"Friendly Premises"
gera...@earthlink.net
premises" -- who discusses their use, what is the correct terminology,
etc. I've read a great deal in books on logic for the layman but
haven't come across anything that corresponds to this issue.
By "friendly premises" I mean premises that people posit (often
unstated) that are necessary to a theory they are building on
circumstantial evidence. That is, they examine circumstantial
evidence, construct a theory that pulls the circumstantial evidence
together plausibly, but the proposal demands certain factual premises.
The author either avoids mentioning them and just praises the
plausibility of his theory, or he mentions them but leaves it up to the
reader to do the research to determine whether they are true or false.
The author may even allege that there is no factual evidence available
as to the truth or falsity of the premises, and hint that the friendly
premises are probably true if their use leads to a theory that sounds
plausible. Is that much clear?
My questions are as follows.
1. Does anyone discuss whose responsibility it is to check friendly
premises? Does a proposer have the right to concoct a theory and
praise its virtues without bothering to verify the truth of his
premises?
2. Proposers sometimes claim that the beauty or consistency or
problem-solving ability of their theory validates their undefended
friendly premises. But aren't there many cases where beautiful /
consistent / problem-solving theories have later been proven to have at
least one fallacious premise? Can you recommend anyone who discusses
this or gives examples?
My questions aren't purely theoretical. I'm trying to assess a
scholarly proposal in an historical field that posits a bunch of
friendly premises that the author considers verified by the
plausibility of the theory he has built upon them. I'm not at all
clear how to analyze the procedure or what are the correct logical
terms involved. Thanks in advance to anyone who responds.
Dan Christensen
<gera...@earthlink.net> wrote in message
news:1122670590.7...@g47g2000cwa.googlegroups.com...
>I have several questions concerning how logicians feel about "friendly
> premises" -- who discusses their use, what is the correct terminology,
> etc. I've read a great deal in books on logic for the layman but
> haven't come across anything that corresponds to this issue.
>
> By "friendly premises" I mean premises that people posit (often
> unstated) that are necessary to a theory they are building on
> circumstantial evidence. That is, they examine circumstantial
> evidence, construct a theory that pulls the circumstantial evidence
> together plausibly, but the proposal demands certain factual premises.
[snip]
Just my two cents, but maybe you are confusing logic or mathematics with
science. Logicians and mathematicians explore questions of "what if,"
constructing useful or at least interesting theoretical systems of numbers,
points, algebraic operators, etc. on paper. Many such systems can be
successfully applied to a scientific analysis of various aspects of physical
reality. It is the job of the scientist to verify any assumptions made about
physical reality, as well as any results predicted by the application of
mathetmatical theory. Contrary results, it should be noted, do not
necessarily indicate a problem with the mathematical theory itself.
I hope this helps.
Dan
Download my DC Proof software at http://www.dcproof.com
Acme Diagnostics
"Dan Christensen" <dch...@allstream.net> wrote:
><gera...@earthlink.net> wrote in message
>> premises" -- who discusses their use, what is the correct terminology,
>> etc. I've read a great deal in books on logic for the layman but
>> haven't come across anything that corresponds to this issue.
>>
>> By "friendly premises" I mean premises that people posit (often
>> unstated) that are necessary to a theory they are building on
>> circumstantial evidence. That is, they examine circumstantial
>> evidence, construct a theory that pulls the circumstantial evidence
>> together plausibly, but the proposal demands certain factual premises.
>
>[snip]
>
>Just my two cents, but maybe you are confusing logic or mathematics with
>science. Logicians and mathematicians explore questions of "what if,"
>constructing useful or at least interesting theoretical systems of numbers,
>points, algebraic operators, etc. on paper.
Ok, but your two cents worth seems most confused. That is not
what logic is. You are mainly describing mathematics here.
>Many such systems can be
>successfully applied to a scientific analysis of various aspects of physical
>reality. It is the job of the scientist to verify any assumptions made about
>physical reality
But Gerald didn't ask about job descriptions. He asked a logic
question. Scientists use logic too, and need to know about it.
>... as well as any results predicted by the application of
>mathetmatical theory. Contrary results, it should be noted, do not
>necessarily indicate a problem with the mathematical theory itself.
Where do you get "mathematical theory" out of the poster's
question? Again, you appear to be confused about what logic is.
Logic has two main branches: formal and informal. There are
two main branches of formal logic: deductive and inductive.
Within the deductive branch are several branches, most
significantly these days predicate logic which breaks down into
sub-branches, one of those being mathematical logic. That appears
to be where you are in your thinking. You seem to think that all
of logic resides in this one branch far down in the chain.
I would be most interested to find out why you think that branch
encompasses all of logic (if so), and more specifically why you
are excluding a question about premises in circumstancial
evidence from logic. I am doing some work in describing these
distinctions.
Other branches of logic use math as quantifiers, but it doesn't
seem as if you're talking about that. Scientists rely heavily on
some of these logics, for instance probability.
Gerald's question is most appropriate for this group titled
"science logic," not "sci.math" or "math logic."
His question falls within two other branches of logic and
can be addressed from either branch. One is inductive logic
which addresses scientific theories among other things.
The other is the branch of informal logic having to do with
argumentation. In fact, the subject of identifying missing
premises also falls within deductive logic.
Gerald is asking for sources within these areas of logic. He's
not asking a math question. I could offer an opinion or two about
his content, but I don't know about sources. I don't think you do
either. Perhaps someone else in this logic group knows of some
sources where Gerald can learn more about the specific areas of
logic which address his question.
Thanks for maintaining reply introductions, for not top-posting,
and for quoting some of Gerald's message.
Larry
Torkel Franzen
> Within the deductive branch are several branches, most
> significantly these days predicate logic which breaks down into
> sub-branches, one of those being mathematical logic.
This is a misunderstanding. Mathematical logic is not a subbranch
of predicate logic, but the study of logic by mathematical means.
Predicate logic is a logical formalism that plays a large role
in mathematical logic.
Herman Jurjus
Ad 1: since this seems to be about the burden of proof in a practical
argumentation, you might dig out Henry Prakken's homepage for further
references. He's interested (a.o.) in formalisms for (practical)
reasoning related to legal practice. Don't expect to find definitive
answers to your practical question, though. But perhaps you can pick up
some ideas and terminology, there.
Ad 2: i had no idea that 'scholars in historical fields' had any such
theories?
Hope this helps a bit.
--
Cheers,
Herman Jurjus
Ross A. Finlayson
Investigate natural deduction.
You might find that there are no non-logical axioms, and with that you
must cope.
ZF is inconsistent. That's right, ZF is inconsistent, and Cantor says
anybody without a universal set is a frickin mathematical crank. Not
being a mathematical crank, I revolutionize the mathematics anyways.
Ha ha!
Deny the infinite, I dare you!
Never speak of it again, then. You either have infinity or not, and
well, where you don't, then I can simulate you on a Pentium, or pebbles
in the sand.
The universe is infinite: infinite sets are equivalent.
Ross
Torkel Franzen
> ZF is inconsistent. That's right, ZF is inconsistent, and Cantor says
> anybody without a universal set is a frickin mathematical crank. Not
> being a mathematical crank, I revolutionize the mathematics anyways.
You are the victim of an illusion. Mathematics does not exist. You
are in fact nibbling on a cupcake, thinking that it contains an
infinite set.
Acme Diagnostics
Perhaps mathematical logic *can* be cast that way and properly
evidenced. However, it is my understanding that predicate logic
is the main logic *prerequisite* of mathematical logic.
Thus, when the context of the discussion is "branches of logic,"
ML can just as easily be cast as an offshoot and result of
predicate logic, though perhaps limiting it only to a "branch"
should be qualified in some way.
I would like to find proper (short-copy) wording for such
qualification while still representing it as a result of
predicate logic, and in context of "branches of logic," that the
branch of logic to most appropriately place mathematical logic is
indeed under predicate logic, more so than any other branch of
logic.
I am uninterested in how "branches of mathematics" or
"branches of foundational mathematics" might apply, nor was that
the context of the poster's question, nor did his question
have anything to do with mathematics (which was the main point
for him and the other responder).
For this I submit that Frege and Russel developed predicate logic
with significant departures from classical logic specifically to
create a logic that could be used to support mathematical
theories and explain at least basic mathematics logically, most
notably common arithmetic.
Four significant departures:
1. Existential import had to go because otherwise math
could not be supported without the "empty set," i.e. in
common understanding the number 0.
2. Replace the word "premise" with "axiom."
3. Replace the word "conclusion" with "theorem."
4. Support self-proving procedures, and perhaps recursive
proofs though I'm not that far along yet.
Now, I don't know these things for sure, and I'm certain to have
made historical and terminological mistakes which are trivial in
context and at this level of description, while I am confident
that you *do* know these things for sure. But you have strong
agendas here that are not necessarily shared by the academic
community at large, and you've as much as said that in
criticizing content on the web which obviously included my
excerpts from well-known university sites.
More significantly, you have argued in bad faith in the past,
i.e. dishonestly, which I can demonstrate, and have demonstrated.
Thus your assertion that might have different interpretations
cannot be taken on faith.
Perhaps you could provide a link to a well-known academic
source written by a logician, not a mathematician, with proper
credentials, and by that I mean some page in front of a
well-known university so that the content reflects directly on
that university's reputation.
Thanks for your response containing some useful explanation.
Larry
Torkel Franzen
> 4. Support self-proving procedures, and perhaps recursive
> proofs though I'm not that far along yet.
What is meant by a self-proving procedure or a recursive proof?
If you're interested in finding out about mathematical logic and
the place of predicate logic within the subject, why not look for
yourself?
ti...@amsta.leeds.ac.uk
Acme Diagnostics wrote:
> Torkel Franzen <tor...@sm.luth.se> wrote:
> >"Acme Diagnostics" <LFinez...@partpostmark.net> writes:
> >
> >> Within the deductive branch are several branches, most
> >> significantly these days predicate logic which breaks down into
> >> sub-branches, one of those being mathematical logic.
> >
> > This is a misunderstanding. Mathematical logic is not a subbranch
> >of predicate logic, but the study of logic by mathematical means.
> >Predicate logic is a logical formalism that plays a large role
> >in mathematical logic.
>
> Perhaps mathematical logic *can* be cast that way and properly
> evidenced. However, it is my understanding that predicate logic
> is the main logic *prerequisite* of mathematical logic.
>
> Thus, when the context of the discussion is "branches of logic,"
> ML can just as easily be cast as an offshoot and result of
> predicate logic, though perhaps limiting it only to a "branch"
> should be qualified in some way.
>
Mathematical logic also contains the mathematically study of other
logics.
eg. constructive mathematics and other weakenings of classical logic
(eg non monotonic)
second (and higher) order logics
infinitary logics
various "uncertain logics" eg. truthfunctional or probabalistic logics
metric structures
and many many more.
First order predicate logic has a special place, true, but this in no
way means that other
I have no idea of your history with the previous poster. I think
however you have set an imposible task: Someone studying any form of
"mathematical logic" (from OP) is surely, by definition, a
mathematician (and a logician).
> Thanks for your response containing some useful explanation.
>
> Larry
Tim
Acme Diagnostics
ti...@amsta.leeds.ac.uk wrote:
>Acme Diagnostics wrote:
>> Torkel Franzen <tor...@sm.luth.se> wrote:
>>>"Acme Diagnostics" <LFinez...@partpostmark.net> writes:
How's the weather in England today, assuming you're from that
part of the UK. In Florida it's been the hottest summer for a
long time.
Thanks very much for your detailed information. It is most useful
to me, and now I think I can compose an appropriate qualification.
I will incorporate it into any future writing on the subject.
My immediate problem is that of composing a chart which lists
areas of logic, but which must specifically exclude theoretical
or symbolic logics, listing the most likely examples specifically.
That distinction slices right into at least two important
logics. One example would need to be mathematical logic because
I'm given to understand it is now a major academic subject.
I do not want to cause my readers to invest either in predicate
logic or mathematical logic, nor any symbolic calculus, and I
have good reasons for that.
I will need to do some research on how mathematical logic
applies to probability and by extension statistics. I'm highly
invested in that area.
>> I am uninterested in how "branches of mathematics" or
>> "branches of foundational mathematics" might apply, nor was that
>> the context of the poster's question, nor did his question
>> have anything to do with mathematics (which was the main point
>> for him and the other responder).
>>
>> For this I submit that Frege and Russel developed predicate logic
>> with significant departures from classical logic specifically to
>> create a logic that could be used to support mathematical
>> theories and explain at least basic mathematics logically, most
>> notably common arithmetic.
I wonder if you'd offer some comment on the above paragraph.
I'm sure it is incorrect in any theoretical detail, but is it
correct in a most general sense? Would it be appropriate to
include just in passing in a much larger text on reasoning, with
only a minor emphasis on logic, even less on formal logic, and
just to make a brief mention about PC and it's implications
for math?
>> Four significant departures:
>>
>> 1. Existential import had to go because otherwise math
>> could not be supported without the "empty set," i.e. in
>> common understanding the number 0.
>> 2. Replace the word "premise" with "axiom."
>> 3. Replace the word "conclusion" with "theorem."
>> 4. Support self-proving procedures, and perhaps recursive
>> proofs though I'm not that far along yet.
Most speculative here. Hehe. With Torkel you have to pull teeth a
little. I was really surprised that 1-3 got past him (he is an
authority on the subject). But then he usually snips everything
but a sentence or two. I wonder if the word "axiom" was really
introduced into logic by Frege, or if he presented the main
introduction of that word into what is now thought of as logic
and not math.
>> Now, I don't know these things for sure, and I'm certain to have
>> made historical and terminological mistakes which are trivial in
>> context and at this level of description, while I am confident
>> that you *do* know these things for sure. But you have strong
>> agendas here that are not necessarily shared by the academic
>> community at large, and you've as much as said that in
>> criticizing content on the web which obviously included my
>> excerpts from well-known university sites.
>>
>> More significantly, you have argued in bad faith in the past,
>> i.e. dishonestly, which I can demonstrate, and have demonstrated.
>> Thus your assertion that might have different interpretations
>> cannot be taken on faith.
>>
>> Perhaps you could provide a link to a well-known academic
>> source written by a logician, not a mathematician, with proper
>> credentials, and by that I mean some page in front of a
>> well-known university so that the content reflects directly on
>> that university's reputation.
>>
>
>I have no idea of your history with the previous poster. I think
>however you have set an imposible task: Someone studying any form of
>"mathematical logic" (from OP) is surely, by definition, a
>mathematician (and a logician).
Well, Torkel is a troll (not always) according to me, and I
believe I've posted sufficient evidence in the past to make that
reasonable inference.
Yes, of course a "mathematical logician" is both a mathematician
and a logician by definition, just as a "bicycle logician" is
both a cyclist and a logician. But just a "logician" is something
else by definition. A mathematical logician is invested in that
area, a bicycle logician is invested in that area, and a logician
is invested in yet another area, the subject in general, i.e. the
next higher level of description above these more specific
areas of logic. Levels of description change a lot of important
things as I'm sure you know.
If you wanted to know if the country is spending too much on
litigation, do you ask a lawyer whose main income is generated
from litigation? I think one would ask someone invested in the
whole field in general, or better yet someone from the next
higher level of description who is well familiar with all the
general details of that issue appropriate for the level of
description in the problem definition, perhaps a pol sci
specialist.
It would be really great if you were a "logician" and
not a "mathematical logician."
These investments create an objectivity issue, which is a matter
of credential or credibility judgment. Someone invested in logic
in general would be more objective about how mathematical logic
really fits into the study of logic in general, and it might be
even better to ask an accomplished philosopher. I do generally
get different answers in the philosophy groups. I'd really like
to nail this one down, but so far I haven't gotten a story that
really adds up from anywhere. Not to say that your information
is contradicted in any way, as it's only a small slice of detail,
but there are contradictions in other information when set
in higher contexts.
I don't know anything for sure and appreciate being corrected.
Thanks again for your useful explanation.
Larry
Acme Diagnostics
Torkel Franzen <tor...@sm.luth.se> wrote:
>"Acme Diagnostics" <LFinez...@partpostmark.net> writes:
>
>> 4. Support self-proving procedures, and perhaps recursive
>> proofs though I'm not that far along yet.
>
> What is meant by a self-proving procedure or a recursive proof?
You know the answers to both those questions. It's just another
example of Torkelling.
My inclination is to write a flame. But it's been called to my
attention that you could really be suffering from some disease or
accident, or are perhaps really such an unbalanced reasoner that
you actually can't figure out those terms. In any case, I can't
take the chance of doing you further harm. Your nonsense isn't
really affecting me in this case, so there's nothing needing to
be undone.
I'm also really kind of sorry about my post to Keith. I think he
is a decent person who just felt sorry for you.
> If you're interested in finding out about mathematical logic and
>the place of predicate logic within the subject, why not look for
>yourself?
The difference between "know" and "think you know."
Sheesh, you are such a lightweight. It's so hard to believe when
you apparently have such a fine education.
Larry
Torkel Franzen
> > What is meant by a self-proving procedure or a recursive proof?
> You know the answers to both those questions.
There is no concept of "self-proving procedure" or "recursive
proof" in logic.
> My inclination is to write a flame.
Right, but such things aside, just what is it you have in mind
when speaking of "self-proving procedure" and "recursive proof"?
Acme Diagnostics
Torkel Franzen <tor...@sm.luth.se> wrote:
>"Acme Diagnostics" <LFinez...@partpostmark.net> writes:
>
>>> What is meant by a self-proving procedure or a recursive proof?
>
>> You know the answers to both those questions.
>
> There is no concept of "self-proving procedure" or "recursive
>proof" in logic.
That statement is incorrect.
>> My inclination is to write a flame.
>
> Right, but such things aside, just what is it you have in mind
>when speaking of "self-proving procedure" and "recursive proof"?
How should I know? The context in which they were used is
missing.
Is this picking of phrases out of context just like what you did
with Dolan's Goedel piece?
Of course, now we all know that you made a large context
error in that case. Especially after that little exchange in
alt.philosophy.debate where I offered the piece to a poster who
appeared to know a lot about mathematical logic, and he thanked
me for it indicating that he inferenced the phrase "true in that
set of axioms" in context of the whole sentence with no problem
whatsoever, and which big Goedel error you normally make a big
stink about, but whereupon there was nothing but deafening
silence from you, though you replied to him about something else,
and which exchange I can link anytime.
Just like the 10 or whatever other people I said I tested it on,
none of them having the least problem inferencing that phrase as
an axiom system or mathematical theory, or as close to that as
they possibly could for their backround, for which there is no
substitute as we all know now after your feeble attempts as
demonstrated, which demonstration you and several other members
of your debating team ignored completely, and which is the genius
behind that particular editing masterpiece.
Which phrase you always misquoted as "true in a set of axioms" so
that even your misquote cluelessly removed any reference to the
rest of the sentence.
