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Re: infinity can't exist
Posted:
Feb 13, 2013 4:19 PM
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fom <fomJUNK@nyms.net> writes:
> On 2/13/2013 11:35 AM, Jesse F. Hughes wrote:
>> fom <fomJUNK@nyms.net> writes:
>>
>>> On 2/13/2013 6:43 AM, Jesse F. Hughes wrote:
>>>> fom <fomJUNK@nyms.net> writes:
>>>>
>>>>> From "Topics"
>>>>> ------------
>>>>>
>>>>> " We must say, then, what a definition, a distinctive
>>>>> property, a genus, and a coincident are.
>>>>>
>>>>> "A definition is an account that signifies the essence.
>>>>> One provides either an account to replace a name or an
>>>>> account to replace an account -- for it is also possible
>>>>> to define some of the things signified by an account.
>>>>> Those who merely provide a name, whatever it is, clearly
>>>>> do not provide the definition of the thing, since every
>>>>> definition is an account. Still, this sort of thing --
>>>>> for example, 'the fine is the fitting' [editor note: Aristotle's
>>>>> reservation here is that replacing one word with another
>>>>> is not really an account] -- should also be counted as
>>>>> definitory. In the same way one should count as definitory
>>>>> a question such as 'Are perception and knowledge the same
>>>>> or different?'; for most of the discussion about definition
>>>>> is occupied with whether things are the same or different.
>>>>> Speaking without qualification, we may count as definitory
>>>>> everything that falls under the same line of inquiry that
>>>>> includes definition.
>>>>>
>>>>> "It is clear immediately that all things just mentioned
>>>>> meet this condition. For if we are able to argue dialectically
>>>>> that things are the same and that they are different, we
>>>>> will in the same way be well supplied to take on
>>>>> definitions; for once we have shown that two things
>>>>> are not the same, we will have undermined the attempted
>>>>> definition. The converse of this point, however, does
>>>>> not hold; for showing that two things are the same is
>>>>> not enough to establish a definition, whereas showing
>>>>> that two things are not the same is enough to destroy a
>>>>> definition."
>>>>
>>>> Thanks for the reference, but I don't think it supports what you said,
>>>> namely
>>>>
>>>> In Aristotle, one finds the discussion that one can never define
>>>> x=y. To be precise, he says that one can never prove a
>>>> definition, but one can destroy a definition.
>>>>
>>>> He does not say "one can never define x=y", since definition of
>>>> equality is not discussed here,
>>>
>>> How is this
>>>
>>> "for most of the discussion about definition
>>> is occupied with whether things are the same or different."
>>>
>>> talking about identity?
>>
>> Yes, he is talking about identity there, but he is not talking about
>> whether one can define identity.
>>
>> To determine whether a definition is "correct", it is necessary, but
>> not sufficient, to show that the extension of the two terms is equal.
>
> I see your point here. My language was somewhat
> inexact -- certainly enough to deserve correction.
>
>
>>
>>>> nor do I think this follows from
>>>> anything he does explicitly say. And he also does not say "one can
>>>> never prove a definition", but rather simply that showing two things
>>>> are the same does not establish a definition.
>>>
>>> How do you interpret
>>>
>>> "showing that two things are the same"
>>>
>>> in the context of a mathematical discussion?
>>
>> I don't understand your question. I suppose that you mean "showing
>> that two things are the same" means showing that they are equal, but I
>> can't guess how this is intended to be relevant to my comments.
>>
>
> Well, it seems that you are focusing on my use
> of "prove". I am merely observing that showing and
> proving are very similar in mathematical contexts.
No, that's fine. I read "show" as more or less synonymous with
"prove", but my comment still stands. I think that since you agreed
with my comment above ("To determine whether a definition is
"correct", it is necessary, but not sufficient, to show that the
extension of the two terms is equal.") that we presumably have no
disagreement here. That's all I was saying.
> Technically, I am certainly wrong. The more formally
> one wishes to pursue the meaning of "to prove" the
> more distant the similarity.
>
>
>>>> This means that one
>>>> approach of establishing a definition does not work, but as far as I
>>>> can tell, Aristotle *does* think one can establish definitions as
>>>> correct, or else there would be little point (from his perspective) in
>>>> discussing them.
>>>
>>> He does. It is a relationship between "essence" and
>>> "substance". It has profoundly influenced the nature of
>>> modern mathematics.
>>
>> Then I'm sure I've no idea why you said, "he says that one can never
>> prove a definition."
>
> Aristotle also says that one cannot know first
> principles. So, his remarks above are not
> substantiated by any example. It might more
> accurately portray his position as thinking
> "one can establish definitions as correct, in
> principle."
>
> But, I admit to my inaccuracies.
>
Eh, it's Usenet. Maybe I shouldn't be so pedantic, but I thought that
your main comments were pretty far from my reading of A.
Not that I had read that passage before yesterday.
--
Jesse F. Hughes
"His name is Crap Talker and he's a bad guy because he doesn't listen.
And he has three faces."
--Quincy P. Hughes (age 5) invents a new super-villain.
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