentation and reasoning,
and to stop calling negations of your biases and dogmas "category
mistakes".
--
<J Q B>
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Phil Roberts, Jr.
I just made a similar proposal in a response to Neil in this thread. Your
comments on the matter would be most appreciated.
--
Phil Roberts, Jr.
Feelings of Worthlessness and So-Called Cognitive Science
http://www.geocities.com/Athens/5476
Jim Balter
Sigh. As I already said, I simply replaced "Jocasta" with
"Oedipus' mother"; the diagram is otherwise identical,
except for fixing the direction of one arrow.
I did not replace any predicates. Please remove your blinders.
> Liebnetz's law permits this.
I'm claiming that that's how you apply it to your diagram. *You*
are the one who denied that the law *fails*. That means *you*
permit it to be applied. *I'm* saying that it *cannot* be applied
without producing an error.
> But the important thing to note is that we
> are in a context where predicates themselves have identity - that's the
> nature of the example. Clearly in this context "nameof (Jocasta)" is
> not identical to "motherof (Oedipus)".
Those are *never* identical, in *any* context, so
Leibniz' Law would not allow such a substitution.
I did not substitute "Jocasta's name" or "`Jocasta'" for or with
"Oedipus' mother". You are making a use/mention error.
> Had we implemented our bot with
> a relational db, then we would have filtered for "knownby(Oedipus)" and
> the predicate "motherof(Oedipus)" would not have cropped up.
The predicate motherof(Oedipus) is in your original diagram.
I merely replaced one way of uniquely identifying a particular fictional character, "Jocasta", with another way of identifying the identical (we are, after all, talking about the Indiscernability of Identicals) fictional character, "Oedipus' mother".
Your talk of implementations and filters seem quite beside the point
being argued. The question is not how we should implement something,
but whether the Indiscernability of Identicals fails when applied
to your diagram. It does, quite straightforwardly.
> Yours and Quine's misuse of Liebniz's law is why we must repeal it for
> across the board application.
I just *showed* that it can't be applied across the board.
It's not *my* application -- I'm *refuting* the application -- I'm
saying it's a misuse. Sheesh.
Again, *you* deny that it fails. If it doesn't fail, why repeal it?
There is no need to add an amendment to the Law that says that it cannot
be used as a string replacement in natural language, or within
intensional contexts, because that amendment is already on the books.
If there is some other problem with its application, then you need
to demonstrate that, but you haven't so far. If your problem is just
with the enforcement of the amendments, I'm all with you, and have
been saying so for years.
> Later to Weinstein you wrote: "But in fact Quine did not apply the
> Identity of Indiscernables to 'the logic of natural language' -- rather,
> he treated the Identity of Indiscernables as a string replacement
> procedure on strings of natural language, and it is hardly surprising
> that it failed."
>
> Yes, it is hardly surprising. But everyone agrees that the meaning and
> reasoning behind the words of natural language is sensitive to the
> context. Then what purpose is served by ignoring that context and doing
> string substitutions into the language string itself? Why would Quine
> spend so much time doing something so patiently worthless? Again, what
> have I missed?
That you aren't the only one who makes mistakes. Go look at the
very long literature on the Sorites paradox if you want to see
how many very bright people have wasted very much time on trying
to apply logical transformations to natural language.
Or read everything that Longley has posted here, especially his
quotations of Quine, to see how much time Longley and Quine spent
on something patently worthless. If they *recognized* that it was
patently worthless, they wouldn't have done it, but, as the bot keeps
telling us, we aren't bots (although bots do this too, truth to tell),
we consistently make mistakes by applying familiar forms, including
assumptions, biases, and dogmas, rather than deductive logic --
even Quine. And Quine's dogma is that natural language can be
transformed into an "ideal language" just by doing away with certain
troublesome items like intension and modality. And Einstein spent most
of his life battling QM based on his dogma that "I cannot believe that
God would choose to play dice with the world ... Raffiniert ist der
Herr Gott, aber boshaft ist Er nicht." Go figure.
--
<J Q B>
Jim Balter
Seth Russell wrote:
>
> Relative to the example: 1) Oedipus knows that his wife is Jocasta. 2)
> Jocasta is Oedipus's mother. Followed by the question: 3) Does Oedipus
> know that his wife is his mother? I say no. Balter says yes.
I missed this misrepresentation the first time. Of course I don't say
yes; the whole point of the example, of the damned play,
is that Oedipus doesn't know that Jocasta is his mother.
What I say is that Leibniz' Law implies yes, therefore, by modus tollens, not(Leibniz' Law). Perhaps someone else can explain to me
how Seth can fail to get this; it certainly is beyond my limited
capabilities to comprehend.
--
<J Q B>
Jim Balter
CDJ wrote:
> It was actually looking to me like Weinstein was just using "cognitive use of
> language" to mean "language use that accords with, say, FOPL". In which case
> it would be trite for him that cognitive uses of language would be governed by
> logic.
I don't see how you got that reading. He is arguing that
all employment of language for giving arguments, reasons, and so forth,
must be "logical", where the rules of that logic need not be
those of FOPL.
> Do you and Rickert hold that there is no significant portion of natural
> language which admits of a translation into the language of FOPL in much the
> manner taught to freshmen logic students?
I can't speak for Rickert, and I don't know what you mean by
"significant", but I would and have stated that some portion translates
directly into FOPL, and I would call it significant. But there is
also a "significant" portion of language that is used in argumentation
and reasoning that does not directly translate into FOPL. Some of it,
such as Quine's example, can be translated, but undergoes important
transformations that make such things as Leibniz' Law inapplicable
to the natural language form. Some, such as Sorites arguments,
looks much like FOPL but cannot be directly translated because the
terms of natural language don't obey the requirements of FOPL in
straightforward ways, e.g., because "predicates" such as "is a heap"
don't predicate, they don't unambiguously confirm or deny -- perhaps
there is a complex fuzzy logic translation, which may in turn be
translated into FOPL. Some, such as "A but B", involve natural
language semantics that are lost with any translation into FOPL --
the translation yields the correct truth values, but truth values
are not all that is of interest in arguments -- people have to be
*convinced*, and that is not a logical process! Some. much,
involves those troublesome intensional contexts -- these again
are "predicates" that do not predicate. Some involves obvious
amphibolies like "better than nothing", and some involves much
more subtle ambiguities. Much is subtly inconsistent.
Much resembles similar logical language but is in fact meaningless,
incoherent.
> Or take an alternative version of the question, if it seems better. Do you and
> Rickert hold that there is not a significant amount of language use that
> admits of this sort of translation?
I would say that a significant amount of language use does not
admit such translation, or that it can only be partially translated.
And I would say that naively treating natural language that resembles
FOPL as if it were the FOPL it resembles, as with Sorites paradoxes
and the vague "predicates" that they involve, leads to quite a bit of
error and useless debate.
> I am not totally clear on just what the disagreement is over.
AW:
"it is only
rather special subclasses of predicates (modal, psychological) that
create contexts recalcitrant to Quine's favored logical apparatus."
He has already assumed that everything that *looks* like a predicate
in natural language *is* one. With such an assumption, Sorites
paradoxes seem quite mysterious, because is_a_heap() is neither
modal nor psychological, so this predicate should be just fine.
But "is a heap" and much other natural language do not obey
the requirements of FOPL or anything like it.
--
<J Q B>
Bill Taylor
Vesa Monisto <ve...@sturman.pp.fi> writes:
|> >-------------------------------------------------------------------------------
|> > Bill Taylor W.Ta...@math.canterbury.ac.nz
|> >-------------------------------------------------------------------------------
|> > Identity of indiscernibles: x = y <==> (P) Px <=> Py
|> > Identity of indiscriminables: P = Q <==> (x) Px <=> Qx
|> >-------------------------------------------------------------------------------
|>
|> Identity of indiscernibles: (P) Px <=> Py ==> x = y
|> Indiscernibility of identicals: x = y ==> (P) Px <=> Py
|> Identity of indiscriminables: (x) Px <=> Qx ==> P = Q
|> Indiscriminability of identicals: P = Q ==> (x) Px <=> Qx
Fair enough!
No wait though, let me tidy it up a little, by allowing ourselves both arrows:-
Identity of indiscernibles: x = y <== (P) Px <=> Py
Indiscernibility of identicals: x = y ==> (P) Px <=> Py
Identity of indiscriminables: P = Q <== (x) Px <=> Qx
Indiscriminability of identicals: P = Q ==> (x) Px <=> Qx
Now, if we could just synonymize the 3 I-words to be of equal length...
======================
And while you're at it, you can find a name for this fancy four:-
U V = V U @ = @
A V = @ A @ = V
(V = universe; @ = empty set; U = union over all members; A = intersection same)
The last one is the only "surprise". There's often a surprise or two in
these bi-dichotomies, (a pet topic of mine, as many will know).
|> Sat sapienti.
Si Vd hablo!
-------------------------------------------------------------------------------
Bill Taylor W.Ta...@math.canterbury.ac.nz
-------------------------------------------------------------------------------
a priori a posteriori
.--------------------------.
synthetic | math | science |
|------------+-------------| The KANT-TAYLOR bi-dichotomy.
analytic | logic | sophistry |
`--------------------------'
-------------------------------------------------------------------------------
CDJ
>Leibnitz's law, IMHO, holds in any context. You have not
>demonstrated a failue by your example. Quine claimed to have
>found a failure in modal contexts. His argument was;
>
>1. The number of planets is 9
>2. It is necessary that (9>7).
>Therefore
>3. It is necessary that (the number of planets >7).
>
>This argument is invalid (see: A. Smullyan 1948), the number
>of planets is a descriptive term and as such according to Russell's
>description theory; It's necessary that (the number of planets >7),
>does not follow as an instance of Leibnitz's law but (The number
>of planets is necessarily greater than 7) does follow and is an
>instance.
Ok, the basic tack taken is to say that 1. does NOT have logically have the
form of an identity claim. In particular phrases like "the number of planets"
are not singular terms, but rather are contextually defined fragments of
sentences.
What do you say to the following questions (some of which are Strawsonian in
origin, and some are original to me, at least as far as I know):
A 1. sure LOOKS to have the form of an identity claim involving two
singular terms. And by LOOKS I mean that in a vast number of other common
situations, one can, without falling into error, treat the claim as an
identity. It's well and good to simply assert that 1. is not an identity, and
conclude that substitutability does not fail, but this conclusion seems to
follow more because the description theory goes a fair ways towards dispensing
with substitution tout court. It seems at least reasonable to ask for an
explanation of why what one might have naturally thought we were doing, viz
making substitution inferences, is not what we were in fact doing.
B Is there a definition of descriptive term handy, or is it just going
to be something like whatever would get us into trouble with LL if it were a
singular term?
C Take the Russellian description language. Skolemize it. Else I am much
confused, which would not be a first, the result tells us that 1. CAN be
viewed as an identity, with what you call the descriptive term being
functional, and hence a singular term. How does this affect your line of
thought?
I think I had more questions, but I forget at the moment. Maybe theyll come
back.
CDJ
Anders N Weinstein
In article <6ns05h$r...@ux.cs.niu.edu>, Neil Rickert <ric...@cs.niu.edu> wrote:
>ande...@pitt.edu (Anders N Weinstein) writes:
>>>I disagree with this. Our argumentation may be done in natural
>>>language, but our reasoning is done in brains. We may be able to
>
>>If it's done silently, call it reasoning, if it's done
>>out loud, call it argumentation. Now it appears there is no important
>>theoretical difference, for anything that could be done in reasoning
>>could be done in argumentation and vice versa.
>
>the purpose of argumentation is to persuade somebody else. I see
>these as very different.
I do not presuppose that argumentation is other-directed or aimed at
convincing someone. One may silently consider the arguments for or
against a claim simply in the course of attempting to reach the right
judgment, with no special interest in persuading others.
Anyway, a difference of *purpose* is not to the point. The point is:
if an inferential transition from p to q is a good one, it cannot
make any difference whether the reasoning is done silently or out loud.
By logical property I mean such things as validity, or more broadly
cogency of support.
>> Since argumentation and
>>reasoning are identical in their logical properties --
>
>Well, that sounds about right. As we mathematicians would say, it is
>vacuously true. In other words, argumentation has no logical
>properties, and reasoning has no logical properties. Therefore these
>are identical in their logical properties.
You are free to make that claim, but it seems absurd. For example,
we say that people have made a faulty inference. Balter delights in
charging me with affirming the consequent.
My point is: if I have indeed affirmed the consequent it makes no
interesting difference whether I have done so in silent reasoning or
overt speech. I have committed the same logical error in both cases.
Now where do you disagree with that? Are you suggesting there is no
such thing as committing a fallacy of affirming the consequent in
*either* reasoning or speech? I must say I don't find this
convincing.
>Now it may be that a particular argument uses logic. And it may be
>that a particular instance of reasoning uses logic. But this would
>not give logical properties to either argumentation or to reasoning.