And there's that little matter of Frege's Context
Principle about the meaning of words depending on entire
sentences, Frege being the God of mathematical logic by
most accounts I've heard.
So I reiterate: Is your snipping of phrases out of context above
a similar case? Because I can always go back and fetch the
context and explicate the meaning of those phrases. But, again
just as with the Goedel piece, the meaning might then be much
different from what you've been able to reason out so far, and
you might not like the result any more than you liked the Goedel
result.
Larry
Torkel Franzen
> > There is no concept of "self-proving procedure" or "recursive
> >proof" in logic.
>
> That statement is incorrect.
OK, so you've invented them. What I'm wondering is, what do you
take them to mean?
Jesse Alama
> Torkel Franzen <tor...@sm.luth.se> wrote:
>>"Acme Diagnostics" <LFinez...@partpostmark.net> writes:
>>
>>>> What is meant by a self-proving procedure or a recursive proof?
>>
>>> You know the answers to both those questions.
>>
>> There is no concept of "self-proving procedure" or "recursive
>>proof" in logic.
>
> That statement is incorrect.
How?
Jesse
--
Jesse Alama (al...@stanford.edu)
Acme Diagnostics
Torkel Franzen <tor...@sm.luth.se> wrote:
>"Acme Diagnostics" <LFinez...@partpostmark.net> writes:
>
>>> There is no concept of "self-proving procedure" or "recursive
>>>proof" in logic.
>>
>> That statement is incorrect.
>
> OK, so you've invented them.
I invented nothing. You said, "There is no concept of
'self-proving procedure' or 'recursive proof' in logic." I
replied, "That statement is incorrect."
That's what is known as a call, i.e. I clearly called your
attention to a statement which I claim to contain a logic error.
You've had all the time you needed to review it.
The correct response was either 1) No, my statement is
correct, or 2) Yes, I made a logic error."
The response "Ok, so you've invented them" is an incorrect
response. It is plainly a weasel response. It says nothing.
Why should I now give you another time slice to correct this
second logic mistake? But ok. Go ahead. You probably are
totally oblivious to the fact that we're conducting logic here
anyway. No equal signs. Ok, special allowance for lightweight
beginners. Take all the time you need. Again.
>What I'm wondering is, what do you
>take them to mean?
Yeah, I'd want to change the subject too. Lots of names for that.
1 or 2, Torkel.
I bet I've pointed out 10 of your logic errors, and certainly at
least 5, yet you have not acknowledged even one of them. I'm
through wasting my good time trying to teach you logic without
any cooperation whatsoever from you.
Larry
p.s. Hope I didn't overdo it! Hehe. Me? Never!
Acme Diagnostics
Jesse Alama <al...@stanford.edu> wrote:
>"Acme Diagnostics" <LFinez...@partpostmark.net> writes:
>> Torkel Franzen <tor...@sm.luth.se> wrote:
>>>"Acme Diagnostics" <LFinez...@partpostmark.net> writes:
>>>
>>>>> What is meant by a self-proving procedure or a recursive proof?
>>>
>>>> You know the answers to both those questions.
>>>
>>> There is no concept of "self-proving procedure" or "recursive
>>>proof" in logic.
>>
>> That statement is incorrect.
>
>How?
Shucks, Jesse, now I have to explain it! I was having fun
trolling Torkel the troll.
But first Torkel has to commit. If he doesn't, I'll wait long
enough so that it becomes apparent that he's defaulted.
Please don't take my posts to Torkel too seriously. I'm mainly
passing a boring Saturday afternoon here. Most posters go home
for the weekend.
I always offer maximum courtesy, cooperation, and good faith to
any new correspondent (which Torkel threw in my face with his
very first reply and ever since then). That at least requires
being responsive and explanatory, thus my obligation to explain.
I apologize for the delay, but I'm sure you don't want to ruin my
fun!
Larry
Jesse Alama
Torkel ignored much of the post
<42eb8beb$0$91626$bb4e...@newscene.com> and called attention to the
part about "self-proving procedures" and "recursive proof". That may
have been a snarky move, but I think Torkel's question needs to be
answered if we are to fully understand your original post. To be
honest, I am with Tokel on this one: I too don't know what you mean by
"self-proving procedures" or "recursive proofs". I presume other
readers of sci.logic are in the same boat. For our sake, tell us what
you mean by "self-proving procedure" and "recursive proof".
--
Jesse Alama (al...@stanford.edu)
Jim Spriggs
> Torkel ignored much of the post
> <42eb8beb$0$91626$bb4e...@newscene.com> and called attention to the
> part about "self-proving procedures" and "recursive proof". That may
> have been a snarky move, but I think Torkel's question needs to be
> answered if we are to fully understand your original post. To be
> honest, I am with Tokel on this one: I too don't know what you mean by
> "self-proving procedures" or "recursive proofs". I presume other
> readers of sci.logic are in the same boat. For our sake, tell us what
> you mean by "self-proving procedure" and "recursive proof".
My guess was that "recursive proof" was an honest mistake for "proof by
induction". "self-proving procedure" intrigues me, where can I buy one?
--
I don't know who you are Sir, or where you come from,
but you've done me a power of good.
Torkel Franzen
> I'm through wasting my good time trying to teach you logic without
> any cooperation whatsoever from you.
I guess I can live with that. But I'm still curious about just what
you had in mind when speaking of "self-proving procedures" and
"recursive proofs".
ti...@amsta.leeds.ac.uk
Acme Diagnostics wrote:
> ti...@amsta.leeds.ac.uk wrote:
> >Acme Diagnostics wrote:
> >> Torkel Franzen <tor...@sm.luth.se> wrote:
> >>>"Acme Diagnostics" <LFinez...@partpostmark.net> writes:
>
> How's the weather in England today, assuming you're from that
> part of the UK. In Florida it's been the hottest summer for a
> long time.
Hi, I am actually working in Germany now. Friday was hot, yesterday
rainy, today humid; it's just like being back at home!
In my experience, mathematical logic is pretty much about studying
symbolic logics and symbolic proofs, and applying theorems about the
logics to the things described by them.
So most of mathematical logic would be excluded from your perview.
I am sure that there are people doing other things, but I don't know
about it.
My justification for calling myself a logician is purely to do with
symbolic languages, all coverd by the ASL.
The American Mathematical Society (ams.org) has a classification system
for mathematics papers. Obviously most papers fall into several
categories, and, well of course there are lots of provisos. Anyway,
here is the list of headings under 03 Mathematical Logic and
foundations:
03-xx | Prev: 01 | Up: Top | Next: 05 |
Mathematical logic and foundations
<snip> headings for history, conference proceedings etc</snip>
03A05 Philosophical and critical {For philosophy of mathematics,
see also 00A30}
03Bxx General logic
03Cxx Model theory
03Dxx Computability and recursion theory
03Exx Set theory
03Fxx Proof theory and constructive mathematics
03Gxx Algebraic logic
03Hxx Nonstandard models [See also 03C62]
Hope this is helpful.
> That distinction slices right into at least two important
> logics. One example would need to be mathematical logic because
> I'm given to understand it is now a major academic subject.
> I do not want to cause my readers to invest either in predicate
> logic or mathematical logic, nor any symbolic calculus, and I
> have good reasons for that.
>
> I will need to do some research on how mathematical logic
> applies to probability and by extension statistics. I'm highly
> invested in that area.
>
I can recomend "the uncertain reasoners companion" by Jeff Paris
ISBN: 0521460891
The subject is to consider reasoning without complete knowledge, for
example if I beleive A is "very likely" to happen and B is "quite
likely" then what should I think (to be consistent) about A and B?
There are various ways of doing this, one is to assign "probabilities"
to A and B, and then there are syntatics restriction on the
"probability" of A and B.
> >> I am uninterested in how "branches of mathematics" or
> >> "branches of foundational mathematics" might apply, nor was that
> >> the context of the poster's question, nor did his question
> >> have anything to do with mathematics (which was the main point
> >> for him and the other responder).
> >>
> >> For this I submit that Frege and Russel developed predicate logic
> >> with significant departures from classical logic specifically to
> >> create a logic that could be used to support mathematical
> >> theories and explain at least basic mathematics logically, most
> >> notably common arithmetic.
>
> I wonder if you'd offer some comment on the above paragraph.
> I'm sure it is incorrect in any theoretical detail, but is it
> correct in a most general sense? Would it be appropriate to
> include just in passing in a much larger text on reasoning, with
> only a minor emphasis on logic, even less on formal logic, and
> just to make a brief mention about PC and it's implications
> for math?
>
I am not really up on my history, I am afraid. What mathematicians call
"classical logic" is, I think, what was developed by Frege and Russel.
Certainly as opposed to "intuistic logic".
> >> Four significant departures:
> >>
> >> 1. Existential import had to go because otherwise math
> >> could not be supported without the "empty set," i.e. in
> >> common understanding the number 0.
What does Existential import mean?
I looked it up online, and I guess it is in reference to "for all"
here,
i.e. "for all x (x=x)"
with EI, implies that there is some x, where as we would not interpret
it without that meaning.
Correct?
>From a mathematical point of view, I think that it doesn't really
matter. i.e. I guess you can express that same things in a language
with EI as you could in one without. The empty set, call it e, is not
really going to cause a problem.
For any formula f(x) we will have
1. forall x f(x)
2. forall x not f(x)
1 and 2 are both true in e, when interpreted without EI but
both false in e, when interpreted with EI
Either way this is going to help you distinguish the empty set.
I am very much a mathematical logician, a model theorist, I am afraid.
> These investments create an objectivity issue, which is a matter
> of credential or credibility judgment. Someone invested in logic
> in general would be more objective about how mathematical logic
> really fits into the study of logic in general, and it might be
> even better to ask an accomplished philosopher. I do generally
> get different answers in the philosophy groups. I'd really like
> to nail this one down, but so far I haven't gotten a story that
> really adds up from anywhere. Not to say that your information
> is contradicted in any way, as it's only a small slice of detail,
> but there are contradictions in other information when set
> in higher contexts.
>
Symbolic logic is, by it's nature a "mathematical persuit" in the broad
sence of the word: What does one do? Looks at some concepts that we
have in real life (sentence, truth, proof, consistency, computability)
and considers a restricted, well defined idealisation. We then see what
we can proove, from "obvious" axioms.
I realise that logic is not part of mathematics, in the same way that
physics is not part of mathematics. The concepts are broader, the
"simple" questions much harder (what is a proof?). However, when one
deals with well defined, idealised situations one can (and does) do
mathematics.
What I do is very much mathematics: much of model theory is about
taking a mathematical structure and a symbolic language. We then apply
the theorems we have about the symbolic logic, and get results about
the mathematical structures.
> I don't know anything for sure and appreciate being corrected.
>
> Thanks again for your useful explanation.
>
> Larry
Bye, enjoy the summer, I am on holiday soon, hurrah!
Acme Diagnostics
Torkel Franzen <tor...@sm.luth.se> wrote:
>"Acme Diagnostics" <LFinez...@partpostmark.net> writes:
>
>> I'm through wasting my good time trying to teach you logic without
>> any cooperation whatsoever from you.
>
> I guess I can live with that.
Hehehehehehe!
Well, you're in a good mood this fine Sunday morning! (Afternoon
for you, I suspect.)
In spite of our two jokes at the top, I'm going to teach you
something important today. But not here.
In 1960's America, when I was a teen, the only nudie flicks were
from Sweden. I thought all the girls in Sweden ran through the
woods naked!
But that's not why I like Sweden so much (well, not the *only*
reason). I had good friends from there. One, who was severely
retarded, was one of the best friends I've ever had. I miss my
friend terribly. They are all gone now.
>But I'm still curious about just what
>you had in mind when speaking of "self-proving procedures" and
>"recursive proofs".
[To other readers in the thread: I've learned that these types of
statements from Torkel are not necessarily sarcastic. He is
sometimes an "accurate reporter," i.e. naively honest. But here
it is probably being sarcastic.]
I responded to that appropriately in my last message and
requested a response from you.
Perhaps you forgot during your morning jog through the woods. And
who wouldn't with all those nude babes running by!!!
- - - - -
>>> There is no concept of "self-proving procedure" or "recursive
>>>proof" in logic.
>>
>> That statement is incorrect.
>
> OK, so you've invented them.
The correct response was either 1) No, my statement is
correct, or 2) Yes, I made a logic error.
The response "Ok, so you've invented them" is an incorrect
response. It is plainly a weasel response. It says nothing.
>What I'm wondering is, what do you
>take them to mean?
Yeah, I'd want to change the subject too. Lots of names for that.
1 or 2, Torkel.
- - - - -
That's now two attempts to change the subject, and
two chances to take responsibility for your assertions
passed up.
I'm sorry Torkel, you got an extra chance, but you have defaulted.
That is worse than affirming or denying. It is a denial of
intellectual responsibility, among other things.
Nothing new there.
But only because Jesse asked, I will explain why your statement
is incorrect, thus reluctantly furthering your education,
assuming you Pay Attention!
Btw, professor, given full attention of the student, a grade of
the student is not a grade of the student, but only a grade of
the teacher. That's right, Torkel, All A is not-A!
Real logic is hard!
I am *certain* that you disagree, and that under any
circumstances a grade of the student is a grade of the student.
For two reasons! (hehe!)
But not at the moment because, being a night person, I got up at
7:30 to get everyone else up to do whatever they do on Sunday
morning. Now I'm going to get the rest of my morning's sleep.
Larry
Acme Diagnostics
Jim Spriggs wrote:
>Jesse Alama wrote:
>
>> Torkel ignored much of the post
>> <42eb8beb$0$91626$bb4e...@newscene.com> and called attention to the
>> part about "self-proving procedures" and "recursive proof". That may
>> have been a snarky move, but I think Torkel's question needs to be
>> answered if we are to fully understand your original post. To be
>> honest, I am with Tokel on this one: I too don't know what you mean by
>> "self-proving procedures" or "recursive proofs". I presume other
>> readers of sci.logic are in the same boat. For our sake, tell us what
>> you mean by "self-proving procedure" and "recursive proof".
>
>My guess was that "recursive proof" was an honest mistake for "proof by
>induction". "self-proving procedure" intrigues me, where can I buy one?
I will answer Jesse's "How?" post this afternoon, i.e. in a few
hours.
- - - - -
Torkel:
>>>> There is no concept of "self-proving procedure" or "recursive
>>>>proof" in logic.
Me:
>>> That statement is incorrect.
Jesse:
>>How?
- - - - -
Larry.
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz.
Jim Spriggs
> >you had in mind when speaking of "self-proving procedures" and
> >"recursive proofs".
>
> [To other readers in the thread: I've learned that these types of
> statements from Torkel are not necessarily sarcastic. He is
> sometimes an "accurate reporter," i.e. naively honest. But here
> it is probably being sarcastic.]
I suspect not. He really doesn't know what you mean by those phrases.
Can you give examples? It may be that you're using unfamiliar jargon
for familiar things.
Jim Spriggs
> Btw, professor, given full attention of the student, a grade of
> the student is not a grade of the student, but only a grade of
> the teacher. That's right, Torkel, All A is not-A!
There's probably a feeble joke lurking here
All A is not A-.
Torkel Franzen
> [To other readers in the thread: I've learned that these types of
> statements from Torkel are not necessarily sarcastic. He is
> sometimes an "accurate reporter," i.e. naively honest. But here
> it is probably being sarcastic.]
An odd notion. Admittedly the subject is peripheral, but I am in
fact curious about what you may have intended.
Martin Shobe
No one seems to have answered these questions, so I will attempt to
throw in my $.02 worth.
>I have several questions concerning how logicians feel about "friendly
>premises" -- who discusses their use, what is the correct terminology,
>etc. I've read a great deal in books on logic for the layman but
>haven't come across anything that corresponds to this issue.
>
>By "friendly premises" I mean premises that people posit (often
>unstated) that are necessary to a theory they are building on
>circumstantial evidence. That is, they examine circumstantial
>evidence, construct a theory that pulls the circumstantial evidence
>together plausibly, but the proposal demands certain factual premises.
>The author either avoids mentioning them and just praises the
>plausibility of his theory, or he mentions them but leaves it up to the
>reader to do the research to determine whether they are true or false.
>The author may even allege that there is no factual evidence available
>as to the truth or falsity of the premises, and hint that the friendly
>premises are probably true if their use leads to a theory that sounds
>plausible. Is that much clear?
>
>My questions are as follows.
>
>1. Does anyone discuss whose responsibility it is to check friendly
>premises?
I don't know who discusses it, but I would say both parties are
responsible. The party supplying the argument should verify that the
premises are "reasonable". In this case, that would mean at least
that factual premises aren't faslifiable (in the sense that we can
examine the real world and see that the real world didn't (doesn't) do
that.) It would also be up to the one receiving the argument to check
up on the premises before being convinced that the conclusion is true.
Note that different people are going to have different ideas of what
is reasonable, and the context of the argument will also add some
restrictions.
> Does a proposer have the right to concoct a theory and
>praise its virtues without bothering to verify the truth of his
>premises?
Yes, but if the premises don't hold, it doesn't matter what other
virtues the theory has.
>2. Proposers sometimes claim that the beauty or consistency or
>problem-solving ability of their theory validates their undefended
>friendly premises. But aren't there many cases where beautiful /
>consistent / problem-solving theories have later been proven to have at
>least one fallacious premise?
Newtonian mechanics comes to mind. Of course, we still use it when we
can show that those premises are "close enough" to what actually
happens.
> Can you recommend anyone who discusses
>this or gives examples?
Nope. Sorry.
Martin
Acme Diagnostics
Sorry for the delay. As usual, it took longer than expected.
>>> There is no concept of "self-proving procedure" or "recursive
>>>proof" in logic.
>>
>> That statement is incorrect.
>
>How?
Ah, more typing practice! <g> Actually, I type about 3,000 wpm.
(Perhaps I exaggerate slightly.)
"a concept...in logic" can be interpreted in two ways: 1) the
concept is a logic concept, or 2) the concept is any concept that
occurs anywhere in a logic process, e.g. a logical argument, i.e.
any concept in the universe.
Obviously, there do not exist particular logic terms for each
concept in the universe.
In a logical argument, which is certainly "in logic," the
"informal logic" branch to be exact, any concept in the universe
can be described with any words sufficient to make the argument
"reliable." (Skip 20 pages on what "reliable" means in this
sense, as it will not apply here.)
That's the easy proof that Torkel's statement is incorrect, and
in fact the one I noticed immediately. It's also why I was so
confident that his statement was logically incorrect that I used
the strongest appropriate denial, "That statement is incorrect."
But "good faith" argumentation requires me to volunteer that,
while that proof is certainly and famously sufficient in context
of Torkel, most qualified real debate judges would not pass that
proof, and I am presenting this proof to others besides Torkel.
The reason it would not usually pass is that it is a
*theoretical* interpretation (commonly, "splitting hairs"), and
logical arguments using language, even one's as short as Torkel's
one statement, are *real world.* (Excluding textbook examples,
etc.)
