Re: Platonism
From: Lester Zick (lesterDELzick_at_worldnet.att.net)
Date: 12/09/04
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Date: Thu, 09 Dec 2004 16:07:08 GMT
On Wed, 8 Dec 2004 23:56:00 +0000 (UTC), Dave Seaman
<dseaman@no.such.host> in comp.ai.philosophy wrote:
>On Wed, 08 Dec 2004 23:36:52 GMT, Lester Zick wrote:
>> On Wed, 8 Dec 2004 19:47:21 +0000 (UTC), Dave Seaman
[. . .]
>>>> I'm talking about everything of equal differences. Ordinality is
>>>> defined by unequal differences.
>
>>>Finite ordinals have equal differences. For example, the ordinal 3 =
>>>{ 0, 1, 2 }. Looks like equal differences to me. For transfinite
>>>ordinals, the notion of "difference" is not even well defined. For
>>>example, w+1 = { 0, 1, 2, ..., w }. What is the last "difference"?
>
>> You're mistaken. Finite ordinals only have equal differences in
>> reference to finite cardinals.
>
>That sentence is ambiguous. I said that finite ordinals have equal
>differences, and one possible reading of what you just said is that you
>are agreeing with me.
Criticism accepted. I find I have to amend my definition of ordinality
to differences alone. Ordinality applies both to the presence and
absence of cardinality.
>>>>Not vague at all and certainly not too
>>>> vague to be the definition of such fundamental properties as these.
>
>>>Your definition is vague, and it's wrong.
>
>> My definition is extremely specific and it's right.
>
>Your definition does not agree with the references I provided, and those
>references are in agreement with standard mathematical usage. That means
>your definition is wrong.
No, it means that your standard of right is wrong.
>>>>>So you see nothing wrong with defining a "turnip" to mean a blue
>>>>>hexagonal elephant? And if other people want to discuss turnips, are you
>>>>>going to insist that their definition is wrong?
>
>>>> There would seem to be some inability to define definition missing
>>>> here. You seem to be defining definition in some rather peculiar form
>>>> akin to whim.
>
>>>No, defining on a whim is exactly what you are doing. I am doing what
>>>most people do, which is to use words with their conventional meanings
>>>instead of making up new ones. It makes communication much simpler when
>>>everyone uses the same definitions.
>
>> Communication of what? Conventional meanings? Go back to studying the
>> number of toes on three toed sloths. I'm sure the answer will occur to
>> you eventually.
>
>>>> I see the definition of definition in terms of
>>>> differences and the absence of self contradiction. You seem to see it
>>>> as some kind of divination.
>
>>>Not at all. I didn't simply make up those definitions; I gave
>>>references.
>
>> And I gave you reasons instead of references. And my reasons are
>> better than your references because you can reason with them instead
>> of just referring to them to find out what others have opined but did
>> not know.
>
>You can't deduce definitions from logical arguments. Logic may be
>involved in making up new definitions, but when definitions already exist
>and are firmly established, there is nothing to be settled by argument.
Logic is involved in making up new and old definitions. Some logic is
just more comprehensive than other logic. The logic involved in making
up old definitions was old logic and it suffered from antiquarian
notions of what was involved in drafting definitions. I have shown you
how the definition of cardinality must be drawn and explained why.
You asked for my definition of cardinality which I gave and explained
why it is correct. If you seriously wish to argue that the basis of
correct definition is standardness (whatever that may be) then I agree
there is nothing further to be argued except your rather quaint
antiquarian notions of right and wrong, correct and incorrect.
>>>> I just ask what the one property peculiar to all cardinals is and what
>>>> they would not be cardinals without and use that as the definition of
>>>> cardinality. If you have some other basis of definition you must
>>>> indeed explain to us all so we don't biject, deject, object, subject,
>>>> and reject your definitions out of hand as so much double talk.
>
>>>The fact that you don't understand something doesn't make it double talk.
>
>> But the fact that you don't understand something yet go on to define
>> it anyway does make it double talk.
>
>I have not defined anything. I have merely pointed out what the correct
>definitions are.
You have merely pointed out what the standard definitions are and
provided no evidence whatsoever that they are correct. I defined
cardinality and ordinality and explained why the definitions are
correct.
Regards - Lester
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