One should not think of logic as a tool to be used
only when it is convenient. Perhaps sometimes it is correct to
affirm the consequent in a chain of inferences, and others not? Can
I then say, oh, I am not using logic on this?
It seems more accurate to me to say that *reasoning* is a method to be
used only when appropriate. (Indeed the main tradition of AI seems to
me to exaggerate vastly the extent to which human understanding is
effected by reasoning.) For example, Balter was able to right his
falling bike by a kind of acquired reflex, but not by reasoning about
it. We do not keep our balance by any kind of reasoning.
That said, it seems rather that logic is the sine qua non of reasoning,
it stands to reasoning something as the rules of chess stand to chess
games -- without the norms it sets, there is no such thing.
>> -- for example,
>>it does not alter the validity of an inference whether it is part
>>of argumentation or reasoning -- it seems to make no theoretical
>>difference whether we consider one or the other.
>
>That may well be correct. Is it relevant?
>
>It seems to me that you are assuming what you are trying to prove --
>namely, that reasoning and argumentation are both a matter of logic.
It is not that both are "a matter of logic". It is, to repeat, that
such things as affirming the consequent are fallacies, invalid
transitions, and the fallacy is exactly the same whether committed in
silent thought or overt argumentation.
What I am saying rests only on the idea that we can evaluate cognitive
transitions in thought and speech for such things as validity. I.e. there
are inferences in both. Logic stands to these transitions as grammar
does to correctness in speech, i.e. it aims to codify them, to make
what is implicit in patterns of inference we accept explicit.
>But that is part of what I have been challenging.
Unpersuasively, it seems to me.
As near as I can tell you seem to me to presuppose that logic must be
something that could be found in a purely formal and disconnected
symbol system, and then attack the significance of logic as so
conceived. But I do not want to use such a conception of logic. I want
to talk about *human* logic, the logical properites to be found in the
operations with symbols conducted by human beings in the course of
concrete activities in the world. Since criticizing someone's reasoning
is clearly something human beings do, I think there must be such a thing.
>> For the reasoning
>>can be articulated and so turned into argumentation; if not, then it
>>has no claim to be called *reasoning* at all.
>
>I must say, I really don't see this. It seems quite wrong. You seem
>to be saying that no matter how excellent are my thought processes,
>and how perfect is the judgement I make with those processes, it
>doesn't count as reasoning unless I can persuade others. It almost
Quite wrong. First whether you do or do not succeed in persuading
others is a purely psychological matter, with no right or wrong about
it: either it happens or it doesn't. Perhaps your audience will be
swayed by fallacies. But whether your reasoning *ought* to be
persuasive is a logical matter. Yet logic is a normative discipline,
concerned with the ought's of correct reasoning not the is's of
merely subjectively persuasive reasoning. That is what is distinctive
about logical properties, that they are not merely psychological,
but normative. If your reasoning is good then it *ought* to persuade
others (but may not); and conversely if it is not.
But mainly, the idea is that a cognitive transition doesn't count as
"reasoning" unless you can articulate it in language so others are in a
position to evaluate it for its cogency. If you say you reasoned your
way to such and such a conclusion, then I can ask you how you did so
and you can tell me; if you tell me the answer was a strong hunch or
came to you in a flash, then you might be reliable and correct, but you
did not do any reasoning, for you cannot answer the question "how" did
you reason, and no one else can evaluate your supposed reasoning
processes for validity. (Of course the can experimentally test the
reliability of your hunches on such matters and discover that they are
worth relying on for unknown reasons.)
As I say, such things as walking and catching fly balls and much else
is not effected by reasoning, that is perfectly true and
uncontroversial. But no one ever suggested that walking had logical
properties. Perhaps the ability to reason is a very small part of human
adaptive competence, but that does not affect what I am saying.
> It almost
>sounds like a claim that the validity of an inference is to be
>determined by majority vote.
Nothing could be further from my position. Validity of reasoning is
taken by us to be objective, not psychological (subjective).
>>I see no reason to think a computer could reason except in the most
>>attenuated of sense (one can speak of the proofs generated by an
>>automated theorem prover, say).
>
>Fair enough. Yet it seems indisputable that computers could argue.
Well I would dispute that. As I say, an automatic theorem prover could
emit symbol strings that we can interpret and treat as arguments, but
that is far from arguing. An AI with a conversational interface might
come closer to carrying on an argument, and perhaps you could say this
was capable of arguments on abstract mathematical topics. It could also
useful to us as a sparring partner in the course of stress-testing our
own reasoning. But I think it could not actually join with us in a
significant debate over whether that thing over there is really a
chair or not without having a similar form of life in the world to
ours, i.e. without basically being something that presents us with an
aspect largely indistinguishable from that of a normal living human
being.
CDJ
In article <35A18941...@sandpiper.net>, Jim Balter <j...@sandpiper.net> said:
>Anders N Weinstein wrote:
>
>> Really I don't know what you are saying when you say there is no
>> reason to expect natural language to be governed by laws of logic.
>> If it's only non-cognitive uses, then it's true but not news. But if
>> it concerns statements that we can argue about, for which reasons can
>> be offered, which one person can second with "that's true", then it
>> is much more problematic. And I found your examples unpersuasive.
>
>Of course it is "much more problematic", but it does not follow
>from the fact that we express logic in natural language that
>all cognitive uses of language "have a logic", but that's the
>argument you gave. Feel free to give a better one.
It was actually looking to me like Weinstein was just using "cognitive use of
language" to mean "language use that accords with, say, FOPL". In which case
it would be trite for him that cognitive uses of language would be governed by
logic.
Do you and Rickert hold that there is no significant portion of natural
language which admits of a translation into the language of FOPL in much the
manner taught to freshmen logic students?
Or take an alternative version of the question, if it seems better. Do you and
Rickert hold that there is not a significant amount of language use that
admits of this sort of translation?
I am not totally clear on just what the disagreement is over.
CDJ
Anders N Weinstein
In article <6ns0qh$dsj$1...@usenet01.srv.cis.pitt.edu>,
CDJ <cdjo...@pitt.edu> wrote:
>In article <6no7jv$5cc$1...@nnrp1.dejanews.com>, oho...@my-dejanews.com said:
>
>>is invalid (see: A. Smullyan 1948), the number
>>of planets is a descriptive term and as such according to Russell's
>>description theory; It's necessary that (the number of planets >7),
>>does not follow as an instance of Leibnitz's law but (The number
>>of planets is necessarily greater than 7) does follow and is an
>>instance.
>
>Ok, the basic tack taken is to say that 1. does NOT have logically have the
>form of an identity claim. In particular phrases like "the number of planets"
>are not singular terms, but rather are contextually defined fragments of
>sentences.
You should check out Stephen Neale's book _Descriptions_ for further
argument for the quantificational view of descriptions. There is also a
brief mention of some considerations in the chapter on Russell in
Evans' _Varieties of Reference_.
I gather, by the way, that a more sophisticated view of syntax means
that unlike Russell one does not have to deny that descriptive NPs are
syntactic units. In fact the quantifier approach is very elegant and
seems to unify (both syntactically and semantically) the description
operator in natural language with several other members of the category
of determiners, devices that combine with (possibly complex) predicates
to form "generalized quantifiers", such as "most" and "at least three",
as well as "everyone who loves someone".
Recall that quantifiers in natural language seem to be binary, to bind
two open sentences to form a sentence. Or as Neale recommends, a
determiner can be viewed as a "unary quantifier former" an expression
that combines with one open sentence to form a quantifier that can bind
another open sentence. Then the semantics for "the x: Fx" can be taken
as comparable to that for "most x: Fx".
>What do you say to the following questions (some of which are Strawsonian in
>origin, and some are original to me, at least as far as I know):
>
>A 1. sure LOOKS to have the form of an identity claim involving two
>singular terms. And by LOOKS I mean that in a vast number of other common
>situations, one can, without falling into error, treat the claim as an
>identity.
But it gives rise to scope ambiguities in the context of other
operators like negation in a way that ordinary identities do not.
Also, remember, it is not as if there is no identity to be found under
the analysis. It is just that the identity holds between a quantified
variable and a singular term.
>B Is there a definition of descriptive term handy, or is it just going
>to be something like whatever would get us into trouble with LL if it were a
>singular term?
I would say "descriptive noun phrase" can be treated as a grammatical
category of surface grammar.
>C Take the Russellian description language. Skolemize it. Else I am much
>confused, which would not be a first, the result tells us that 1. CAN be
>viewed as an identity, with what you call the descriptive term being
>functional, and hence a singular term. How does this affect your line of
>thought?
I am not sure that the existence of an alternative logical device for
saying the same thing shows the logico-semantic category of a bit of
syntax n the original notation. As I mentioned above, descriptive
terms give rise to scoping phenomena: there are two readings of "NOT
G[THE x.Fx]".
Anders N Weinstein
In article <35A18941...@sandpiper.net>,
Jim Balter <j...@sandpiper.net> wrote:
>Of course it is "much more problematic", but it does not follow
>from the fact that we express logic in natural language that
>all cognitive uses of language "have a logic", but that's the
>argument you gave. Feel free to give a better one.
OK, but I didn't mean to be arguing from the fact that we express
*logic* in natural language. I was arguing from the fact that we
express *arguments* in natural language, some of which depend only
on a structure determined by the little logical words like "or" and
"not".
More generally one could insist that the propositions of natural language
are in practice taken to stand in logical relations like implication
and incompatibility.
For example, suppose one person says "that's red" and another
person says "that's blue". Already they are making apparently
incompatible claims. Insofar as they understand the terms, they
will likely take this to be a conflict in the further course of the
conversation. It is one that might be resolved in several ways or given up
but such that they cannot simply leave both claims standing without
repair. One person might say, "look closer", "is your vision normal?"
the other one "the light is funny" or whatever.
At no point do they have to appeal to explicit logical rules, much less
a formal system; yet there are logical properties -- incompatibilities
-- to be found implicit in this exchange. Possibly one person will
get exasperated and say "look you *can't* say its both red and blue".
The "can't" is the crucial word here, the one that gives expression
to the notion of logical necessity ("the hardness of the logical must")
as it functions implicit in the practice. Similar expressions can be
found when people say "look, if it's a dog it *has* to be an animal".
To repeat, I am taking the logic in language to be something implicit,
not something necessarily appealed to by the participants. I think
there is logic in natural language even if the folks arguing have never
studied logic, just as people speak prose all their lives without
ever learning a grammar for their language.
>A similar problem applies to Sorites Paradoxes. We can
>apply induction to the form
>
>assume: not heap(1)
>assume: not heap(i) -> not heap(i+1)
>conclude: (n) not heap(n)
>
>The logic is fine *as long as* heap() is a logical predicate
>which yields a unique truth value for every value in its domain.
>But the English word "heap" simply doesn't *have* that attribute.
Then this formalization is inadequate to the logic oments with
predicates like "heap".
>impossible. Whatever the "logic" of "heap" might be,
>it seems that it is to be found in the complexities of ways we use the
>term in practice, rather than following rules of logic. Perhaps it
I don't understand this. At the beginning of your sentence you
are appealing to the idea that there is a logic of "heap" implicit in
our practice with the word. That is all I was suggesting. On the
other hand you do not explain what that logic is or in what terms
to theorize it adequately.
>work and Leibniz' Law arguments don't work in intensional contexts
>or certain natural language modal expressions.
Leibniz law holds where it holds; that defines extensionality. Quine's
question is how to formalize reasoning using predicates for which it
doesn't holds. The problem is not so much is that it doesn't hold for
x. It is rather that then we lack an account of the logic of x
comparable in achievement to the logic we seem to have of AND, OR, NOT,
and FOR ALL.
CDJ
In article <6ns71p$ehm$1...@usenet01.srv.cis.pitt.edu>, ande...@pitt.edu (Anders
N Weinstein) said:
>You should check out Stephen Neale's book _Descriptions_ for further
>argument for the quantificational view of descriptions. There is also a
>brief mention of some considerations in the chapter on Russell in
>Evans' _Varieties of Reference_.
Thanks. I will check it out tomorrow.
>But it gives rise to scope ambiguities in the context of other
>operators like negation in a way that ordinary identities do not.
>As I mentioned above, descriptive
>terms give rise to scoping phenomena: there are two readings of "NOT
>G[THE x.Fx]".
To talk about the scope ambiguity phenomenon requires that I show some of my
hand.
I think these noun phrases, or whatever they are commonly called, are good
Brandomian singular terms. They have a function\argument structure. In the
Grundlagen, for example, I take it that Frege told us a whole lot about the
structure of the function THE NUMBER OF. The manner in which he did this was
mathematical standard, by looking at a quotient structure. The same structure
is given in freshmen thermo class, where one of the first things heard is that
the relation IS IN THERMAL EQUILIBRIUM WITH is transitive. The point of saying
this is to permit, via looking at the quotient structure, the introduction of
the THE TEMPERATURE OF function.