If you are unfamiliar with "real-world reasoning," just think
"informal logic." Close enough, but keep in mind the there
are parts of rhetoric not primarily intended to be logical, also
very big real-world parts of formal logic like probability,
statistics (inductive) and minor parts of classical logic which
are typically studied in "formal logic" courses, books, etc.
I would be making the exact same mistake that Torkel made
when, upon reading the following sentence:
[Goedel] proved that any set of axioms at least as rich
as the axioms of arithmetic has statements which are true
in that set of axioms, but cannot be proved by using that
set of axioms.
he excerpted "true in that set of axioms" out of context, changed
it (like in 5 or 10 repetitions even after being corrected) to
read "true in a set of axioms" (thus removing the reference to
the context), and interpreting that phrase *theoretically*. Of
course after those changes it makes no sense theoretically.
(Actually, I'm told, but am unqualified to even "think I know,"
that it does in some rare context(s), but I conceded that point
anyway since it doesn't matter).
However, the statement was always intended in the real-world
sense considering venue and intended readers. That was explained
myriad times in myriad ways, including in its original
presentation here. Further, in a sufficient number of
*real-world* tests (one now being fortunately linkable)
the entire sentence was inferenced correctly every time.
Now getting back to Torkel's assertion at the top, most qualified
judges would instead require me to assume that Torkel was not so
stupid as to make that mistake, even though he seems challenged
enough at reasoning, e.g. the Goedel example, to make it. Thus I
volunteer to supply charity to improve his assertion to admit
only interpretation #1. The simplest way to improve his assertion
for that is (emphasis added):
>>>There is no *logic* concept of "self-proving procedure"
>>>or "recursive proof" in logic.
This is the statement that I will prove incorrect. Unfortunately
for any readers, that takes a bit longer. I get to practice my
logical refutations.
This is the end of Torkel's lesson. Whether correct or
incorrect, the rest is over his head by about 10 stories. I see
no reason why it should be over anyone else's head. It's length
should not be a reading challenge for any readers qualified to
post here except those for whom English is a second language.
I apologize to them for length. I'd probably do a summary if one
should ask. One of my medical textbooks has paragraphs as long
as this whole post, for instance, and about a 25-character
average word length. Perhaps I exaggerate slightly again.<g>
- - - - -- - - - -
REFUTING THE ASSERTION:
"There is no logic concept of 'self-proving procedure' or
'recursive proof' in logic."
First I will explicate the definitions of words in the above
statement only to clarify them and open up my proof to criticism.
I will then show that, using these words, a true statement
can be constructed "in logic" that contradicts the assertion.
The contradicting statement that I construct will contain the
exact phrasing I used, which phrasing the assertion labels a
"concept," now improved to "logic concept," and will demonstrate
that the phrasing does in fact describe a logic concept, and that
this logic concept does in fact occur "in logic."
These facts will be demonstrated within the definitions because,
in this particular refutation, they are highly related.
There will be no attempt whatsoever to show that either of the
two quoted phrases occur in any glossary of logic terms because
I would not be so stupid as to refute a completely different
assertion from the one I was given to refute, e.g. "There is no
logic glossary containing the terms 'self-proving procedure' or
'recursive proof' in logic." I mention this only because I
suspect that at least one reader expects this to be the assertion
to be refuted. There is a good well-known logic term for that:
"Wishful Thinking." <g>
1. "Logic"
This will be a logical refutation of Torkel's above (improved)
statement proving it to be incorrect. This logical refutation
will use language and thus be governed by the rules of logical
argumentation.
Such a logical refutation is within the logic branch of logical
argumentation which is, in at least one standard logic
definition, within the logic branch of informal logic, which is
within logic. This satisfies the condition "in logic" for these
definitions.
2. "In"
This has already been partly defined at the top. To refute the
improved version of Torkel's assertion, I must demonstrate a
"logic concept." This can be any logic concept that occurs
in logic, Since Torkel has quantified over his entire complex
proposition with the universal "no," and since in context we
can eliminate the usual real-world "soft universal"
interpretation, I need only demonstrate one counter-example. I
will choose the logic concept of "logic system" for my
counter-example.
I personally know this to be a standard concept in at least one
area of logic and I believe it passes as a fact on shared
experience.
However, "to crack unreasoning resistance" as we sometimes
say in the real debate world, I quote from a logic textbook:
"These rules form a system called the propositional
calculus. (The term means simply 'system for performing
calculations with propositions.')"
Note that the word "system" is used as a general
word, twice, using it's common definition, not a technical
defintion. Also note that a logic textbook occurs "in logic,"
Of course the terms "axiom system" or "axiomatic
system" are often used in sci.logic, also on the web, and I'm
sure that mathematical theories are described generally as
"systems" in at least one textbook somewhere, though I don't have
an example, nor do I need one. Torkel didn't say "in XYZ logic,"
he said "in logic."
Because I need to anyway, I will provide an additional example
of "system" used in a general sense along with the next
definition.
Thus I am satisfied that any qualified debate jury would accept
"logic system" as a legitimate example of a "logic concept" "in
logic."
3. "Self-"
The prefex "self-" can mean anything I want it to mean among
all the common definitions of the prefix "self-" as long as it
is sufficient to describe any logic system whatsoever.
I choose for it to mean "self-contained" in the context of a
"logic system," and to simply refer to any logic system
whatsoever that does not require input from outside that system
to apply any of it's rules of inference; and additionally this
implies that all elements needed for that application are within
the system.
For instance, in a system of syllogisms composed of syllogistic
arguments, or in the whole system of syllogistic logic, if the
premises are true, then in all valid arguments the conclusions
must be true. Nothing from outside the system, i.e. the
syllogisms, (or syllogistic logic) is needed to infer that.
Additionally, nothing from outside the system can change it
without changing the system itself, and my definition including
"a system" precludes that one thing. Thus, "self-" in this
context implies a self-contained system.
4. "Procedure".
A procedure is a finite successive sequence of steps, also
sometimes described as a finite successive step-by-step process.
That's probably obvious enough, since it only needs to apply
to any logic system of any kind.
5. "Proving."
Note: In logical argumention, the quantifiers "some" and
"sometimes" minimally require one case.
Accurately condensing, but not paraphrasing, more text than I
care to type until further challenged, another quote from a logic
textbook:
"A deduction in logic is sometimes defined as a finite successive
step-by-step process applying rules of a logic system to a series
of premises or formulas. In some of these cases where deduction
is so defined, the word "deduction" is used synonymously with the
word 'proof'. The two terms will be used interchangeably in this
text."
This textbook is well-distributed. Whether it is accurate or not
is irrelevant. I don't need to prove that the concept occurs in
"correct" logic, just that it occurs in logic. Any
well-distributed logic textbook occurs "in logic."
[End definitions]
Now using these words and the explicated definitions all from
within logic, and assuming agreement for the meaning of "there,"
"is," and "of," I can construct the sentence: "There is a
logic concept of 'self-proving procedure' in logic" which is a
meaningful sentence in a logical refutation (but perhaps not
in any theoretical or symbolic logic), thus qualifies as
"occuring in logic," as defined. It is meaningful because it is
at least sufficient to disprove by counter-example the universal
assertion, "There is no logical concept of 'self-proving
procedure' in logic."
According to the "OR" operator as used in logical argumentation,
Torkel has asserted that neither of the two quoted terms occurs
in logic. Thus I need only prove that one of them occurs to
provide the counter-example proving his statement incorrect.
A proper refutation, even of this size, would take at least a
week and better a month. This is not my best work. I reserve the
right to correct any errors that may be found.
To my assertion "That statement is incorrect," which now stands
proved in this group until refuted, Torkel said:
> OK, so you've invented them.
I did not invent any concepts. All concepts herein were well
establish long before I arrived on the planet. That goes for
all the words in the assertion and counter-example as well.
Nor did I invent any terms. My use of the phrases were not
"quoted" (below). *Torkel* added the quotes. The confusion about
both concepts *and* terms is his own doing.
And a big reason for that is his constant habit of *snipping
necessary context* and *inaccurate quoting*.
- - - - -
Now for the benefit of the three posters who have so far asked,
I will explain the meaning of the two phrases *in context*.
Quoting myself, the context is as follows:
>>For this I submit...
<snip some of what I "submit" and continuing with the rest of
what I "submit">
>>1. Existential import had to go because otherwise math
>> could not be supported without the "empty set," i.e. in
>> common understanding the number 0.
>>2. Replace the word "premise" with "axiom."
>>3. Replace the word "conclusion" with "theorem."
>>4. Support self-proving procedures, and perhaps recursive
>> proofs though I'm not that far along yet.
>>
>>Now, I don't know these things for sure, and I'm certain to have
>>made historical and terminological mistakes <snip>
Notice that I only "submitted," and did not "assert." Notice that
I don't know these things for sure. Notice that, re: "recursive
proofs" - "perhaps...not that far along yet." Notice that "I'm
sure to have made terminological mistakes."
Most of all, notice the lack of quotes around those two phrases.
Additional important context is that I posted this to a troll,
but who is however an expert who knows answers. I may thus
legitimately overstate my "submission" to provoke a reply
which might tell me something about the accuracy of these
statements.
Given all that context, there is no use for an explanation. I
don't know anything about Frege or Russell or predicate logic or
how it applies to mathematical logic. I've picked up the
"recursive proof" lingo on Usenet. It googles and obvious
variations google, but not that many pages. Do that and you'll
know what I know.
I've known that math is self-proving, as people from outside the
field of math often say not needing to split any Goedel hairs,
forever. For reasoning in a philosophical sense, it's the main
distinction between math and most other professions.
Thanks Jesse for the opportunity to present my case on
these issues.
Larry
Torkel Franzen
[...]
A remarkable harangue! Could you possibly condense it into a brief
explanation of what you mean by "self-proving procedure" and
"recursive proof"?
> I've known that math is self-proving, as people from outside the
> field of math often say not needing to split any Goedel hairs,
> forever.
What do you mean by "math is self-proving"?
Martin Shobe
<LFinez...@partpostmark.net> wrote:
[Snip]
In other words, a "self-proving procedure" is nothing other than a
proof.
[Snip]
Martin
Keith Ramsay
|Torkel Franzen <tor...@sm.luth.se> wrote:
|>"Acme Diagnostics" <LFinez...@partpostmark.net> writes:
|>
|>> 4. Support self-proving procedures, and perhaps recursive
|>> proofs though I'm not that far along yet.
|>
|> What is meant by a self-proving procedure or a recursive proof?
|
|You know the answers to both those questions. It's just another
|example of Torkelling.
No, he doesn't. I don't. Even after reading your explanation
of what you meant by one of them, I still don't know what
you mean by it. You're free to assume this is dishonest, but
it's not. I'm not even convinced you have a definite idea of
what you mean by it.
|My inclination is to write a flame.
You do seem to hate him.
|But it's been called to my
|attention that you could really be suffering from some disease or
|accident, or are perhaps really such an unbalanced reasoner that
|you actually can't figure out those terms. In any case, I can't
|take the chance of doing you further harm.
{sarcasm} How kind and charitable you are!
|Your nonsense isn't
|really affecting me in this case, so there's nothing needing to
|be undone.
|
|I'm also really kind of sorry about my post to Keith. I think he
|is a decent person who just felt sorry for you.
I planned to leave the issue alone, since I think I
previously explained my point of view well enough for people
who, unlike you, don't have an enormous axe to grind. But I
see here that you are again attempting to "reposition" me
a little bit. No, I didn't "feel sorry" for him; this is
just your imagination.
Afterward, I realized what you remind me of. You seem to
me like the moral equivalent of the town gossip. "Did
you hear what so-and-so said about so-and-so?" "So-and-so?
Oh, well, we _all_ know what _he's_ like, don't we?" "I
shouldn't say too much-- I wouldn't want to hurt him, you
know, but, well, I've been told that so-and-so may possibly
be, you know, not quite well in the head if you know what
I mean?"
These are not the exact phrases you use, of course, but
it all seems to be of this flavor. This great relish at
retelling old stories over and over (spun in your favor of
course). The thinly disguised pleasure at finding a way
to make something sound more dramatic than it really is.
The kind of rationalization you offer is just the kind of
rationalization that a town gossip has to offer too. "I
don't like to say bad things about people, but I want to
protect you, so you should know what so-and-so is like."
But of course you enjoy saying these things. You appear
to *love* doing so. You manage to work it into a thread
on the most tenuous of excuse.
The town gossip often does try to reframe any attempt to
confront him for his gossipy behavior as something other
than that. It must be because the critic is some kind of
bleeding heart who doesn't want to confront the harsh
truth about the people around him. Or maybe he's secretly
in league with some of them. Or whatever. Anything to make
the gossip's own enthusiasm for attempting to make certain
people look bad from being the issue.
|> If you're interested in finding out about mathematical logic and
|>the place of predicate logic within the subject, why not look for
|>yourself?
|
|The difference between "know" and "think you know."
|
|Sheesh, you are such a lightweight. It's so hard to believe when
|you apparently have such a fine education.
Your desire to make him look bad is transparent. That's
essentially all this is.
Keith Ramsay
dch...@netcom.ca
Acme Diagnostics wrote:
> "Dan Christensen" <dch...@allstream.net> wrote:
> ><gera...@earthlink.net> wrote in message
> >> premises" -- who discusses their use, what is the correct terminology,
> >> etc. I've read a great deal in books on logic for the layman but
> >> haven't come across anything that corresponds to this issue.
> >>
> >> By "friendly premises" I mean premises that people posit (often
> >> unstated) that are necessary to a theory they are building on
> >> circumstantial evidence. That is, they examine circumstantial
> >> evidence, construct a theory that pulls the circumstantial evidence
> >> together plausibly, but the proposal demands certain factual premises.
> >
> >
> >Just my two cents, but maybe you are confusing logic or mathematics with
> >science. Logicians and mathematicians explore questions of "what if,"
> >constructing useful or at least interesting theoretical systems of numbers,
> >points, algebraic operators, etc. on paper.
>
> Ok, but your two cents worth seems most confused.
Quite possible.
> That is not
> what logic is. You are mainly describing mathematics here.
>
[snip]
Does it matter? Assumptions or premises about physical systems
("friendly" or otherwise) can be stated in the language of logic and
mathematics. It is not, however, the job of logic or mathematics to
verify such assumptions, only to draw to reasonable conclusions from
them. That was my point.
Dan
Download my DC Proof software http://www.dcproof.com
Acme Diagnostics
"Keith Ramsay" <kra...@aol.com> wrote:
>Acme Diagnostics wrote:
>>Torkel Franzen <tor...@sm.luth.se> wrote:
>>>"Acme Diagnostics" <LFinez...@partpostmark.net> writes:
>>>
>>>> 4. Support self-proving procedures, and perhaps recursive
>>>> proofs though I'm not that far along yet.
>>>
>>> What is meant by a self-proving procedure or a recursive proof?
>>
>>You know the answers to both those questions. It's just another
>>example of Torkelling.
>
>No, he doesn't. I don't. Even after reading your explanation
>of what you meant by one of them, I still don't know what
>you mean by it. You're free to assume this is dishonest, but
>it's not. I'm not even convinced you have a definite idea of
>what you mean by it.
The answer is "I don't know." Torkel knew that because
my "I don't knows" (in so many words) surrounded the comment.
You obviously didn't read that post. But Torkel did because
he quoted it in his message.
The real question becomes, why did he snip all my qualifications
about not knowing and ask the question when he already knew the
answer was "I don't know?"
Besides that, if anybody can figure out any meaning from those
phrases, it is Torkel. So why didn't he just post what *he knew*
about them?
(Answer: sandbagging. It googles in this group.)
You can deny that evidence if you like, but others won't. You
can bet on that, and that's a performance parameter.
You didn't do your homework on this one.
>>My inclination is to write a flame.
>
>You do seem to hate him.
Then why would I compliment him when he announced his new book,
and say, "That's very impressive, regardless of anything."
And there have been lots of other compliments. None of them
necessary. You haven't done your homework here, either.
In fact, I have high respect for Torkel, mostly for his
performances. secondly for his publisher, his excellent web site,
etc., etc., which I've posted several times. I've listed his
accomplishments for other people. I've encouraged them to talk to
him for those reasons.
Regarding performance, I am well on record as only considering
the very best instances. However inconsistent a performer is is
irrelevant to me, and that's probably not that typical among
performers. Google my nick and "groove holmes" (the hammond
organ group) as one instance I remember of posting this. Torkel
has turned in some very good performances.
People are complex and have good attributes and bad ones. I
have acknowledged both the good and the bad. I've implied or
directly stated that I'm no better numerous times. You just
haven't read those posts. But his posting style, e.g. the
sandbagging, hurts people, and his intellectual dishonesty
aggravates people, and damages this group as well as himself.
The frequency of my criticisms and mentions of Torkel lately have
all been initiated by Torkel in one way or another. I have
feelings too, Keith. It's hard for me to stand by and do nothing.
This is a matter of record, but you have to read sequentially and
not select those that support your point of view.
You initiated this one here, and by that I only mean that if you
hadn't done this post, I wouldn't be replying to it and talking
about Torkel.
I do not hate Torkel. I dislike some things he does here. I'd
like to meet him and buy him a beer so we can both have a big
laugh about Usenet nonsense, and he could tell me more great
things about Sweden than I already know. You need to keep things
in context. Nobody with half-a-brain could have such a strong
emotion as "hate" here.
Here's one great reason:
http://thor.prohosting.com/~chrismay/usenet.gif
I've well-published that I'm only a 5, btw. You're welcome to
post your guess. Milt says the one on the bottom right is his
license foto.<g>
People are not the same here as they are in real life. Just like
their personalities change when sitting in a traffic jam.
>>But it's been called to my
>>attention that you could really be suffering from some disease or
>>accident, or are perhaps really such an unbalanced reasoner that
>
>{sarcasm} How kind and charitable you are!
No. My brother was sitting right beside me and advised me to
dump a flame I had written on exactly those grounds. One other
poster, highly respected here and in other groups, has made the
same caution, but needing to be inferenced.
Torkel gave me a Christmas present last year! (i.e. even my
mom has read some Torkel messages.)
My point is that people who know me sometimes read my content
and I have to answer to them, just like you would have to answer
to the people you know here and in real life.
Here, you don't see any posters invested in mathematical logic,
or academics in general, on my side of this issue. DUH!!!
But there are plenty of posters here, and people in my real life,
who do agree with me about Torkel at least in part. I have links.
You just haven't done your homework again.
I'm a big advice asker - to accomplished people. Including on
Usenet. I routinely post compliments. I've posted that I only
have average intelligence many times and have never posted
privilege-asserting things that would raise my stock in this
group considerably, nor do they google. I've listed my faults
including some you are naming here. You are reading highly
selected messages of mine. You have got me wrong, at least to
some substantial degree.
