Proof of logic?
hol...@delphi.com
one know that logic is a valid means of deriving facts?
This may seem a ridiculous question, but when you think about it, it's not.
Every means I can think of for proving that logic is a valid method uses
logic to prove that. (That's what a proof is, innit?) Thus one must
accept the validity of logic before one can prove the validity of logic.
Hence logic must be accepted on faith.
In Barbara Branden's biography of Ayn Rand, she noted that Rand would argue
vehemently over any topic except with those who refused to accept the validity
of reason. This sounds like a cop-out, like someone afraid to argue because
they know they can't win. But then again, as I have shown, it really isn't
possible to argue the validity of logic, since one must already have accepted
logic.
If it's true that logic must be accepted on faith, that it is a premise or
postulate and not something to be proved, what about all the other things
which must be accepted without proof? Mysticism, religion, etc. Objectivists
dismiss these things because they cannot be proved by logic. Yet one must
assume logic. One might as well assume Zen. How is one to know that logic
is better than these other methods?
Then again, if there was a reason logic was better, that would constitute
a logical proof, wouldn't it?
Somehow I get the feeling that this matter is one which would be answered by
"MU".
Charles Hollingsworth
Enright
: Thus one must
: accept the validity of logic before one can prove the validity of logic.
: Hence logic must be accepted on faith.
: One might as well assume Zen. How is one to know that logic
: is better than these other methods?
In all seriousness, run some controlled experiments.
Try them both. Try the unlogical things in a safe environment.
Observe people who try unlogical things on a big scale.
Observe people who try logical things on a big scale.
See who lives and dies. I mean, that's one of Rand's main
points in Atlas Shrugged.
--
-------------------------------------------------------------
John Enright from address: jenr...@home.interaccess.com
-------------------------------------------------------------
Jimmy -Jimbo- Wales
>one know that logic is a valid means of deriving facts?
>
>This may seem a ridiculous question, but when you think about it, it's not.
Oh, I think this is not a ridiculous question at all! Lots of people
have this question and lots of professional philosophers get tangled
up on this point. I have found discussions of it to be very interesting
and helpful!
>Every means I can think of for proving that logic is a valid method uses
>logic to prove that. (That's what a proof is, innit?) Thus one must
>accept the validity of logic before one can prove the validity of logic.
>Hence logic must be accepted on faith.
You are pretty much o.k. up until this last line. Does it really follow?
I don't think so.
Laws of logic are among the widest kind of abstractions, but they are
still abstractions, identifications of the facts of reality. Leonard
Peikoff gives a very nice explanation of the process of coming to know
the law of noncontradiction in "Aristotle's 'Intuitive Induction'",
_The New Scholasticism_, 1985.
Essentially, in Peikoff's presentation, the process goes like this:
I perceive (directly, via observation) that "this man is not both
white and nonwhite" (at the same time and in the same respect, of
course). I see that this pail of water is not both wet and non-wet.
At a later point in time, I abstract from the particulars that I've
observed and note that "No being is both A and non-A." This holds
no matter what being and what attribute is being considered.
>If it's true that logic must be accepted on faith, that it is a premise or
>postulate and not something to be proved, what about all the other things
>which must be accepted without proof? Mysticism, religion, etc. Objectivists
>dismiss these things because they cannot be proved by logic. Yet one must
>assume logic. One might as well assume Zen. How is one to know that logic
>is better than these other methods?
Keep in mind that "validation" is a broader concept that "proof."
As Peikoff put it many years ago, "'Validation' in the broad sense
includes any process of relating mental contents to the facts of
reality. Direct perception, the method of validating axioms, is one
such process. 'Proof' designates another type of validation. Proof
is the process of deriving a conclusion logically from antecedent
knowledge." (Quoted in the AR Lexicon under 'validation'.)
--Jimbo
Jeffrey Allan Miller
> hol...@delphi.com wrote:
> : Thus one must
> : accept the validity of logic before one can prove the validity of logic.
>
> : Hence logic must be accepted on faith.
>
> : One might as well assume Zen. How is one to know that logic
> : is better than these other methods?
>
> In all seriousness, run some controlled experiments.
> Try them both. Try the unlogical things in a safe environment.
And how do you analyze the evidence of the experiment without
the logic you have yet to confirm?
The only answers to this very good question I have ever really
heard was that logic was an axiom confirmed by evidence. No
one has ever explained how they were able to confirm it without
using any logic in the process. I have always contended that
the primacy of logic is an assumption, not an axiom, that we
make based upon internal feelings of happiness.
Jeff Miller
Jeff Dalton
>hol...@delphi.com wrote:
>: Thus one must
>: accept the validity of logic before one can prove the validity of logic.
>
>: Hence logic must be accepted on faith.
>
>: One might as well assume Zen. How is one to know that logic
>: is better than these other methods?
>
>In all seriousness, run some controlled experiments.
>Try them both. Try the unlogical things in a safe environment.
>
>Observe people who try unlogical things on a big scale.
>Observe people who try logical things on a big scale.
>
>See who lives and dies. I mean, that's one of Rand's main
>points in Atlas Shrugged.
Rand's performed these experiments, has she? She's noticed
that all the Zen masters died while Objectivists live, what,
forever?
Jeff Dalton
>Laws of logic are among the widest kind of abstractions, but they are
>still abstractions, identifications of the facts of reality. Leonard
>Peikoff gives a very nice explanation of the process of coming to know
>the law of noncontradiction in "Aristotle's 'Intuitive Induction'",
>_The New Scholasticism_, 1985.
>
>Essentially, in Peikoff's presentation, the process goes like this:
>I perceive (directly, via observation) that "this man is not both
>white and nonwhite" (at the same time and in the same respect, of
>course). I see that this pail of water is not both wet and non-wet.
Really? As a child, say, did you ever find yourself thinking "this
pail of water is not both wet and non-wet"?
>At a later point in time, I abstract from the particulars that I've
>observed and note that "No being is both A and non-A." This holds
>no matter what being and what attribute is being considered.
But that's not all there is to logic.
So I find this account frustratingly incomplete.
Dr. Michael M. Cohen
>In article <Bm+ODfg...@delphi.com>, hol...@delphi.com writes:
>|> Thoughts, anyone?
>|>
>|> Charles Hollingsworth
>
>Sure, the whole law excluded middle issue only applies to propositions
>that can evaluated as TRUE or FALSE. Emotions, which drive most human
>behavior, are thus outside the laws of logic. Since i have a great interest
>in humans the laws of logic are of little use. And if fuzzy logic is used,
>as it must be to solve any useful problems, then the importance of "No
>being
>is both A and non-A." is further reduced.