Function have arguments. It is a often a discovery that a given function has
more arguments than used to be thought. The first example coming to mind is
the Gleick discussion about the function THE LENGTH OF. The conclusion, to my
way of speaking, is that for certain purposes, one needs to supplement this
function not only with the item whose length is to be measured, but also with
something like a zoom level.
Many functions of multiple arguments have some of the places filled with
defaults, when nothing in the context of utterance overrides. Frege in the
Grundlagen discussed this for the case of THE NUMBER OF INHABITANTS OF
GERMANY. As we use this function, and many others, the time argument defaults
to NOW, when not overridden by context.
So take a case of scope ambiguity.
The president of the United States will be black in the year 2000.
(this is copped from Brandom)
According to this way of speaking, what we know as scope ambiguity is actually
ARGUMENT ambiguity. In this case, whether or not the provided time reference
is supposed to be counted as taking the argument place in the THE PRESIDENT OF
function, which is one of those which, as standardly used, has a NOW default
argument, or not.
One standard way of indicating that an argument is meant to supplement a
function, overridding its default, if any, is by putting the argument right
next to the function. Thus the following goes a good distance towards clearing
up the ambiguity.
The president of the United States in the year 2000 will be black.
The basic reason for the possibility of this sort of ambiguity was given by
Frege in his Function and Concept. For a given judgement content, there are in
general lots of ways to discern function\argument structure. Lambda provides a
picture of this as well.
Advantages to this way of speaking, primarily by contrast with the Russellian
manner and its variants.
In the presence of Brandoms ideas of singular terms, a more fully articulated
version of the above is an overwhelmingly natural continuation of those ideas.
It does so happen however that in the presence of an articulated description
of the above way of talking, Brandoms chapter 7 stands in drastic need of
revision.
It is elegant and Russell is ugly. Think of, for example the point of Skolem
functions, as described in logic books. Then think of what it would be like,
after speaking the Skolemized language, to deSkolemize it and continue
speaking. How tedious. Thought of this way, the claim is that, as it were, we
actually live in a Skolemized language, which Russell and Quine were kind
enough to deSkolemize for us.
This way of speaking asks no question why it looks like we do with noun
phrases what we, according to Brandom, do with, say, names. It looks like this
because it is so. Functional singular terms are caught up in substitution
inferences just like the paradigmatic proper name. Indeed, on this way of
speaking, the general form of an identity claim is f(a)=g(b). The case a=b is
special, a limiting case.
Other things, like the matter of the informativeness of identities, find
natural expression in the above way of speaking as well.
None of the above has any bearing on the substitutivity of identicals. That
is, as far as I can tell, explained solely by using Brandoms language of
perspectivalness. Note that in every example of failure there are two people
involved, the attributor and the attributee. Classical formal logic makes many
idealizations. Among them is that there is only one speaking in a
conversation. Or more sharply, that there is only one set of commitments in
play in a given conversation. Loosely, the possibility of failure of
substitutivity exists when, and only when, at least one of the attributors
commitments differs from the attributees.
CDJ
oho...@my-dejanews.com
In article <35A143A0...@sandpiper.net>,> > In article <359FFED9...@sandpiper.net>,
> > Jim Balter <j...@sandpiper.net> wrote:
> > >
> > > oho...@my-dejanews.com wrote:
> > >
> > > > Leibnitz's law, IMHO, holds in any context. You have not
> > > > demonstrated a failue by your example. Quine claimed to have
> > > > found a failure in modal contexts. His argument was;
> > > >
> > > > 1. The number of planets is 9
> > > > 2. It is necessary that (9>7).
> > > > Therefore
> > >
> > > Natural language does not follow rules of logic and no one,
> > > certainly not Quine, should expect it to.
> > >
> > > A hamburger is better than heaven."
> >
> > I don't think anyone would consider the above (hamburger thing)
> > as a sensible argument.
>
> Of course not; such examples are intended to provide obvious,
> unarguable instances of a class that contains less obvious,
> arguable instances. For instance, application of rules of logic
> to natural language as if they were string procedures defined on
> any strings, rather than only on WFFs.
>
> > Ever since Aristotle, it has been clear
> > that language has to be more formal than natural language to deal
> > with logic.
>
> Which was my point.
Not very well made.
> > Quine's use of Leibnitz's law is not as trivial as
> > not formalizing language within his argument.
>
> Had he formalized the language, he would have had no argument.
Nonsense; To sugesst that Quine cannot formalize language enough
for this argument is just plain silly. He may be wrong but he
most definitely can express beyond you and me.
> > He wants to say
> > that (the x such that Fx)=y->G(the x such that Fx)<->Gy, for
> > every G, fails in formalized modal context.
>
> He wants to say it because the natural language argument above
> seems to lead to it, not because he has a formal argument.
>
> > Smullyan, and others
> > have pointed out that Quine is wrong....that was my point.
>
> Quine applied the Identity of Indiscernables to natural language
> by doing a string replacement of "the number of planets" for "9".
> But IofI is only defined as a string replacement on logical forms,
> not natural language. Since "the number of planets" is a descriptive
> term, it is not preserved as a string when the language is
> formalized. This really isn't that much more complicated than
> the amphiboly of "nothing".
WOW, I wish that I had the capacity to dismiss anyone with the
reputation from Harvard that Dr.W.V.Quine has in the way that you do.
> <J Q B>
>
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Jim Balter
> >demonstrated a failue by your example. Quine claimed to have
> >found a failure in modal contexts. His argument was;
> >
> >1. The number of planets is 9
> >2. It is necessary that (9>7).
> >Therefore
> >3. It is necessary that (the number of planets >7).
> >
> >of planets is a descriptive term and as such according to Russell's
> >description theory; It's necessary that (the number of planets >7),
> >does not follow as an instance of Leibnitz's law but (The number
> >of planets is necessarily greater than 7) does follow and is an
> >instance.
>
> Ok, the basic tack taken is to say that 1. does NOT have logically have the
> form of an identity claim. In particular phrases like "the number of planets"
> are not singular terms, but rather are contextually defined fragments of
> sentences.
>
> origin, and some are original to me, at least as far as I know):
>
> A 1. sure LOOKS to have the form of an identity claim involving two
> singular terms. And by LOOKS I mean that in a vast number of other common
> situations, one can, without falling into error, treat the claim as an
> conclude that substitutability does not fail, but this conclusion seems to
> follow more because the description theory goes a fair ways towards dispensing
> with substitution tout court. It seems at least reasonable to ask for an
> explanation of why what one might have naturally thought we were doing, viz
> making substitution inferences, is not what we were in fact doing.
Take (1) as shorthand for "the number of planets, according
to [entire array of theory and evidence that led to the conclusion],
is 9".
Then the substitution works. Due to the nature of the shortcut,
namely removing the sufficiency conditions of the description,
using the shortcut fails in modal contexts.
[Note that this is still a string replacement, and will fail
for many other ways of expressing the same thing.]
The problem in this case, as I see it, is that natural language makes
very frequent use of such contextual elisions and a host of other
mechanisms that are not allowed in FOPL, precisely because
they make context-free analysis impossible. Requiring full
context, however, makes it effectively impossible to express
all that we wish to express in natural language. The whole
point of natural language is that it is used among systems
that are driven by, make constant use of, and maintain a large
memory of, context. Trying to reduce natural language to FOPL or any
other set of context-independent rules is another aspect of the GOFAI
problem.
Jim Balter
> Function have arguments. It is a often a discovery that a given function has
> more arguments than used to be thought.
For instance, the_number_of_planets_in_a_system requires
all the relevant empirical data to be represented in its arguments,
or at least enough to be sufficient to yield a unique answer.
If sufficiency isn't maintained, substitution may fail in
modal contexts.
> None of the above has any bearing on the substitutivity of identicals. That
> is, as far as I can tell, explained solely by using Brandoms language of
> perspectivalness. Note that in every example of failure there are two people
> involved, the attributor and the attributee. Classical formal logic makes many
> idealizations. Among them is that there is only one speaking in a
> conversation. Or more sharply, that there is only one set of commitments in
> play in a given conversation. Loosely, the possibility of failure of
> substitutivity exists when, and only when, at least one of the attributors
> commitments differs from the attributees.
And how often does that happen in our use of natural language?
And what sorts of mistakes might arise if multiple perspectives
were idealized out of our language?
--
<J Q B>
David Longley
there may be something awry within our folk psychology. It is one
part of the case I make in "Fragments". We have plenty of other
evidence to support the thesis, and we have good reasons for
pursuing the development of a behavioural science from the
extensional stance. One reason is that it's in the interest of
the unity and integrity of science, but the more mundane one is
that it just works better (Dawes, Faust and Meehl 1989, SCIENCE).
--
David Longley (check end reply line #)
Longley Consulting London, UK
Behaviour Assessment & Profiling Technology,
Research, Data Analysis and Training Services,
Small IT Systems http://www.longley.demon.co.uk
CDJ
>CDJ wrote:
>
>> Function have arguments. It is a often a discovery that a given function has
>> more arguments than used to be thought.
>
>all the relevant empirical data to be represented in its arguments,
>or at least enough to be sufficient to yield a unique answer.
>If sufficiency isn't maintained, substitution may fail in
>modal contexts.
If I understand this, I would attenuate it to the need to ensure uniqueness in
a given conversational context. Different conversations have different
standards. If I ask my contractor how long my window sill is, and he tells me
that it is really a very complicated chaos theoretical question, I would
probably smack him.
>> None of the above has any bearing on the substitutivity of identicals. That
>> is, as far as I can tell, explained solely by using Brandoms language of
>> perspectivalness. Note that in every example of failure there are two people
>> involved, the attributor and the attributee. Classical formal logic makes
> many
>> idealizations. Among them is that there is only one speaking in a
>> conversation. Or more sharply, that there is only one set of commitments in
>> play in a given conversation. Loosely, the possibility of failure of
>> substitutivity exists when, and only when, at least one of the attributors
>> commitments differs from the attributees.
>
>And how often does that happen in our use of natural language?
>And what sorts of mistakes might arise if multiple perspectives
>were idealized out of our language?
It never happens. That is the point. Idealization is just about synonymous
with useful falsehood.
There would not be anything recognizable as language if there were not
different sets of commitments.
It can still be useful to be explicit about just which idealization is
responsible for a given failure of a proof idea. Or better, to discover that
in using a proof idea one has made an idealization. In this way, idealization
is just another word for hidden lemma, out of Lakatos mouth.
CDJ
Seth Russell
> Seth Russell wrote:
> >
> > Relative to the example: 1) Oedipus knows that his wife is Jocasta. 2)
>
> > Jocasta is Oedipus's mother. Followed by the question: 3) Does Oedipus
>
> > know that his wife is his mother? I say no. Balter says yes.
>
> I missed this misrepresentation the first time. Of course I don't say
> yes; the whole point of the example, of the damned play,
> is that Oedipus doesn't know that Jocasta is his mother.
Yes, Greek tragedy at its best.
Jim Balter Wrote:
What I say is that Leibniz's Law implies yes, therefore, by modus tollens,
not (Leibniz' Law). Perhaps someone else can explain to me how Seth can
fail to get this; it certainly is beyond my limited capabilities to
comprehend. [sorry had to retype this because of some strange characters
introduced in transmission]
Seth Russell writes:
You substituted "is-mother-of(Oedipus)" for the name "Oedipus" in a context
where the distinction between name and predicate was the matter at hand.
If "Oedipus" is identical to "is-mother-of(Oedipus)" in *all* contexts,
then Leibniz would have allowed the substitution, but that is clearly not
the case.
My point is that there is meaning behind natural language. The objects
which must obey Leibnetz's law are those meanings. If we have two
identical photo copies of a document, those copies can be substituted for
each other with no consequence to the facts of the matter. When the
objects are the objects of a mind, we must be very careful to distinguish
their properties - for example a name is *not* a predicate. If we bear
this in mind, then Leibnitz law works just fine, if it did not, then we
would be living in a very bazaar world. String substitutions in natural
language do not preserve the meaning of the statements. There must be a
parser (reading comprehension) between the natural language string and the
meaning behind it. It is that meaning behind the language which I seek.
David Longley
sought for the problem of failure of substitution salva veritate
within intensional contexts. But finding solutions amount to
restriction to extensional contexts. The analysis is explicative,
ie that what is characteristic of so called mental or
psychological verbs is the fact that they *do* flout the above,
rendering inference, via quantification in, unreliable in such
contexts.
Investigating how and why such failures occur is of course, part
of the business of empirical psychology.
One of my points is that it has implications for certain
approaches to AI, and certain assumptions of AI.