>>I'm also really kind of sorry about my post to Keith. I think he
>>is a decent person who just felt sorry for you.
>
>I planned to leave the issue alone, since I think I
>previously explained my point of view well enough for people
>who, unlike you, don't have an enormous axe to grind. But I
>see here that you are again attempting to "reposition" me
>a little bit. No, I didn't "feel sorry" for him; this is
>just your imagination.
Well, Keith, now that you mention it, replying to my post did
entail you admitting quite a significant error in your judgment
of Torkel. Forget it. No big deal. But let's not discuss "plans"
and "repositioning" for why you didn't reply, ok? That's about
as lame as a George Bush debate.
Why do you think I keep bringing up the Goedel piece? Torkel
refuses to acknowledge errors. This is his single worst habit.
Worse than the trolling (because it brings him and the group
down so much).
Any *uncooperative* poster, i.e. engaged in debate with me,
who refuses to acknowledge errors (or at least address them
responsive and explanatory) has justified *any behavior*
within Usenet rules, and I am fanatical about playing by
the rules. I can have a grandstanding field day,
practice flaming, be dramatic, be goofy, be the town gossip,
do anything at all that I like. Everything is justified to an
uncooperative poster who has invested you but then will
not acknowledge errors or at least address them responsive
and explanatory.
You've justified that too, QED. But you're a special case. Your
feelings get hurt.
I don't give out many free passes on that issue.
If my posts about Torkel bother you so much, why not email
him and try to get him to be responsive and explanatory? Or
at least find out why he can't be and email me. I guarantee
confidence. That will be the end of it.
You can change my behavior too. Nothing could be easier.
Do some homework. Post evidence and short logic. These
easy opinion pieces are not persuasive.
>Afterward, I realized what you remind me of. You seem to
>me like the moral equivalent of the town gossip. "Did
>you hear what so-and-so said about so-and-so?" "So-and-so?
>Oh, well, we _all_ know what _he's_ like, don't we?" "I
>shouldn't say too much-- I wouldn't want to hurt him, you
>know, but, well, I've been told that so-and-so may possibly
>be, you know, not quite well in the head if you know what
>I mean?"
Hehe. Entertaining. At least it's creative. Flame me some
more, seriously. I like it. There's a poster I know who people
flame just for the honor of being flamed *by* him!
>The thinly disguised pleasure at finding a way
>to make something sound more dramatic than it really is.
What's wrong with that? Nothing I can see. You don't
seem to understand performance at all.
And to balance that out, I have lots and lots of links
to original contributions I've made to this group on the
subject of logic. Some have been acknowledged, so I
don't think you can impreach that remark.
I just posted an example of what a logical refutation in
language looks like (by request) and it took me over two hours.
It couldn't have been all that bad. The tally so far is:
Reviewers: 3
Probable reviewers: 10
Errors: 0
<snip more on "town gossip" though entertaining>
>But of course you enjoy saying these things. You appear
>to *love* doing so. You manage to work it into a thread
>on the most tenuous of excuse.
Again, you seem not to understand about performance.
<more on "town gossip">
The gossip angle is entertaining but it lacks demonstration.
All you can demonstrate is lots and lots of posts of all
kinds inferencing down to two faults of one troll.
I grandstand, I'm a ham. I've posted it often. You are highly
selecting the posts of mine that you've read or choose to notice.
>Your desire to make him look bad is transparent. That's
>essentially all this is.
I want to make him look bad as a direct result of things that
he does that: 1) bring down an otherwise accomplished
fellow performer with a great deal to offer (i.e. himself), 2)
hurt people, 3) aggravate people, 4) denigrates the subject of
logic, and 5) otherwise hurts this group in general. (I dropped
one as he seems to have responded.)
I have a long list of posts having nothing to do with me where
other posters have accused him of some of the same things as I.
Do you know what sandbagging is? If you'd done your homework you
would.
I have two linkable instances where he has engaged in his cryptic
way, aggravated, provoked an error, then announcing that he has
just written a book on the subject. That's sandbagging.
The example of sandbagging in the post we're forgetting is
just as as good. Plain for all to see.
I have instances of normal engagements, Torkel comes in and
then there is corruption, aggravation, insulting. I'm not
involved.
I don't get involved in the theoretical discussions, but I have
examples from there too. One with a very highly credentialed
poster who did nothing at all wrong - had done nothing but
contribute.
You were heavily involved in the May "If all bananas are
green..." etc. thread. Torkel was trolling, or being Torcrates,
or however nicely you'd like to put it, the new
poster. No question you saw it - you replied to it and answered
the question Torkel wouldn't in at least two replies instead
posting cryptic one-liners. You saw the newbie's aggravation.
Did I make a peep? No. If I hated him, why not? I didn't come in
until the newbie posted his compilation about "cryptic responses"
and "mind games" etc. I didn't compile that! The newbie did!
You have blanked that one out of your mind too. You ignored it
with me and G.D. too. I am not in denial about Torkel's good
points as I can demonstrate in the record. But you appear to
be in denial about anything that does not support your point of
view on this issue.
Also, I acknowledge my errors, which I can also demonstrate
in the record, including in my very last post to you which we
are ignoring.
I had not gone out of my way to criticize Torkel in a long time.
Then I discovered that a great and accomplished poster, respected
in many groups, G.D., had similar issues with Torkel for *four
years* (three more than I). How do you explain that? Find me one
instance of G.D. not being responsive and explanatory, but
"creating" an issue with anybody anywhere! He's one of the most
laid back and evenly responsive posters on Usenet. He routinely
ignores insults and gets the discussion back on track. Post lots
of content, i.e. isn't afraid of criticism. Highly accomplished
logician to boot, especially wrt argumentation.
You haven't done your homework on G.D. You've only seen his
messages with Torkel, apparently. You have had an emotional
response to those.
I didn't seek Torkel out this time either. He replied to a post
of mine. It was a trolling post again. That's what started this
last round.
Why should I let an intellectually dishonest troll, who has
aggravated any number of people in this newsgroup troll me? It
makes no sense.
Last, and perhaps most important, you do not understand about
performance. Torkel is a performer, and so am I. You're not.
There's just the remotest possibility at this point that this is
your motivation, i.e. to be a performer too. I hope that isn't
the case because you're beating your head against a brick wall.
Torkel and I understand things that you don't because of this
attribute that he and I share. You are misinterpreting things
because of that.
I see that you are being honest and posting from the heart, but
most of it is based on ignorance, plus a denial of facts, i.e.
the last post of mine that you cannot address plus the companion
post to G.D. You are suffering for no good reason at all. The
solution is to educate yourself a little.
I'm sorry to cause you more pain here, Keith. One thing needed
to be addressed for intellectual reasons, and that invoked the
whole reply not to agree to the rest by default. When you lay
down with dogs, you wake up with fleas.
Larry
This post was typed fast and not edited much. I believe there
may be unfair or unfounded remarks. I reserve the right to
retract if such errors are brought to my attention.
Acme Diagnostics
Torkel Franzen <tor...@sm.luth.se> wrote:
>"Acme Diagnostics" <LFinez...@partpostmark.net> writes:
>
> [...]
>
> A remarkable harangue! Could you possibly condense it into a brief
>explanation of what you mean by "self-proving procedure" and
>"recursive proof"?
It's not apparent what you mean by "remarkable." What specific
comments of mine are you referring to?
>> I've known that math is self-proving, as people from outside the
>> field of math often say not needing to split any Goedel hairs,
>> forever.
>
> What do you mean by "math is self-proving"?
"Math is self-proving" means that it proves itself.
Acme Diagnostics
ti...@amsta.leeds.ac.uk wrote:
>Acme Diagnostics wrote:
>> ti...@amsta.leeds.ac.uk wrote:
>>>Acme Diagnostics wrote:
>>
>> My immediate problem is that of composing a chart which lists
>> areas of logic, but which must specifically exclude theoretical
>> or symbolic logics, listing the most likely examples specifically.
>
>In my experience, mathematical logic is pretty much about studying
>symbolic logics and symbolic proofs, and applying theorems about the
>logics to the things described by them.
>
>So most of mathematical logic would be excluded from your perview.
Thanks for increasing my confidence about that.
>I am sure that there are people doing other things, but I don't know
>about it.
>
>My justification for calling myself a logician is purely to do with
>symbolic languages, all coverd by the ASL.
>
>The American Mathematical Society (ams.org) has a classification system
>for mathematics papers. Obviously most papers fall into several
>categories, and, well of course there are lots of provisos. Anyway,
>here is the list of headings under 03 Mathematical Logic and
>foundations:
>
>03-xx | Prev: 01 | Up: Top | Next: 05 |
>Mathematical logic and foundations
>
><snip> headings for history, conference proceedings etc</snip>
>
> 03A05 Philosophical and critical {For philosophy of mathematics,
>see also 00A30}
> 03Bxx General logic
> 03Cxx Model theory
> 03Dxx Computability and recursion theory
> 03Exx Set theory
> 03Fxx Proof theory and constructive mathematics
> 03Gxx Algebraic logic
> 03Hxx Nonstandard models [See also 03C62]
>
>Hope this is helpful.
Very enlightening. Some good googles.
People sometimes wonder why I don't just get a book or google
things, so this is to them, not you. I do sometimes do that, but
I have some goals here involving a learning dogma that I'm
probably going to be publishing. At least I'm spending a lot of
time on it lately. I'm trying to learn things in a certain way to
learn about that kind of learning, also for practice with that
kind of learning.
(Though at my age that involves a fact not in evidence.<g>)
>> I will need to do some research on how mathematical logic
>> applies to probability and by extension statistics. I'm highly
>> invested in that area.
>
>I can recomend "the uncertain reasoners companion" by Jeff Paris
> ISBN: 0521460891
>The subject is to consider reasoning without complete knowledge, for
>example if I beleive A is "very likely" to happen and B is "quite
>likely" then what should I think (to be consistent) about A and B?
>There are various ways of doing this, one is to assign "probabilities"
>to A and B, and then there are syntatics restriction on the
>"probability" of A and B.
Thanks for the reference. Two of my dogmatic ritual words
<g> in that short title! I will definitely read that book. I
just finished "How to lie with statistics." <g> Otherwise, I'm
quite familiar with that and see no difference from what I
learned decades ago, though I'm sure Jeff's book would have
some, with that title. Still, what you didn't say tells me
something.
>I am not really up on my history, I am afraid. What mathematicians call
>"classical logic" is, I think, what was developed by Frege and Russel.
>Certainly as opposed to "intuistic logic".
Hehe. I'm *really* no historian at all, but I think I can claim
that classical logic was mostly about Aristotle. Perhaps both
of us are poking in the dark. <g>
>>>> Four significant departures:
>>>>
>>>> 1. Existential import had to go because otherwise math
>>>> could not be supported without the "empty set," i.e. in
>>>> common understanding the number 0.
>
>What does Existential import mean?
>I looked it up online, and I guess it is in reference to "for all"
>here,
>i.e. "for all x (x=x)"
>with EI, implies that there is some x, where as we would not interpret
>it without that meaning.
>
>Correct?
A universal affirmative in classical logic implies the existence
of at least one member of the subject. "All dogs are mammals"
implies that there exists at least one dog. But to extend that
(and other logics) to a logic that supports math, what about
propositions involving zero? "All 0 is X". It doesn't work. This
is just my very naive guess. I don't know that at all, or even if
the number zero is significant at all. I have read that in
predicate logic something like "All dogs are mammals" does not
imply the existence of any dogs at all. Why is that? There must
be a reason. I suspect that the reason has something to do with
math.
>> If you wanted to know if the country is spending too much on
>> litigation, do you ask a lawyer whose main income is generated
>>
>> It would be really great if you were a "logician" and
>> not a "mathematical logician."
>I am very much a mathematical logician, a model theorist, I am afraid.
My above comment was stupidly put. Both "logician" and "math
logician" are equally respectable! Sorry I created this issue out
of thin air. You seem most objective to me, also very
knowledgeable and helpful.
>Symbolic logic is, by it's nature a "mathematical persuit" in the broad
>sence of the word: What does one do? Looks at some concepts that we
>have in real life (sentence, truth, proof, consistency, computability)
>and considers a restricted, well defined idealisation. We then see what
>we can proove, from "obvious" axioms.
I'm unqualified to comment. I naively think that any logic
involving axioms and theorems is obviously a mathematical
persuit. I encountered those a lot in my schooling (40 years ago)
and in every last case it was a math course.
>I realise that logic is not part of mathematics, in the same way that
>physics is not part of mathematics. The concepts are broader, the
>"simple" questions much harder (what is a proof?). However, when one
>deals with well defined, idealised situations one can (and does) do
>mathematics.
Agree about logic and physics. Unqualified about the rest. Thanks.
In the real world, I guess the logic/math question is sort of
like which came first, chicken or the egg. As soon as you find
some logic, e.g. cause and effect or some probability event,
you also need to quantify it.
>What I do is very much mathematics: much of model theory is about
>taking a mathematical structure and a symbolic language. We then apply
>the theorems we have about the symbolic logic, and get results about
>the mathematical structures.
Sounds like great fun and very interesting. I loved math in my
youth, but never thought of it as very income producing. <g>
>Bye, enjoy the summer, I am on holiday soon, hurrah!
Same to you. Have fun! I'm always on holiday. I play with
my computer and people send me checks. Small checks,
but you can't beat the working conditions!
Larry
Acme Diagnostics
I can't really know since I am grossly unqualified, but it
naively seems to me that if there's such a thing as a
self-proving procedure in logic, then it would be a proof, and
that the word "self" would imply a little more information than
just "proof." I only proved that the "concept" existed within
logic, just playing with words, i.e. logic.
Thanks for reading.
Larry
Acme Diagnostics
dch...@netcom.ca wrote:
>Acme Diagnostics wrote:
>> "Dan Christensen" <dch...@allstream.net> wrote:
>>><gera...@earthlink.net> wrote in message
>>>> premises" -- who discusses their use, what is the correct terminology,
>>>> etc. I've read a great deal in books on logic for the layman but
>>>> haven't come across anything that corresponds to this issue.
>>>>
>>>> By "friendly premises" I mean premises that people posit (often
>>>> unstated) that are necessary to a theory they are building on
>>>> circumstantial evidence. That is, they examine circumstantial
>>>> evidence, construct a theory that pulls the circumstantial evidence
>>>> together plausibly, but the proposal demands certain factual premises.
>>>
>>>[snip]
>>>
>>>Just my two cents, but maybe you are confusing logic or mathematics with
>>>science. Logicians and mathematicians explore questions of "what if,"
>>>constructing useful or at least interesting theoretical systems of numbers,
>>>points, algebraic operators, etc. on paper.
>>
>> Ok, but your two cents worth seems most confused.
Sorry for that wording, btw. "Incorrect" would have been much
better.
>
>Quite possible.
>
>
>> That is not
>> what logic is. You are mainly describing mathematics here.
>>
>[snip]
>
>Does it matter? Assumptions or premises about physical systems
>("friendly" or otherwise) can be stated in the language of logic and
>mathematics. It is not, however, the job of logic or mathematics to
>verify such assumptions, only to draw to reasonable conclusions from
>them. That was my point.
I can't really be responsive because some of my relevant
comments appear to be missing. I don't think I can follow
the exchange well enough.
But I'd like to post two examples. I don't know if they relate to
that, perhaps they do, but I think they might at least be
helpful in some way to the original poster:
Case #1
Betty Hill claimed to have been abducted by a UFO. As the
story goes, sometime later under hypnosis she drew a star map
from the perspective of the supposed home planet. Then, as
the story goes, somebody put the map on the computer. Close,
but no cigar. One of the stars she drew wasn't there, though the
others matched up. But then, as the story continues, a few years
later, that star was discovered.
Big load of crap, of course. But let's just suppose that star
map, hypnosis, etc., and computer work really could be verified
to be legit, and they certainly could be if someone went to the
trouble. (No, nobody has gone to the trouble! <g>) Ok, so now you
have facts, i.e. premises.
You apply logic to the facts. The new star is predicted, but what
does that mean? Only logic can tell you what it means. The
abduction is proved, but not by scientific verification. That
only provided source facts, i.e. true premises for the argument.
In this case, you only have a conclusion, but no scientific
verification, for one of the most important discoveries in
history. That's one reason logic is important in these real-world
theories. One way of putting this is that a theory achieves
"logical significance." I.e. logic tells you that it is
nearly impossible not to be true - at least as reliable and
probably more so than a scientific verification.
Most people wouldn't believe it. They would require scientific
verification. But a practicing logician would believe it. They'd
have no choice because experience requires them to accept that
such simple logic always works, turns out to be true, can risk
your life on it (emergency workers and military do it, double-ace
fighter pilots and there you are talking about some very complex
logic in the sense of reasoning), etc. To get the best
information, then, you could legitimately ask in a logic group.
Case #2
Let's say there is a kook posting in a newsgroup (not here). Over
time, you learn things about this kook, including some personal
history and current real life circumstances. As you learn things,
you write down observations in the form of rough psychiatric
speculations and any trivia whether it seems relevant or not.
Then one day, you get an email to check out a
certain site which describes a particular psychiatric disorder.
Bingo! Immediately symptoms match up. Since you already wrote
down these symptoms, they were predictive, which is an absolute
requirement. When do you have a positive diagnosis? Well, you
need to use coincidental probability for that (or some similar
probability alternative). Also it would help if you were a
qualified psychiatrist (!), but this is just an example.
Probability is a branch of logic, i.e. the inductive branch.
Applied math for quantification, and then there is a lot of
logic having to do with independence of premises (probably
the single most important thing), possible effects from outside
the system (or theory), etc. There are just all kinds of logic
issues in problems of this nature, i.e. anything having to do
with applied probability or statistics, and having nothing to do
with the underlying logic theory of probability itself.
Now having that diagnosis, and your list of various information,
all information about the disorder might be predictive. For
instance, 95% of people with this disorder have been
incarcerated. Now knowing that, a piece of information with a
well-known prison name becomes coincidental. Is it independent?
What logical relationships might exist? The two pieces of
information work together to both increase the probability of the
diagnosis and the probability of incarceration. In this way,
logic can be used to discover "secret premises," or premises that
are made more probable or even discovered (because you are caused
to look or look at them in a new context) only because the
"theory" is so good.
So, yes, according to this example, a theory can certainly bear
on the reliability of premises or supply new premises just
because the theory is "good." But it would help for the OP
to post a more detailed problem definition.
Ok, so most of this logic is specific to the application, and you
could say that it doesn't belong in logic proper, but in the
logic of whatever application. But suppose you are in the
business of solving these types of problems, i.e. expert at the
generalized logic that can affect any such theories or systems?
Then you would be mainly a logician ready to apply your logic
knowledge to a wide range of applications. But don't quote me on
that. <g>
Larry
Torkel Franzen
> It's not apparent what you mean by "remarkable." What specific
> comments of mine are you referring to?
