It helps to differentiate between “real” and “existant”. Mathematics is as real as the laws of logic—neither, however, exists.
What is “real” is that which proscriptively constraints that which exists. That which exists is that which interacts directly with other phenomena which also exist (that also interact).
When we say “2+3=5” what we are doing is engaging in the definition of real patterns of that which exists. So while, yes, the patterns themselves are external to us; the terms we assign them are subjective. In mathematics we ‘understand’ what happens when you add 2 and 3 together. But these are just symbols; just representations by which we predict outcomes based upon our understanding of those constraining patterns. In other words; we define 0 as none of a thing, and 1 as a single thing. We therefore define 2 as 1+1, 3 as 1+1+1, etc., etc.. (The dots).
However, if we were to encounter a person who defined 6 as 1+1+1+1+1, and we were to continue definining 1+1+1+1+1 as five, then neither would agree with one another, and both would be correct. This is, given the understanding involved of the difference between “real” and “existent”, neither exceptional nor inscrutable. It’s a trick of definition—much as is the Law of Identity and the Law of the Excluded Middle. (That which I define as “only-A” cannot ever simultaneously be “not-A”.)
It helps to differentiate between “real” and “existant”. Mathematics is as real as the laws of logic—neither, however, exists.
What is “real” is that which proscriptively constraints that which exists. That which exists is that which interacts directly with other phenomena which also exist (that also interact).
When we say “2+3=5” what we are doing is engaging in the definition of real patterns of that which exists. So while, yes, the patterns themselves are external to us; the terms we assign them are subjective. In mathematics we ‘understand’ what happens when you add 2 and 3 together. But these are just symbols; just representations by which we predict outcomes based upon our understanding of those constraining patterns. In other words; we define 0 as none of a thing, and 1 as a single thing. We therefore define 2 as 1+1, 3 as 1+1+1, etc., etc.. (The dots).
However, if we were to encounter a person who defined 6 as 1+1+1+1+1, and we were to continue definining 1+1+1+1+1 as five, then neither would agree with one another, and both would be correct. This is, given the understanding involved of the difference between “real” and “existent”, neither exceptional nor inscrutable. It’s a trick of definition—much as is the Law of Identity and the Law of the Excluded Middle. (That which I define as “only-A” cannot ever simultaneously be “not-A”.)