Difficult to evaluate, with potential yellow flags.
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Greetings, the question I want to explore is whether mathematics is discovered, invented, or some combination of both. I've been wondering about this question for a while now. I've come across people from both sides of the debate. So, I wanted to get deeper into it. I wanna share my logic at first;
According to Kurt Gödel's incompleteness theorem, a language can not describe itself, but math can-within a set of rules of course.
Gödel's incompleteness theorem provides an interesting lens: if mathematics were merely a language, it couldn't consistently reference itself.
So Math itself is not just a language, if it were, it couldn't have described itself. Mathematics includes linguistic properties, but it also functions with the ability to formalize itself makes it a framework, a broader network that is. That's because it is a language, and guess what, Gödel's incompleteness theorem works cause of the supposition of math being a language. (I did say this just to not get out of the theorem's rules.)
Hence, it is not just a language while also being a language. We explain the nature and describe math itself with it, so instead of a closed language, it is a framework for us to explain both itself, and the nature, universe... Thus, mathematics is not merely a language, but a framework for describing both itself and the structures of the universe.
According to Platonists' views, mathematical objects and structures exited, independent to us, we discover them and that's how we attain the knowledge. But formalists' views tell the opposite: "These structures get built by the systems that were created by our mind. " To me, its only possible if its a mix of both of them. Mathematical orders, ratios, and harmonies existed in the universe; our frameworks give them explicit form and communicability.
So it had already existed, as a structure, but we shaped it. Still, both of them are considered Math so it is mixed with both. That was my view, I want to see others' views so I'll be sharing this as my first post. Hope you had fun while reading!
Greetings, the question I want to explore is whether mathematics is discovered, invented, or some combination of both. I've been wondering about this question for a while now. I've come across people from both sides of the debate. So, I wanted to get deeper into it. I wanna share my logic at first;
According to Kurt Gödel's incompleteness theorem, a language can not describe itself, but math can-within a set of rules of course.
Gödel's incompleteness theorems
Gödel's incompleteness theorem provides an interesting lens: if mathematics were merely a language, it couldn't consistently reference itself.
So Math itself is not just a language, if it were, it couldn't have described itself. Mathematics includes linguistic properties, but it also functions with the ability to formalize itself makes it a framework, a broader network that is. That's because it is a language, and guess what, Gödel's incompleteness theorem works cause of the supposition of math being a language. (I did say this just to not get out of the theorem's rules.)
Hence, it is not just a language while also being a language. We explain the nature and describe math itself with it, so instead of a closed language, it is a framework for us to explain both itself, and the nature, universe... Thus, mathematics is not merely a language, but a framework for describing both itself and the structures of the universe.
According to Platonists' views, mathematical objects and structures exited, independent to us, we discover them and that's how we attain the knowledge.
But formalists' views tell the opposite: "These structures get built by the systems that were created by our mind. "
To me, its only possible if its a mix of both of them.
Mathematical orders, ratios, and harmonies existed in the universe; our frameworks give them explicit form and communicability.
So it had already existed, as a structure, but we shaped it.
Still, both of them are considered Math so it is mixed with both.
That was my view, I want to see others' views so I'll be sharing this as my first post. Hope you had fun while reading!