I had in mind your general approach, as manifested in the posting at
issue.
> "Math is self-proving" means that it proves itself.
This terse explanation is certainly preferable to a lengthy tirade
to the same effect.
Torkel Franzen
> The answer is "I don't know." Torkel knew that because
> my "I don't knows" (in so many words) surrounded the comment.
No, I didn't know that you don't know what is meant by
"self-proving procedure" or "recursive proof". Why then
use these odd terms in your posting?
As for your lengthy comments about me, who could possibly care
about this stuff? You must have better things to do with your time.
Acme Diagnostics
Torkel Franzen <tor...@sm.luth.se> wrote:
>"Acme Diagnostics" <LFinez...@partpostmark.net> writes:
>
>> It's not apparent what you mean by "remarkable." What specific
>> comments of mine are you referring to?
>
> I had in mind your general approach, as manifested in the posting at
>issue.
Yes, but "remarkable?" I certainly had no intention to make you
envious. Hmmm, where did I spot that word "envy" recently?
For some reason it seemed to be attention-getting. Well, age
takes it's toll on memory.
Anyhow, it's not really a fair comparison because I had the
advantage of the best trainers money could buy.
>> "Math is self-proving" means that it proves itself.
>
> This terse explanation is certainly preferable to a lengthy tirade
>to the same effect.
Thanks! I'd also like to acknowledge your generously free
teaching. Of course I learned the above technique by carefully
studying your recent reply to the question, "What is a false
axiom?"
Your reply, "A false axiom is an axiom that is false" was
remarkably terse. It provoked quite a bit of aggravation on the
part of the questioner too, we noticed.
By the way, I've been accused of aggravating you. I apologize
if that's the case. You're obviously special.
Larry
Hmmm, where have I spotted that word "special" recently?
It also seemed to be attention-getting. I need to eat more
blueberries.
Martin Shobe
<LFinez...@partpostmark.net> wrote:
Not really. Your definition of "procedure" is directly included in
your definition of "proof". Since you pulled your definition of
"proof" from a logic textbook, it is almost certain that your
definition of "self" is included in the definition of proof as well.
(Somewhere, it almost certainly states that the formulas must either
be things proven already, or axioms. At that point, your definition
of "self" is included.)
Martin
George Dance
> Acme Diagnostics wrote:
> > ti...@amsta.leeds.ac.uk wrote:
> > >Acme Diagnostics wrote:
> > >> Torkel Franzen <tor...@sm.luth.se> wrote:
> > >>>"Acme Diagnostics" <LFinez...@partpostmark.net> writes:
snip
> > >> For this I submit that Frege and Russel developed predicate logic
> > >> with significant departures from classical logic specifically to
> > >> create a logic that could be used to support mathematical
> > >> theories and explain at least basic mathematics logically, most
> > >> notably common arithmetic.
> >
> > I wonder if you'd offer some comment on the above paragraph.
> > I'm sure it is incorrect in any theoretical detail, but is it
> > correct in a most general sense? Would it be appropriate to
> > include just in passing in a much larger text on reasoning, with
> > only a minor emphasis on logic, even less on formal logic, and
> > just to make a brief mention about PC and it's implications
> > for math?
>
> I am not really up on my history, I am afraid. What mathematicians call
> "classical logic" is, I think, what was developed by Frege and Russel.
> Certainly as opposed to "intuistic logic".
In light of what Acme says about existential import down below, I think
that what he's calling 'classical logic' is Aristotelian logic.
Standard predicate logic (as developed by Frege, Russell et al) rests
on the Boolean interpretation of incorporates of normal language
statements, which departs quite drastically from the Aristotelian
interpretation in some ways.
> > >> Four significant departures:
> > >>
> > >> 1. Existential import had to go because otherwise math
> > >> could not be supported without the "empty set," i.e. in
> > >> common understanding the number 0.
>
> What does Existential import mean?
> I looked it up online, and I guess it is in reference to "for all"
> here,
> i.e. "for all x (x=x)"
> with EI, implies that there is some x, where as we would not interpret
> it without that meaning.
> Correct?
In predicate logic with Universal Instantian and Existential
Generalization (or Existential Introduction), "for all x (x=x)" implies
that there is some x. (Not sure which you meant by EI, but neither of
those alone would be sufficient for the implication).
> >From a mathematical point of view, I think that it doesn't really
> matter. i.e. I guess you can express that same things in a language
> with EI as you could in one without. The empty set, call it e, is not
> really going to cause a problem.
> For any formula f(x) we will have
>
> 1. forall x f(x)
> 2. forall x not f(x)
>
> 1 and 2 are both true in e, when interpreted without EI but
> both false in e, when interpreted with EI
>
> Either way this is going to help you distinguish the empty set.
Interpreting both 1 and 2 as true (ie, asserting "Everything is an f
and everything is not an f" is simply asserting an absurdity; so it's
of no help in distinguishing the empty set. OTOH, interpreting both 1
and 2 as false is equivalent to asserting that some things are f's and
some things are not f's; which again is of no help in distinguishing
the empty set.
I suspect that you and Acme are actually thinking of the same thing:
the Boolean interpretation of statements like "All F are G" as (x)(Fx
-> Gx), which does eliminate existential import without any absurdity
and without any dependence on EI.
Interpreting both "All F is G" and "All F is not G" as true, in the
Boolean interpretation, does help distinguish the empty set (as both
are true iff there are no Fs). However, interpeting both as false does
not (as both would also be false if there were some Fs that were Gs and
some that were not).
snip
George Dance
> Acme Diagnostics wrote:
> > ti...@amsta.leeds.ac.uk wrote:
> > >Acme Diagnostics wrote:
> > >> Torkel Franzen <tor...@sm.luth.se> wrote:
> > >>>"Acme Diagnostics" <LFinez...@partpostmark.net> writes:
snip
> > >> For this I submit that Frege and Russel developed predicate logic
> > >> with significant departures from classical logic specifically to
> > >> create a logic that could be used to support mathematical
> > >> theories and explain at least basic mathematics logically, most
> > >> notably common arithmetic.
> >
> > I wonder if you'd offer some comment on the above paragraph.
> > I'm sure it is incorrect in any theoretical detail, but is it
> > correct in a most general sense? Would it be appropriate to
> > include just in passing in a much larger text on reasoning, with
> > only a minor emphasis on logic, even less on formal logic, and
> > just to make a brief mention about PC and it's implications
> > for math?
>
> I am not really up on my history, I am afraid. What mathematicians call
> "classical logic" is, I think, what was developed by Frege and Russel.
> Certainly as opposed to "intuistic logic".
In light of what Acme says about existential import down below, I think
that what he's calling 'classical logic' is Aristotelian logic.
Standard predicate logic (as developed by Frege, Russell et al)
incorporates the Boolean interpretation of universal statements, which
departs quite drastically from the Aristotelian one.
> > >> Four significant departures:
> > >>
> > >> 1. Existential import had to go because otherwise math
> > >> could not be supported without the "empty set," i.e. in
> > >> common understanding the number 0.
>
> What does Existential import mean?
> I looked it up online, and I guess it is in reference to "for all"
> here,
> i.e. "for all x (x=x)"
> with EI, implies that there is some x, where as we would not interpret
> it without that meaning.
> Correct?
In predicate logic with Universal Instantian and Existential
Generalization (or Existential Introduction), "for all x (x=x)" implies
that there is some x. (Not sure which you meant by EI, but neither of
those alone would be sufficient for the implication).
> >From a mathematical point of view, I think that it doesn't really
> matter. i.e. I guess you can express that same things in a language
> with EI as you could in one without. The empty set, call it e, is not
> really going to cause a problem.
> For any formula f(x) we will have
>
> 1. forall x f(x)
> 2. forall x not f(x)
>
> 1 and 2 are both true in e, when interpreted without EI but
> both false in e, when interpreted with EI
>
> Either way this is going to help you distinguish the empty set.
Interpreting both 1 and 2 as true (ie, asserting "Everything is an f
and everything is not an f" is simply asserting an absurdity; so it's
of no help in distinguishing the empty set. OTOH, interpreting both 1
and 2 as false is equivalent to asserting that some things are f's and
some things are not f's; which again is of no help in distinguishing
the empty set.
I suspect that you and Acme are actually thinking of the same thing:
the Boolean interpretation of statements like "All F are G" as (x)(Fx
-> Gx), which does eliminate existential import without any absurdity
and without affecting the generalization or instantiation rules.
Acme Diagnostics
Yes of course. The definitions are obviously a build. One is to
be used in the next.
No, as implied in the rest of your comment (below), there is no
occurence of "procedure" in the (full) text I used for "proof."
I connected the phrase in the textbook with "procedure" myself.
I did just copy the definition out of the proof definition and
include it in the previous definition of "procedure." And I
purposely tacked it onto the end of another definition in an
off-handed way, "...also sometimes described as..." And I did
that for a very good reason: hostile reviewers.
When reading the definition of "procedure" and encountering "a
finite successive step-by-step process," the hostile reviewer,
not knowing what is to come in the next definition, is expected
to accept that as one legitimate definition of "procedure." And
why not, since it is, and since they have no reason not to (yet).
But then when they get to the definition of "proof" and encounter
that same exact wording, and realize they've already accepted it,
then they cannot refuse the definition in honesty.
Whether you approve of that tactic or not, it is no point of
logic. The refutation stands.
>Since you pulled your definition of
>"proof" from a logic textbook, it is almost certain that your
>definition of "self" is included in the definition of proof as well.
Nope. That was not included anywhere. "Self-proving" in context
of math is just a phrase I've always known and encountered
throughout my life.
>(Somewhere, it almost certainly states that the formulas must either
>be things proven already, or axioms. At that point, your definition
>of "self" is included.)
Thanks for demonstrating an instance of the concept of "self-"
occuring in logic. I hereby incorporate that into the refutation
under definition "3. 'Self-'".
Larry
Acme Diagnostics
Torkel Franzen <tor...@sm.luth.se> wrote:
>"Acme Diagnostics" <LFinez...@partpostmark.net> writes:
>
>> The answer is "I don't know." Torkel knew that because
>> my "I don't knows" (in so many words) surrounded the comment.
>
> No,
The sentence you snipped in context as I posted it:
>>>>For this I submit... <snip>
>>>>4. Support self-proving procedures, and perhaps recursive
>>>> proofs though I'm not that far along yet.
>>>>Now, I don't know these things for sure, and I'm certain to have
>>>>made historical and terminological mistakes <snip>
>
> I didn't know that you don't know what is meant by
>"self-proving procedure" or "recursive proof".
You write English well enough. You have no problem
interpreting sarcasm and responding in kind in correct context
of the sarcasm, which responses can be demonstrated in the
posting record. Sarcasm is more difficult to inference than the
above straightforward explanatory text. Since you accurately
snipped the sentence out of that context, it is a reasonable
given that you also read the context. So to take your question as
honest only results in contradictions.
>Why then use these odd terms in your posting?
For the same reason, this does not add up. At best, it's just
an attempt to spread your dogma about terminology, e.g. that only
"formal" logic matters, by which you probably mean predicate
logic and it's variations, that it requires correct academic
terminology, blah blah blah. You're not the first person on
Usenet to have such an agenda. David L0ngley, famous kook.troll
of comp.ai.philosophy, posted the word "extensional" many
thousands of times over an 8-year period. He used to call phrases
like the ones I used "folk psychology" and posted that phrase
thousands of times too. Whenever someone disagreed with him, they
were using "folk psychology." Whenever someone agreed with them,
they were using correct terminology no matter how informal. This
is a matter of posting record in comp.ai.philosophy, including
google counts of these favorite phrases.
> As for your lengthy comments about me, who could possibly care
>about this stuff? You must have better things to do with your time.
I for one am not going to sing along with that hymn so that
I would be programmed to share that belief.
But to answer the implied question of why I keep posting
comments about you, it's the same answer that all of the most
experienced Usenet posters will give you: you like it. Otherwise
you would not keep provoking it. But it is entirely possible,
even likely, that you are totally unaware of that fact. That is
the typical case.
Larry
Note to Keith: I would not have answered this message
if not for the point of fact at the top that needed to be
corrected. I had to answer the rest not to appear to
agree by default.
Torkel Franzen
> The sentence you snipped in context as I posted it:
Well, then I just wonder why you posted a lengthy commentary on
"self-proving procedure" instead of just remarking that you didn't
know what it meant when you used it.
George Dance
Jim Spriggs wrote:
> Jesse Alama wrote:
>
> > Torkel ignored much of the post
> > <42eb8beb$0$91626$bb4e...@newscene.com> and called attention to the
> > part about "self-proving procedures" and "recursive proof". That may
> > have been a snarky move, but I think Torkel's question needs to be
> > answered if we are to fully understand your original post. To be
> > honest, I am with Tokel on this one: I too don't know what you mean by
> > "self-proving procedures" or "recursive proofs". I presume other
> > readers of sci.logic are in the same boat. For our sake, tell us what
> > you mean by "self-proving procedure" and "recursive proof".
>
> My guess was that "recursive proof" was an honest mistake for "proof by
> induction". "self-proving procedure" intrigues me, where can I buy one?
The first thing that occurred to me was procedures such as: "Construct
a proof of []p -> p in modal T."
Acme Diagnostics
Jim Spriggs wrote:
>Jesse Alama wrote:
>
>> Torkel ignored much of the post
>> <42eb8beb$0$91626$bb4e...@newscene.com> and called attention to the
>> part about "self-proving procedures" and "recursive proof". That may
>> have been a snarky move, but I think Torkel's question needs to be
>> answered if we are to fully understand your original post. To be
>> honest, I am with Tokel on this one: I too don't know what you mean by
>> "self-proving procedures" or "recursive proofs". I presume other
>> readers of sci.logic are in the same boat. For our sake, tell us what
>> you mean by "self-proving procedure" and "recursive proof".
>
>My guess was that "recursive proof" was an honest mistake for "proof by
>induction". "self-proving procedure" intrigues me, where can I buy one?
Hi Jim,
Seeing George's message reminded me that I had intended
to compliment your two statements, before getting sidetracked.
"Honest mistake" is exactly correct. Also appropriate considering
that I qualified my statement with "perhaps... though I'm not
that far along yet... I'm certain to have made ... terminological
mistakes."
"Where can I buy one" has just the right touch of humor to cancel
any implied insult. I obviously made a mistake there too, since I
intended to use a phrase that posters could figure out easily
enough, failing miserably.
Nor did I have any problem with Jesse's comments, even though
he tended to agree with Torkel. I choose who to agree with too!
If you or anyone else might be a little perplexed at my use of
terminology and other activites, I was thinking I might post a
little necesarry bio and appropriate explanation. I think my
activities here must strike some people as somewhat odd, to put
it nicely. Typically, posters couldn't care less about those
things.
I like them, though.
"Little" in my case usually winds up being 200 lines or so. <g>
Larry
George Dance
> On 31 Jul 2005 14:57:03 -0500, "Acme Diagnostics"
> <LFinez...@partpostmark.net> wrote:
>
> [Snip]
>
> >3. "Self-"
> >
> >The prefex "self-" can mean anything I want it to mean among
> >all the common definitions of the prefix "self-" as long as it
> >is sufficient to describe any logic system whatsoever.
> >
> >I choose for it to mean "self-contained" in the context of a
> >"logic system," and to simply refer to any logic system
> >whatsoever that does not require input from outside that system
> >to apply any of it's rules of inference; and additionally this
> >implies that all elements needed for that application are within
> >the system.
[...]
> >4. "Procedure".
> >
> >A procedure is a finite successive sequence of steps, also
> >sometimes described as a finite successive step-by-step process.
> >
> >That's probably obvious enough, since it only needs to apply
> >to any logic system of any kind.
> >
> >5. "Proving."
> >
> >Note: In logical argumention, the quantifiers "some" and
> >"sometimes" minimally require one case.
> >
> >Accurately condensing, but not paraphrasing, more text than I
> >care to type until further challenged, another quote from a logic
> >textbook:
> >
> >"A deduction in logic is sometimes defined as a finite successive
> >step-by-step process applying rules of a logic system to a series
> >of premises or formulas. In some of these cases where deduction
> >is so defined, the word "deduction" is used synonymously with the
> >word 'proof'. The two terms will be used interchangeably in this
> >text."
[...]
> In other words, a "self-proving procedure" is nothing other than a
> proof.
> [Snip]
> Martin
Apparently; which makes the assertion in question equivalent to:
There is no concept of "proof" in logic.
Torkel Franzen
> Apparently; which makes the assertion in question equivalent to:
> There is no concept of "proof" in logic.
Why would you make this bold assertion?
George Dance
Sorry for your misunderstanding; I should have made it clear that I was
referring to someone else's assertion.
I hope that the following edit clears things up:
Apparently; which makes the assertion in question equivalent to:
"There is no concept of 'proof' in logic."
(Perhaps you'd see that as an example of how learning to write only
confuses and bewilders my kind, causing us to make absurd assertions.)
Torkel Franzen
> Sorry for your misunderstanding; I should have made it clear that I was
> referring to someone else's assertion.
Surely you are eagerly affirming the proposition that there is no
such thing as proof in logic?
George Dance
Surely not. I am pointing out that, if Mr. Shobe is correct that the
concepts of 'self-proving procedure' and 'proof' refer to the same
things, then asserting (as you did) "There is no concept of
'self-proving procedure' in logic" is equivalent to asserting "There is
Torkel Franzen
> Surely not. I am pointing out that, if Mr. Shobe is correct that the
> concepts of 'self-proving procedure' and 'proof' refer to the same
> things, then asserting (as you did) "There is no concept of
> 'self-proving procedure' in logic" is equivalent to asserting "There is
> no concept of 'proof' in logic."
No, I think you're really eagerly affirming that there is no such
thing as proof in logic.
George Dance
Well, I think you're being silly.
Torkel Franzen
> Well, I think you're being silly.
Sure I am. But not as silly as you!
George Dance
> Acme Diagnostics wrote:
> |Torkel Franzen <tor...@sm.luth.se> wrote:
> |>"Acme Diagnostics" <LFinez...@partpostmark.net> writes:
> |>
> |>> 4. Support self-proving procedures, and perhaps recursive
> |>
> |> What is meant by a self-proving procedure or a recursive proof?
> |
> |You know the answers to both those questions. It's just another
> |example of Torkelling.
>
> No, he doesn't. I don't. Even after reading your explanation
> of what you meant by one of them, I still don't know what
> you mean by it. You're free to assume this is dishonest, but
> what you mean by it.
I found the explanation perfectly clear: a 'procedure' is a
step-by-step method for doing something, while 'self-proving' means
proving something without any external assumptions. So a 'self-proving
procedure' would be a way of proving something without bringing in any
outside assumptions. What part of that is giving you trouble?
> You do seem to hate him.
>
> {sarcasm} How kind and charitable you are!