Neil Rickert
>In article <6ns05h$r...@ux.cs.niu.edu>, Neil Rickert <ric...@cs.niu.edu> wrote:
>>ande...@pitt.edu (Anders N Weinstein) writes:
>>>If it's done silently, call it reasoning, if it's done
>>>out loud, call it argumentation. Now it appears there is no important
>>>theoretical difference, for anything that could be done in reasoning
>>>could be done in argumentation and vice versa.
>>For me, the purpose of reasoning is to make a wise decision, while
>>the purpose of argumentation is to persuade somebody else. I see
>>these as very different.
>I do not presuppose that argumentation is other-directed or aimed at
>convincing someone. One may silently consider the arguments for or
>against a claim simply in the course of attempting to reach the right
>judgment, with no special interest in persuading others.
>Anyway, a difference of *purpose* is not to the point.
I think it is important. However, let's put that to one side for the
present.
> The point is:
>if an inferential transition from p to q is a good one, it cannot
>make any difference whether the reasoning is done silently or out loud.
I agree, although I don't see this as providing much support for your
position in our disagreement.
>By logical property I mean such things as validity, or more broadly
>cogency of support.
I'll readily grant that it is possible to use the term "logic" so
broadly that the word loses its usefulness.
>>> Since argumentation and
>>>reasoning are identical in their logical properties --
>>Well, that sounds about right. As we mathematicians would say, it is
>>vacuously true. In other words, argumentation has no logical
>>properties, and reasoning has no logical properties. Therefore these
>>are identical in their logical properties.
>You are free to make that claim, but it seems absurd. For example,
>we say that people have made a faulty inference. Balter delights in
>charging me with affirming the consequent.
Inferences which reach wrong conclusions can be considered faulty,
whether or not they are logical inferences. Balter's charges are
that you organize your arguments into an invalid logical form.
>My point is: if I have indeed affirmed the consequent it makes no
>interesting difference whether I have done so in silent reasoning or
>overt speech. I have committed the same logical error in both cases.
Agreed. But I don't see this as providing much support for your
case. Apparently there is an implicit assumption in the above
arguments that reasoning is logic. But it is that implicit
assumption that is being disputed.
>>Now it may be that a particular argument uses logic. And it may be
>>that a particular instance of reasoning uses logic. But this would
>>not give logical properties to either argumentation or to reasoning.
>One should not think of logic as a tool to be used
>only when it is convenient.
I don't. Rather, I think of logic as a tool to be used where it is
useful.
> Perhaps sometimes it is correct to
>affirm the consequent in a chain of inferences, and others not?
Perhaps so. But if it is correct to do so, that is not a matter of
logic.
> Can
>I then say, oh, I am not using logic on this?
It wouldn't help. You were, after all, giving an argument. And an
argument presented in the form of a fallacious logical step is never
very convincing.
>It seems more accurate to me to say that *reasoning* is a method to be
>used only when appropriate.
Who could argue with that?
> We do not keep our balance by any kind of reasoning.
Generally correct, although there may be exceptions. I expect that
there is a certain amount of reasoning involved in the work of a
tightrope walker, although maintaining balance is still not
exclusively a matter of reasoning.
>That said, it seems rather that logic is the sine qua non of reasoning,
>it stands to reasoning something as the rules of chess stand to chess
>games -- without the norms it sets, there is no such thing.
Well that has been your implicit assumption. I haven't yet seen any
good argument for this.
>>It seems to me that you are assuming what you are trying to prove --
>>namely, that reasoning and argumentation are both a matter of logic.
>It is not that both are "a matter of logic". It is, to repeat, that
>such things as affirming the consequent are fallacies, invalid
>transitions, and the fallacy is exactly the same whether committed in
>silent thought or overt argumentation.
That using fallacious logical forms is evidence of incompetent
reasoning would not seem to demonstrate that all valid reasoning is
logic.
>What I am saying rests only on the idea that we can evaluate cognitive
>transitions in thought and speech for such things as validity. I.e. there
>are inferences in both. Logic stands to these transitions as grammar
>does to correctness in speech, i.e. it aims to codify them, to make
>what is implicit in patterns of inference we accept explicit.
And, just as I am skeptical on grammar as codifying proper speech, I
am skeptical on logic as codifying good reasoning.
>As near as I can tell you seem to me to presuppose that logic must be
>something that could be found in a purely formal and disconnected
>symbol system, and then attack the significance of logic as so
>conceived.
A little confused, I think. In particular, I do not attack the
significance of logic, so conceived. On the contrary, I readily
agree that logic, so conceived, can be quite useful.
> But I do not want to use such a conception of logic. I want
>to talk about *human* logic, the logical properites to be found in the
>operations with symbols conducted by human beings in the course of
>concrete activities in the world.
But what I am disagreeing with, is precisely the claim that human
reasoning is a matter of operations with symbols.
> Since criticizing someone's reasoning
>is clearly something human beings do, I think there must be such a thing.
That would support the idea that people are able to use natural
language to communicate aspects of their reasoning, and that when
this communication is successful, the listeners are able to do
'similar' reasoning. (I use scare quotes, because 'similar' is a
very tricky concept). But I don't see any basis there for the
apparent claim that reasoning is a matter of operations with
symbols.
> First whether you do or do not succeed in persuading
>others is a purely psychological matter, with no right or wrong about
>it: either it happens or it doesn't. Perhaps your audience will be
>swayed by fallacies. But whether your reasoning *ought* to be
>persuasive is a logical matter. Yet logic is a normative discipline,
>concerned with the ought's of correct reasoning not the is's of
>merely subjectively persuasive reasoning.
It would seem that you would require some sort of neuroscope, or
electro-encephalograph, and apply the logic to the output of that
machine if logic is to be a normative discipline concerned with
reasoning. Has this ever been done successfully?
> That is what is distinctive
>about logical properties, that they are not merely psychological,
>but normative. If your reasoning is good then it *ought* to persuade
>others (but may not); and conversely if it is not.
This sounds like standard philosophical dogma. I cannot say that I
find any basis for it.
In what I take to be the standard meaning of 'logic', it is a matter
of procedures one follows to go from premises to a conclusion. But
it seems to me that most reasoning starts before there are premises.
And if logic is to be used, then part of the reasoning is in coming
up with suitable premises. And it seems to me that part of
argumentation is involved with trying to persuade others to accept
your premises.
Part of what I am suggesting, is that often we reach a conclusion
first. Then we attempt to come up with premises from which we could
deduce the conclusion. That is, we often retrofit a logical form to
our reasoning.
>But mainly, the idea is that a cognitive transition doesn't count as
>"reasoning" unless you can articulate it in language so others are in a
>position to evaluate it for its cogency.
I am inclined to think this is unnecessarily strict. It seems to me
that we can sometimes persuade people of the validity of our
reasoning by making an unsuspected prediction, and having that
prediction turn up to be correct. With this form of persuasion, the
reasoning itself may never be fully articulated. I would think that
the professional judgement of experts is often evaluated in this
manner.
In any case, lets temporarily accept your idea. That would provide
evidence that language can be used to convey to other people enough
information that they can carry out 'similar' reasoning, and reach
'similar' conclusions. It would fall far short of demonstrating that
the reasoning itself was a matter of operations with symbols.
>As I say, such things as walking and catching fly balls and much else
>is not effected by reasoning, that is perfectly true and
>uncontroversial.
I think that is false. For sure, a great deal of ordinary walking
does not involve reasoning. But try to walk on slippery ice, or try
to step on a sequence of rocks to walk across a stream without
getting wet, and I think you cannot do it without reasoning. I'm not
an expert in baseball, but I would be surprised if catching fly balls
did not sometimes involve reasoning.
Neil Rickert
>Do you and Rickert hold that there is no significant portion of natural
>language which admits of a translation into the language of FOPL in much the
>manner taught to freshmen logic students?
Jim Balter has answered this pretty well. I'm not sure what would
count as "significant."
>Or take an alternative version of the question, if it seems better. Do you and
>Rickert hold that there is not a significant amount of language use that
>admits of this sort of translation?
Again, "significant" is a little unclear here.
Let me put the problem this way. Unless there are clear objective
criteria by which we can decide whether a part of language is
suitable for logic, it would not seem to matter. Jim has presented
several arguments, given in an apparent logical form, which reach
foolish conclusions. Weinstein complains that these are invalid
arguments. I am asking whether there are objective,
non-psychological criteria to detect when an argument is invalid,
even though it seems to fit a logical form. If there are not such
criteria, then it seems to me to be a better explanation to say that
people reach their conclusions on a basis other than logic, and then
declare an argument to be invalid if that argument conforms to an
apparent logical form but contradicts the conclusion already
reached.
Neil Rickert
>In some of these exchanges it appears that a *solution* is being
>sought for the problem of failure of substitution salva veritate
>within intensional contexts.
I don't think either Jim Balter or I are looking for solutions.
Perhaps we are suggesting that this is a pseudo-problem that does not
require solutions.
Jim Balter
> You substituted "is-mother-of(Oedipus)" for the name "Oedipus" in a
No, I never did that. Nor did I substitute "is-mother-of(Oedipus)"
for "Jocasta".
> context
> where the distinction between name and predicate was the matter at hand.
> If "Oedipus" is identical to "is-mother-of(Oedipus)" in *all* contexts,
Jocasta is identical to Oedipus' mother. Period.
But you can't do the substitution of terms in intensional contexts
because their meaning depends not just on what is referenced but on
the form of the reference itself. It's a bit like "pass by name"
vs. "pass by reference" in programming languages.
> then Leibniz would have allowed the substitution, but that is clearly not
> the case.
What is clearly the case is that you are too sloppy a thinker
for me to effectively communicate with.
--
<J Q B>
Anders N Weinstein
Jim Balter <j...@sandpiper.net> wrote:
>AW:
>"it is only
>rather special subclasses of predicates (modal, psychological) that
>create contexts recalcitrant to Quine's favored logical apparatus."
>
>in natural language *is* one. With such an assumption, Sorites
I don't see where I make such an error. Perhaps there is some
special baggage attached to your use of "predicate" that is not in mine.
Of course you can always argue that contrary to appearances, such and
such is not really a predicate (existence comes to mind). But then
you have to make the case.
>paradoxes seem quite mysterious, because is_a_heap() is neither
>modal nor psychological, so this predicate should be just fine.
Hmm. You don't actually seem to be denying that is_a_heap() is a predicate.
Of course there are many different ways a locution can be resistant to
formalization in standard logic. All I meant was that it is
non-extensionality that is Quine's bete noire. Vague predicates also
pose problems, albeit different ones.
>But "is a heap" and much other natural language do not obey
>the requirements of FOPL or anything like it.
Doesn't the sorites arise from the apparently plausible "inductive"
axiom "IF a pile of n grains constitutes a heap then a pile of n-1
grains [still] constitutes a heap"? But that is not a logical
axiom, and it is not a requirement of FOPL that predicates be governed
by it.
Jim Balter
> Let me put the problem this way. Unless there are clear objective
> criteria by which we can decide whether a part of language is
> suitable for logic, it would not seem to matter. Jim has presented
> several arguments, given in an apparent logical form, which reach
> foolish conclusions. Weinstein complains that these are invalid
> arguments. I am asking whether there are objective,
> non-psychological criteria to detect when an argument is invalid,
> even though it seems to fit a logical form.
Yes, this is vital point that I was thinking of but never wrote down.
AW would have it that there are just these recalcitrant special
subclasses that we have identified. CDJ says that they are explained
by multiple perspectives, and then agrees that virtually all
natural language includes multiple perspectives. What grounds, then,
do we have for saying that the areas identified are the only ones, or
to imply that these are a small portion of language? What about all
the discussions here about consciousness, intelligence, and so on,
with no consensus? Don't these reflect the involvement of multiple
perspectives? These different perspectives are an *empirical*
matter, not a logical matter, in that they reflect people's
different experiences, including different exposure to word usage.
Logic can help untangle some of this, but not all, especially when
very few humans are adept at its use, and those who are, are often
the least aware of its limitations, a bit like surgeons who love
to cut.
> If there are not such
> criteria, then it seems to me to be a better explanation to say that
> people reach their conclusions on a basis other than logic, and then
> declare an argument to be invalid if that argument conforms to an
> apparent logical form but contradicts the conclusion already
> reached.
Well, I would say that logic is just one basis among several that
people use. It's that old analytic/synthetic thang.
--
<J Q B>
Jim Balter
The only problem is that some people who have taken a freshman
course in logic, and other assorted logicists, try to apply such
substitutions inappropriately and otherwise naively treat natural
language that resembles FOPL as if it *were* FOPL.
Henny Youngman gave the solution.
--
<J Q B>
Anders N Weinstein
>ande...@pitt.edu (Anders N Weinstein) writes:
>>In article <6ns05h$r...@ux.cs.niu.edu>, Neil Rickert <ric...@cs.niu.edu> wrote:
>>>ande...@pitt.edu (Anders N Weinstein) writes:
>
>>By logical property I mean such things as validity, or more broadly
>>cogency of support.
