Re: [jboske] Aristotelian vs. modern logic

[John Cowan <cowan@ccil.org>]

Jordan DeLong scripsit:

> Why do we want to use an outdated logic? We already have features
> of modern logic which Aristotle didn't have (bu'a, lambda stuff,
> whatnot). Should we give those up too?

Every bit of Aristotle's logic is consistent and compelling by modern
standards, once you get past the broken "some S is not P" reading for O.
Aristotle's original and correct reading "not every S is P" has the
correct non-import semantics.

We should not give anything up, *including* Aristotelian logic.

> Aristotle used XOR for "or" also---I don't see you saying we should
> be doing that.

We have both or and xor. What's the issue?

> Yes, but those things are useless. Modern logicians have a much
> simpler "square", and it hasn't hurt them any.

They are not "useless". They support widely accepted varieties of
common-sense reasoning.

> But we don't want to have to write that. I want to be able to say things
> like
> ro pavyseljirna cu blabi
> and have it be exactly the same as
> ro da zo'u ga da na pavyseljina gi da blabi
> and
> ro da poi pavyseljirna zo'u da blabi

And so? You do, but I do not. I want "ro pavyseljirna cu blabi" to
count as false, not true, and ditto with "ro pavyseljirna cu zirpu".
At the common-sense level, there *aren't* any unicorns, white, purple
or otherwise. (I am not here talking about possible or fictional worlds
in which there are unicorns -- substitute "even primes > 2" if you like.)

> Yeah, that case is nonimportant---I didn't know back when we were
> discussing this last. But in a system of modern logic, it can be
> proven as a theorem that the universe is nonempty (or at least it
> can in Quine's). And it can also be shown intuitivly: we have a
> set of all things, which is a thing, and a set of nothings, which
> is another thing---so we can't have an empty universe.

If sets count as things, then the "set of all things" will not work:
see Cantor's paradox, which shows that the notion "set of all sets"
is ill-formed.

-- 
And through this revolting graveyard of the universe the muffled, maddening
beating of drums, and thin, monotonous whine of blasphemous flutes from
inconceivable, unlighted chambers beyond Time; the detestable pounding
and piping whereunto dance slowly, awkwardly, and absurdly the gigantic
tenebrous ultimate gods -- the blind, voiceless, mindless gargoyles whose soul
is Nyarlathotep. (Lovecraft) John Cowan|jcowan@reutershealth.com|ccil.org/~cowan