>
> I planned to leave the issue alone, since I think I
> previously explained my point of view well enough for people
> who, unlike you, don't have an enormous axe to grind. But I
> see here that you are again attempting to "reposition" me
> a little bit. No, I didn't "feel sorry" for him; this is
> just your imagination.
>
> Afterward, I realized what you remind me of. You seem to
> me like the moral equivalent of the town gossip. "Did
> you hear what so-and-so said about so-and-so?" "So-and-so?
> Oh, well, we _all_ know what _he's_ like, don't we?" "I
> shouldn't say too much-- I wouldn't want to hurt him, you
> know, but, well, I've been told that so-and-so may possibly
> be, you know, not quite well in the head if you know what
> I mean?"
>
> These are not the exact phrases you use, of course, but
> it all seems to be of this flavor. This great relish at
> retelling old stories over and over (spun in your favor of
> course). The thinly disguised pleasure at finding a way
> to make something sound more dramatic than it really is.
> The kind of rationalization you offer is just the kind of
> rationalization that a town gossip has to offer too. "I
> don't like to say bad things about people, but I want to
> protect you, so you should know what so-and-so is like."
> But of course you enjoy saying these things. You appear
> to *love* doing so. You manage to work it into a thread
> on the most tenuous of excuse.
>
> The town gossip often does try to reframe any attempt to
> confront him for his gossipy behavior as something other
> than that. It must be because the critic is some kind of
> bleeding heart who doesn't want to confront the harsh
> truth about the people around him. Or maybe he's secretly
> in league with some of them.
Or maybe it's clear that the "critic" is simply gossiping as well.
> Or whatever. Anything to make
> the gossip's own enthusiasm for attempting to make certain
> people look bad from being the issue.
>
> Your desire to make him look bad is transparent. That's
> essentially all this is.
There's also an unresolved question of whether there are any
self-proving procedures in logic. Let's hope that isn't forgotten.
George Dance
> "George Dance" <george...@yahoo.ca> writes:
>
> > Well, I think you're being silly.
>
> Sure I am.
Glad we cleared that up.
> But not as silly as you!
Sorry, but I can't really see any silliness in statements like the
following:
<unsnip>
> > I am pointing out that, if Mr. Shobe is correct that the
> > concepts of 'self-proving procedure' and 'proof' refer to the same
> > things, then asserting (as you did) "There is no concept of
> > 'self-proving procedure' in logic" is equivalent to asserting "There is
> > no concept of 'proof' in logic."
</us>
Perhaps you could point it out?
Torkel Franzen
> Perhaps you could point it out?
Consider it an exercise in intensional logic.
George Dance
Aha. So let's remove the intensionality:
<unsnip>
> > I am pointing out that, if Mr. Shobe is correct that the
> > concepts of 'self-proving procedure' and 'proof' refer to the same
> > things, then "There is no concept of
> > 'self-proving procedure' in logic" is equivalent to "There is
Torkel Franzen
> Aha. So let's remove the intensionality:
What sense of "equivalent to" are you using here?
H. J. Sander Bruggink
> Surely not. I am pointing out that, if Mr. Shobe is correct that the
> concepts of 'self-proving procedure' and 'proof' refer to the same
> things, then asserting (as you did) "There is no concept of
> 'self-proving procedure' in logic" is equivalent to asserting "There is
> no concept of 'proof' in logic."
>
Let's do a little word game:
I am pointing that, if the words 'bloem' and 'flower'
refer to the same things, then asserting "there is no
word 'bloem' in English" is equivalent to asserting
"there is no word 'flower' in English."
Do you agree with this? :-)
groente
-- Sander
George Dance
> I have several questions concerning how logicians feel about "friendly
> premises" -- who discusses their use, what is the correct terminology,
> etc. I've read a great deal in books on logic for the layman but
> haven't come across anything that corresponds to this issue.
>
> By "friendly premises" I mean premises that people posit (often
> unstated) that are necessary to a theory they are building on
> circumstantial evidence. That is, they examine circumstantial
> evidence, construct a theory that pulls the circumstantial evidence
> together plausibly, but the proposal demands certain factual premises.
Speaking for myself, rather than logicians, I'd describe (and have
described) logic as a way to uncover and examine those premises. Logic
investigates 'valid' arguments or reasoning, those in which it's
impossible for the premises to be true and the conclusion false. Logic
alone cannot say which extraneous premises are false; only that if an
argument is valid, and its conclusion is false, at least one of the
premises is false.
Logic can tell you whether someone's argument for a theory is valid.
If it is, and there's a reason to think that the conclusion (the
theory) is false, that means there's also a reason to think that one of
the premises is false. If it is not, and there's reason to think that
the conclusion is false, there's reason to think that the theorist is
assuming unstated premises (which would give him a valid argument); and
at least trying to make those premises explicit by repairing the
argument so that it is valid.
> The author either avoids mentioning them and just praises the
> plausibility of his theory, or he mentions them but leaves it up to the
> reader to do the research to determine whether they are true or false.
If the author avoids stating all his premises, then he's given an
invalid argument (though it might appear valid to those who share the
same unstated premises). If one's corresponding with him (say, on
Usenet), one can point out that the argument is invalid; at which point
he can repair it himself by making his additional premises explicit.
If one's simply reading an author, the best one can do is try to
identify the hidden premises oneself.
If the author simply declares his premises as true, without supporting
them in any way, it becomes a matter of trying to discover his reasons
for believing them. (In either of the same two ways.)
> The author may even allege that there is no factual evidence available
> as to the truth or falsity of the premises, and hint that the friendly
> premises are probably true if their use leads to a theory that sounds
> plausible. Is that much clear?
The author cannot plausibly claim that any of his premises are true
*because*, as a consequence of them, his theory is true; that's nothing
but circular reasoning. He can claim that a premise is true because
it's necessary for the truth of some other theory (which the reader
also accepts); that can be a good inductive argument.
> My questions are as follows.
>
> 1. Does anyone discuss whose responsibility it is to check friendly
> premises? Does a proposer have the right to concoct a theory and
> praise its virtues without bothering to verify the truth of his
> premises?
He has a legal right of course; but not, I'd say, an epistemic one.
Someone who believes an assertion for no reason should not expect to be
taken seriously when he asserts it.
> 2. Proposers sometimes claim that the beauty or consistency or
> problem-solving ability of their theory validates their undefended
> friendly premises. But aren't there many cases where beautiful /
> consistent / problem-solving theories have later been proven to have at
> least one fallacious premise? Can you recommend anyone who discusses
> this or gives examples?
One applicable point, which I've read widely (but can't remember the
original source - I think it was Popper), is that any fact can be
explained by an infinite number of theories. So that a theory explains
a fact is not, by itself, a sufficient reason to believe the theory.
I'd see considerations of 'beauty' etc. entering in only where one has
two inconsistent theories which both fully explain the same facts. In
cases like that, eg, it's quite in order to choose between them on the
basis of criteria like Occam's Razor, believing the simplest one (the
one with the fewest premises) eg.
> My questions aren't purely theoretical. I'm trying to assess a
> scholarly proposal in an historical field that posits a bunch of
> friendly premises that the author considers verified by the
> plausibility of the theory he has built upon them. I'm not at all
> clear how to analyze the procedure or what are the correct logical
> terms involved.
To sum up, I'd say the correct procedure would be:
1) State the author's argument for the theory in semi-formal form (as a
list of premises and conclusion). Is the argument valid? If not, what
other premises would be required for it to be valid?
2) State the author's argument for each controversial premise in the
same form. Are those valid? If so, what are the premises for those
premises (the premises^2)?
3) If the author's only stated premise(^2) for any premise is that
without it his theory is incorrect, that's not a valid argument for the
premise. To be valid, it would have to be recast as a modus tollens
argument:
1. If premise X is not correct, then theory Y is not correct.
2. [Theory Y is correct.]
----------
3. Premise X is correct.
Which is a valid argument. However, if the author then goes on to
argue for theory Y on the basis of premise X, he's given nothing but a
circular argument.
Thanks in advance to anyone who responds.
[BTW, it may be just me, but I find that last a bit rude; it sounds
like, "I couldn't be bothered to write and thank you after you've
answered my question."]
George Dance
Well, yes, but we weren't talking about words but concepts. The fact
that an English-speaker doesn't use the word 'bloem' does not show that
English-speakers have no such concept. In fact they do, even though
they use a different word ('flower') for it.
George Dance
> H. J. Sander Bruggink wrote:
> > I am pointing that, if the words 'bloem' and 'flower'
> > refer to the same things, then asserting "there is no
> > word 'bloem' in English" is equivalent to asserting
> > "there is no word 'flower' in English."
> >
> > Do you agree with this? :-)
>
Oops! Should have been, "Well, no, but..."
Once again we see the apparent power of writing to confuse and bewilder
my kind.
Jim Spriggs
>
> Jim Spriggs wrote:
> >Jesse Alama wrote:
> >
> >> Torkel ignored much of the post
> >> <42eb8beb$0$91626$bb4e...@newscene.com> and called attention to the
> >> part about "self-proving procedures" and "recursive proof". That may
> >> have been a snarky move, but I think Torkel's question needs to be
> >> answered if we are to fully understand your original post. To be
> >> honest, I am with Tokel on this one: I too don't know what you mean by
> >> "self-proving procedures" or "recursive proofs". I presume other
> >> readers of sci.logic are in the same boat. For our sake, tell us what
> >> you mean by "self-proving procedure" and "recursive proof".
> >
> >My guess was that "recursive proof" was an honest mistake for "proof by
> >induction". "self-proving procedure" intrigues me, where can I buy one?
>
> Hi Jim,
>
> Seeing George's message reminded me that I had intended
> to compliment your two statements, before getting sidetracked.
>
> "Honest mistake" is exactly correct.
So, when you wrote "recursive proof" you meant precisely "proof by
induction"?
> Also appropriate considering
> that I qualified my statement with "perhaps... though I'm not
> that far along yet... I'm certain to have made ... terminological
> mistakes."
>
> "Where can I buy one" has just the right touch of humor to cancel
> any implied insult.
Certainly no insult was intended.
> I obviously made a mistake there too, since I
> intended to use a phrase that posters could figure out easily
> enough, failing miserably.
Can you give an alternative to "self-proving procedure"? Or give an
example, or a reference? Do you mean something like:
Mathematicians use mathematics to prove things about logic
while at the same time founding their mathematics on logic.
--
I don't know who you are Sir, or where you come from,
but you've done me a power of good.
George Dance
"Has the same truth value as".
Acme Diagnostics
First, let me compliment you on your much stronger
demonstration that "proof" is not equivalent to "Self-proving
procedure" that occurs in Torkel's (reduced) assertion:
"There is no concept of 'self-proving procedure' in logic."
by constructing the necessary inference from the assumption
"'proof' is equivalent to 'self-proving procedure'":
"There is no concept of 'logic' in logic."
which is obviously absurd. In my reply to Mr. Shobe, I could
only say it "naively seems to me" that "self-" implied more
information than just "proof." I'm can make a proof by
absurdity, but I just didn't see it!
Also, I compliment H. J. Sander Bruggink who appears to
be arguing cooperatively and knowledgeably for the opposition
here. Maybe we can make some progress, then, as opposed to
just being "silly."
Doesn't the analogy also contain a level-of-description (LOD)
error?
For background, I remind other readers that 1) LOD is a test in
real-world logical reasoning (RW) 2) RW includes everything in
the real-world, i.e. it includes "theory." The two are not
mutually exclusive. 3) LOD is only ever valid in a context, I'll
try to make context obvious where necessary.
Mr. Shobe, who made the (paraphrase) "'self-proving procedure' is
equivalent to 'proof.'" assertion, appeared to use "proof" only
in the sense of a deductive formal logic proof. For one thing he
was commenting on a textbook quote about the "deductive" process
that seemed obviously within formal logic.
"Self-proving procedure" is RW. The latter contains the word
"proof" but that word is used in the RW sense, and includes both
formal deductive proofs and other kinds of "proofs" as (loosely
and perhaps incorrectly) used in other logic contexts. "Self-"
and "procedure" are both intended (regardless of how poorly) to
invoke the formal deductive interpretation of proof in context of
predicate/math logic (and don't forget I was confused about that
relationship), by readers who are assumed to be qualified to make
that conversion, by someone (me) who doesn't know the correct
terminology to use and thus cannot make that conversion. (As I
clearly stated with the original introduction of the phrase.)
"Proof" is then "formal deductive logic in English" while
"self-proving procedure" is "English," even though it was
(attempted to be) shaded to the best of my meager ability
in such a way as to induce the above hoped for conversion.
Also note that, since I wanted to induce that conversion, I also
needed it to be somewhat obviously incorrect - and that should go
down in Usenet history as one of the most tortured excuses ever
for confused terminology!).
The LOD for "proof" is "formal deductive logic in English"
The LOD for 'self-proving procedure' is "English"
Because "formal deductive logic," when containing English
language (at least), occurs within "English," there is an LOD
change to the next higher LOD. Thus the comparison "proof" v.
"self-proving procedure" contains a change in LOD.
The two terms cannot be equivalent if there is a change in
LOD.
Also, it was recently explained to me that, linguistically, the
word "Formal" excludes language by definition. I don't know if
that applies here, but if it does, then that's another end of the
story (besides yours). 'Self-proving procedure" cannot be
equivalent to 'proof" in the formal deductive sense.
I continue with an aside about this proof (refutation) by analogy.
If there is indeed an LOD change between 'proof' and
'self-proving procedure' then I think the analogy must fail
because I don't think there is an LOD change in the analogy.
However, if the LOD change above does fail, then the analogy
would hold with respect to LOD only.
I don't know all the things that would be in a higher
LOD for "English." But I'm speculating that the obvious one
in context of the jumbled word in the analogy would be
"character set." Here, the context includes: character set,
words, resulting meaning, logic using words, natural language
using words, theory v. RW.
Both "Bloem" and "flower" occur in "character set." That
alone does not establish that they are in the same LOD
(what I wish to demonstrate). But it establishes that they
are in the same system, i.e. if there is a difference in LOD
in context of "characters set," one is contained within the
other (which I suspect is not the case.)
The LOD for 'Flower" is "English."
The LOD for 'bloem" is "Nonsense."
But "English" does not occur within "Nonsense" (I speculate.)
"English" does not occur within "nonsense" because you
cannot have "Nonsense" without "English" (whereas you
*can* have English without formal deductive logic in the original
comparison which is being analogized).
In other words, the character set "abcde...", however arranged
is not "nonsense." It remains just a character set, and it's
perfectly sensible to invent a character set. It cannot be
"nonsense" until "sense" is introduced, i.e. "English." "Sense"
(i.e. English) is in the same level of description as "nonsense."
Thus (I speculate) the analogy fails because: 1) there is a
failure to maintain LOD in the analogy, and 2) LOD is one of the
attributes of the comparison being analogized, i.e. "proof" v.
"self-proving procedure." which is a deciding attribute of the
proposition in question, i.e. whether the two terms are
equivalent.
Again, this whole line of reasoning, presented for George's
(or anyone's) review, is speculative.
Larry
Acme Diagnostics
"George Dance" <george...@yahoo.ca> wrote:
>Torkel Franzen wrote:
A little compilation to repair the snippage, with comment.
>>>>>>>>>>>>>Martin Shobe wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>>> In other words, a "self-proving procedure" is nothing other than a
>>>>>>>>>>>>>> proof.
>>>>>>>>>>>>>> [Snip]
For the rest, George starts with the odds:
>>>>>>>>>>>>>Apparently; which makes the assertion in question equivalent to:
>>>>>>>>>>>>>There is no concept of "proof" in logic.
George is replacing 'self-proving procedure' with 'proof' in
Torker's original statement which asserted: "There is no concept
of 'self-proving procedure' in logic."
Tokel with the evens:
>>>>>>>>>>>>Why would you make this bold assertion?
Classic Torkelling. It is only too obvious above why George
constructed the absurd statement.
>>>>>>>>>>> Sorry for your misunderstanding; I should have made it clear that I was
>>>>>>>>>>> referring to someone else's assertion.
George has made an attempt to repair and convert to cooperative
argument.
>>>>>>>>>>Surely you are eagerly affirming the proposition that there is no
>>>>>>>>>>such thing as proof in logic?
>>>>>>>>
>>>>>>>>> Surely not. I am pointing out that, if Mr. Shobe is correct that the
>>>>>>>>> concepts of 'self-proving procedure' and 'proof' refer to the same
>>>>>>>>> things, then asserting (as you did) "There is no concept of
>>>>>>>>> 'self-proving procedure' in logic" is equivalent to asserting "There is
>>>>>>>>> no concept of 'proof' in logic."
Explaining as if to a child.
>>>>>>>> No, I think you're really eagerly affirming that there is no such
>>>>>>>>thing as proof in logic.
A very young child.
>>>>>>>Well, I think you're being silly.
>>>>>>
>>>>>>Sure I am. But not as silly as you!
I submit that it is obvious to every reader who is being silly.
<snip and repear a broken exchange>
>>>>> Perhaps you could point it [reason for silly] out?
>>>>
>>>> Consider it an exercise in intensional logic.
Torkel changes the subject. But George does not make
the call, so Torkel gets away with it.
>>>Aha. So let's remove the intensionality:
>>>
>>><unsnip>
>>>>> I am pointing out that, if Mr. Shobe is correct that the
>>>>> concepts of 'self-proving procedure' and 'proof' refer to the same
>>>>> things, then "There is no concept of
>>>>> 'self-proving procedure' in logic" is equivalent to "There is
>>>>> no concept of 'proof' in logic."
>>>>></us>
>>
>>What sense of "equivalent to" are you using here?
Another change of subject. Weaseling, plain and simple.
>"Has the same truth value as".
A very, very young child. But of course this is just obvious
trolling activity.
This compilation and commentary brought to you by Acme
Diagnostics.
George Dance
> "George Dance" <george...@yahoo.ca> wrote:
> >H. J. Sander Bruggink wrote:
> >> George Dance wrote:
>
> First, let me compliment you on your much stronger
> demonstration that "proof" is not equivalent to "Self-proving
> procedure" that occurs in Torkel's (reduced) assertion:
>
> "There is no concept of 'self-proving procedure' in logic."
>
> by constructing the necessary inference from the assumption
> "'proof' is equivalent to 'self-proving procedure'":
>
> "There is no concept of 'logic' in logic."
>
> which is obviously absurd.
I think you misunderstood what I managed to prove here: not that
Shobe's statement was incorrect, but that his and Torkel's original one
could not both be correct - which leaves Torkel the options of either
denying Shobe's statement, or retracting his original one.
That's complicated a bit by the fact that you're denying Shobe's
statement yourself, but I think that (even if the statements don't say
the same thing), the relation between them is such that they're still
equivalent. (More on that in its place below).