>
>I'll readily grant that it is possible to use the term "logic" so
>broadly that the word loses its usefulness.
Why does this lose its usefulness? There are cognitive transitions that
in which one proposition is inferred from others and the transition
can be evaluated for correctness. That is where logic is found.
>>>> Since argumentation and
>>>>reasoning are identical in their logical properties --
>
>>>Well, that sounds about right. As we mathematicians would say, it is
>>>vacuously true. In other words, argumentation has no logical
>>>properties, and reasoning has no logical properties. Therefore these
>>>are identical in their logical properties.
>
>>You are free to make that claim, but it seems absurd. For example,
>>we say that people have made a faulty inference. Balter delights in
>>charging me with affirming the consequent.
>
>Inferences which reach wrong conclusions can be considered faulty,
>whether or not they are logical inferences.
As I am sure you know, an inference can be criticized in different
ways. It might have valid logical form but still reach a false
conclusion (because the premises are false). And an inference of
invalid logical form can stumble by accident as it were into a true
conclusion. So I would say your statement is too crude, it blurs
the distinctions we can make between soundness and validity. Evaluating
reasoning is not solely a matter of the rightness of the conclusion.
>>My point is: if I have indeed affirmed the consequent it makes no
>>interesting difference whether I have done so in silent reasoning or
>>overt speech. I have committed the same logical error in both cases.
>
>Agreed. But I don't see this as providing much support for your
>case. Apparently there is an implicit assumption in the above
>arguments that reasoning is logic. But it is that implicit
>assumption that is being disputed.
I don't even understand the claim "reasoning is logic". I mean only that
reasoning is a norm-governed transition in thought from premises to
conclusion that can be evaluated in certain ways. Logic aims to make explicit
a certain sort of goodness of the inferential transitions (validity in terms
of logical form). One can speak of the logic of material predicates
too, e.g. a logic of color terms.
>> Can
>>I then say, oh, I am not using logic on this?
>
>It wouldn't help. You were, after all, giving an argument. And an
>argument presented in the form of a fallacious logical step is never
>very convincing.
Here again you slide from an objective property like validity to a
subjective one like convincing. But it seems to me that invalid
arguments are often quite convincing ("if you oppose the
anti-flag-burning amendment, you must be in favor of burning the
flag"). Anyway it is clear that what is convincing to a particular audience
need not be the same as what is a good argument, so the point is irrelevant.
>That using fallacious logical forms is evidence of incompetent
>reasoning would not seem to demonstrate that all valid reasoning is
>logic.
No. But why don't you indicate some examples of what you mean by reasoning
for which a notion of validity is defined that "is not logic"? Do you
mean material validity, ie. validity dependent on the logic of the
extra-logical predicates? That still counts as logic in the broad sense
I was using.
>> But I do not want to use such a conception of logic. I want
>>to talk about *human* logic, the logical properites to be found in the
>>operations with symbols conducted by human beings in the course of
>>concrete activities in the world.
>
>But what I am disagreeing with, is precisely the claim that human
>reasoning is a matter of operations with symbols.
Actually I do not hold that reasoning is an operation with symbols.
The relevant operation with symbols is *expressing* or *articulating*
one's reasoning. I am recommending the view that our concept of reasoning
is the concept of something essentially *expressible* in language. The
reasoning can occur in a flash, as we say, as long as it can be unpacked
into symbols so that anyone can evaluate its cogency.
>> Since criticizing someone's reasoning
>>is clearly something human beings do, I think there must be such a thing.
>
>That would support the idea that people are able to use natural
>language to communicate aspects of their reasoning, and that when
>this communication is successful, the listeners are able to do
>'similar' reasoning. (I use scare quotes, because 'similar' is a
Mainly that the others can evaluate and criticize the cogency of
the inferential transitions that constitute the bit of reasoning.
>very tricky concept). But I don't see any basis there for the
>apparent claim that reasoning is a matter of operations with
>symbols.
Again, I don't claim reasoning *is* an operation with symbols. I
claim that reasonings are expressibilia, potentialities for being expressed,
and public language vehcicles constitute the medium of expression
into which they get poured.
>> First whether you do or do not succeed in persuading
>>others is a purely psychological matter, with no right or wrong about
>>it: either it happens or it doesn't. Perhaps your audience will be
>>swayed by fallacies. But whether your reasoning *ought* to be
>>persuasive is a logical matter. Yet logic is a normative discipline,
>>concerned with the ought's of correct reasoning not the is's of
>>merely subjectively persuasive reasoning.
>
>It would seem that you would require some sort of neuroscope, or
>electro-encephalograph, and apply the logic to the output of that
>machine if logic is to be a normative discipline concerned with
>reasoning. Has this ever been done successfully?
I really have no idea what you are talking about here. Certainly a
neuroscope would be completely irrelevant. Mathematicians when they
check a proof do not need to apply a neuroscope to the mathematician.
The logical properties of an argument are quite indepenent of the
electro-chemical properties of the arguer. If I don't understand what
you are saying, looking inside your brain would be of no help.
>In what I take to be the standard meaning of 'logic', it is a matter
>of procedures one follows to go from premises to a conclusion. But
Not quite procedures. More like constraints. The rules of chess are not
procedures for playing chess, for they are "non-deterministic", they do
not determine a course of play. Similarly norms of correct reasoning do
not determine the actual course of your thought, they have no "control
structure".
>it seems to me that most reasoning starts before there are premises.
I'm not clear what this means. Can you give me an example of how
some reasoning proceeds from a point before there are premises?
>And if logic is to be used, then part of the reasoning is in coming
>up with suitable premises. And it seems to me that part of
>argumentation is involved with trying to persuade others to accept
>your premises.
I agree there can be such a thing as trying to provoke others into accepting
certain premises. Perhaps someone cannot see the dalmatian in that
famous washed out spotted picture, and so does not share a certain premise
of yours to the effect that it is a dog-picture. Then you have to cajole
them in various ways to help them acquire a premise, to be able to see it
as the dog-picture it is. But again, it is not so clear that is reasoning
or even persuasion.
>Part of what I am suggesting, is that often we reach a conclusion
>first. Then we attempt to come up with premises from which we could
>deduce the conclusion. That is, we often retrofit a logical form to
>our reasoning.
That seems compatible with what I've been saying. On the other hand it
is a question whether there is any good basis for the conclusion until
the support is found.
>>But mainly, the idea is that a cognitive transition doesn't count as
>>"reasoning" unless you can articulate it in language so others are in a
>>position to evaluate it for its cogency.
>
>I am inclined to think this is unnecessarily strict. It seems to me
>that we can sometimes persuade people of the validity of our
>reasoning by making an unsuspected prediction, and having that
>prediction turn up to be correct. With this form of persuasion, the
>reasoning itself may never be fully articulated. I would think that
>the professional judgement of experts is often evaluated in this
>manner.
That is what I called empirically evaluating someone's reliablity.
But if the person is just going by what feels to them like a hunch,
then however reliable it is, however well-grounded in terms of operations
in their neurons, it is not clear to me we should call it reasoning
performed by the person.
>In any case, lets temporarily accept your idea. That would provide
>evidence that language can be used to convey to other people enough
>information that they can carry out 'similar' reasoning, and reach
>'similar' conclusions. It would fall far short of demonstrating that
>the reasoning itself was a matter of operations with symbols.
As I say, the point is not so much whether others can reproduce it as
whether they can evaluate it, and I agree that reasoning is not
itself an operation with symbols, but I insist that reasoning as we
conceive it is governed by objective norms, that makes it essential
to reasoning that it be intersubjectively evaluable and so must
*expressible*. Then our theoretical handle on the reasoning comes by
way of its overt expression, even if the reasoning is one thing and
the expression another.
Jim Balter
>
> ande...@pitt.edu (Anders N Weinstein) writes:
> >In article <6ns05h$r...@ux.cs.niu.edu>, Neil Rickert <ric...@cs.niu.edu> wrote:
> >>Well, that sounds about right. As we mathematicians would say, it is
> >>vacuously true. In other words, argumentation has no logical
> >>properties, and reasoning has no logical properties. Therefore these
> >>are identical in their logical properties.
>
> >You are free to make that claim, but it seems absurd. For example,
> >we say that people have made a faulty inference. Balter delights in
> >charging me with affirming the consequent.
It's not exactly delight; I'd prefer to have no cause to make the
charge.
> Inferences which reach wrong conclusions can be considered faulty,
> whether or not they are logical inferences. Balter's charges are
> that you organize your arguments into an invalid logical form.
>
> >My point is: if I have indeed affirmed the consequent it makes no
> >interesting difference whether I have done so in silent reasoning or
> >overt speech. I have committed the same logical error in both cases.
>
> Agreed. But I don't see this as providing much support for your
> case. Apparently there is an implicit assumption in the above
> arguments that reasoning is logic. But it is that implicit
> assumption that is being disputed.
Anders points out something that he thinks follows from his position
as support of his position. Which is, of course, an example of
affirming the consequent.
It is undisputed that affirming the consequent is the same
logical error whether done silently or not. It *does not follow*
that either reasoning or argumentation "have logical properties",
nor that they have "identical logical properties", nor that they
have "no important theoretical difference". To show those, one must
argue for why they follow from something agreed to, not mention
something agreed to and expect anyone to therefore accept the premise.
> > Perhaps sometimes it is correct to
> >affirm the consequent in a chain of inferences, and others not?
>
> Perhaps so. But if it is correct to do so, that is not a matter of
> logic.
Of course. One can affirm the consequent all one wants.
If it is affirmable, it is affirmable. But the antecedent doesn't
thereby follow.
> > Can
> >I then say, oh, I am not using logic on this?
Right, you're not -- logic is the application of inference rules,
and you applied no inference rule. Unless, as I've suggested
many times before, you are a Martian who thinks that affirmation of
the consequent is an inference rule, but *you* are the one who
insisted that we wouldn't even *recognize* such Martians to be using
logic (perhaps you have forgotten that contradiction among your
positions; with so many, I'm sure its hard to keep track).
I'll concede, we don't recognize them to be using logic,
because they aren't. But we could recognize that they are using
something that they *take* to be logic, which of course is my complaint
about mistaking natural language for FOPL. Which is not to say
that one cannot apply inference rules to natural language, as long
as the particular natural language has the (rather restrictive)
properties required by FOPL.
[snipped too much to comment on with too little time,
and it's all been said before]
> >As I say, such things as walking and catching fly balls and much else
> >is not effected by reasoning, that is perfectly true and
> >uncontroversial.
>
> I think that is false. For sure, a great deal of ordinary walking
> does not involve reasoning. But try to walk on slippery ice, or try
> to step on a sequence of rocks to walk across a stream without
> getting wet, and I think you cannot do it without reasoning. I'm not
> an expert in baseball, but I would be surprised if catching fly balls
> did not sometimes involve reasoning.
This is at the wrong level. The question is whether such things
as walking etc. can be *modeled* as reasoning, and there is no
reason to think that they can't (else people couldn't have built
GOFAI robot walkers), even if that isn't the most effective sort of model.
--
<J Q B>
Jim Balter
>
> In article <35A1C0BF...@sandpiper.net>,
> Jim Balter <j...@sandpiper.net> wrote:
> >AW:
> >"it is only
> >rather special subclasses of predicates (modal, psychological) that
> >create contexts recalcitrant to Quine's favored logical apparatus."
> >
> >He has already assumed that everything that *looks* like a predicate
> >in natural language *is* one. With such an assumption, Sorites
>
> I don't see where I make such an error. Perhaps there is some
> special baggage attached to your use of "predicate" that is not in mine.
> Of course you can always argue that contrary to appearances, such and
> such is not really a predicate (existence comes to mind). But then
> you have to make the case.
I have repeatedly pointed out that predicates provide an unambiguous
truth value for every argument in their domain. The law of the
excluded middle and the law of non-contradiction are either axioms of
or consequences of FOPL, depending upon how it is formulated.
> >paradoxes seem quite mysterious, because is_a_heap() is neither
> >modal nor psychological, so this predicate should be just fine.
>
> Hmm. You don't actually seem to be denying that is_a_heap() is a predicate.
"With such an assumption ...". Sheesh, are you blind?
> Of course there are many different ways a locution can be resistant to
> formalization in standard logic. All I meant was that it is
> non-extensionality that is Quine's bete noire. Vague predicates also
> pose problems, albeit different ones.
Yes, indeedy. We call something a heap and then deal with it as
an abstract entity. But there is no truth value as to which things
are heaps -- we do not go around trying to decide what things are
heaps and what things are not, except in the silly exercises of
logicists. "Logical" arguments that try to reach a deductive
conclusion about heaps based upon treating "heap" like a logical
predicate fail, because that's not the role that "heap" plays
in English. "heap" is used for *communication*, a sharing of
experience, not for logical deduction. The "perspectivalness"
that CDJ mentioned is not something we can "idealize" away,
something we can ignore except in the "special subclasses" of
modal and psychological contexts -- it is at the *heart* of
natural language.
