Re: Rules of deduction.

David Canzi <dmcanzi@xxxxxxxxxxxxxxxxxxxx> wrote:

The operators and quantifiers in systems of symbolic logic are
derived from words in spoken language, eg. if, not, all, some.
The rules of inference in symbolic logic are derived from methods
of inference we use in spoken language.

We are born without language, We learn how the words of our
language are used by observing how others use them. We come to
expect that the words will continue to be used as we have heard
them being used. This includes the words from which the operators
and quantifiers of symbolic logic are derived.

We learn the rules of deduction by induction.

This is arguable. We may have these rules innately, that is, they may be
Kantian synthetic aprioria, but at the same time evolutionary a
posterioria. Individually I don't "learn" to use deduction or grammar
(logical or natural), I am born already able to employ these. What I do
is map hypotheses about local grammars and logic to my prior categories.

This used to be called the "Laws of Thought" hypothesis. I think instead
we have a *partial* syntax that we individually develop into local
languages and logics.

Incidentally, it is very interesting to see how quantification differs
in the Greek texts from how it is employed in the Latinate texts. There
is less stress on the scope of quantification in Aristotle than in the
modern logics (post medieval). The universal quantifier applies to a
predicate rather than an entity.
--
John S. Wilkins, Postdoctoral Research Fellow, Philosophy
University of Queensland - Blog: scienceblogs.com/evolvingthoughts
"He used... sarcasm. He knew all the tricks, dramatic irony, metaphor,
bathos, puns, parody, litotes and... satire. He was vicious."

.

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