Re: Platonism

From: patty (pattyNO_at_SPAMicyberspace.net)
Date: 11/27/04 

Date: Sat, 27 Nov 2004 00:24:12 GMT

Eray Ozkural exa wrote:
> Neil W Rickert <rickert+nn@cs.niu.edu> wrote in message news:<co59g8$6hg$1@usenet.cso.niu.edu>...
>
>>examachine@gmail.com (Eray Ozkural exa) writes:
>>
>>
>>>I agree. However, as evidenced by this newsgroup most mathematicians
>>>are naive platonists. They don't understand the distinction between
>>>the reality of a table and mathematical ideas.
>>
>>Nonsense! Of course mathematicians understand the distinction.
>
>
> Well, I don't think most of them have even an inkling. Otherwise, they
> would stop suggesting that PCs are not models of Turing Machines, or
> that real numbers "exist" or other silly Platonism.
>
> In particular, they should acknowledge that consistency alone is no
> indication of reality. That is the issue. I can come up with a
> completely consistent, and a completely fabricated story, like the
> Bible. But that is a fairy tale. It is not real. Likewise,
> mathematicians can come up with consistent and un-real stories. Most
> mathematicians do not appreciate that whatever idea they can think
> about is not automatically "real".
>

This is a follow up to my previous posting on this matter. The
semantics of language works such that if we refer to a thing it must
exist in our interpretation (world or model). But if we want to
restrain our interpretive world to be a bit more realistic (for some
interpretation of realistic) we can choose a more restrictive criteria.
  As we do this we will be consigning references outside the chosen
scope of the additional criteria to the nonsense heap. I would like to
consider several kinds of interpretations (worlds or models) according
to reasonable criteria for existence in those worlds ... working from
one extreme to the other ...

fictional worlds
  no - physical - things located in time/space
  no - effective - procedures exist for identification
  no - objective - can be verified by multiple agents

mental worlds
  yes - physical - things located in time/space
  no - effective - procedures exist for identification
  no - objective - can be verified by multiple agents

mathematical worlds
  no - physical - things located in time/space
  yes - effective - procedures exist for identification
  yes - objective - can be verified by multiple agents

physical worlds
  yes - physical - things located in time/space
  yes - effective - procedures exist for identification
  yes - objective - can be verified by multiple agents

Note that in all the worlds considered here, if things are effective
they are also objective. Perhaps those are the same criteria, perhaps
not; if not then we should be able to describe those worlds distinct
from the ones i mentioned.

Also note that in all cases we are talking about *things* in whatever
kind of world of which we speak. We are not talking of the marks which
stand for those things in some other world. For example the marks which
comprise a work of fiction are not usually allowed to exist in the world
created by the interpretation of those marks.

Constructive comments and critique gladly accepted.

patty

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