Thursday, March 01, 2018

The Death of Logic

A hundred years ago (more or less) logic died.

It was either logic and transcendent Creator,
or neither... And atheism was in the ascendant
a hundred years ago (while the Creator shown, logically, to exist
was not that of the embattled religions of those war-faring days).

Prima facie, though, logic took off at that time: it was formalized,
and we now have lots of formal logics, within Analytic Philosophy.
But, what's so logical about reacting to the Liar paradox by redefining "truth"?
And what's so logical about having each ordinal, but not having every ordinal?

We may begin with physics: nowadays we have String Theory.
Suppose we get a really good String Theory, say "S," one day.
There's no guarantee that we won't need a better theory later,
so why would we use S to redefine all our physical entities?
If the description of electrons in S was E, for example, then
we could replace "electron" with "E,"  but why should we?
A very good reason why not is that electrons are electrons.
(A better theory of them won't be any sort of theory of E.)

And mathematics is a subset of the properties of possible objects:
one object and another object is (one plus one) objects, and so on.

But for a hundred years, science has replaced "1" with "{{}}."
Did not the logician Frege refute Mill's description of "1"?

It turns out that he did not; and he could not have,
because 1 is, basically, Mill's 1.

Set Theory mimics mathematics,
so for applications it hardly matters; but,
do the best mathematicians really believe
that 1 is nothing like Mill's 1, is really {{}}?
We all learn what 1 really is at an early age.
{{}} was chosen following Cantor's paradox,
but it also followed that logic had to be replaced.
Logically, there was that paradoxical proof; and
while the Liar paradox is nowadays interpreted
as another reason to replace truth, and its logic,
with something formal, that is not really scientific:
science pursues truth, and logic takes truths to truths
(where to say, of what is, that it is, is to speak the truth).

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