>
>>Jimmy -Jimbo- Wales <jwa...@silver.ucs.indiana.edu> writes:
>>
>>Essentially, in Peikoff's presentation, the process goes like this:
>>I perceive (directly, via observation) that "this man is not both
>>white and nonwhite" (at the same time and in the same respect, of
>>course). I see that this pail of water is not both wet and non-wet.
>>At a later point in time, I abstract from the particulars that I've
>>observed and note that "No being is both A and non-A." This holds
>>no matter what being and what attribute is being considered.
>
>
>Wetness is NOT an attribute of water, it only exists in relation to
>an entity that perceives wetness. Does a fish perceive wetness? If not,
>does wetness exist? How do i measure wetness if i'm wearing gloves?
>Will wetness be different for me if i'm a very hairy person, live in the
>desert, or live in the artic? Abstraction from particulars is a very
>messy business, as anyone who builds realities knows. Given the same
>particulars no two people will consistently abstract the same.
>
>--
>Todd Hoff
To quote Lotfi Zadeh:
"When the only tool you have is a hammer,
everything begins to look like a nail"
This seems to be a central problem of Objectivism.
That is to say, with only binary logic, one
can only see extremes. What fuzzy logic gives us
is not wishy-washy thinking, but rather precision.
Of course, it makes the world a simpler place
if you have binary vision. Easier to call people
good or evil, easier to make "moral" judgments
and philosophical pronouncements. But evil and evading
if evil entails disregarding information.
For more information of Fuzzy logic I've put
a couple of documents on fuzzy.ucsc.edu in pub
for anonymous ftp:
----------------------------------------------------------------------------
-rw-r--r-- 1 0 1 59032 Apr 24 03:39 fuzzy_logic_faq
-rw-r--r-- 1 0 1 23199 Apr 24 03:39 fuzzy_systems_tutorial
----------------------------------------------------------------------------
If Objectivism has a refutation for fuzzy
logic, I'd be interested to hear about it.
Cheers, MMCohen
--
======================================================================
= Dr. Michael M. Cohen mmc...@dewi.ucsc.edu =
= Program in Experimental Psychology mmc...@fuzzy.ucsc.edu =
= 68 Clark Kerr Hall 408-459-2655 VOICE =
= University of California - Santa Cruz 408-459-2700 MESSAGES =
= Santa Cruz, CA 95064 USA 408-459-3519 FAX =
= WWW URL: http://mambo.ucsc.edu/psl/mmc.html =
Dr. Michael M. Cohen
>In article <Bm+ODfg...@delphi.com>, hol...@delphi.com writes:
>|> Thoughts, anyone?
>|>
>|> Charles Hollingsworth
>
>Sure, the whole law excluded middle issue only applies to propositions
>that can evaluated as TRUE or FALSE. Emotions, which drive most human
>behavior, are thus outside the laws of logic.
Don't know that that's so. Perhaps we simply don't
yet understand the logic of emotions...
Otherwise I agree. MMC
Paul Michael Szpunar
Metaphysics (sorry, I don't have it on me to give the passages) was to
point out that any attempt to refute or deny it necessarily involved the
affirmation of the principle. This is how Rand defended her three
primary axioms. I think something similar would apply to logic as a
whole. Any attempt to refute it would necessarily involve the use of
logic. I'm assuming that any attempt to refute logic would involve
argumentation against logic, which would seem to involve logic to have
any hope of being successful.
Tibor Machan has written an excellent essay on this subject called
"Evidence for Necessary Existence", published in _Objectivity_, Vol 1,
No.4.
Sorry if this post was a little too brief and unclear. However, I really
must study for my final exam in my Aristotle class tomorrow :-)
--
***************************************************************************
Paul Szpunar "I'm fearless in my heart.
University of Michigan They will always see that in my eyes.
ah...@umich.edu or: I am the Passion; I am The Warfare.
paul szp...@um.cc.umich.edu I will never stop...Always constant,
accurate and intense." -- Steve Vai
***************************************************************************
hol...@delphi.com
>I perceive (directly, via observation) that "this man is not both
>white and nonwhite" (at the same time and in the same respect, of
>course). I see that this pail of water is not both wet and non-wet.
>At a later point in time, I abstract from the particulars that I've
>observed and note that "No being is both A and non-A." This holds
>no matter what being and what attribute is being considered.
on logic, how do you know that, just because you've observed two things which
cannot be A and non-A, that *nothing* can be A and non-A? You can demonstrate
this with a logical proof, but not just from observation.
Another example of how logic might not be valid is Lewis Carrol's "Two-point
invention": Say you have a proof:
A) Things that are equal to the same are equal to each other.
B) The two sides of this triangle are things that are equal to the same.
Z) The two sides of this triangle are equal to each other.
If you've already accepted logic and the rules that come with it as valid,
Z follows from A and B. But what if you haven't? You would need a third
point to show that it does follow:
C) If A and B are true, Z must be true.
But you can't use logic-- because you haven't assumed it as true. No rule
states that if A, B, and C are true, Z must be true. So let's make one:
D) If A, B, and C are true, Z must be true.
So on, ad infinitum.
Thoughts, anyone?
Charles Hollingsworth
Enright
: Rand's performed these experiments, has she?
Not that I know of. No one would bother to perform them unless
they doubted the principles of logic. Most people regard them
as self-evident. But Jimmy Wales' comments on the kinds of
observations that validate logic are very much to the point.
: She's noticed
: that all the Zen masters died while Objectivists live, what,
: forever?
Some Objectivists die young. And I suppose most Zen masters
are already old when they attain mastery. I hope you don't
really think I meant that logic guarantees longevity. Would
that it were so.
What would you regard as an illogical act? I would regard
standing in the path of an oncoming train, in the hope
that it would pass through me without harming me, to be
highly illogical.
Also, I'm not sure it's fair to regard Zen masters as
illogical. A-logical would be more like it.
John Enright
--
-------------------------------------------------------------
from address: jenr...@home.interaccess.com
-------------------------------------------------------------
Todd Hoff
|> Thoughts, anyone?
|>
|> Charles Hollingsworth
Sure, the whole law excluded middle issue only applies to propositions
that can evaluated as TRUE or FALSE. Emotions, which drive most human
behavior, are thus outside the laws of logic. Since i have a great interest
in humans the laws of logic are of little use. And if fuzzy logic is used,
as it must be to solve any useful problems, then the importance of "No
being
is both A and non-A." is further reduced.
