Re: syllogism

From: patty (pattyNO_at_SPAMicyberspace.net)
Date: 09/30/04 

Date: Thu, 30 Sep 2004 11:23:15 GMT

Wolf Kirchmeir wrote:

> patty wrote:
>
>> Wolf Kirchmeir wrote:
>>
>>>
>>> The reason logical identity is such a powerful tool is that it is
>>> really a double implication. To say "A==B" is to say that "If A, then
>>> B; and if B, then A".
>>
>>
>>
>> ... well not totally exactly. To say "A==B" is to say that "A" and
>> "B" are names of the same thing ... in other words we cannot
>> distinguish between them. If we say "If A, then B; and if B, then A",
>> A can still be quite distinguishable from B ... for instance "A" could
>> be the trunk of an elephant and "B" could be the tail of the elephant.
>>
>> Logical identity means that you can recognize something, and then
>> recognize it again the next time you see it; and that you realize it
>> is the same thing. It is a powerful tool - some might say too
>> powerful. If you are *absolutely* certain that you can reidentify
>> something, well then you can use the law of the excluded middle (LEM)
>> too. If you are not *absolutely* certain (as in most cases in real
>> life), then you really shouldn't use LEM; but people frequently do
>> anyway.
>>
>> ... sometimes i like to show off, but sometimes when i show off i end
>> up looking stupid, hopefully this won't be one of those times :(
>>
>> patty
>
>
> Well, to say A==B does not mean that we cannot distinguish between them.

Well in my book things are identical if, and only if, they *are*
indistinguishable.

> The statement that asserts indistiguishable identity is A==A. To say
> that A==B is to say that either term can replace the other without
> affecting the truthvalue of statement in which it occurs. That's not
> exactly the same thing as "they are the same thing." For one thing, A==B
> must be proven, while A==A is a tautology.
>

The only trouble i have with that, is that in real life we can rarely
assume A==A. A case in point is below. You wrote (A-->B) and i read it
not to mean the same (A-->B) as you wrote. That may be the subtle point
that i am trying to make here.

[snip a paragraph about something else]

>
> BTW, (A==B) == (A-->B AND B-->A) is the definition of logical identity.
> IOW, (A==B) is inferred from an argument that has shown both that
> (A-->B) and (B-->A). See?
>

Well i see where we are stumbling over the rather ambiguous (A-->B). I
was interpreting it as a first order term with *one* property and no
quantification (Fa => Fb); but now i see you meant it as (for *all*
properties F, Fa <=> Fb) which *is* a coding of the definition of the
identity of a and b:

   "x = y if, and only if, x has every property which y has,
   and y has every property which x has."

<http://huizen.dto.tudelft.nl/deBruijn/grondig/equality.htm>

> Proving A==B is useful because it allows the replacement of either
> expression with the other wherever they occur, which, for example, may
> simplify calculations, or proofs of theorems, etc. It's necessary when
> you ant to use LEM, as you correctly note -- but note that merely
> asserting A==B isn't good enough. Many people assert the identity, they
> don't prove it, hence the fallacy. :-)

Merely assuming A==A is no better. I know that you will feel
uncomfortable with thinking about it this way; but i feel uncomfortable
with a logic that assumes it is always playing with all its balls inside
the court. Assuming A always is the same A, seems to me to break down
too frequently - especially when more than one person is talking - and
almost always when you are talking to me :( Incidentally i intend to
skip the lecture about the distinction between formal logic and applied
logic because i fed the texbook to my dog.

patty

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