Re: Platonism

From: Mitch Harris (harrisq_at_tcs.inf.tu-dresden.de)
Date: 12/07/04 

Date: 7 Dec 2004 20:36:07 GMT

Lester Zick <lesterDELzick@worldnet.att.net> wrote:
>On Tue, 07 Dec 2004 10:09:53 +0100, Mitch Harris
>>Lester Zick wrote:
>>>
>>> Tautologies are necessarily composed of empirical observations.
>>
>>I really can't buy that. Not with generally accepted definitions of
>>the terms.
>>
>>Are you saying that the atomic propositions that make up a tautology
>>must be empirical? They can certainly be mathematical propositions.
>>
>>Are you then implying that all mathematical propositions are
>>empirical (that is, their truth is contingent on experience)?
>
>Well, at least you make pertinent observations, Mitch. All positive
>observations are empirical including mathematical observations.

Yes. I agree with you there. All we know of math is from observation (most
of it introspective). Using one of your (later examples) we observe that
6+2=8, and we can also observe that a formalization of this, and also
observe a proof of it, either internally or externally.

But (and I suppose this is what might be labelled Platonic) those
mathematical facts themselves are not contingent on our observing them.

>But
>the reason isn't evident in conventional definitions for empirical
>observations because these are analytically imprecise and rely on
>tautologically vague notions like experience etc.
>
>For any given tautology such as t:[subject][not subject] the first or
>positive half of t is an empirical observation because that's what an
>empirical observation is. If we take an observation such as "6+2=8" or
>"the interior angles of a plane triangle add up to a straight angle"
>or "e=mcc", these are all empirical observations subject to proof or
>disproof through the second or negative half of the tautology in
>conjunction with other tautologies.

I'm not sure I follow your terminology here about "second or negative
half" or "in conjunction with other tautologies".

>The sole and exclusive difference between empirical and tautological
>sciences is that empirical sciences only rely on the empirical half of
>tautologies and argue that an empirical observation is true if there
>are no empirical counter examples.

What's the empirical part of a tautology?

>Now, this might be true, but it
>cannot be proven true through the same mechanisms as are used in
>tautological sciences, which prove the consistency of any empirical
>observation with other empirical observations analytically through
>consideration of the implications of the tautology as a whole.
>
>In point of fact, this is why and how the so-called empirical sciences
>derive from the philosophy of positivism. Positivism just relies on an
>assumption of truth from consistency of empirical observation whereas
>tautological sciences do not.

I'm not sure what positivism is here. Is it the principle of
verificationism (or falsificationism)?

>There is nothing to stop tautological
>sciences from behaving as if they were empirical.

And they do. Lakatos, Proofs and Refutations. The history of analysis.

Mitch

Relevant Pages

  • Re: Platonism
    ... >>Are you saying that the atomic propositions that make up a tautology ... They can certainly be mathematical propositions. ... >sciences is that empirical sciences only rely on the empirical half of ... >derive from the philosophy of positivism. ...
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  • Re: Platonism
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  • Re: Platonism
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