>Jimmy -Jimbo- Wales <jwa...@silver.ucs.indiana.edu> writes:
>
>Essentially, in Peikoff's presentation, the process goes like this:
>I perceive (directly, via observation) that "this man is not both
>white and nonwhite" (at the same time and in the same respect, of
>course). I see that this pail of water is not both wet and non-wet.
>At a later point in time, I abstract from the particulars that I've
>observed and note that "No being is both A and non-A." This holds
>no matter what being and what attribute is being considered.
Color is on a scale. Almost no one is white as almost no one is black.
Enright
: Aristotle's defense of the principle of noncontradiction in the
: Metaphysics...
I'm thinking I misunderstood the initial question here.
In my youth, I went through a period where I definitely had my
doubts about the principle of noncontradiction. And one of the things
that finally convinced me it was true, was watching how it worked
in practice.
My mention of doing experiments may have seemed odd, but from my
personal perspective, I do such experiments on a daily basis,
as part of earning my living. When I write logical code, it
works. When I write illogical code (by accident) it doesn't
work. Curiously, this never fails to impress me.
But these are things that impress a person of an empirical
bent, such as myself. I think the initial question here,
however, was designed to elicit replies of the analytical
variety. So that pointers to Aristotle's approach, and
Peikoff's approach, are more relevant.
On the subject of fuzzy logic, I just want to say that it
doesn't really contradict the law of the excluded middle,
but that it takes a different approach to the issue.
Obviously fuzzy logic is compatible with binary logic,
since it is typically implemented on binary logic machines.
Dr. Michael M. Cohen
> ...
>On the subject of fuzzy logic, I just want to say that it
>doesn't really contradict the law of the excluded middle,
>but that it takes a different approach to the issue.
>
I think that it does contradict: If X=0.5, not(X)=X
[ with the definition not(X)=1.0-X ]
>
>Obviously fuzzy logic is compatible with binary logic,
>since it is typically implemented on binary logic machines.
>
Compatible to the degree that one can represent analog quantities digitally.
Jawaid Bazyar
>Here's something which has been bothering me for some time: how does
>one know that logic is a valid means of deriving facts?
>This may seem a ridiculous question, but when you think about it, it's not.
>Every means I can think of for proving that logic is a valid method uses
>logic to prove that. (That's what a proof is, innit?) Thus one must
>accept the validity of logic before one can prove the validity of logic.
>Hence logic must be accepted on faith.
No. The "proof" of logic is all around you, you use the results every
days. You walk in the streets of a city built by reason and logic; you
drive a car that has steadily improved over 100 years by reason and
logic; the computer you're typing on had its foundation in _pure logic_
in the 1930's (the fundamentals of how computers work were laid down
in the 30's by mathematical theoreticians, 10-15 years before the first
modern computers were actually built).
To attempt to claim that the products of humanity are no proof of
the validity of reason, is to attempt to claim that progress is
made by chance, or luck. One might point to the "infinite number of
monkeys" quote and say that that is how humanity achieves; but the facts
of the tremendous, unparalleled progress of the last two centuries
in the United States show that logic and reason do in fact exist, work,
and will continue to do so.
One can come to an incorrect conclusion, either by not thinking
properly, or by having facts which are not, but that does not mean
that logic itself is flawed; rather, it simply shows that logic is
not an instinct, that it is a process of thought, which is not
an easy enterprise.
>Charles Hollingsworth
--
Jawaid Bazyar | Like UNIX? Like your Apple IIGS? Then ask
Procyon, Inc. | me about GNO/ME for the Apple IIgs!
baz...@netcom.com | P.O Box 620334
--Apple II Forever!-- | Littleton, CO 80162-0334 (303) 781-3273
Jawaid Bazyar
>In all seriousness, run some controlled experiments.
>Try them both. Try the unlogical things in a safe environment.
>Observe people who try unlogical things on a big scale.
>Observe people who try logical things on a big scale.
Good point, but the experiment has already been done, and the
results are plain to anyone who cares to open their eyes.
Jawaid Bazyar
>Don't know that that's so. Perhaps we simply don't
>yet understand the logic of emotions...
Some of us do.
Enright
: jenr...@interaccess.com (Enright) writes:
: > ...
: >On the subject of fuzzy logic, I just want to say that it
: >doesn't really contradict the law of the excluded middle,
: >but that it takes a different approach to the issue.
: >
: I think that it does contradict: If X=0.5, not(X)=X
: [ with the definition not(X)=1.0-X ]
If the two systems use different definitions of "Not X",
then they don't really disagree about whether something
can be both white and not white at the same time in the
same respect.
If something is half-white and half-red, a checkered
table-cloth let us say, is it white or not? Aristotelians,
approaching this question, are inclined to say that the
table-cloth is white in one respect, but not in another.
Fuzzy logic approaches the problem differently - by
approaching it numerically, and giving the table-cloth
a 50% membership in the set of "white things".
These are different procedures, and one or the other may
be the more productive in any given case. But do they
necessarily involve substantial disagreement?
If we take the table-cloth square by square, so that each
piece we consider is all white or all black, so that the
fuzzy approach assigns 100% class membership in one color
or the other, then the traditional Aristotelian exclusions
arise as a special case within the fuzzy method. That is,
if a piece of cloth is 100% white, then it is 0% non-white.
Tom Radcliffe
|> In article <2pk2rg$q...@mailhost.interaccess.com> jenr...@interaccess.com (Enright) writes:
|> > ...
|> >On the subject of fuzzy logic, I just want to say that it
|> >doesn't really contradict the law of the excluded middle,
|> >but that it takes a different approach to the issue.
|> >
|>
|> I think that it does contradict: If X=0.5, not(X)=X
|> [ with the definition not(X)=1.0-X ]
|>
Sorry, are you asserting this is a true statement? And not a false one?
Fuzzy logic is a generalization of Boolean logic, and is an extremely
powerful tool for dealing with situations where there is incomplete
or imperfect information. In cases where information is complete and
error-free, it becomes Boolean logic. So where's the contradiction?
|> >
|> >Obviously fuzzy logic is compatible with binary logic,
|> >since it is typically implemented on binary logic machines.
|> >
|>
|> Compatible to the degree that one can represent analog quantities digitally.
|>
That is to say, with almost arbitrarily high accuracy.
