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Wherein Virgil once more moans and groans that there is no truth to
axioms and definitions in modern math, a position which we don't
dispute at all.
On Wed, 30 Aug 2006 22:38:55 -0600, Virgil <virgil@xxxxxxxxxxx> wrote:
>In article <pksbf2ljq7h442gj4m88lbv4esihafsb9f@xxxxxxx>,
> Lester Zick <dontbother@xxxxxxxxxxx> wrote:
>
>> On Tue, 29 Aug 2006 22:06:19 -0600, Virgil <virgil@xxxxxxxxxxx> wrote:
>>
>
>> > I am not aware of any definition in mathematics that assumes anything,
>>
>> Well if defintions are neither true nor false I don't exactly see how
>> they cannot assume everything they say.
>
>Nor how they need to assume anything. Show us a definition that assumes
>something, Zick!
>>
>> >except a moderate proficiency in English, or the definer's native
>> >tongue.
>> >
>> >Perhaps Zick has some examples in mind?
>>
>> Zick tends to concentrate on the truth or falsity of definitions and
>> leave definitional assumptions to those who cannot.
>
>As there is foundationfor truth or falsity to be involved in
>definitions, as Zick has claimed, his claim about assumptions being
>involved will prove to be equally ill founded.
>>
>> >> They remain undemonstrated problematic
>> >> assumptions regardless.
>> >
>> >For example?
>>
>> For example those things which can be neither true nor false.
>
>Such as? Avoiding the question, as Zick keeps doing, leads one to
>conclude that either Zick doesn't know what he is talking about or knows
>he is wrong but won't admit it.
>>
>> >> And whether they save time and space is totally
>> >> irrelevant.
>> >
>> >It may be irrelevant to whether they are valid, but not to whether they
>> >are useful.
>>
>> Jesus are you dense.
>
>What is the point of abbreviations which save neither time not space?
>Interested minds want to know!
>>
>> >> >> >All definitions are essentially no more than abbreviations, and can
>> >> >> >be
>> >> >> >eliminated by opting to do without the brevity they provide.
>> >> >>
>> >> >> Or you could keep the abbreviation and do without the contradiction
>> >> >> involved.
>> >> >
>> >> >What contradiction can be involved in keeping them if one can keep them
>> >> >without contradiction?
>> >>
>> >> Huh? Do you actually read what you write? By all means go ahead and
>> >> keep the ones without contradictions. Then tell us how you demonstrate
>> >> which ones they are.
>> >
>> >First show me that there can be ones WITH a contradiction.
>>
>> I already have.
>
>Not to the satisfaction of anyone but Zick.
>
>And if Zick wants only a monologue supporting his own biases and
>prejudices, he need not bother to post at all.
>
>> >> >> A squircle is a square circle.
>> >> >
>> >> >You have defined something, but there is no implication in that
>> >> >definition that the thing defined need exist, and , in this case, it
>> >> >does not.
>> >>
>> >> Yeah look, Virgil, this comment is nothing but doubletalk offered as
>> >> an excuse the fact that you're wrong on this aspect of definitions.
>> >
>> >Mathematics has no problems with definitions like that. If Zick does,
>> >perhaps he needs to get some tutoring in logic.
>>
>> You mean modern math has no problems with doubletalk and I agree.
>
>While the Greeks would have has to have it stated in Greek, those such
>as Archimedes would have no trouble with my comments at all.
>>
>> >> >Vacuous definitions do not of themselves create problems
>> >> >unless one tries to incorporate instantiation as a part of the
>> >> >definition, but that is not proper in definitions.
>> >>
>> >> Oh so now we move on from just keeping valid definitions without
>> >> contradictions to more pressing concerns about vacuous definitions and
>> >> totally nugatory incorporations of instantiations in definitions? And
>> >> here I thought all along that definitions could not be evaluated true
>> >> or false. My mistake.
>> >
>> >While Zick makes many mistakes, thinking that definitions are neither
>> >true nor false is not one of them.
>>
>> Yeah, yeah, whatever.
>
>My , my, such penetrating logic!
>>
>> >> >> >> >Does LZ have any examples of mathematical definitions that include
>> >> >> >> >requirements that the thing defined exists or not exist? I know of
>> >> >> >> >none.
>> >> >> >>
>> >> >> >> I didn't imagine you would. Do you maintain that definitions
>> >> >> >> inclusive
>> >> >> >> of contradictory statement combinations are not false?
>> >> >
>> >> >Give me an example. If your "squircle" is an example of what you mean,
>> >> >then "NO"! The definition is not "false" it is merely not instantiated.
>> >>
>> >> Oh horseshit, Virgil. I gave you a false definition. Now you
>> >> arbitrarily extend the demand from definition to instantiation.
>> >> Instantiation is not and can never be an aspect of definition because
>> >> you can't instantiate what you can't define.
>> >
>> >But one can certainly define what one cannot instantiate.
>> >Zick's "squircle" is a good example.
>>
>> Sure it is. Problem is though that you can't instantiate what you
>> can't define.
>
>Who needs to? The issue is whether sentences of the form
>"Let 'A' represent 'B' ." can be true or false.
>mathematics and mathematicians say no.
>What Zick's mathematikers say we would have to ask Zick to explain, as
>we have no other access to them except through him.
>
>> >> More instantiation nonsense. I really don't understand where you get
>> >> such quaint ideas regarding definitions.
>> >
>> >From dictionaries, and texts on logic, and tests on mathematics, and
>> >from that uncommon common sense that Zick seem to be utterly lacking.
>>
>> You mean facile common sense assumptions of truth.
>
>That may be what Zick means, but why he should put his ideas in other
>mouths is something only he knows.
>
>> >> I'd say self contradictory definitions are pretty much false.
>> >
>> >Then you would say wrongly.
>>
>> And you would say rightly that they're not false?
>
>As I have never seen one, and cannot conceive of one, I would not say
>that they even exist.
~v~~
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