From: shmage-AT-pipeline.com
Date: Mon, 9 Mar 1998 00:31:33 -0500
Subject: Re: M-TH: Dialectics and Paraconsistent Logic


James Farmelant writes:

>I found the following article in the Stanford Internet Encyclopedia of
>Philosophy.  The question that interests me is to what extent can
>the systems of paraconsistent logic can help us to understand
>the nature of dialectical reasoning as understood by Marxism?
>Can the notions of contradiction in paraconsistent logic help
>us to clarify the notion of dialectical contradiction as understood
>by Marxists?  And does the theory of paraconsistent logic help
>to give us a better understanding of the relationships between
>formal logic and dialectics?

Because the word "image" cannot satisfactorily replace any of the images
for which it stands, I cannot make enough sense of the article to venture
an answer to your question.  But I would like to point  out two conspicuous
fallacies  in its exposition and one conspicuous omission in its
references.

=46allacy One

>   ... A plausible example of dialetheia is the liar paradox.
>   Consider the sentence: This sentence is not true. There are two
>   options: either the sentence is true or it is not. Suppose it is true.
>   Then what it says is the case. Hence the sentence is not true.
>   Suppose, on the other hand, it is not true. This is what it says.
>   Hence the sentence is true. In either case it is both true and not
>   true.

The "sentence" "This sentence is not true" is neither true nor not true. It
is simply a defective sentence saying nothing.  Why?  The phrase "this
sentence" is pronominal.  Every pronoun must be replaced by the noun for
which it stands when explication of the sentence in which it is imbedded is
demanded. What does "this sentence" stand for?  Obviously the "sentence"
"This sentence is not true."  So the demanded explication yields "the
sentence 'This sentence is not true' is not true."  But the prenominal
phrase has *not* been replaced--it remains in the putatively explicated
version.  Every further demand for explication will yield only a longer
sentence containing the devilish phrase "this sentence."  The ensuing
infinite regression proves its meaninglessness.

=46allacy Two:

>   Notoriously, people have inconsistent beliefs. They may even
>   be rational in doing so. For example, there may be apparently
>   overwhelming evidence for both something and its negation. There may
>   even be cases where it is in principle impossible to eliminate such
>   inconsistency. For example, consider the "paradox of the preface". A
>   rational person, after thorough research, writes a book in which they
>   claim A1, ... , An. But they are also aware that no book of any
>   complexity contains only truths. So they rationally believe ~(A1 & ...
>   & An) too.

Suppose A1, ... , An stands for a series of 195 propositions each of which
is worthy of belief because it has been established at a .98 significance
level (ie., the probability of its truth is .98) and this is taken as the
established criterion for belief-worthiness.  By elementary laws of
probability, we know that the probability of all 195 propositions being
true is .02--ie.,  there is a .98 probability that not all of the
propositions are true.  Thus there is no contradiction at all.  The claims
A1, ... , An and ~(A1 & ... & An) are rigorously consistent.

=46allacy One, again:


>  THE PHILOSOPHICAL SIGNIFICANCE OF G=96DEL'S THEOREM

>   ... The heart of G=96del's theorem is, in fact, a paradox that
>   concerns the sentence, G, `This sentence is not provable'. If G is
>   provable, then it is true and so not provable. Thus G is proved. Hence
>   G is true and so unprovable.

Conspicuous Omission:

>  MANY-VALUED SYSTEMS
>
>   Perhaps the simplest way of generating a paraconsistent logic, first
>   proposed by Asenjo, is to use a many-valued logic, that is, a logic
>   with more than two truth values. The formulas which hold in a
>   many-valued interpretations are those which have a value said to be
>   designated. A many-valued logic will therefore be paraconsistent if
>   it allows both a formula and its negation to be designated. The
>   simplest strategy is to use three truth values: true (only) and false
>   (only), which function as in classical logic, and both truth and
>   false (which, naturally, is a fixed point for negation). Both
>   varieties of truth are designated. This is the approach of the
>   paraconsistent logic LP. If one adds a fourth value, neither true nor
>   false, which behaves in an appropriate way, one obtains Dunn's
>   semantics for First Degree Entailment.

=46our-valued logic was first expressed, as far as we know, more than 2,500
years before Dunn--by the Buddha Himself.  Those basic references in
English with which I'm familiar are "Buddhist Logic" by Scherbatsky and
"The Central Philosophy of Buddhism" bu Murti.

Shane Mage

When we read on a printed page the doctrine of Pythagoras that all things
are made of numbers, it seems mystical, mystifying, even downright silly.

When we read on a computer screen the doctrine of Pythagoras that all
things are made of numbers, it seems self-evidently true.




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