Paul Michael Szpunar
: Perhaps the argument requires only _part_ of logic. That is, you
: could use one part of logic to show there was something wrong with
: other parts. Don't suppose that arguing against logic must use
: all the logical principles the argument questions: work it out.
: Moreover, if someone constructs a valid logical argument against
: logic, this shows there's something wrong with logic. Saying "he's
: using logic to argue against logic and is therefore assuming what he's
: arguing against" does not show he is wrong. If there's no mistake in
: the argument itself, the argument shows there's something wrong with
: logic. If anything is shown to be self-refuting in this case, it's
: logic, not the argument against logic.
: If there are logical arguments against logic, and there are no
: errors in the arguments, then logic is in trouble. Note that
: using logic is *not* an error in the argument.
OK, I messed up here. Actually, what I wanted to say is that any attempt
to refute the principle of non-contradiction ends up affirming the
principle. The principle states that things have a distinct nature, and
that they are distinct from other things; there is difference. Attempts
to refute the principle necessarily involve its use. I can't remember
the specific examples Aristotle gives to clarify this point. What he
claims is that *any* action affirms the principle. When one speaks, say,
predicating a property of something, one is predicating some property
rather than another to some subject rather than another. If one refuses
to speak, one still affirms the principle. One can designate difference
by body language and other physical actions just as well as one can with
speech.
Of course, the principle of non-contradiction is not all of logic, but it
is certainly its foundation. One could demonstrate that some part of
logic is erroneous, but to reject logic as a whole, or even very large
chunks of it, would probably eventually result in an attack on the
principle of non-contradiction.
Enright
: Enright wrote:
: >
: >: Rand's performed these experiments, has she?
: >
: >Not that I know of. No one would bother to perform them unless
: >they doubted the principles of logic. Most people regard them
: >as self-evident.
: 1. I was responding to an article that said:
: In all seriousness, run some controlled experiments.
: Try them both. Try the unlogical things in a safe environment.
: Perhaps not so serious after all?
I was serious. I was recommending this approach as a way of verifying
the principles of logic, for someone who seemed to have some doubt
about it. As I've said elsewhere, I have myself been in that position,
and found this approach useful. Most people never get in that position.
: 2. It's hardly self evident that people who try unlogical things die.
: Remember that I was responding to:
: Observe people who try unlogical things on a big scale.
: Observe people who try logical things on a big scale.
: See who lives and dies. I mean, that's one of Rand's main
: points in Atlas Shrugged.
: > But Jimmy Wales' comments on the kinds of
: >observations that validate logic are very much to the point.
: At most for a tiny part of logic.
: >: She's noticed
: >: that all the Zen masters died while Objectivists live, what,
: >: forever?
: >
: >Some Objectivists die young. And I suppose most Zen masters
: >are already old when they attain mastery. I hope you don't
: >really think I meant that logic guarantees longevity. Would
: >that it were so.
: It sure looked to me like we had a claim that people who did
: unlogical things died.
If you look again, I suggested observing the results of large
scale logical action, as opposed to large scale illogical action.
I said to watch who lived and died. A clear trend will emerge,
but it will be a trend and not a guarantee of success or doom.
: >What would you regard as an illogical act? I would regard
: >standing in the path of an oncoming train, in the hope
: >that it would pass through me without harming me, to be
: >highly illogical.
: >
: >Also, I'm not sure it's fair to regard Zen masters as
: >illogical. A-logical would be more like it.
: But wouldn't "unlogical" include a-logical?
What I had in mind here was the fact that Zen, like its
close relative, Taoism, developed in a culture which
had not yet discovered logic. So that as belief systems,
they do not originally have positions on logic as we
understand it. I'm sure that Zen masters, like most
people, are logical some of the time, and less than
logical on other occasions. All that being said,
I'll be glad to grant that certain aspects of Zen
Buddhism are basically illogical. And that many of
its modern Western adherents adopt a staunchly
anti-logical attitude.
But how many will stand in the path of the oncoming train?
Todd Hoff
Radcliffe) writes:
|> |> I think that it does contradict: If X=0.5, not(X)=X
|> |> [ with the definition not(X)=1.0-X ]
|> |>
|>
|> Sorry, are you asserting this is a true statement? And not a false
|> one?
|> Fuzzy logic is a generalization of Boolean logic, and is an extremely
|> powerful tool for dealing with situations where there is incomplete
|> or imperfect information. In cases where information is complete and
|> error-free, it becomes Boolean logic. So where's the contradiction?
|>
Take the classic example: is X tall? How can the response map down to
TRUE or FALSE? What more information do you need? What is imperfect?
Other questions: Is X sexy? Is X smart? Is that curtain red?
Fuzzy logic captures aspects of reality boolean logic fails to capture.
It is not useful only in situations where information is incomplete
or imperfect, it is useful because reality is analog, not digital, and
cannot be fully explained digitally.
--
Todd Hoff
Dr. Michael M. Cohen
>In article <2pka27$a...@darkstar.UCSC.EDU>, mmc...@dewi.ucsc.edu (Dr. Michael M. Cohen) writes:
>|> In article <2pk2rg$q...@mailhost.interaccess.com> jenr...@interaccess.com (Enright) writes:
>|> > ...
>|> >On the subject of fuzzy logic, I just want to say that it
>|> >doesn't really contradict the law of the excluded middle,
>|> >but that it takes a different approach to the issue.
>|> >
>|>
>|> I think that it does contradict: If X=0.5, not(X)=X
>|> [ with the definition not(X)=1.0-X ]
>|>
>
>Sorry, are you asserting this is a true statement? And not a false one?
Yes, if X is 0.5, it is true that not(X) = X
i.e. 0.5 = 0.5
Or as the Oists say A = A
>Fuzzy logic is a generalization of Boolean logic, and is an extremely
>powerful tool for dealing with situations where there is incomplete
>or imperfect information.
A situation which is pretty common....
> In cases where information is complete and
> error-free, it becomes Boolean logic. So where's the contradiction?
>
Only if the information in question is binary in nature.
When, as is often the case, the information is continuous
in nature, then the fuzzy logic rules apply.
MMCohen
Dr. Michael M. Cohen
Sounds similar to the question:
"Are you still beating your wife?"
Is the principle of the argument different?
MMC
Chris Wolf
>If it's true that logic must be accepted on faith, that it is a premise or
>postulate and not something to be proved, what about all the other things
>which must be accepted without proof? Mysticism, religion, etc.
>Objectivists dismiss these things because they cannot be proved by logic.
