[lit-ideas] Re: Numbers

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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