> >But "is a heap" and much other natural language do not obey
> >the requirements of FOPL or anything like it.
>
> Doesn't the sorites arise from the apparently plausible "inductive"
> axiom "IF a pile of n grains constitutes a heap then a pile of n-1
> grains [still] constitutes a heap"? But that is not a logical
> axiom, and it is not a requirement of FOPL that predicates be governed
> by it.
Huh? Mathematical induction follows from FOPL!
And Sorites can (of course!) be formulated without induction.
It is well-established that Sorites paradoxes arise out of vagueness;
here's a reference:
http://plato.stanford.edu/archives/fall1997/entries/sorites-paradox/
--
<J Q B>
Seth Russell
> Seth Russell wrote:
>
> > You substituted "is-mother-of(Oedipus)" for the name "Oedipus" in a
> No, I never did that. Nor did I substitute "is-mother-of(Oedipus)"
> for "Jocasta".
Go back and look at your diagram and then tell me you did not make that exact
substitution. Incidentally, obviously "Oedipus' mother" ==
"is-mother-of(Oedipus)" with the only distinction being notation.
> > context
> > where the distinction between name and predicate was the matter at hand.
> > If "Oedipus" is identical to "is-mother-of(Oedipus)" in *all* contexts,
>
> Jocasta is identical to Oedipus' mother. Period.
Well that is dead wrong. Jocasta is the name of Oedipus's wife and his
mother. The *whole symbol* comprising all the predicates that this mind
example knows about Joscata points (refers) to an entity outside of that mind
example. That is the predicament of mental symbols. The word "Jocasta" is
not the only part of that symbol. Of course if you don't accept that, then I
understand why you would say that "Jocasta is identical to Oedipus' mother.
Period.". Please bear in mind that we are playing with my definition of
symbol and my diagram. Sorry the game is kind of rigged. But I think this
symbol/diagraming (I call it mentography) helps people understand and see
through this thought problem without confusion.
> But you can't do the substitution of terms in intensional contexts
> because their meaning depends not just on what is referenced but on
> the form of the reference itself. It's a bit like "pass by name"
> vs. "pass by reference" in programming languages.
Some extensional verbs when substituted for "knows" would salva veritate and
others would not. For example "Oedipus is-yourger-than his mother" is true,
whereas "Oedipus divorced his mother" would be false. "Divorced" is a legal
term that is quite extensional (right?) and the legal papers would read
"Jocasta". I assume that any level of inference not contained in the example
is irrelevant to the example. Actually in this case I realize that I am on
shaky grounds. You can see clearly the distinction between extensional and
intensional verbs in the SVO diagram. However, the real question is whether
all predicates with the subject Jocasta apply within the context of the
original verb. As extensional verbs are usually independent of context, they
all should work. So I see the problem as one of context-independence or
context-sensitiveity rather than extensionality and intensionality.
But all of that is immaterial to the fact that you are substituting strings
into language and expecting their referents to be preserved in the deep
meaning. I claim that is a category error of the first magnitude.
> > then Leibniz would have allowed the substitution, but that is clearly not
> > the case.
>
> What is clearly the case is that you are too sloppy a thinker
> for me to effectively communicate with.
Well if you were more interested in matching facts and correcting errors than
in proving me a sloppy thinker, we might actually be able to get somewhere.
Maybe I should just admit it ... I am a sloppy thinker ... now let's get back
to business.
Jim Balter
>
> Jim Balter wrote:
>
> > Seth Russell wrote:
> >
> > > You substituted "is-mother-of(Oedipus)" for the name "Oedipus" in a
> > No, I never did that. Nor did I substitute "is-mother-of(Oedipus)"
> > for "Jocasta".
>
> Go back and look at your diagram and then tell me you did not make that exact
> substitution. Incidentally, obviously "Oedipus' mother" ==
> "is-mother-of(Oedipus)" with the only distinction being notation.
No it is not. is-mother-of-Oedipus() has a boolean value.
> Well that is dead wrong. Jocasta is the name of Oedipus's wife and
use/mention. "Jocasta" is her name; Jocasta is his wife.
> Well if you were more interested in matching facts and correcting errors than
> in proving me a sloppy thinker, we might actually be able to get somewhere. Maybe I should just admit it ... I am a sloppy thinker ... now let's get back
> to business.
It does no good to correct errors for someone too sloppy
even see that they are errors and corrections. If the business
is to have a rational dialog, I find that hopeless with you.
If the business is for you to spout your ill-conceived preconceptions,
you can do that without me.
--
<J Q B>
Neil Rickert
>In article <6ntgon$e...@ux.cs.niu.edu>, Neil Rickert <ric...@cs.niu.edu> wrote:
>>But what I am disagreeing with, is precisely the claim that human
>>reasoning is a matter of operations with symbols.
>Actually I do not hold that reasoning is an operation with symbols.
>The relevant operation with symbols is *expressing* or *articulating*
>one's reasoning.
But I don't agree that expressing one's reasoning is working with
symbols.
>I really have no idea what you are talking about here. Certainly a
>neuroscope would be completely irrelevant. Mathematicians when they
>check a proof do not need to apply a neuroscope to the mathematician.
Mathematicians are not concerned with reasoning. They are concerned
with proofs. One should avoid confusing the two.
>>it seems to me that most reasoning starts before there are premises.
>I'm not clear what this means. Can you give me an example of how
>some reasoning proceeds from a point before there are premises?
It seems to me that in this thread we are arguing, and presumably
backing our arguing with reasoning, yet we have no agreement on
premises.
Jim Balter
> By "predicate" I just mean a phrase (more generally, an open sentence)
> of natural language that is predicable, that can be attached to a
> singular term to form a sentence. (A sharper definition would call for
> lots of work.) For example, if I say "that's a heap", in my sense I am
> appying the predicate "is a heap" to the demonstrated object. So for me
> it can be an open question whether the logic of predicates of natural
> language can be captured with the sharply defined predicates of FOPC.
"logic of predicates" begs the question. And its an open question
for you because you keep ignoring the answer -- they can't, because
they don't have truth values.
> >> >paradoxes seem quite mysterious, because is_a_heap() is neither
> >> >modal nor psychological, so this predicate should be just fine.
> >>
> >> Hmm. You don't actually seem to be denying that is_a_heap() is a predicate.
> >
> >"With such an assumption ...". Sheesh, are you blind?
>
> I think this just stems from the fact that we are using "predicate" in
> different ways. See above.
No, it stems from you're being blind, or acting that way.
I said "With such an assumption [that "is a heap" is a predicate] ...".
Of course I "don't actually seem to be denying" that, if "is a heap"
is a predicate, then "is a heap" is a predicate! It doesn't
matter what I mean by it.
[snip too much stuff to unwrap and it won't matter a hill of beans
whether I do or not]
> >> Doesn't the sorites arise from the apparently plausible "inductive"
> >> axiom "IF a pile of n grains constitutes a heap then a pile of n-1
> >> grains [still] constitutes a heap"?
> >It is well-established that Sorites paradoxes arise out of vagueness;
>
> I wasn't disagreeing with that.
Whatever you say, Anders. But there are no grounds for denying
the inductive axiom, there are no specifiable cases where it fails.
Rather, the paradox arises from the assumption that *whether*
a pile of n grains constitutes a heap has a precise answer.
There is no need to doubt that *if* n grains form a heap, so do n-1.
Of course, you can absolutely flatly deny that 1 grain forms a
heap, and then you are forced to question the step from 2 to 1,
and either say that 2 grains is a heap and its an invalid step,
acknowledge that there is no precise answer to whether 2 grains is a
heap, or flatly deny that 2 is a heap and go on to the step from
3 to 2. Somewhere along the line your either admit to imprecision
or deny a step. But since there is no clear basis, from the word
"heap", for denying any particular step, we are left with the
clear recognition that "is a heap" does not provide a clear answer,
which makes "argumentation" somewhat pointless.
--
<J Q B>
Jim Balter
> >> Doesn't the sorites arise from the apparently plausible "inductive"
> >> axiom "IF a pile of n grains constitutes a heap then a pile of n-1
> >> grains [still] constitutes a heap"?
Hey, I missed this affirmation of the consequent:
If there's something wrong with the inductive step, then we get a
paradox. We have a paradox. Therefore, there's something wrong with
the inductive step.
You are in good and broad company on that one. Notably, though,
independent grounds for thinking that there is anything wrong with
the inductive step are not in evidence.
> But that is not a logical
> >> axiom, and it is not a requirement of FOPL that predicates be governed
> >> by it.
> >
> >Huh? Mathematical induction follows from FOPL!
I somehow misread you as referring to mathematical induction
in general, rather than the specific inductive hypothesis; sorry.
--
<J Q B>
Seth Russell
> Seth Russell wrote:
> > Go back and look at your diagram and then tell me you did not make
> > that exact substitution. Incidentally, obviously "Oedipus' mother" ==
> > "is-mother-of(Oedipus)" with the only distinction being notation.
>
> No it is not. is-mother-of-Oedipus() has a boolean value.
The syntactic structure "Oedipus's mother" can be transformed to the
predicate is-mother-of-Oedipus() without altering its meaning in any way -
both expressions denote the same thing and are therefore identical. That
your FOPC notation associates a truth value to a predicate and you haven't
though of associating a truth value to a possessive noun clause is
"beauty-in-the-eye-of-Balter" quite apart from the meaning the clause
denotes. The fact of the matter is anything you say about something can be
true of that thing or not. For example: the subject of the sentence
"Balter's shit for brains wants always to be right." obviously points to
the substance between your ears and the vernacular idiom with which I
characterize that substance can be true of it or not. That is a predicate,
like it or not. Note, we are discussing Leibniz's law, which deals with
substances and not with your current notions of syntactic structures.
David Longley
j...@sandpiper.net "Jim Balter" writes:
> The only problem is that some people who have taken a freshman
> course in logic, and other assorted logicists, try to apply such
> substitutions inappropriately and otherwise naively treat natural
> language that resembles FOPL as if it *were* FOPL.
>
All sorts of (educated and uneducated) people do it. People make
inferences about what people *must* believe in epistemic
contexts, what they must want etc. They are often surprised as a
consequence. They substitute in such contexts. They make
inferences in such contexts - they try to quantify in - and it's
just a mistake to do so. Such people have no courses in logic,
and have no idea what the predicate calculus is - it's just the
way that natural language operates.
The mark of the mental is not the mind (Quine 1960;1990;,1992),
it's the "that" clause, the fact that people naturally try to
substitute salva veritate and quantify in. Examples of failure
include failure of transitivity. Yet people still think one can
make sense of individual preferences.
You need to look to the empirical data on behaviour first.
You and some others continue to miss the point.
Anders N Weinstein
Jim Balter <j...@sandpiper.net> wrote:
>Anders N Weinstein wrote:
>>
>> >He has already assumed that everything that *looks* like a predicate
>> >in natural language *is* one. With such an assumption, Sorites
>>
>> I don't see where I make such an error. Perhaps there is some
>> special baggage attached to your use of "predicate" that is not in mine.
>> Of course you can always argue that contrary to appearances, such and
>> such is not really a predicate (existence comes to mind). But then
>> you have to make the case.
>
>I have repeatedly pointed out that predicates provide an unambiguous
>truth value for every argument in their domain. The law of the
>excluded middle and the law of non-contradiction are either axioms of
>or consequences of FOPL, depending upon how it is formulated.
Ok, you are using "predicate" to mean "predicate in FOPC". I
don't use it that way.
By "predicate" I just mean a phrase (more generally, an open sentence)
of natural language that is predicable, that can be attached to a
singular term to form a sentence. (A sharper definition would call for
lots of work.) For example, if I say "that's a heap", in my sense I am
appying the predicate "is a heap" to the demonstrated object. So for me
it can be an open question whether the logic of predicates of natural
language can be captured with the sharply defined predicates of FOPC.
>> >paradoxes seem quite mysterious, because is_a_heap() is neither
>> >modal nor psychological, so this predicate should be just fine.
>>
>> Hmm. You don't actually seem to be denying that is_a_heap() is a predicate.
>
>"With such an assumption ...". Sheesh, are you blind?
I think this just stems from the fact that we are using "predicate" in
different ways. See above.
>> Of course there are many different ways a locution can be resistant to
>> formalization in standard logic. All I meant was that it is
>> non-extensionality that is Quine's bete noire. Vague predicates also
>> pose problems, albeit different ones.
