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On Sat, Jan 11, 2003 at 11:23:07AM -0500, John Cowan wrote:
> 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 Why do we want to use an outdated logic?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.
Sure, but those semantics aren't consistent with the way DeMorgan is
supposed to work according to CLL. CLL clearly says that
naku ro broda cu brodo ==
su'o broda naku brodo
This is consistent with modern logic, OTOH.
> We should not give anything up, *including* Aristotelian logic.
Aristotle has nothing to offer that symbolic logic doesn't offer.
> > 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?
But OR is given preferential treatment in terms of cmavo assignment.
> > 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.
They are useless in that they provide no additional use. You can
build theorems all the way up to laws of addition and such things
with symbolic logic without using any such square stuff.
Furthermore, the "widely accepted" bit is completely bogus; infering
based on A and I as subalterns is considered a common enough error
of reasoning that they have a specific name for it: "The Existential
Fallacy".
[...]
> > 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.
[...]
I *think* Quine solves this with some fidling around with the
definition of what can be a member of something. I know (he claims)
russel's paradox is solved by his doing this, because it excludes
certain sets from being considered as things which can be members
of other things.
I don't remember explicit mention of cantor's paradox in the book,
so I don't know if it applies or what.
He doesn't have a power set function in his system, but it can be
created using his abstraction stuff. For set of all subsets of x:
â(a < x)
('<' as containment). So it would certainly be a problem for the
system if the power set of a set is an element (which I am not adept
enough to determine).
--
Jordan DeLong - fracture@hidden.email
lu zo'o loi censa bakni cu terzba le zaltapla poi xagrai li'u
sei la mark. tuen. cusku
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