Discovery vs. Invention: A Confusion

I have a strange relationship with philosophy, which I think is the case for most people who have an amateur interest in the subject. Many of the topics and ideas seem fascinating, but many other ideas seem like pointless semantics. In my case, most of the big topics in the philosophy of math are uninteresting. In particular, is math invented or discovered? Or in other words, are mathematical concepts a type of platonic ideal, or are they a construct of human imagination?

I think many mathematicians (particularly pure mathematicians) have to some degree a belief in mathematical concepts as platonic ideals. People who do mathematics for its own sake, myself included, don’t often feel that they are playing an elaborate man-made game, but that there is something organic (for lack of a better word) about the study of mathematics. The emergence of deeper patterns is the main draw for studying mathematics for me.

I suppose it’s the mathematician nature in me that always goes back to the question, “What is existence?” whenever I hear this question. And somehow, trying to determine what existence is prior to what seems like a hopelessly futile task. Regardless of whether material existence is prior to abstract concepts or vice versa, it doesn’t affect how we would go about studying math. It seems to me that these philosophical ideas are two distinct systems of axioms which have different theorems but are the same for all tangible purposes.

But perhaps the main point is that by expressing different ideas for the ultimate questions about reality, we put into context our own beliefs about the matter, and we are made aware of our unconscious assumptions about reality. And we are confronted with the idea that our beliefs aren’t at all universally held.


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