>
>Yes, indeedy. We call something a heap and then deal with it as
>an abstract entity. But there is no truth value as to which things
>are heaps -- we do not go around trying to decide what things are
>heaps and what things are not, except in the silly exercises of
>logicists. "Logical" arguments that try to reach a deductive
>conclusion about heaps based upon treating "heap" like a logical
>predicate fail, because that's not the role that "heap" plays
>in English. "heap" is used for *communication*, a sharing of
>experience, not for logical deduction. The "perspectivalness"
This dichotomy is somewhat dubious. Either the 'experience' in question
is brute given sensation, in which case it is not really shareable, or
it is *conceptually informed* experience, as in Kant's "intutions
without concepts are blind". But in that case it has a content that is
subject to logic in a broad sense. For concepts are what they are in
part by playing combinatory roles in forming judgements which stand in
inferential relations.
To take an example, as Sellars suggested in EPM, you don't have a
*conceptual* experience of something *as* blue (in the loose everyday
sense) unless you are master of a set of inferential relations, at
minimum say that you understand that it's being blue is incompatble
with its being red (say); also of the idea that things can look other
than they are in strange light.
So communication of conceptualized experience requires that the
other person share some of the same network of inferential relations
and appreciate that the experience has "logical properties" insofar
as it has a propositional content.
>that CDJ mentioned is not something we can "idealize" away,
>something we can ignore except in the "special subclasses" of
>modal and psychological contexts -- it is at the *heart* of
>natural language.
CDJ is alluding to the role of perspectivalness in Brandom's theory of
conceptual content and objectivity. But *that* is a *thoroughly* logical
(inferential) matter. On Brandom's account, you are an inference engine, I am
an inference engine, but because we may have wound up with different
contexts of background premises ("perspectives"), one proposition
may be very different in inferential consequences for you and for me.
Just as an X-ray has different import (consequences) for an expert and
a lay person. There are further issues about the fact that we may have
different inference rules. For Brandom, objectivity emerges in the
process whereby we negotiate these differences. But it hardly points
to a divergence of natural language from logic in that account.
>> >But "is a heap" and much other natural language do not obey
>> >the requirements of FOPL or anything like it.
>>
>> Doesn't the sorites arise from the apparently plausible "inductive"
>> axiom "IF a pile of n grains constitutes a heap then a pile of n-1
>> grains [still] constitutes a heap"? But that is not a logical
>> axiom, and it is not a requirement of FOPL that predicates be governed
>> by it.
>
>Huh? Mathematical induction follows from FOPL!
I don't know what you are referring to here. Logicism? The fact that
set theory was not distinguished from logic in its early days?
Anders N Weinstein
>ande...@pitt.edu (Anders N Weinstein) writes:
>>In article <6ntgon$e...@ux.cs.niu.edu>, Neil Rickert <ric...@cs.niu.edu> wrote:
>
>>>But what I am disagreeing with, is precisely the claim that human
>>>reasoning is a matter of operations with symbols.
>
>>Actually I do not hold that reasoning is an operation with symbols.
>>The relevant operation with symbols is *expressing* or *articulating*
>>one's reasoning.
>
>symbols.
Can you explain? I mean, if I ask you how you reasoned your way to
a conclusion, either you can tell me "I thought this, therefore that"
or not. Then I can say "good job" or "but that doesn't follow".
The words that come out of your mouth in response are the symbols
I was talking about. What's the problem?
Bill Taylor
|> > --------------------
|> > ------| Oedipus |
|> > | --------------------
|> > [knows that] ^ ^
|> > | | |
|> > -->[is wife of] [is mother of]
|> > | |
|> > ---------------------
|> > | Oedipus' mother |
|> > ---------------------
Yes, your approach by using *predicates* as separate reified objects
is fine, if perhaps a little metaphysical for my taste. I prefer a
simpler approach involving people-with-qualities, which I posted about
six months or so ago. Probably amounts to much the same thing.
|> Yours and Quine's misuse of Liebniz's law is why we must repeal it for
|> across the board application.
Yes, it's hard to see why Quine and his followers get so knicker-twisted
about this issue. It's not as if it isn't VERY easy to determine when
substitution is valid and when it isn't. If there were any really
dangerous examples, there might be some justification for getting all bent
out of shape about it. But long winded types refuse to give any; nor have I
ever seen Quine (or other) give any such examples.
|> But everyone agrees that the meaning and
|> reasoning behind the words of natural language is sensitive to the context.
Zackerly.
|> Why would Quine
|> spend so much time doing something so patiently worthless?
Hah! Serendipitous typo! Truly, Quine has been patiently worthless here.
That "patience" of a pig-headed father, pompously instructing his sons,
endlessly and painedly, on something they know far more about than he does.
Remind you of anyone else?
|> Again, what have I missed?
Not a lot, old son, not a lot. Nothing significant.
The attitude of these extensionalists is truly baffling.
-------------------------------------------------------------------------------
Bill Taylor W.Ta...@math.canterbury.ac.nz
-------------------------------------------------------------------------------
The reason human beings invented language was
to get away from point-and-click interfaces.
-------------------------------------------------------------------------------
Jim Balter
>
> Jim Balter wrote:
>
> > Seth Russell wrote:
> > > Go back and look at your diagram and then tell me you did not make
> > > that exact substitution. Incidentally, obviously "Oedipus' mother" ==
> > > "is-mother-of(Oedipus)" with the only distinction being notation.
> >
> > No it is not. is-mother-of-Oedipus() has a boolean value.
>
> The syntactic structure "Oedipus's mother" can be transformed to the
> predicate is-mother-of-Oedipus() without altering its meaning in any way -
> both expressions denote the same thing and are therefore identical.
mother-of(Oedipus) = Jocasta.
is-mother-of(Oedipus) = <nonsense>.
I mistakenly replaced your nonsense with the wrong sensical thing.
[irrelevant blather snipped; hopefully no one else is senseless enough
to be reading this stuff anyway]
--
<J Q B>
Oliver Sparrow
"" If we have two
"" identical photo copies of a document, those copies can be substituted for
"" each other with no consequence to the facts of the matter. When the
"" objects are the objects of a mind, we must be very careful to distinguish
"" their properties - for example a name is *not* a predicate.
Is this not the principle of substitutability of particle physics, under an
older guise? If so, then the important distinctions between internal and
external symmetries matter, and some substitutions are gauge invariant and
some are not, from which the whole ball o' wax. That is, the Law isn't a law,
just a regularity in one part of the woods.
______________________________________
Oliver Sparrow
Oliver Sparrow
"" Mathematicians are not concerned with reasoning. They are concerned
"" with proofs. One should avoid confusing the two.
Neil: unbundle that worrying statement for us a little, please. Intuition
agrees, but Reason is concerned.
______________________________________
Oliver Sparrow
Seth Russell
> Seth Russell wrote:
> >
> > Jim Balter wrote:
> >
> > > Seth Russell wrote:
> > > > Go back and look at your diagram and then tell me you did not make
> > > > that exact substitution. Incidentally, obviously "Oedipus' mother" ==
>
> > > > "is-mother-of(Oedipus)" with the only distinction being notation.
> > >
> > > No it is not. is-mother-of-Oedipus() has a boolean value.
> >
> > The syntactic structure "Oedipus's mother" can be transformed to the
> > predicate is-mother-of-Oedipus() without altering its meaning in any way -
>
> > both expressions denote the same thing and are therefore identical.
> is-mother-of-Oedipus(Jocasta) = true.
> mother-of(Oedipus) = Jocasta.
> is-mother-of(Oedipus) = <nonsense>.
> I mistakenly replaced your nonsense with the wrong sensical thing.
Hey, we all can make mistakes, and "mother-of(Oedipus) = Jocasta" is
another. A name is not a predicate, a predicate is not a name, they are not
the same thing, they are not identical. We must be consistent. Expressions
which can be transformed into each other are allowable transformations and can
be substituted for each other. But there is no way to transform "Jocasta"
into "mother-of(Oedipus)" there is not enough information there - that is
unless you reach into your own mind and make connections that are not in our
example mind and that is not allowed. Now as to the name of the predicate ...
well there I have not been consistent ... i've been choosing whatever string
crops into my brain hole ... sorry ... so that "mother-of" or "is-mother-of"
are to me arbitrary designations and interchangeable ... but let's be
consistent and go with your "mother-of". Hopefully we will be able to go
back to the original example and see what I am talking about. These symbols
really do have a logic and you can think within them, but you do need to be
consistent and think a little like a machine and follow the rules - my rules -
sorry about that.
Jim, I really do appreciate this dialogue, and respect your greater depth of
knowledge of the historical ways of logic, and greater abilities to make
distinctions and ascertain allowable facts, and not get confused. If you can
only indulge me long enough to work through this one example arriving at a
consensus between us, then I think you will see that there is a point behind
this confusion that will justify the efforts. It might help for you to know
that there was once a real computer system that was built on these symbols,
and it did work, and it was consistent, although its mind was limited to 64k
bytes, including the operating system.
Thanks again for the dialogue ....
Neil Rickert
>In article <6nulfa$2...@ux.cs.niu.edu>, Neil Rickert <ric...@cs.niu.edu> wrote:
>>>>But what I am disagreeing with, is precisely the claim that human
>>>>reasoning is a matter of operations with symbols.
>>>Actually I do not hold that reasoning is an operation with symbols.
>>>The relevant operation with symbols is *expressing* or *articulating*
>>>one's reasoning.
>>But I don't agree that expressing one's reasoning is working with
>>symbols.
>Can you explain?
I think it very misleading to say that natural language words are
symbols.
> I mean, if I ask you how you reasoned your way to
>a conclusion, either you can tell me "I thought this, therefore that"
>or not.
Right. And if you are not impressed, I might try a different set of
words. So what I am doing is trying to induce some state of your
mind. The words are merely tools I use for that purpose. If words
were symbols, and if I was working with symbols, then I would have to
stick to the exactly right words (or symbols). I am working with
states of mind, rather than with symbols.
Neil Rickert
> ric...@cs.niu.edu (Neil Rickert) wrote:
>"" Mathematicians are not concerned with reasoning. They are concerned
>"" with proofs. One should avoid confusing the two.
>Neil: unbundle that worrying statement for us a little, please. Intuition
>agrees, but Reason is concerned.
Reasoning is a process that goes on in a person's mind, or in the
interaction of several persons. A proof is a formal instrument. The
mathematician is not much concerned with what processes are going on
within minds or between minds. However, the mathematician is
concerned with the contents of the formal instrument.
Sergio Navega
>
>In what I take to be the standard meaning of 'logic', it is a matter
>of procedures one follows to go from premises to a conclusion. But
>up with suitable premises. And it seems to me that part of
>argumentation is involved with trying to persuade others to accept
>your premises.
>
>first. Then we attempt to come up with premises from which we could
>deduce the conclusion. That is, we often retrofit a logical form to
>our reasoning.
>
Well, sorry, I took again this thread in the middle but I couldn't
resist commenting on these phrases. I utterly *agree* with these
paragraphs. In fact, if philosophers grasped the real depth of this,
most of them would be ashamed. Thanks again, Neil.
Logic and rules and "normative" thinking are often the last thing
that appears in one's mind. The "direction" in which our thought
flows is not determined by logic: it is determined by vague
goals, suspicions and intuitive clues. When these "pressures"
become strong enough, one start "paving" the floor with rules
and logical reasoning. Logic is used to justify our most
inner suspicions. It is that paved "road" that is subjectively
communicable through language. And if the listener is not
able to ground each rule (received through language) in his
own ground of suspicions, he (the listener) will not believe
on what he read. He may agree with the logic entailment, but
he will refuse to accept it. This newsgroup is the live proof
of this situation.
The main part of our thoughts is not, IMHO, the result of
logic entailment. It is almost always the result of "intuitive"
entailment (whatever that may mean). Denying the importance
of this intuitive mechanism is committing the sin of GOFAI:
implementing logic and rules and failing to grasp the
essence, which results in brittle and inflexible implementations.
Sure, "intuition" is a folk psychological concept. But that
is not a strong enough reason to avoid trying to understand
it *scientifically*. It is not because intuition is basically
subjective that we should avoid thinking about it and even
explain how it works.
Extensional and normative reasoning is, undoubtedly, the goal
to be attained when one is developing a theory. Critical
thinking should, in my opinion, be taught in high-school,
and we know that presently it is not. This is certainly a
great failure of our educational system.
But it is very important not to associate the need of critical
thinking with the *invalidity* of subjective intuition.
They are *complementary*, they should work *together* because
the results of using one alone are almost always unproductive
(examples abound).
With this I want to reinforce my point of view: throughout
the times we have studied extensively logic, their implications,
sound reasoning, etc. But we know very little of these
intuitive mechanisms. Cognitive Science is heroically pursuing
this understanding and it is the work of psychologists that's
shedding new light on this subject.
Watson and Crick's discovery of the double-helix structure of
DNA is a classical example of what I'm talking. Yes, there
was a moment of "aha!", in which the helical structure
suddenly appeared in their minds. But this was the result
of hard work, where "normative" and "extensional" procedures
were also employed. When one reads the history of this discovery
it becomes clear that most scientific discoveries happen
this way: interwoven logic reasoning with intuitional leads.
It is a process that should not be restrained, but emphasized.