I get your point about LOD's, and I'd agree: 'proof' is a technically
defined term used within logic to denote certain sets of formulas;
whereas 'self-proving procedure' is a non-technical description from
outside the field of the process of constructing a (technical) proof
which uses the word 'proving' in a completely non-technical sense (so
you have not given a circular definition).
> "Proof" is then "formal deductive logic in English" while
> "self-proving procedure" is "English," even though it was
> (attempted to be) shaded to the best of my meager ability
> in such a way as to induce the above hoped for conversion.
As I commented before, I certainly understood that; though I was
thinking of one-line proofs of axioms or tautologies. But, again, it's
not necessary that all proofs be self-proving procedures or vice versa;
only that some things be both.
> Also note that, since I wanted to induce that conversion, I also
> needed it to be somewhat obviously incorrect - and that should go
> down in Usenet history as one of the most tortured excuses ever
> for confused terminology!).
OK. Worked for me.
> The LOD for "proof" is "formal deductive logic in English"
> The LOD for 'self-proving procedure' is "English"
> Because "formal deductive logic," when containing English
> language (at least), occurs within "English," there is an LOD
> change to the next higher LOD. Thus the comparison "proof" v.
> "self-proving procedure" contains a change in LOD.
>
> The two terms cannot be equivalent if there is a change in
> LOD.
I'm going to continue, in the discussion with Torkel (and Shobe, should
he choose to respond) with the hypothesis that Shobe is correct and the
two terms do mean the same thing; but I'll point out that my argument
goes through, even if there are some 'self-proving procedures' that are
not logical proofs and vice versa, as long as there are some things one
can point to that are both.
> Also, it was recently explained to me that, linguistically, the
> word "Formal" excludes language by definition. I don't know if
> that applies here, but if it does, then that's another end of the
> story (besides yours). 'Self-proving procedure" cannot be
> equivalent to 'proof" in the formal deductive sense.
> I continue with an aside about this proof (refutation) by analogy.
> If there is indeed an LOD change between 'proof' and
> 'self-proving procedure' then I think the analogy must fail
> because I don't think there is an LOD change in the analogy.
> However, if the LOD change above does fail, then the analogy
> would hold with respect to LOD only.
I agree that Mr. Sander Bruggink's [SB] analogy fails, but for a
different reason.
> I don't know all the things that would be in a higher
> LOD for "English." But I'm speculating that the obvious one
> in context of the jumbled word in the analogy would be
> "character set." Here, the context includes: character set,
> words, resulting meaning, logic using words, natural language
> using words, theory v. RW.
>
> Both "Bloem" and "flower" occur in "character set." That
> alone does not establish that they are in the same LOD
> (what I wish to demonstrate). But it establishes that they
> are in the same system, i.e. if there is a difference in LOD
> in context of "characters set," one is contained within the
> other (which I suspect is not the case.)
>
> The LOD for 'Flower" is "English."
> The LOD for 'bloem" is "Nonsense."
My own belief (which I haven't bothered to check) is that 'bloem' is
actually Dutch (for flower). Which means you'll have to modify your
refutation below. Pace "Austin Powers in Goldmember", Dutch and
nonsense are distinct concepts.
> But "English" does not occur within "Nonsense" (I speculate.)
>
> "English" does not occur within "nonsense" because you
> cannot have "Nonsense" without "English" (whereas you
> *can* have English without formal deductive logic in the original
> comparison which is being analogized).
>
> In other words, the character set "abcde...", however arranged
> is not "nonsense." It remains just a character set, and it's
> perfectly sensible to invent a character set. It cannot be
> "nonsense" until "sense" is introduced, i.e. "English." "Sense"
> (i.e. English) is in the same level of description as "nonsense."
>
> Thus (I speculate) the analogy fails because: 1) there is a
> failure to maintain LOD in the analogy, and 2) LOD is one of the
> attributes of the comparison being analogized, i.e. "proof" v.
> "self-proving procedure." which is a deciding attribute of the
> proposition in question, i.e. whether the two terms are
> equivalent.
>
> Again, this whole line of reasoning, presented for George's
> (or anyone's) review, is speculative.
> Larry
I'm glad to see you thinking this through, even though (IMO) you got a
couple of things wrong. I already have, as well; I don't mind you
jumping and correcting me in turn, of course. (Just don't save my
errors in a file and continue to repost them for years, a la
Torkelmada. 8)
Acme Diagnostics
"George Dance" <george...@yahoo.ca> wrote:
>Acme Diagnostics wrote:
>>
>> demonstration that "proof" is not equivalent to "Self-proving
>> procedure" that occurs in Torkel's (reduced) assertion:
>
>Shobe's statement was incorrect, but that his and Torkel's original one
>could not both be correct - which leaves Torkel the options of either
>denying Shobe's statement, or retracting his original one.
Yes of course. Thanks for correcting me.
("LOD" = level of description)
>> The LOD for "proof" is "formal deductive logic in English"
>> The LOD for 'self-proving procedure' is "English"
<snip>
>> The two terms cannot be equivalent if there is a change in
>> LOD.
>
>I'm going to continue, in the discussion with Torkel (and Shobe, should
>he choose to respond) with the hypothesis that Shobe is correct and the
>two terms do mean the same thing; but I'll point out that my argument
>goes through, even if there are some 'self-proving procedures' that are
>not logical proofs and vice versa, as long as there are some things one
>can point to that are both.
Well, Torkel's assertion was a universal, so it is refuted if
they can be the same in just one case. But I only had to
demonstrate that 'self-proving procedures' described one "logic
concept." It seems you'll have to demonstrate that there is at
least one proof that qualifies as a 'self-proving procedure.' I'm
sure there is, but I'm unqualified to argue it. I leave it up to
you.
Re: LOD, Two things in different LODs can refer to the same
thing, e.g. a proof, especially if the one in the lower LOD is
a proof. <g> I think a formal deductive proof would qualify,
since that seemed to be Shobe's context that you can demonstrate.
If you were to put 'formal deductive proof' in Torkel's
assertion, I think it would be just as absurd.
<snip>
>> The LOD for 'Flower" is "English."
>> The LOD for 'bloem" is "Nonsense."
>
>My own belief (which I haven't bothered to check) is that 'bloem' is
>actually Dutch (for flower). Which means you'll have to modify your
>refutation below. Pace "Austin Powers in Goldmember", Dutch and
>nonsense are distinct concepts.
Hehe! No tulips here in Florida. <g>
>> Again, this whole line of reasoning, presented for George's
>> (or anyone's) review, is speculative.
>> Larry
>
>I'm glad to see you thinking this through, even though (IMO) you got a
>couple of things wrong.
Ok. Hope any distinctions along the way help.
>I already have, as well; I don't mind you
>jumping and correcting me in turn, of course. (Just don't save my
>errors in a file and continue to repost them for years, a la
>Torkelmada. 8)
Yours aren't nearly as entertaining as his. <g>
I'd just like to share my opinion with you that Torkel's has
reverted to pushing his terminological dogma here, since
everything else has failed. But since that dogma is a loser too,
it really doesn't matter whether he expands on his "intensional"
and "informal" comedy or not. I'd ignore it (or have fun with
it), but maybe you're willing to pull it out inch by inch in
XX "silly" posts. <g>
I've argued all aspects of that dogma with D.L. already, but more
significantly a few excellent arguers like Bill M0dlin, and so
far my arguments have stood. No "Bill M0dlins" in Torkel's
"priesthood" that I've seen.
Larry
Acme Diagnostics
Jim Spriggs wrote:
>Acme Diagnostics wrote:
>> Jim Spriggs wrote:
>>>Jesse Alama wrote:
>>>
>>>> Torkel ignored much of the post
>>>> <42eb8beb$0$91626$bb4e...@newscene.com> and called attention to the
>>>> part about "self-proving procedures" and "recursive proof". That may
>>>> have been a snarky move, but I think Torkel's question needs to be
>>>> answered if we are to fully understand your original post. To be
>>>> honest, I am with Tokel on this one: I too don't know what you mean by
>>>> "self-proving procedures" or "recursive proofs". I presume other
>>>> readers of sci.logic are in the same boat. For our sake, tell us what
>>>> you mean by "self-proving procedure" and "recursive proof".
>>>
>>>My guess was that "recursive proof" was an honest mistake for "proof by
>>>induction". "self-proving procedure" intrigues me, where can I buy one?
>>
>> Hi Jim,
>>
>> Seeing George's message reminded me that I had intended
>> to compliment your two statements, before getting sidetracked.
>>
>> "Honest mistake" is exactly correct.
>
>So, when you wrote "recursive proof" you meant precisely "proof by
>induction"?
No, I only referred to the "honest mistake" part. I have no idea
what "proof by induction" means. It sounds like an oxymoron
to me, but I have seen it legitimately used in context of
some logic somewhere, so I know it is not an oxymoron in some
sense. I vaguely remember some textbook somewhere saying
something like "this is called a proof by induction but that's a
misnomer because it is really a deductive process" or something
like that. This goes back a while, and was (probably still is)
irrelevant to my goals in logic.
>> I obviously made a mistake there too, since I
>> intended to use a phrase that posters could figure out easily
>> enough, failing miserably.
>
>Can you give an alternative to "self-proving procedure"? Or give an
>example, or a reference? Do you mean something like:
>
> Mathematicians use mathematics to prove things about logic
> while at the same time founding their mathematics on logic.
No, not at all.
There are systems of logic where results can be changed from
outside the system. "Results" are often called proofs, though
not in the same sense as a theoretical math proof. For instance,
in business, or in the military including in the most complex
systems imaginable, someone will often say "prove it" and someone
will just produce some empirical evidence which is then accepted
as "proof," or it could just a point of short logic. Well, to get
closer to what some people would be more willing to accept as a
"logic system," it also happens in the programming world. There
you prove your logic with the "run" button. A more "theoretical"
example would be statistical prediction of stocks or commodity
prices. There you make theoretical calculations which are proved
in the sense of exact probability calculations. But when applied
in the real-world, new logic can completely invalidate that
"theory." (I know some statistical formulas are unproven
mathematically but lets not go there. It's just a "more
theoretical" example than the business example.) Then there are
dogmas of all varieties including religious dogmas, and you'll
find that "logic" occurs as every third word (or whatever) in
some of them. They are routinely "disproved" from outside those
systems. I think you get the idea.
In logic or math theories never intended to apply in the
real-world (and perhaps some that are - I don't know), a system
can be constructed so that there is no possibility of anything
outside the system changing results, or at least that's what I've
been told, including here. That is what I meant by
"self-proving." That has been called "self-proving" at various
points thoughout my life from a variety of sources. None of them
being in predicate or math logic, though.
Since the idea of "proofs" had to be introduced into logic
at some point, there is no reason for me to conclude that
they were introduced as the "theoretical" self-provng kind
all at once. For all I know, there may be other or intermediate
logics that have some other definition of "proved" that can
in some circumstance whatsoever be affected from outside
the system. I think that would be a foolish assumption to
make until one exhausts the historical record. I haven't even
started on the historical record. <g>
"Procedure" just means a step-by-step process. Lot's of
synonyms could have been used. Some word seemed necessary
to complete the phrase "self-proving..." since by itself it's
just an adjective. Other than that, I didn't mean to attach any
special importance to the word. "Self-proving mechanism" or
"self-proving process" or "self-proving method" or "self-proving
system" all would probably have worked as well in my mind. I saw
no reason not to use "procedure," since that's one thing that a
deductive proof is according to my textbook excerpt. I had
probably read that excerpt (and others) in the past and probably
"finite successive step-by-step process" (and variations) was
just read as "procedure" in my mind, since that's what it is.
Larry
dch...@netcom.ca
> dch...@netcom.ca wrote:
> >Acme Diagnostics wrote:
> >> "Dan Christensen" <dch...@allstream.net> wrote:
> >>><gera...@earthlink.net> wrote in message
> >>>> premises" -- who discusses their use, what is the correct terminology,
> >>>> etc. I've read a great deal in books on logic for the layman but
> >>>> haven't come across anything that corresponds to this issue.
> >>>>
> >>>> By "friendly premises" I mean premises that people posit (often
> >>>> unstated) that are necessary to a theory they are building on
> >>>> circumstantial evidence. That is, they examine circumstantial
> >>>> evidence, construct a theory that pulls the circumstantial evidence
> >>>> together plausibly, but the proposal demands certain factual premises.
> >>>
> >>>
> >>>Just my two cents, but maybe you are confusing logic or mathematics with
> >>>science. Logicians and mathematicians explore questions of "what if,"
> >>>constructing useful or at least interesting theoretical systems of numbers,
> >>>points, algebraic operators, etc. on paper.
> >>
> >> Ok, but your two cents worth seems most confused.
>
> Sorry for that wording, btw. "Incorrect" would have been much
> better.
> >
> >Quite possible.
> >
> >
> >> That is not
> >> what logic is. You are mainly describing mathematics here.
> >>
> >[snip]
> >
> >Does it matter? Assumptions or premises about physical systems
> >("friendly" or otherwise) can be stated in the language of logic and
> >mathematics. It is not, however, the job of logic or mathematics to
> >verify such assumptions, only to draw to reasonable conclusions from
> >them. That was my point.
>
> I can't really be responsive because some of my relevant
> comments appear to be missing. I don't think I can follow
> the exchange well enough.
>
> But I'd like to post two examples. I don't know if they relate to
> that, perhaps they do, but I think they might at least be
> helpful in some way to the original poster:
>
> Case #1
>
> Betty Hill claimed to have been abducted by a UFO. As the
> story goes, sometime later under hypnosis she drew a star map
> from the perspective of the supposed home planet. Then, as
> the story goes, somebody put the map on the computer. Close,
> but no cigar. One of the stars she drew wasn't there, though the
> others matched up. But then, as the story continues, a few years
> later, that star was discovered.
>
> Big load of crap, of course. But let's just suppose that star
> map, hypnosis, etc., and computer work really could be verified
> to be legit, and they certainly could be if someone went to the
> trouble. (No, nobody has gone to the trouble! <g>) Ok, so now you
> have facts, i.e. premises.
>
> You apply logic to the facts. The new star is predicted, but what
> does that mean? Only logic can tell you what it means.
[snip]
In this case, logic tells you only that the two sets of data giving the
location of the new star were consistent. Nothing about alien
abductions, etc. Or how this Betty may actually have obtained the data.
Maybe she discovered the star herself through her own astronomical
research and, for fun, is perpetrating a little hoax on a gullible
public. ;^)
And what if her map was wrong? Would this disprove her story of an
alien abduction? Strictly speaking, no.
Your other example is complicated by considerations of probability, but
I suspect a similar analysis may apply.
Dan
Download my DC Proof software at http://www.dcproof.com
Torkel Franzen
<unsnip>
> > I am pointing out that, if Mr. Shobe is correct that the
> > concepts of 'self-proving procedure' and 'proof' refer to the same
> > things, then "There is no concept of
> > 'self-proving procedure' in logic" is equivalent to "There is
> > no concept of 'proof' in logic."
</us>
Is "the concepts of 'self-proving procedure' and 'proof' refer to
the same things" another way of saying "all self-proving procedures
are proofs and all proofs are self-proving procedures"?
Torkel Franzen
> No, I only referred to the "honest mistake" part. I have no idea
> what "proof by induction" means.
Or what "recursive proofs" means?
H. J. Sander Bruggink
> H. J. Sander Bruggink wrote:
>
>>George Dance wrote:
>>
>>>I am pointing out that, if Mr. Shobe is correct that the
>>>concepts of 'self-proving procedure' and 'proof' refer to the same
>>>things, then asserting (as you did) "There is no concept of
>>>'self-proving procedure' in logic" is equivalent to asserting "There is
>>>no concept of 'proof' in logic."
>>
>>Let's do a little word game:
>>
>> I am pointing that, if the words 'bloem' and 'flower'
>> refer to the same things, then asserting "there is no
>> word 'bloem' in English" is equivalent to asserting
>> "there is no word 'flower' in English."
>>
>>Do you agree with this? :-)
>
> Well, yes, but we weren't talking about words but concepts.
The problem in your argument is the referring to; what is being referred
to by what it not important. I changed "concept" into "word" because
concepts do not refer to anything, but words do.
> The fact
> that an English-speaker doesn't use the word 'bloem' does not show that
> English-speakers have no such concept. In fact they do, even though
> they use a different word ('flower') for it.
True. But that doesn't mean that anyone will understand you when you say
"bloem" in an English-speaking country (except, perhaps, for a few Dutch
tourists :-).
groente
-- Sander
George Dance
H. J. Sander Bruggink wrote:
> George Dance wrote:
> > H. J. Sander Bruggink wrote:
> >
> >>George Dance wrote:
> >>
> >>>I am pointing out that, if Mr. Shobe is correct that the
> >>>concepts of 'self-proving procedure' and 'proof' refer to the same
> >>>things, then asserting (as you did) "There is no concept of
> >>>'self-proving procedure' in logic" is equivalent to asserting "There is
> >>>no concept of 'proof' in logic."
> >>
> >>Let's do a little word game:
> >>
> >> I am pointing that, if the words 'bloem' and 'flower'
> >> refer to the same things, then asserting "there is no
> >> word 'bloem' in English" is equivalent to asserting
> >> "there is no word 'flower' in English."
> >>
> >>Do you agree with this? :-)
> >
[edited as per my posted correction]
>
> The problem in your argument is the referring to; what is being referred
> to by what it not important. I changed "concept" into "word" because
> concepts do not refer to anything, but words do.
More precisely, (a) concepts "refer to" objects, (b) words "symbolize"
concepts, and ergo (c) words "stand for" objects:
http://originresearch.com/sd/sd4.cfm
I realize that we're on sci.logic, not alt.philosophy; but I'd like you
to understand that those distinctions aren't merely pedantic:
1) Just before I sat down to write this, I made myself some coffee. To
do so, I had to find coffee, filters, machine, water tap, cup, and
spoon. How could I have done any of that - identified any of those
objects - except by using concepts which referred to them? Not by
words, as the entire process was non-verbal.
2) Say you're reading an English book and come across the sentence,
"Some tulips are pink." You know that's synthetically true, because
you know the Dutch equivalent is synthetically true; you don't have to
suspend belief until you can go out and observe some tulips. Why do
you know that the two sentences are equivalent? Because they're
talking about the same things - <tulips> and <pink>.
What kind of things are <tulips> and <pink>? They can't be merely the
physical objects, pink tulips; for (I'll stipulate) at the time you
were reading, there were no such objects in the room for you to
observe. And what if the sentence you'd read had been: "Some unicorns
are gold." You'd know that one was false (in both English and Dutch
equivalents), but not by reference to certain objects - there are no
such objects as unicorns for you to observe, period.
3) Finally, consider a case in which humans simply could not
conceptualize; they could still make sounds and write strings of
characters, but none of those sounds or characters symbolized any
concepts (there being none). In that case, what objects could the
sounds and strings possibly stand for or 'refer to'?
> > The fact
> > that an English-speaker doesn't use the word 'bloem' does not show that
> > English-speakers have no such concept. In fact they do, even though
> > they use a different word ('flower') for it.