>Yet one must assume logic. One might as well assume Zen. How is one to
>know that logic is better than these other methods?
It's not true that logic must be accepted on faith. You are falling victim
to the fallacy of the false alternative; the choice is not simply between
'proof' and 'faith.' To 'prove' something means to demonstrate that it
corresponds to reality. This proof is accomplished via reason, logic, and
axioms. It is then natural to ask, "What proof do we have that logic and
axioms are correct?" As you have correctly pointed out, there is no proof
of these things, because they are the precondition of all proof. So how
does one demonstrate the validity of logic and axioms?
Here is where the more fundamental concept of self-evident comes in. The
concept of self-evident preceeds the concept of proof. Self-evident simply
means that the mere perception of something is enough to establish its
existence. Take the fact that you exist. How do you know that you exist?
It is a self-evident fact. You validate this fact simply by being aware of
yourself. Your existence is a self-evident, inescapable fact. Even the
*attempt* to attack this fact requires that you implicitly accept it as
true. The same is true of logic. Logic is a self-evident truth that
follows from the fundamental axioms of existence.
The understanding and acceptance of self-evident truths is absolutely
essential for a rational man. If you reject the concept of self-evident,
then you have nowhere to go but into subjectivism. You will be forced to
take your most fundamental axioms on faith. And you will have no reason to
accept logic over mysticism, religion, zen, etc. You will have totally cut
your mind off from its only anchor to reality. Sad to say, this inability
to accept the self-evident is quite common among modern-day philosophers
and intellectuals. If you have ever wondered how a contemporary philosopher
can make the claim, "I can prove you have no hands," then you have seen
first-hand the inability to accept the self-evident.
The reason we do not accept mysticism or religion as a self-evident truth
is because there is nothing self-evident about them. There is nothing
about opening your eyes and looking around to suggest the existence of
mysticism, or God. There is *everything* to suggest the existence of
reality. If someone says, "I do not accept reality as a self-evident
truth," then that person is not rational, and cannot be dealt with.
To take something on faith is to believe without any evidence. Accepting
the existence of reality, or logic, because they are self-aware, is not an
act of faith. The evidence for the existence of reality and logic is more
than overwhelming. It is total.
This is not to say that the concept of self-evident is easy to understand.
Sometimes it seems that it is one of the hardest concepts to grasp and
accept. Some people never seem to get it. I would strongly urge you to
read Dr. Leonard Peikoff's book *Objectivism: The Philosophy of Ayn Rand*
for a more complete discussion of the self-evident.
Chris Wolf
cwo...@delphi.com
Enright
Jeff Dalton (je...@aiai.ed.ac.uk) wrote:
: If you want to understand Objectivism, pay attention to Jawaid's
: posts. The Kelley-ites are far too reasonable to give you a true
: picture of Objectivism.
: Take such posts, apply the $-notation (as in "Some of us do
: understand the $logic of $emotion"), and you are well on your way.
Is the proposal self-referential? Should the beginning of this read:
If you want to understand $Objectivism... ?
Where "$Objectivism" refers to Jeff Dalton's usage of the term, which
excludes proponents he regards as too reasonable.
Todd Hoff
writes:
|> jenr...@interaccess.com (Enright) writes:
|>
|> >In all seriousness, run some controlled experiments.
|> >Try them both. Try the unlogical things in a safe environment.
|>
|> >Observe people who try unlogical things on a big scale.
|> >Observe people who try logical things on a big scale.
|>
|> Good point, but the experiment has already been done, and the
|> results are plain to anyone who cares to open their eyes.
|>
Let's see, in my business i work with hords of logical people. Yet
most projects in this industry fail. Is this logical?
A preacher of god's word can say homosexuals must die? Is this logical?
Nixon can say "let's go rob some secrets" even though he was almost
assured
of reelection. Is this logical?
An intelligent middle class person can chose to be homeless. Is this
logical?
Everyday humans say of the other, the other religion, the other nation,
let's kill them. Is this logical?
--
Todd Hoff
Jeff Dalton
>
>: Rand's performed these experiments, has she?
>
>Not that I know of. No one would bother to perform them unless
>they doubted the principles of logic. Most people regard them
>as self-evident.
1. I was responding to an article that said:
In all seriousness, run some controlled experiments.
Try them both. Try the unlogical things in a safe environment.
Perhaps not so serious after all?
2. It's hardly self evident that people who try unlogical things die.
Remember that I was responding to:
Observe people who try unlogical things on a big scale.
Observe people who try logical things on a big scale.
See who lives and dies. I mean, that's one of Rand's main
points in Atlas Shrugged.
> But Jimmy Wales' comments on the kinds of
>observations that validate logic are very much to the point.
At most for a tiny part of logic.
>: She's noticed
>: that all the Zen masters died while Objectivists live, what,
>: forever?
>
>Some Objectivists die young. And I suppose most Zen masters
>are already old when they attain mastery. I hope you don't
>really think I meant that logic guarantees longevity. Would
>that it were so.
It sure looked to me like we had a claim that people who did
unlogical things died.
>What would you regard as an illogical act? I would regard
>standing in the path of an oncoming train, in the hope
>that it would pass through me without harming me, to be
>highly illogical.
>
>Also, I'm not sure it's fair to regard Zen masters as
>illogical. A-logical would be more like it.
But wouldn't "unlogical" include a-logical?
-- jd
Jeff Dalton
>Aristotle's defense of the principle of noncontradiction in the
>Metaphysics (sorry, I don't have it on me to give the passages) was to
>point out that any attempt to refute or deny it necessarily involved the
>affirmation of the principle. This is how Rand defended her three
>primary axioms. I think something similar would apply to logic as a
>whole. Any attempt to refute it would necessarily involve the use of
>logic. I'm assuming that any attempt to refute logic would involve
>argumentation against logic, which would seem to involve logic to have
>any hope of being successful.
Perhaps the argument requires only _part_ of logic. That is, you
could use one part of logic to show there was something wrong with
other parts. Don't suppose that arguing against logic must use
all the logical principles the argument questions: work it out.
Moreover, if someone constructs a valid logical argument against
logic, this shows there's something wrong with logic. Saying "he's
using logic to argue against logic and is therefore assuming what he's
arguing against" does not show he is wrong. If there's no mistake in
the argument itself, the argument shows there's something wrong with
logic. If anything is shown to be self-refuting in this case, it's
logic, not the argument against logic.
In short, this whole approach to defending logic is wrong-headed.
