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Non-Contradiction

 
 
joefromchicago
 
  1  
Reply Wed 24 Mar, 2004 09:38 pm
fresco wrote:
However a reading of Kosco's "Fuzzy Thinking" yields a specific rejection of the law of the excluded middle (which I believe is related to non-contradiction).

The law of the excluded middle (x is either A or not-A) is similar to the law of non-contradiction (x cannot be both A and not-A), but they are not the same thing. Your apparent confusion, however, can be excused: after all, Kosko makes this mistake all the time.
0 Replies
 
fresco
 
  1  
Reply Thu 25 Mar, 2004 12:48 am
Relative,

I have no problem with your analysis if I accept your starting point "consciousness is a product of logic". (I hope I got this the right way round ?)

For me, for reasons of nondualist considerations of observer-observed, this is a non starter, and the corollary is more likely to be the case.

There is an interesting analysis of "decision making" in Capra (Web of Life) where he rejects information theoretic (binary) concepts with respect to the emergence of "structure" (organic, conscious, perceptual etc). This is where he evokes Prigogene (structural dynamics) and Von Foerster (second order cybernetics) as alternative formal paradigms. However I feel an understanding of this does depend on the reader taking on board a Buddhist type "rejection of objective reality."
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fresco
 
  1  
Reply Thu 25 Mar, 2004 01:15 am
Joe,

Neither Kosco nor I need an excuse if "similarity" and "difference" lie in the eye of the beholder. :wink:
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Relative
 
  1  
Reply Thu 25 Mar, 2004 06:45 am
Joe:
Quote:
The law of the excluded middle (x is either A or not-A) is similar to the law of non-contradiction (x cannot be both A and not-A), but they are not the same thing. Your apparent confusion, however, can be excused: after all, Kosko makes this mistake all the time.


I made the same mistake in my posts and I now realize I should've been more careful.

EM:)The law of the excluded middle (x is either A or not-A) defines the binarity of logic , and is more a definition than anything.

NC:)The law of non-contradiction (x cannot be both A and not-A) is a fundamental axiom of any known logic to me.

EM does not follow from NC, and vice versa.
If you replace EM with something else, you can get N-valent logic etc.
If you adopt non-NC, however, you get terrible results.


fresco:
Quote:
I have no problem with your analysis if I accept your starting point "consciousness is a product of logic". (I hope I got this the right way round ?)


I believe there is logic involved in everything, so consequentially also in consciousness. That is, if you carefully map the principles, axioms, rules of procedure, theorems and definitions of formal logic to any real system, you will see that logic models the real system perfectly well. I believe any problems you may find will arise from incorrect mapping.

In other words, I believe logic is everywhere If you want it to be, and you can base models of anything on logic.
But to say "consciousness is a product of logic" is maybe a bit strong, because it gives an impression that the mere logic of it somehow invokes consciousness which I don't believe. It is like saying that "gravity is a product of logic" which it is certainly not.
We must be careful here because algorithms are not produced by logic also; you get algorithms from logic, set theory, and additional definitions which conjure the whole theory into existence. It is the definitions and additional axioms that do the trick, not logic itself.
While I don't believe that theory of algorithms explains consciousness, and I believe that consciousness is NOT itself an algorithm, I believe that consciousness is nonetheless logical. It is the additional axioms and definitions that don't fit and yield, and we need something stronger.

I have to do some reading; the second-order cybernetics will be a good place to start. Thank you for valuable references.
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joefromchicago
 
  1  
Reply Thu 25 Mar, 2004 09:36 am
fresco wrote:
Joe,

Neither Kosco nor I need an excuse if "similarity" and "difference" lie in the eye of the beholder. :wink:

Kosko wrote a book in which he purported to refute the law of non-contradiction, but instead spent much of his time attacking the law of the excluded middle. Either that's lazy scholarship or deliberate distortion. In either case, it is inexcusable.
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joefromchicago
 
  1  
Reply Thu 25 Mar, 2004 09:43 am
Relative wrote:
EM:)The law of the excluded middle (x is either A or not-A) defines the binarity of logic , and is more a definition than anything.

NC:)The law of non-contradiction (x cannot be both A and not-A) is a fundamental axiom of any known logic to me.

EM does not follow from NC, and vice versa.
If you replace EM with something else, you can get N-valent logic etc.
If you adopt non-NC, however, you get terrible results.

I agree. EM is not derived from NC; I believe that Aristotle derived both from the law of identity (A = A). Philosophers have long noted the problems with EM, even coming up with "tertium quid" to identify something that doesn't fit into its "either A or not-A" rule. EM can be abandoned without much trouble; NC, in contrast, is disregarded at one's peril.
0 Replies
 
fresco
 
  1  
Reply Thu 25 Mar, 2004 11:18 am
Joe,

Which book do you refer to ?

("Fuzzy Thinking" 1993 has only two references to "noncontradiction" and one to "excluded middle" in 300 pages)
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JLNobody
 
  1  
Reply Thu 25 Mar, 2004 11:35 am
truth
Relative, I have virtually no training in formal logic and mathematics, so my comments here are based purely on naive intuition. I agree that consciousness (as pure awareness) is not derived from logic, but consciousness as "meaningful" perception is, if we define logic very broadly to include all meaning construction such as the "logics" of a cultural construction of reality.
But I do not "feel" that "logic is involved in everything", as a property of the world. It is, however, the major way we construct meaning or impose order onto our experience (we cook our raw experience with various forms of logic). As such, logic is in our heads not in the world beyond our heads. It's part of the grammar with which we talk to ourselves and others about the world, not part of the architecture of the world.
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joefromchicago
 
  1  
Reply Thu 25 Mar, 2004 12:15 pm
fresco wrote:
Joe,

Which book do you refer to ?

