"khanster" wrote: [quote="at1with0"]I don't know if this answers your questions but numbers still exist (or don't exist) regardless of whether or not there are things to count.

If there are things to count then numbers must exist.

Any discernible difference between "things" is a number.

There are different concepts (e.g., triangles and circles) therefore numbers exist. hehe
Reality exists implies that the number 1 exists for in that scenario, at least one thing exists.

Then 2 exists because "reality exists" and ""reality exists" is true" are two true statements.

Similarly, all natural numbers exist.

It takes some effort but all numbers can be defined in terms of natural numbers.

However, to say that there is a SET of all natural numbers can not be proved it must be assumed (axiom of infinity).

"DIss0n80r" wrote: [quote="at1with0"]I don't know if this answers your questions but numbers still exist (or don't exist) regardless of whether or not there are things to count.

How do you differentiate between things to count and numbers?

It would seem to be better that we reduce the number of undefined primitive notions to a minimum; therefore, let's stick with sets being that one undefined notion.

Natural numbers are defined (Or can be defined) in terms of sets
http://en.wikipedia.org/wiki/Natural_nu ... set_theory
In this way, natural numbers are viewed as specific sets.

To answer your question, not all things are sets but numbers, in this line of thought, are sets thus things to count and numbers are entirely different categories of real.

As a simplistic analogy, say we have a perception of self = 1 dimension

a perception of perspective of other than self = 2nd dimension

a perception of duration which gives depth, which some might call "time" = 3rd dimension

A two dimensional holographic encoding plus time gives three dimensions.

Long live the Droids :clap:

Perhaps it would help to view dimensions as degrees of freedom.