If there are logical arguments against logic, and there are no
errors in the arguments, then logic is in trouble. Note that
using logic is *not* an error in the argument.
-- jd
Jeff Dalton
If you want to understand Objectivism, pay attention to Jawaid's
posts. The Kelley-ites are far too reasonable to give you a true
picture of Objectivism.
Take such posts, apply the $-notation (as in "Some of us do
understand the $logic of $emotion"), and you are well on your way.
For an amusing example where Rand just doesn't get it, see what
she says about "You can't measure love" in the Intro to Objectivist
Epistemology. When people say things like that (you can't measure
Love), what they have in mind is something like assigning specific
numeric values. One of the episodes of the tv series Square
Pegs had a good example. Someone had invented a machine that,
when two people were attached, would measure, on a numeric scale,
how strongly they felt about each other. That's an example of
measureing love in the sense that (some) people say can't be done.
But what does Rand say? Does she defend that sort of measuring?
Of course not. Instead, she takes the approach that I'm starting
to think is standard with Objectivists. She reads "You can't
measure love" as "You can't $meaure love", where $measure is
the Objectivist notion of measuring, and proceeds to defend the
possibility of measuring love in that sense. That this is an
almost complete misunderstanding of the original claim doesn't
seem to occur to her.
Moreover, even her defense of $measuring love is odd. In an earlier
section, she talked about measurement, measurement omission, units,
and so on. Then she turns to "You can't measure love". Now, does
she apply the stuff she's just been saying about measurement?
Noooooo. Instead, she introduces a bunch of new stuff. There
was no suggestion earlier that this sort of extension would be
needed, so one is left with the impression that you can't measure
love even in the Objectivist sense that was just introduced!
That is, you have to elaborate the Objectivist notion further
before love can be handled.
-- jd
Robert J. Kolker
......snip.....
>My mention of doing experiments may have seemed odd, but from my
>personal perspective, I do such experiments on a daily basis,
>as part of earning my living. When I write logical code, it
>works. When I write illogical code (by accident) it doesn't
>work. Curiously, this never fails to impress me.
sense it causes your computer to do something, if that something
is to go into an un-interruptable wait state ( = halt). Badly
written code is code that does not achive your objective. If you set
out to write a square root routine and you in-advertently write
a cube root extractor, in what sense is the code illogical. Not in
the internal sense. The dissonance occurs between what you wrote
(the means) and what you wanted to happend (the end). That is not
the same as asserting A & -A is true.
......snip....
>On the subject of fuzzy logic, I just want to say that it
>doesn't really contradict the law of the excluded middle,
>but that it takes a different approach to the issue.
in fuzzy and in probalistic logics and propositon and its denial
can have equal fuzz value. This denies that one or the other must
be definite. On the other hand neither logic would assert the
conjunction of the two is definite true.
.....rest snipped...
--
Conan the Libertarian
"Taxation is Theft. "
"There are no good governments, only bad ones and worse ones"
"If you can't love the Constitution, then at least hate the Government"
Jawaid Bazyar
>In article <bazyarCo...@netcom.com>, baz...@netcom.com (Jawaid Bazyar)
>writes:
>|> jenr...@interaccess.com (Enright) writes:
>|>
>|> >In all seriousness, run some controlled experiments.
>|> >Try them both. Try the unlogical things in a safe environment.
>|>
>|> >Observe people who try unlogical things on a big scale.
>|> >Observe people who try logical things on a big scale.
>|>
>|> Good point, but the experiment has already been done, and the
>|> results are plain to anyone who cares to open their eyes.
>|>
>Let's see, in my business i work with hords of logical people. Yet
>most projects in this industry fail. Is this logical?
Certainly. You have bad managers, bad executives, bad employees,
or combinations of the three.
>A preacher of god's word can say homosexuals must die? Is this logical?
No.
>Nixon can say "let's go rob some secrets" even though he was almost
>assured
>of reelection. Is this logical?
I don't recall that Nixon ever authorized the Watergate breakins
beforehand.
>An intelligent middle class person can chose to be homeless. Is this
>logical?
Are you asking why anyone would choose to lower their quality
of living? That question has a number of answers. It doesn't make
sense to me, and giving up one's wealth to become a beggar certainly
goes against my grain. If they want to do that it's not my problem.
>Everyday humans say of the other, the other religion, the other nation,
>let's kill them. Is this logical?
No.
I never claimed that everyone acts rationally all the time, and
never claimed that the proof of the validity of logic depended
on every human being completely rational all the time.
Jawaid Bazyar
>If you want to understand Objectivism, pay attention to Jawaid's
>posts. The Kelley-ites are far too reasonable to give you a true
>picture of Objectivism.
I don't yet claim to be an Objectivist. Things that I say are
not to be taken as "Official Tenets of Objectivism", nor "
The Word of Ayn Rand as Given Us By Jawaid". I'm still learning,
and I'll make mistakes. Don't fool yourself into thinking
you're actually attacking Objectivism when you go after _my_
vulnerabilities. When and if I claim to be an Objectivist, then
you can attack Objectivism for the things I say.
I could just as easily attack Objectivism by calling Rush Limbaugh
an Objectivist.
Shall we try again?
>Take such posts, apply the $-notation (as in "Some of us do
>understand the $logic of $emotion"), and you are well on your way.
Since the rest of your post is based on this interesting leap
of "logic" (which seems to denounce values, the dollar, and the
United States all in one fell swoop), I'm not even going to bother.
I mean, really.
Enright
: Let's see, in my business i work with hords of logical people. Yet
: most projects in this industry fail. Is this logical?
: A preacher of god's word can say homosexuals must die? Is this logical?
: Nixon can say "let's go rob some secrets" even though he was almost
: assured of reelection. Is this logical?
Affirming that logic is valid is not the same as affirming that
all people are perfectly logical all the time. Would that they
were.
Nor is it an affirmation that all logical people will be
successful in all of their ventures. Would that it were.
Todd Hoff
(Enright) writes:
|> Todd Hoff (t...@darla.asd.sgi.com) wrote:
|>
|> : Let's see, in my business i work with hords of logical people. Yet
|> : most projects in this industry fail. Is this logical?
|>
|> : A preacher of god's word can say homosexuals must die? Is this
|> logical?
|>
|> : Nixon can say "let's go rob some secrets" even though he was almost
|> : assured of reelection. Is this logical?
|>
|> Affirming that logic is valid is not the same as affirming that
|> all people are perfectly logical all the time. Would that they
|> were.
|>
|> Nor is it an affirmation that all logical people will be
|> successful in all of their ventures. Would that it were.