>
> True. But that doesn't mean that anyone will understand you when you say
> "bloem" in an English-speaking country (except, perhaps, for a few Dutch
> tourists :-).
Actually, I suspect that most of us would: as a reflection of our
mongrel heritage, we the word "bloom" as well as "flower" in our
language (and most of us understand that both words symbolize the same
concept, and therefore stand for the same objects).
Some would not, of course: that very issue arose in response to your
earlier post, with one person arguing that 'bloem' symbolized the
concept <flower>, and the other that 'bloem' was nonsense that
symbolized nothing. Obviously one was right and the other wrong; which
couldn't be the case if there were no concepts that referred to
objects.
The distinction between 'concepts' and 'words' is not only non-pedantic
(as I hope I've shown; I was trying for brevity, so may have sacrificed
some clarity), but also (contrary to what you hint above) important to
the discussion. If in fact the claim in question had dealt with words
rather than concepts - if the claimant had said only, "There's no such
term as 'self-proving procedure' in logic" -
then we probably wouldn't even be having a discussion.
> groente
G'day to you (as we say in Canada).
George Dance
It looks to me like Mr. Shobe was saying "all"; but you can interpret
his statement as well as I can:
"In other words, a "self-proving procedure" is nothing other than a
proof."
However, the equivalence follows no matter how one quantifies: if some
but not all Fs were Gs and vice versa, "There are no Fs" and "There are
no Gs" would still have the same truth value.
H. J. Sander Bruggink
>>The problem in your argument is the referring to; what is being referred
>>to by what it not important. I changed "concept" into "word" because
>>concepts do not refer to anything, but words do.
>
> More precisely, (a) concepts "refer to" objects, (b) words "symbolize"
> concepts, and ergo (c) words "stand for" objects:
Ok, I see, your "concept" is similar to Frege's "Sinn", but I
thought "Sinn" is usually translated as "Sense" in English.
Doesn't matter though, the problem is, as I said, the
"referring to", not what refers to what. Just because two
concepts refer to the same thing, doesn't meen they are both
concepts from logic.
[snip]
>
>>groente
>
> G'day to you (as we say in Canada).
I think you say "vegetables" in Canada. ;-)
groente
-- Sander
Torkel Franzen
> However, the equivalence follows no matter how one quantifies: if some
> but not all Fs were Gs and vice versa, "There are no Fs" and "There are
> no Gs" would still have the same truth value.
So we can take "the concepts of 'self-proving procedure' and 'proof'
refer to the same things" to mean "all self-proving procedures are
proofs and all proofs are self-proving procedures". Can we similarly
eliminate the word "concept" from the statement "There is no concept
of 'self-proving procedure' in logic"?
Jim Spriggs
>
>.... I vaguely remember some textbook somewhere saying
> something like "this is called a proof by induction but that's a
> misnomer because it is really a deductive process"
Probably a confusion about two kinds of induction; mathematical
induction and (what one might call) Baconian induction.
I can make no sense of the rest of your post. In particular, I do not
know what you mean by "recursive proof" and "self-proving procedure" nor
can I even guess any more.
Acme Diagnostics
dch...@netcom.ca wrote:
>Acme Diagnostics wrote:
>>
>> Betty Hill claimed to have been abducted by a UFO. As the
>> story goes, sometime later under hypnosis she drew a star map
>> from the perspective of the supposed home planet. Then, as
>> the story goes, somebody put the map on the computer. Close,
>> but no cigar. One of the stars she drew wasn't there, though the
>> others matched up. But then, as the story continues, a few years
>> later, that star was discovered.
>>
>> Big load of crap, of course. But let's just suppose that star
>> map, hypnosis, etc., and computer work really could be verified
>> to be legit, and they certainly could be if someone went to the
>> trouble. (No, nobody has gone to the trouble! <g>) Ok, so now you
>> have facts, i.e. premises.
>>
>> You apply logic to the facts. The new star is predicted, but what
>> does that mean? Only logic can tell you what it means.
>
>[snip]
>
>In this case, logic tells you only that the two sets of data giving the
>location of the new star were consistent.
And that a prediction was correctly made that must be
explained in such a way that all logical contradictions are
removed. Since there will always be multiple explanations that
can accomplish this, we examine the probabilities of each being
the correct explanation.
Obviously here, the comparison is expected to reduce to the
probability of a nonrandom event. Similar to someone predicting a
winning lottery number after investing, let's say, $200,000 for
that privilege. That would reduce the number of guessers
considerably, in fact probably to zero considering the odds. But
the odds here can be many orders-of-magnitudes less depending
on how one fills in the detail.
It must be acknowledged that this is a real-world example.
In the real world, there is no such thing as 100% certainty. We
can find contractions absolutely, but conclusions about
explanations always have a probability attached. The resulting
probabilities can only achieve reliability. In a nutshell,
reliability means a probability to satisfy the importance and
circumstances of the subject.
In this example, we are comparing the reliability of scientific
verifications to the reliability of logical conclusions, more
specifically whether a logical conclusion is as reliable as
a scientific verification in the absence of the latter.
>Nothing about alien
>abductions, etc.
Nothing is proved regarding alien abductions. Only a prediction
is reliably proved. An alien abduction just becomes more probable
than other explanations of that prediction.
>Or how this Betty may actually have obtained the data.
>Maybe she discovered the star herself through her own astronomical
>research and, for fun, is perpetrating a little hoax on a gullible
>public. ;^)
One is expected to fill in the detail of the example in such
a way as to best support the example, i.e. the comparison between
scientific verifications and logical conclusions as described.
This detail would reliably preclude such infections. The detail
required will vary per reader depending on each reader's
interpretation of "reliable."
For some that is quite easily done, while for others it would be
impossible. By that I don't necessarily imply a difference in
abilities or attitude, but also a difference in point-of-view.
For instance, a: 1) textbook's, 2) real-world's, or 3) God's POV
about the probability of a coin toss. Or a juror's POV as opposed
to a commentator's POV after a verdict. More topically, from a
scientist's POV, the probability of ET is "n.a." (not
applicable). But from a senator's POV who was forced to decide
funding for the SETI project, a probability can be factored out
of the cost/benefit calculation.
One could make Betty's map so old that the prediction
is 50 years into the future. One could supply along with the map
precise numeric coordinates out to any number of decimal places
sufficient to satisfy the probability that will reliably overcome
the random event for that person. One could place the predicted
star beside or within (from our perspective) some object that
astronomers routinely examine. And so forth.
In other words, the example is only for the cooperative reader,
but then only if it survives criticism like you are kindly
providing. For uncooperative readers, it is useless in any case,
and I doubt that a purist scientist would even entertain the
example. I certainly wouldn't if I was wearing my science hat
today. But logic is not science, just as it isn't math. I think
it was you who said that already.
>And what if her map was wrong? Would this disprove her story of an
>alien abduction? Strictly speaking, no.
If the story didn't include that, we would not be discussing it.
>Your other example is complicated by considerations of probability, but
>I suspect a similar analysis may apply.
I'm certain that a similar analysis would apply. But I don't know
anything for sure. <g>
Thanks,
Larry
George Dance
Sounds reasonable. Which I tentatively suggest would yield:
"There are no self-proving procedures in logic."
Torkel Franzen
> Sounds reasonable. Which I tentatively suggest would yield:
> "There are no self-proving procedures in logic."
You were pointing out, then that if all self-proving procedures are
proofs and all proofs are self-proving procedures, then there are
self-proving procedures in logic if and only if there are proofs in
logic. This is certainly so. It does not, however, affect the
observation that there is no such concept as 'self-proving procedure'
in logic.
George Dance
>
> >>The problem in your argument is the referring to; what is being referred
> >>to by what it not important. I changed "concept" into "word" because
> >>concepts do not refer to anything, but words do.
> >
> > More precisely, (a) concepts "refer to" objects, (b) words "symbolize"
> > concepts, and ergo (c) words "stand for" objects:
>
> Ok, I see, your "concept" is similar to Frege's "Sinn", but I
> thought "Sinn" is usually translated as "Sense" in English.
'Sense' is used in that way; eg, if we were talking about happiness,
say, and disagreeing on virtually everything, one of us might ask the
other, "Just what sense of 'happiness' do you mean?" (IOW, just what
concept are you talking about and calling 'happiness'?).
I suppose that's a matter of what Acme was calling "levels of
description" (LOD): If we were epistemologists engaged in a technical
discussion, I suppose, we'd stick with the word 'concept'; but for
laymen not primarily interested in epistemology, 'sense' works just
fine. (And in general: as long as it's clear what concepts are being
discussed, the words used for them aren't all that important.)
> Doesn't matter though, the problem is, as I said, the
> "referring to", not what refers to what. Just because two
> concepts refer to the same thing, doesn't meen they are both
> concepts from logic.
This seems to be the nub of our disagreement, which (I think) comes
down to the same matter of LOD's.
An epistemologist might object to my use of the word 'sense' in a
conversation with him about his subject, by telling me that there's no
such concept in epistemology - meaning that 'sense' simply doesn't
have a technical meaning, that it's not a defined term, that there's
nothing to which epistemologists attach the label 'sense'. Or he might
question me, learn what I meant by 'sense' in that case, and tell me
that there is indeed such a concept, but that the correct label for it
is 'concept.'
Similarly, a logician might tell me that there's no concept of
'self-proving procedure in logic, meaning roughly the same: that the
words have no technical meaning, nothing to which they're attached as a
label. Or again, he might discover what I meant by a 'self-proving
procedure', and inform me that there is such a concept, but that the
correct label for it is 'deductive proof'.
In both cases, I'd say that the second expert was correct, while the
first was conflating words (labels) with concepts (ideas).
George Dance
> "George Dance" <george...@yahoo.ca> writes:
>
> > Sounds reasonable. Which I tentatively suggest would yield:
> > "There are no self-proving procedures in logic."
>
> You were pointing out, then that if all self-proving procedures are
> proofs and all proofs are self-proving procedures, then there are
> self-proving procedures in logic if and only if there are proofs in
> logic. This is certainly so.
Thank you; though that's agreement on only one premise, I'm encouraged
to go further. My next premise would be "There are proofs in logic,"
which of course would imply that the first quoted sentence was false.
> It does not, however, affect the
> observation that there is no such concept as 'self-proving procedure'
> in logic.
Now this genuinely puzzles me; just after we've agreed to drop the word
'concept,' you reintroduce it to reassert the very claim I've been
challenging. My first thought is that you're using it in a different
way from what I was before, to refer to some other concept (sorry for
the self-reference); and perhaps, that you've been using it
that way all along.
So let me ask you: just what do you mean by "concept" in the above?
The same thing as "term," perhaps?
Acme Diagnostics
Jim Spriggs wrote:
>Acme Diagnostics wrote:
>>
>>.... I vaguely remember some textbook somewhere saying
>> something like "this is called a proof by induction but that's a
>> misnomer because it is really a deductive process"
>
>Probably a confusion about two kinds of induction; mathematical
>induction and (what one might call) Baconian induction.
I'll just continue to think of them as logic induction, heat
induction, selective service induction, and mathematical
induction. One more isn't going to break my back.<g>
>I can make no sense of the rest of your post. In particular, I do not
>know what you mean by "recursive proof"
I advised you to google it. It gets 524 hits. I've posted that I
only have a vague notion of it. But you, and just about
every other poster, are much more qualified than I to read those
pages, so I'm neither going to explain nor excerpt them. I only
wonder why you are not explaining it to me. I'm having some
trouble figuring out why you keep asking me to explain that
phrase in light of this.
>and "self-proving procedure" nor can I even guess any more.
Well, I explained it in excruciating detail in my refutation of
Torkel's assertion, and just gave you an overview with several
example systems. I'm having a tough time figuring out why
you can't understand those explanations.
Maybe Goedel's Incompleteness Theorem is throwing you off.
I was careful to explain that I had never heard the
term in the fields of predicate or mathematical logic, but only
by those "not needing to split Goedel hairs." So it is irrelevant
to my explanations so far if you might be thinking that some math
systems are not self-proving in that sense.
Larry
Acme Diagnostics
If it was just an oversight, I'd prefer the term to be quoted to
make it a better approximation of the original. But please ignore
me if you have a reason not to quote it.
Just for the record, I would not call a quoted version incorrect.
I needed "concept" for that.
Larry
Chris Menzel
<LFinez...@partpostmark.net> said:
>>I can make no sense of the rest of your post. In particular, I do not
>>know what you mean by "recursive proof"
>
> I advised you to google it. It gets 524 hits.
A quick look suggests that in almost every case it simply means "proof
by recursion", which is just a generalization of mathematical induction.
Since you recently noted that you don't know what mathematical induction
is, it seems likely that "proof by recursion" is not what you meant by
"recursive proof", so the Google hits don't clear things up.
Chris Menzel
George Dance
I can't see any reason not to quote the actual statements in question.
Here they are: (Torkel even, you odd):
<quote>
>>> For this I submit that Frege and Russel developed predicate logic
>>> with significant departures from classical logic
[snip]
>>> Four significant departures:
[snip]
>>> 4. Support self-proving procedures, and perhaps recursive proofs though I'm not that far along yet.
>> There is no concept of "self-proving procedure" or "recursive
>>proof" in logic.
> That statement is incorrect.
</q>
Acme Diagnostics
>
>>>I can make no sense of the rest of your post. In particular, I do not
>>>know what you mean by "recursive proof"
>>
>> I advised you to google it. It gets 524 hits.
>
>A quick look suggests that in almost every case it simply means "proof
>by recursion", which is just a generalization of mathematical induction.
Great! That clears up "What is a 'recursive proof'" which is
exactly what several posters have been asking including Jim.
>Since you recently noted that you don't know what mathematical induction
>is, it seems likely that "proof by recursion" is not what you meant by
>"recursive proof", so the Google hits don't clear things up.
Nope. I googled, I gave the google, I said "Read them and you'll
know what I know." It's in the record.
Here's the post Torkel wanted to divert everyone's attention from
(must be some lucky guesses in there!):
>>I am uninterested in how "branches of mathematics" or
>>"branches of foundational mathematics" might apply <snip>
>>Thus, when the context of the discussion is "branches of logic,"
>>ML can just as easily be cast as an offshoot and result of
>>predicate logic, though perhaps limiting it only to a "branch"
>>should be qualified in some way.
>>For this I submit that Frege and Russel developed predicate logic
>>with significant departures from classical logic specifically to
>>create a logic that could be used to support mathematical
>>theories and explain at least basic mathematics logically, most
>>notably common arithmetic.
>>
>>Four significant departures:
>>
>>1. Existential import had to go because otherwise math
>> could not be supported without the "empty set," i.e. in
>> common understanding the number 0.
>>2. Replace the word "premise" with "axiom."
>>3. Replace the word "conclusion" with "theorem."
>>4. Support self-proving procedures, and perhaps recursive
>> proofs though I'm not that far along yet.
>>
>>Now, I don't know these things for sure, and I'm certain to have
>>made historical and terminological mistakes <snip>
After writing my explanation to Jim, I think I know what was
going through my mind when I decided to write "self-proving
procedures" rather than "proofs." The entire message to him
explains about some of the different kinds of proofs with which
I'm familiar, but the most applicable part is this:
>>Since the idea of "proofs" had to be introduced into logic
>>at some point, there is no reason for me to conclude that
>>they were introduced as the "theoretical" self-provng kind
>>all at once. For all I know, there may be other or intermediate
>>logics that have some other definition of "proved" that can
>>in some circumstance whatsoever be affected from outside
>>the system. I think that would be a foolish assumption to
>>make until one exhausts the historical record. I haven't even
>>started on the historical record. <g>
I think I said "self-proving procedures" to avoid that pitfall,
and used procedures just to provide a noun for the adjective
that could describe the proof process but which was otherwise
neutral to "self-proving."
Larry
Torkel Franzen
> Now this genuinely puzzles me; just after we've agreed to drop the word
> 'concept,' you reintroduce it to reassert the very claim I've been
> challenging.
Well, you wanted to remove the intensionality from your observation.
But perhaps we haven't yet managed to do this. After all, "there are
proofs in logic" isn't obviously a statement free of intensionality.
How are we to understand this statement?
Torkel Franzen
> Nope. I googled, I gave the google, I said "Read them and you'll
> know what I know."
So what you know is that there are 524 hits for the phrase
"recursive proofs"? It's unclear how you concluded from this piece
of information that supporting "recursive proofs" may have been
a feature of the Frege-Russell departure from "classical logic".
George Dance
A few suggestions:
Some proofs are things in logic.
Some things in logic are proofs.
There's at least one thing that is both a proof and is in logic.
Pick one or suggest another. I'm intrigued to see where you're going
with this.
Torkel Franzen
> A few suggestions:
> Some proofs are things in logic.
> Some things in logic are proofs.
> There's at least one thing that is both a proof and is in logic.
These are all good extensional formulations provided we can explain
what is meant by the predicate "x is in logic".
George Dance
OK. "x is in logic" can't mean "a has the value x, and a occurs in
logic text P or logical system Q" - that's too restrictive, as Acme
made it clear he meant logic in general. At the same time, we can't
have it mean "a has the value x, and a occurs in any writing at all
about logic" - that's too broad, as it would mean that not only proofs
but self-proving procedures (spp's) were "in logic" by definition (as
Acme was writing about logic when he mentioned spp's).
My first suggestion would be: "a has the value x, and a occurs
in (or is implied by) any sound or complete system of logic."
I'm not completely happy with that, so feel free to critique it; after
all, "in logic" was a term that you originally introduced into the
discussion, so I'd expect you to have a more precise idea of it than I.
Torkel Franzen
> I'm not completely happy with that, so feel free to critique it; after
> all, "in logic" was a term that you originally introduced into the
> discussion, so I'd expect you to have a more precise idea of it than
> I.
As regards the non-occurrence of the concept "self-proving
procedure", certainly. But that observation cannot be expressed as
one about the non-occurrence of self-proving procedures in logic.
Torkel Franzen
> That refutation has been reviewed by several logicians and
> stands in this group.
Surely you mean that you are happily nibbling away at a particularly
delicious cupcake, dreaming of better times!
Acme Diagnostics
Torkel Franzen <tor...@sm.luth.se> wrote:
>"George Dance" <george...@yahoo.ca> writes:
>
>> I'm not completely happy with that, so feel free to critique it; after
>> all, "in logic" was a term that you originally introduced into the
>> discussion, so I'd expect you to have a more precise idea of it than
>> I.
>
> As regards the non-occurrence of the concept "self-proving
>procedure",
That assertion was refuted here:
That refutation has been reviewed by several logicians and
stands in this group.
So your repetition above is a false statement, making the rest of
your commentary irrelevant.
>certainly. But that observation cannot be expressed as
>one about the non-occurrence of self-proving procedures in logic.
Ditto. These are meaningless comments.
Larry