What is the nature of Mathematical concepts?

[RationalEgoistSG]

I openly profess that I do not know much about mathematics or the philosophy of mathematics. However, I have been curious about one important point. Are mathematical objects (such as the number 2 or an equation, etc.) existents in reality or are they like objective concepts that describe the relationship between physical existents? (Or are they something else altogether?)

It would seem to me that mathematical objects are the latter, concepts that describe the relationship between physical existents.

I may be way out of my league here, but I was curious as to whether or not anyone has any interesting ideas on the subject.

[MinorityOfOne]

They're abstractions, so numbers per se don't exist apart from consciousness, if that's what you mean.

Ron Pisaturo has done a lot of work on this topic. I read his articles in The Intellectual Activist on mathematics a long time ago, and found them interesting, though I'd have to reread them again to say much about them. Here are a few links you might find useful.

Pisaturo's summary of his theory:

http://www.cs.nyu.edu/pipermail/fom/2003-M...rch/006313.html

(Not directly related to your problem, but the solution lies in applying the Objectivist theory of concepts to mathematics. Here, he gives an indication of part of how it's done.)

Some brief excerpts from Pisaturo's essays on math:

http://pages.prodigy.net/rpisaturo/MathExc...cerpts.htm#FOM1

(Again, you'd have to get the actual essays in order to get much from this.)

An article by Travis Norsen on (among other things) how bad ideas in mathematics are related to bad ideas in physics:

http://www.apor.info/articles/tn_mathematics1.htm

(Also not directly related to your problem, but it might help indirectly.)

Also, take a look in the appendex to ITOE. I think Rand had some comments on this in there.

[ernie]

I would have to agree. They describe relationships. Certain mathematical principles may turn out to be absolute, but only in relation to other principles which exist in the same system.

[Guest Tracy]

They're abstractions, so numbers per se don't exist apart from consciousness

Not per se, no, but they do have reference, namely equal parts describing object collections, dimensions, intensities, intervals, or any other type of measurement.

In order to form such concepts, you have to omit the particular *existents* involved.

Many people think Objectivism has no answer for how concepts of quantities are formed because they take "measurement omission" too literally.