My reply was specifically to the "look all around" you response
for the a priori validity of logic. The answer to my questions is
that yes, every instance i sighted is perfectly logical within the
context of the person doing the reasoning, it's only from alien
reference frames that logic appears to fail.
--
Todd Hoff
Enright
: Badly
: written code is code that does not achive your objective. If you set
: out to write a square root routine and you in-advertently write
: a cube root extractor, in what sense is the code illogical. Not in
: the internal sense. The dissonance occurs between what you wrote
: (the means) and what you wanted to happend (the end). That is not
: the same as asserting A & -A is true.
Agreed.
The code is not truly illogical. Rather my thinking,
in writing the code, contained some logical error.
No, it's not the same as asserting A & -A...
unless I was so foolish as to keep insisting that
the routine was a square-root extractor in spite
of the fact it was returning cube roots. At least,
asserting that square-roots always = cube roots,
is perilously close to asserting A & -A.
Enright
: My reply was specifically to the "look all around" you response
: for the a priori validity of logic. The answer to my questions is
: that yes, every instance i sighted is perfectly logical within the
: context of the person doing the reasoning, it's only from alien
: reference frames that logic appears to fail.
Thanks. I didn't get it. I still have a question, about, say,
your Nixon example and your preacher example.
I'll agree with you that RMN must have _thought_ that his early
Watergate coverup activities were logical... But I'm not
sure that makes it fair to say his thought processes were
perfectly logical in his own context, and only wrong from
alien reference frames. Are you saying a person can never
detect his own logical errors?
As to wacky preachers, there are some Christians who hold
beliefs that they recognize as non-logical, indeed, as
apparently nonsensical - "mysteries" accepted on faith.
Would you agree that such Christians' beliefs do NOT
appear logical, even from their own frame of reference?
Jeff Dalton
>
>Jeff Dalton (je...@aiai.ed.ac.uk) wrote:
>: If you want to understand Objectivism, pay attention to Jawaid's
>: posts. The Kelley-ites are far too reasonable to give you a true
>: picture of Objectivism.
>
>: Take such posts, apply the $-notation (as in "Some of us do
>: understand the $logic of $emotion"), and you are well on your way.
>
>Is the proposal self-referential? Should the beginning of this read:
>
> If you want to understand $Objectivism... ?
No.
>Where "$Objectivism" refers to Jeff Dalton's usage of the term, which
>excludes proponents he regards as too reasonable.
$X always refers to the Objectivist notion of X.
Of course, Kelley-ites can approach Randroid-ness when pushed.
See, e.g., Chris Wolf's recent post on logic, in which we find
the following:
It's not true that logic must be accepted on faith. You are falling victim
to the fallacy of the false alternative; the choice is not simply between
'proof' and 'faith.' To 'prove' something means to demonstrate that it
corresponds to reality. [...]
This is $proof, not proof.
Here is where the more fundamental concept of self-evident comes in. The
concept of self-evident preceeds the concept of proof. Self-evident simply
means that the mere perception of something is enough to establish its
existence.
This is $self-evidence, and probably $perception and $existence as well.
Take the fact that you exist. How do you know that you exist?
It is a self-evident fact. You validate this fact simply by being aware of
yourself. Your existence is a self-evident, inescapable fact. Even the
*attempt* to attack this fact requires that you implicitly accept it as
true. The same is true of logic. Logic is a self-evident truth that
follows from the fundamental axioms of existence.
Straight orthodox Objectivism. Note too the Peikoff ref at the end
[not in what I quote].
And, of course, it's $logic he's talking about, not logic.
The understanding and acceptance of self-evident truths is absolutely
essential for a rational man. If you reject the concept of self-evident,
then you have nowhere to go but into subjectivism.
What happened to that fallacy of the false alternative? But perhaps
it's not a false alternative if he means $self-evident and $subjectivism.
I've never quite been able to figure out whether Objectivism is
consistent in its own terms.
You will be forced to
take your most fundamental axioms on faith. And you will have no reason to
accept logic over mysticism, religion, zen, etc.
So if logic isn't self-evident, I can have "no reason"? I can't,
just for instance, determine that logic is correct by doing some
intellectual work?
Since this stuff is so obviously false if interpreted according to the
ordinary meanings of words, we're pretty much forced to use special,
Objectivist meanings if we want to see what's true in this kind of
account.
You will have totally cut
your mind off from its only anchor to reality. Sad to say, this inability
to accept the self-evident is quite common among modern-day philosophers
and intellectuals. If you have ever wondered how a contemporary philosopher
can make the claim, "I can prove you have no hands," then you have seen
first-hand the inability to accept the self-evident.
Another standard Objectivist technique: the bizarre example.
Seriously, how many of you have ever heard such a claim from
a contemporary philosopher? I certainly haven't.
Etc.
Jeff Dalton
>
>>If you want to understand Objectivism, pay attention to Jawaid's
>>posts. The Kelley-ites are far too reasonable to give you a true
>>picture of Objectivism.
>
> I don't yet claim to be an Objectivist. Things that I say are
>not to be taken as "Official Tenets of Objectivism", nor "
>The Word of Ayn Rand as Given Us By Jawaid". I'm still learning,
>and I'll make mistakes.
You have the right _style_.
> Don't fool yourself into thinking
>you're actually attacking Objectivism when you go after _my_
>vulnerabilities.
But I didn't really go after you. Indeed, most of my article
was directed against ITOE.
>When and if I claim to be an Objectivist, then
>you can attack Objectivism for the things I say.
Really? All you have to do is *claim* to be an Objectivist?
>>Take such posts, apply the $-notation (as in "Some of us do
>>understand the $logic of $emotion"), and you are well on your way.
>
> Since the rest of your post is based on this interesting leap
>of "logic" (which seems to denounce values, the dollar, and the
>United States all in one fell swoop), I'm not even going to bother.
>I mean, really.
The rest of my post tells the truth about one aspect of the ITOE.
If you think not, address what I said.
Charles Dlhopolsky
>
>Fuzzy logic approaches the problem differently - by
>approaching it numerically, and giving the table-cloth
>a 50% membership in the set of "white things".
>
>John Enright
>
Perhaps the law of the excluded middle extended to Fuzzy logic is
just:
If x is the fuzzy percentage of a thing having property A
and y is the fuzzy percentage of a thing NOT having property A
then it is always the case that x+y = 100%
Which for example means that a thing cannot be both 60% white and 55%
non-white, nor can it be 40% white and 40% non-white.
