[lit-ideas] Re: Numbers
- From: Robert Paul <robert.paul@xxxxxxxx>
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Wed, 18 Jan 2006 21:04:44 -0800
Alex wrote:
I believe that numbers are mental phenomena. Basic, fundamental units of
perception, with no existence outside of the mind. I am familiar with Plato,
whose influence is inescapable, and aware of the view, held my many throughout
the ages, which says that numbers exist somewhere in a realm of Platonic
forms. However, I do not regard Platonic forms as a comprehensible concept, or
as any kind of understandable "space" where things like "numbers" reside, or
belong. I regard it more as an elaborate metaphor or mystical concept which is
impossible to pin down or understand--a religious concept in a way.
I can see that one might be tempted to say that numbers were 'mental
phenomena' because of the difficulty of identifying them with objects in
the 'physical world.' But what are mental phenomena if not mental
objects, the sorts of things Anselm appealed to when he said that a
being whose existence was 'in the mind' wouldn't be as great as (would
have less perfection than) one whose existence was outside the mind as
well? If what Peter happily calls the glyph 3, referred to a mental
object of some sort, then whatever was true of the number three would
also be true of that mental object, and this raises difficulties.
The first is that mental objects are discontinuous and numbers are
thought not to be. That mental objects are discontinuous (their
existence is episodic) follows from their being mental objects some
person has, or many persons, or all persons have, at particular times
and places. There are no mental objects which no person has (Berkeley
aside), although there are possibile mental objects, i.e., mental
objects many people could have, simultaneously or not, e.g. the sudden
thought that the burner is still on under the teakettle.
One could give such a thought a name, â, and say that â referred to the
sudden thought in question, but this wouldn't be analogous to saying
that 3 referred to a particular mental object, viz., the number three.
The difference is that there just is no such thought if no one is
'thinking' it; it's merely a possible thought. Yet if even if no one is
(I'm not sure of the verb here) entertaining the number three, three
isn't a mere possible number, it's a full-fledged number.
My suggestion is that a mental phenomenon is a mental object, i.e., an
object whose existence is either essentially mental (a thought) and
contingently had (the thought that the kettle will boil dry); objects
whose existence is mental aren't stable enough to support our intuitions
about even the natural numbers: if you 'have' the mental phenomenon, or
mental object three, that it is greater than the mental phenomenon, or
object, two, could only be understood by appealing to something other
than a mental phenomenon. If two and three and the rest were merely
mental phenomena, familiar arithmetical operations would be somewhat
hard to describe: three plus three is six (ordinarily) but to say that
the sum of two mental phenomena is a further mental phenomenon would
require that this sum be a number, and not a sudden thought, such as â;
yet how is this to be determined? By an appeal to the properties of
numbers, surely, and (in this case) to the meaning of the + sign. That
the properties of numbers can be read off mental phenomena, and mental
phenomena alone needs more support than I see here.
Talk about presence and absence, being and non-being may have to wait.
Thanks to Alex for these thoughts.
Robert Paul
Reed College
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