("Fuzzy Thinking" 1993 has only two references to "noncontradiction" and one to "excluded middle" in 300 pages)

Fuzzy Thinking: The New Science of Fuzzy Logic

There is a reference to "non-contradiction" on practically every page. The book's index clearly does not reflect this fact (look instead at the entries for "bivalence," "A and not-A," and "A or not-A").

A good example of Kosko's inability to understand the difference between the law of non-contradiction and the law of the excluded middle can be found on page 6 (which is not identified in the index as dealing with non-contradiction or with the excluded middle), where he states [my comments in brackets]:
    Aristotle's binary logic came down to one law: A or not-A. Either this or not this. The sky is blue or not blue[[i]that's the law of the excluded middle[/i]]. It can't be both blue and not blue. It can't be A and not-A [[i]that's the law of non-contradiction[/i]]. Aristotle's "law" defined what was philosophically correct for over two thousand years.

His confusion is manifest: he calls this "one law," when, in fact, he is describing two very different laws. Kosko then proceeds to attack the law of the excluded middle and, in the end, he proclaims his victory over the law of non-contradiction.

Evidently, he is either confused or he's being deliberately deceitful (I will leave any tertium quid to your imagination).
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fresco
 
  1  
Reply Thu 25 Mar, 2004 12:53 pm
Joe, I accept your references info but...

Is it not the case that:

~(A or ~A)=(A and ~A)

i.e. isn't negation of EM logically equivalent to the opposite of NC ?
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Relative
 
  1  
Reply Thu 25 Mar, 2004 01:06 pm
fresco: uhh, you are just saying

not true = false
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joefromchicago
 
  1  
Reply Thu 25 Mar, 2004 01:09 pm
fresco wrote:
Joe, I accept your references info but...

Is it not the case that:

~(A or ~A)=(A and ~A)

i.e. isn't negation of EM logically equivalent to NC ?

I don't believe so.

~(A or ~A) is the equivalent of: "for all x's, it is not the case that x is either A or not-A." Under that formulation x could be B (the previously excluded middle). That would not be the same thing as saying: "for all x's, it is the case that x is both A and not-A."
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Relative
 
  1  
Reply Thu 25 Mar, 2004 01:12 pm
EM can be expressed formally as:

EM: A or ~A

The fact that this assertion is true is a technical way of saying "either A or not A is always true."


NC: ~(A and ~A)

The fact that this assertion is true is a technical way of saying "A and not A cannot be."



Now, surprise:

~(A and ~A) = ~(fresco is a dualist)

Does this mean, then, that the law of excluded middle is the same as you being a nondualist Wink
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twyvel
 
  1  
Reply Thu 25 Mar, 2004 01:40 pm
Relative wrote:

Quote:
I believe that consciousness is nonetheless logical.


Whatever does that mean?
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Relative
 
  1  
Reply Thu 25 Mar, 2004 01:54 pm
twyvel:

I honestly don't know what it means! Which brings me to the topic of 'what is reality?'.
See, for the body of excellent English speakers such as you folks are around here, this statement
"I believe that consciousness is nonetheless logical"
means something, and I can't be sure what. That is because I am looking at the reality of English language on this forum through my thinking which developed and still lives in Slovenian. And i can, using this dualism' know and explore 'reality' of English! Of course, sometimes I might produce a dud.

What I meant to say is (in simpler words):
I believe that the ordinary, formal mathematical logic, is a good way to describe consciousness. The laws of logic apply to it perfectly, although consciousness might be something very much advanced compared to logic, set theory, algorithms or (neural networks = algorithms). I think we can know things, and discuss them, about being conscious using mentioned logic. If we logically deduce a property of consciousness, it will eventually turn out that consciousness really has this property in reality.

That is what I wanted to say Smile
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fresco
 
  1  
Reply Thu 25 Mar, 2004 02:01 pm
Joe and Relative,

The point at issue is that Kosco's demolition of EM appears to be logically equivalent to rejection of NC, based on simple truth table models. Hence by his own criteria Joe's argument against Kosco fails.
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Relative
 
  1  
Reply Thu 25 Mar, 2004 02:13 pm
fresco:

I agree that NC is logically linked to EM in the following sense:
If you can prove any false statement in logic, you prove everything else.

That means that ONE contradiction in logic causes ALL OTHER false statements to become truths and vice versa, rendering all logic useless. We can replace all logic symply by a single statement: A is true and false.
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fresco
 
  1  
Reply Thu 25 Mar, 2004 02:14 pm
Relative,

If Slovenian has any relationship to Russian allow me to recommend the works of the developmental psychologist Luria, who like Piaget, saw logic as an end product of mature consciousness rather than an a priori.
These writers also saw "reality" in terms of interaction between observer and observed (neither subjective nor objective).
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twyvel
 
  1  
Reply Thu 25 Mar, 2004 02:19 pm
You are doing fantastic with english Relative
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fresco
 
  1  
Reply Thu 25 Mar, 2004 02:21 pm
Relative (re your last)

That is exactly the Zen position ! The key word in your statement becomes "IS" ....i.e. the nature of existence

However, a less mystical path can be taken from there using either Hegelian type dialectic, or other "transcendent" modes such as second order cybernetics.
0 Replies
 
 

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