This generalizes to boolean logic very nicely, in that x and y must
have either the value 100% or 0%. A thing cannot be both white (x =
100%) and not white (y = 100%) because x+y= 200 in that case...
-charlie
Tom Radcliffe
|> In article <CoxLy...@knot.ccs.queensu.ca>, t...@mips2.phy.queensu.ca (Tom
|> Radcliffe) writes:
|>
|> |> |> I think that it does contradict: If X=0.5, not(X)=X
|> |> |> [ with the definition not(X)=1.0-X ]
|> |> |>
|> |>
|> |> Sorry, are you asserting this is a true statement? And not a false
|> |> one?
|> |> Fuzzy logic is a generalization of Boolean logic, and is an extremely
|> |> powerful tool for dealing with situations where there is incomplete
|> |> or imperfect information. In cases where information is complete and
|> |> error-free, it becomes Boolean logic. So where's the contradiction?
|> |>
|>
|> Take the classic example: is X tall? How can the response map down to
|> TRUE or FALSE? What more information do you need? What is imperfect?
|> Other questions: Is X sexy? Is X smart? Is that curtain red?
|>
I need information that would define a binary standard of tallness.
If I define tall as ``greater than 180 cm'' then there is no problem
doing the Boolean thing. It would not be a very good representation
of how we think about these things, but that is just the point: sometimes
you are better off, uh, omitting the measurements.
Dr. Michael M. Cohen
But why throw away information?
Why deal with binaries when finer resolution is available?
I want to stress that fuzzy logic was not made to deal with
cases of "incomplete or imperfect information". I was made to
deal with cases where we have precise, continuous data.
To me, throwing away precision is evasion of reality.
MMCohen
mike...@liberty.com
Well, Charles, I really don't like Peikoff's presentation of this point
(as you have quoted him).
While it's true enough that you cannot understand logic without
empirical observation, logic is a kind of secondary process, something
you do once you're convinced that things are stable.
You use empirical observation to note that, gee whiz, a man has 2
ears and a nose, and by golly the second man I see has that also. Then,
eventually, man as a species differs from other species by its means of
survival, by the use of the rational faculty to create wealth.
While you take due note of differences within men, some being
smart, some retards, some even having just one ear or no
nose...nontheless, it seems pretty clear to you what you mean by a
"healthy" man, i.e., having all intact body parts functioning with no
sign of disease. You may look far and wide among men, but your
definition of healthy man doesn't seem to need any change in describing
all people born a certain way with certain genes.
It's the same thing when studying the sun. Hot during the day, it
recedes at night to one's vision and feel. You can study the gases that
compose it or how far away it is. It changes constantly, but only in
certain limits with certain potentialities. Within those limits, there
is no change.
Within the limits of potential for man, there is no change.
Everything, but everything, is stable in this sense, having its
own internal logic and consistency. Never changing fundamentally. (Yes,
fundamental change is possible, in which case you're talking about a
totally different object...as when ore is heated to liquid state, and
poured into a mold, to make coins).
That is where empirical observation comes in. You look at the
world. The sun. Moon. flowers. dirt. men. homes. Eventually, you become
convinced that reality is stable, that everything has its own specific
identity with characteristics that are stable over time.
After the law of identity hits you hard, as a result of all this
empirical observation (you might also note that every success that you
have in life, from typing on the computer to moving your body off the
bed, is done when you act on the premise that A is A and that it exists
in stable form independently of your awareness... when you try to act
against your own knowledge, you run into problems, quickly!), THEN you
can use logic to get answers to questions.
Logic says that since reality is stable, once you know something
about the reality you're studying at the moment, your later inferences
must not conflict with that certain knowledge. If there is a conflict,
then if your knowledge is certain, your later inference is wrong. Or, if
you're fairly sure about your inference, maybe your initial "knowledge"
was not, in effect, knowledge about the reality under consideration. Of
course, there is always the possiblity that both your earlier
"knowledge" and your later inference are both wrong.
The context of all these remarks about stability are: at a given
time and in a certain respect. A thing cannot both b and not-b at the
same timein the same respect. At different times or in different
respects, things can change, of course.
Hope that my ramblings help clarify this issue a mite.
Best Wishes,
Mike Rael
ac...@kbb.com
Todd Hoff
|> your Nixon example and your preacher example.
|>
|> I'll agree with you that RMN must have _thought_ that his early
|> Watergate coverup activities were logical... But I'm not
|> sure that makes it fair to say his thought processes were
|> perfectly logical in his own context, and only wrong from
|> alien reference frames. Are you saying a person can never
|> detect his own logical errors?
|>
i've never committed a logical error. in retrospect i have been
wrong, but at the time i made the decisions my decisions made
perfect sense, they were all perfectly logical. Now were the
decisions logical in the classical mathematical sense? Probably not.
But i as a human find it quite easy to pursue two contradictory goals
at the same time. I think nixon was in this same place.
Nixon's group of thugs, lead by Liddy, were itching to do some sort of
black bag job, and if you've read Liddy's bio this is not hard to believe.
They proposed several wild and expensive schemes which were
nixed because they were too wild or too expensive. Then the watergate
job was proposed. It was accepted because it was cheap and fairly
straight forward. Now why was it accpeted? It was surely a stupid thing
to do and would benifit Nixon not a whit. One explanation i accept
is that the reason is human nature. The explanation is based on the
pattern of making your first bid high, then a counter bid is made, and
you settle somewhere in the middle. People are very reluctant to refuse
what is considered a fair offer after several rejections have been made.
This is a possible explanation of why the watergate job was approved.
Several elaborate jobs were proposed and rejected. Then when a more
reasonable job was proposed it made it almost impossible not to accept it.
Is this logical? Yes, very, within the framework of human behavior. Is
it logical according to classical logic? Does it matter?
|> As to wacky preachers, there are some Christians who hold
|> beliefs that they recognize as non-logical, indeed, as
|> apparently nonsensical - "mysteries" accepted on faith.
|> Would you agree that such Christians' beliefs do NOT
|> appear logical, even from their own frame of reference?
|>
|> John Enright
Like Pascal they've made the decision that faith is a reasonable
basis for decision making. Faith is as good a source of facts and axioms
as the scientific method.
--
Todd Hoff
Tom Radcliffe
Although good design practice dictates that the sum of the membership
values of all fuzzy sets defined on an axis be less than or equal to
one at all points, there is nothing inheirent in fuzzy logic that
makes this a requirement.