It is the process that should be duplicated in computers (or
robots) to achieve intelligence artificially.
Don't tell me that intuition is not worth studying because
it is intentional (Skinner's "we don't want such a science").
For me, this is the worse part of behaviorism, something
as damaging as imposed religious beliefs. Let's not be
afraid of what seems incomprehensible or even vulgar to us.
Our list of victories in previously "inexpugnable" subjects
is very large. The only way of growing with this list is
keeping our minds open.
Regards,
Sergio Navega.
David Longley
> mat...@math.canterbury.ac.nz (Bill Taylor) writes:
>
> >Yes, it's hard to see why Quine and his followers get so knicker-twisted
> >about this issue. It's not as if it isn't VERY easy to determine when
> >substitution is valid and when it isn't. ...
>
> >The attitude of these extensionalists is truly baffling.
>
> There is always the possibility that evangelical extensionalists
> actually do not find it easy to determine when substitution is
> valid.
>
>
So, does that mean we are going to see more quotation and respect
for evidence from you and Taylor in place of the inferences,
imputations, attributions and such like about what others think
and believe etc.?
Or doesn't the restriction apply to you <g>?
David Longley
So reasoning is not a formal process or instrument, relying on
quantification (Frege 1879), rather it is "a process that goes on
in a person's *mind*...." So in your view, Frege's explication of
reasoning as inference, as a mechanical process relying on
quantification was not perhaps such a breakthrough.
Where computers perform "automated reasoning" (cf. Wos et al.'s
text of that title), they are not instantiating the above,
mechanical, algorithmic, machine processes? The are somehow doing
it in a "mind" or "between minds". Does that make reasoning an
irreducable "mental" phenomenon?
Wht are "mental" phenomena? Are they characterised by intensional
contexts?
David Longley
>
> Don't tell me that intuition is not worth studying because
> it is intentional (Skinner's "we don't want such a science").
> For me, this is the worse part of behaviorism,
Skinner says no such thing. You have to be careful to distinguish
what other people think he said. What Skinner suggested was that
we don't want a science of *behaviour*, ie it's too much of a
threat. As to intuition, there are very powerful behavioural
explications of this in terms of contingencies. The main point
that the radical behaviourist makes is that there are some of our
experiences which just aren't readily accessible to the verbal
community, so we are unable to talk about such processes as well
as we can other aspects of behaviour. It's a technical point.
Since most people initially come to hear about what behaviourism
is all about from the perspective of natural language and its
conceptual scheme, one only really comes to see what the real
points are as one comes to learn more of what the research in the
operant field is all about. If you think about it, this is true
of all learning - one's preconceptions are gradually revised and
replaced.
Most professionals don't bother trying to make this clear to
people beyond a cursory comment or two - they have no need to or
reason to.
It's a profound, and generally unappreciated point, bit natural
language and common sense are an impediment to grasping some
quite simple facts about the nature of behaviour and its control.
Seth Russell
> Neil Rickert wrote:
Well said gentlemen, well said !!
I would hasten to add that intuition must inevitably be
restrained by public regularities and point matches. At
the same time we should not, must not, reject intuition or
cast doubt on its validity. We should do this not because
we can reason or rationalize or empericize that judgment,
for we cannot, but by dint of a choice from the being of
our humanity.
Neil Rickert
>Well said gentlemen, well said !!
>I would hasten to add that intuition must inevitably be
>restrained by public regularities and point matches.
Absolutely. I insist that intuition is developed from experience
acting in the world and perceiving that world. Because of that
basis, the regularities of the world become embedded in our
intuition.
> At
>the same time we should not, must not, reject intuition or
>cast doubt on its validity.
As a scientist, I prefer to say that we should be prepared to be
skeptical of everything, including our own intuition.
Neil Rickert
>So, does that mean we are going to see more quotation and respect
>for evidence from you and Taylor in place of the inferences,
>imputations, attributions and such like about what others think
>and believe etc.?
I can't speak for Bill Taylor.
I shall continue to have high respect for evidence and considerable
skepticism for opinions which defy common sense. I shall continue to
criticize those who are unable to distinguish between evidence and
the opinions they have derived from that evidence. I shall continue
to value relevant citations, and to resent the unwarranted dumping of
large quotations on the newsgroup. I shall continue my practice of
being cautious about attributing any beliefs to others, yet I shall
continue discussing the issues and challenging opinions, even if
doing so requires my using the language of attribution.
>Or doesn't the restriction apply to you <g>?
I predict that Longley will continue to misinterpret my position, and
to ascribe to me beliefs that I do not hold.
Neil Rickert
>In article <6o02c6$3...@ux.cs.niu.edu> ric...@cs.niu.edu "Neil Rickert" writes:
>> Reasoning is a process that goes on in a person's mind, or in the
>> interaction of several persons. A proof is a formal instrument. The
>> mathematician is not much concerned with what processes are going on
>> within minds or between minds. However, the mathematician is
>> concerned with the contents of the formal instrument.
>So reasoning is not a formal process or instrument, relying on
>quantification (Frege 1879), rather it is "a process that goes on
>in a person's *mind*...."
Right.
> So in your view, Frege's explication of
>reasoning as inference, as a mechanical process relying on
>quantification was not perhaps such a breakthrough.
That sounds like an appropriate evaluation of Frege's work.
>Where computers perform "automated reasoning" (cf. Wos et al.'s
>text of that title), they are not instantiating the above,
>mechanical, algorithmic, machine processes? The are somehow doing
>it in a "mind" or "between minds". Does that make reasoning an
>irreducable "mental" phenomenon?
On the contrary, the term "automated reasoning" is a misnomer for the
type of work you mention. Those systems were useful in helping us
understand what we can automate. And they have been valuable when
used by mathematicians for doing formal work with a higher accuracy
than is readily achievable by humans. But I do not consider them to
be reasoning systems.
>Wht are "mental" phenomena? Are they characterised by intensional
>contexts?
"Mental phenomena" is a vague term, used mainly by philosophers. The
term is of only very limited usefulness because of this vagueness.
One of the aims of a cognitive science should be to find a more
precise language for discussing the underlying mechanism of human
behavior. For that matter, the expression "intensional contexts" is
not of much use either.
Seth Russell
A fine choice indeed. Perhaps you and Longley will discuss
the repercussions of self-fulfilling prophecies in the light
of that choice. Since I still don't believe Longley is
capable of dialogue, I still don't believe I will be
responding to him.
David Longley
> Seth Russell <seth...@clickshop.com> writes:
> >Sergio Navega wrote:
> >> Neil Rickert wrote:
>
> >Well said gentlemen, well said !!
>
> >I would hasten to add that intuition must inevitably be
> >restrained by public regularities and point matches.
>
> Absolutely. I insist that intuition is developed from experience
> acting in the world and perceiving that world. Because of that
> basis, the regularities of the world become embedded in our
> intuition.
>
But the problem is that we don't sample the world
representatively, so our intuitions (functional approximations
bet modelled currently by ANNs) are unreliably, and resistant to
logical inference via quantification.
> > At
> >the same time we should not, must not, reject intuition or
> >cast doubt on its validity.
>
> As a scientist, I prefer to say that we should be prepared to be
> skeptical of everything, including our own intuition.
>
Saying so doesn't alas, make it so - as the experimental evidence
- Wason (modus tollens), Tversky (transitivity), Kahneman and
Tversky (the conjunction law), plus all the studies between 1944
and 1991 (Dawes, Faust and Meehl. My point is that it is just a
context specific intellectualist myth) to claim rationality
prevails outside of trained professional roles or "context".
Without evidence from the extensional stance we are frequently
not in a position to put such scepticism into effect - one needs
a relation to be able to do that.
http//www.longley.demon.co.uk/Frag.htm
David Longley
> Da...@longley.demon.co.uk (David Longley) writes:
>
> >So, does that mean we are going to see more quotation and respect
> >for evidence from you and Taylor in place of the inferences,
> >imputations, attributions and such like about what others think
> >and believe etc.?
>
> I can't speak for Bill Taylor.
>
> I shall continue to have high respect for evidence and considerable
> skepticism for opinions which defy common sense. I shall continue to
> criticize those who are unable to distinguish between evidence and
> the opinions they have derived from that evidence. I shall continue
> to value relevant citations, and to resent the unwarranted dumping of
> large quotations on the newsgroup. I shall continue my practice of
> being cautious about attributing any beliefs to others, yet I shall
> continue discussing the issues and challenging opinions, even if
> doing so requires my using the language of attribution.
>
Turning over a new leaf then? It's taken long enough.
I look forward to seing you citing evidence and references, and
greater retraint in attribution. Of course "opinions" are not the
same as conjectures, so if you *are* going to challenge informed
scientific conjecturs, I hope you wil present the evience to
substantiate such challenges (as is the norm in science).
> >Or doesn't the restriction apply to you <g>?
>
> I predict that Longley will continue to misinterpret my position, and
> to ascribe to me beliefs that I do not hold.
>
I have no idea what beliefs you hold, I just see what you write
and I am refering to that. There's a difference, one is public
the other not.
David Longley
But you say "Reasoning is a process that goes on in a person's
mind". I'm trying to understand what you are referring to when
you say 'in a person's mind'. I'm also tryig to understand what
you are referring to when you write of 'reasoning'.
You seem to reject the classic line taken to this - ie the
Fregian explication of the modus operandi of inference in his
"Begriffsschrift" (1879) ...
Phil Roberts, Jr.
>
> Seth Russell <seth...@clickshop.com> writes:
> >Sergio Navega wrote:
> >> Neil Rickert wrote:
>
> >Well said gentlemen, well said !!
>
> >I would hasten to add that intuition must inevitably be
> >restrained by public regularities and point matches.
>
> Absolutely. I insist that intuition is developed from experience
> acting in the world and perceiving that world. Because of that
> basis, the regularities of the world become embedded in our
> intuition.
>
One regularity which has become embedded in nearly all primitive
cultures, many of whom have had virtually no contact with each
other, is the meme of the psychical self, as evidenced by the
belief in spirits etc. in nearly all primitive cultures. On
these grounds, given your statement above, I would assume you
might entertain the possibility that there might be some
"substance" to this meme.
> > At
> >the same time we should not, must not, reject intuition or
> >cast doubt on its validity.
>
> As a scientist, I prefer to say that we should be prepared to be
> skeptical of everything, including our own intuition.
Would that include what, from my perspective, is the purely
intuitionist conclusion that the ultimate nature of reality
is going to turn out to be physical, and therefore that the
meme of the psychical self is purely fictitious?
--
Phil Roberts, Jr.
Feelings of Worthlessness and So-Called Cognitive Science
http://www.geocities.com/Athens/5476
Neil Rickert
>In article <6o0brl$3...@ux.cs.niu.edu> ric...@cs.niu.edu "Neil Rickert" writes:
>> Da...@longley.demon.co.uk (David Longley) writes:
>> >So, does that mean we are going to see more quotation and respect
>> >for evidence from you and Taylor in place of the inferences,
>> >imputations, attributions and such like about what others think
>> >and believe etc.?
>> I shall continue to have high respect for evidence and considerable
>> skepticism for opinions which defy common sense. I shall continue to
>> criticize those who are unable to distinguish between evidence and
>> the opinions they have derived from that evidence. I shall continue
>> to value relevant citations, and to resent the unwarranted dumping of
>> large quotations on the newsgroup. I shall continue my practice of
>> being cautious about attributing any beliefs to others, yet I shall
>> continue discussing the issues and challenging opinions, even if
>> doing so requires my using the language of attribution.
>Turning over a new leaf then? It's taken long enough.
Evidently Longley cannot read. What I said in the above, is that I
shall continue using c.a.p. in much the way I have done in the past.
Neil Rickert
>In article <6o0crv$3...@ux.cs.niu.edu> ric...@cs.niu.edu "Neil Rickert" writes:
>> "Mental phenomena" is a vague term, used mainly by philosophers. The
>> term is of only very limited usefulness because of this vagueness.
>> One of the aims of a cognitive science should be to find a more
>> precise language for discussing the underlying mechanism of human
>> behavior. For that matter, the expression "intensional contexts" is
>> not of much use either.
>But you say "Reasoning is a process that goes on in a person's
>mind". I'm trying to understand what you are referring to when
>you say 'in a person's mind'. I'm also tryig to understand what
>you are referring to when you write of 'reasoning'.
Finding the detailed nature of that process is part of a research
program. You should not expect final answers at this stage, and you
should not take informal reference to that process as a claim to have
a final answer.
>You seem to reject the classic line taken to this - ie the
>Fregian explication of the modus operandi of inference in his
>"Begriffsschrift" (1879) ...
It is possible to define "inference" more narrowly than reasoning.
It could be defined narrowly enough to accept Frege's version. For
myself, I find it useful to keep the term "inference" as imprecise,
and use the term "logic" or "logical inference" for the narrower
concept.