Is maths invented or discovered?
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Quoted By: >>11232039 >>11232042 >>11232072 >>11232081
I saw this question posed by some random image someone posted on /adv/.
And this is what I think:
>The principles of maths are DISCOVERED (such as Pythagoras's Theorem)
>But the syntax of maths is INVENTED
Obviously humans invented the syntax of maths. We invented the symbols and gave them meanings. But the mathematical truths, like Pythagoras's Theorem, or the quadratic equation, are discovered.
Also, I would argue that maths is not a priori knowledge like Kant thought it was ("a priori" meaning that it's independent of experience; you can just grasp it through pure reasoning). I would say that maths is a posteriori (knowledge gained from experience). Because every mathematical truth is simply a description of our empirical reality. Maths is ultimately just a language for describing reality, just like English is. Maths is of course heavily used in physics, because it can describe the reality that physics is trying to describe. "1 + 1 = 2" simply means that when you put two single objects together, you now have a pair of objects. That's an empirical observation. Of course we can use maths to deduce things that we don't know directly from experience, sure. E.g. if I see a bank statement of yours from last month saying you had £2,000 in your account, and I know that you've spent £500 since then, then obviously I can deduce that you have £1,500 left in your account, without having to see your bank balance first hand. Sure. So that sort of knowledge could possibly be called a priori. But the fundamental axioms of maths must be a posteriori. They are descriptions of our empirical world.
What do you think, /sci/?
And this is what I think:
>The principles of maths are DISCOVERED (such as Pythagoras's Theorem)
>But the syntax of maths is INVENTED
Obviously humans invented the syntax of maths. We invented the symbols and gave them meanings. But the mathematical truths, like Pythagoras's Theorem, or the quadratic equation, are discovered.
Also, I would argue that maths is not a priori knowledge like Kant thought it was ("a priori" meaning that it's independent of experience; you can just grasp it through pure reasoning). I would say that maths is a posteriori (knowledge gained from experience). Because every mathematical truth is simply a description of our empirical reality. Maths is ultimately just a language for describing reality, just like English is. Maths is of course heavily used in physics, because it can describe the reality that physics is trying to describe. "1 + 1 = 2" simply means that when you put two single objects together, you now have a pair of objects. That's an empirical observation. Of course we can use maths to deduce things that we don't know directly from experience, sure. E.g. if I see a bank statement of yours from last month saying you had £2,000 in your account, and I know that you've spent £500 since then, then obviously I can deduce that you have £1,500 left in your account, without having to see your bank balance first hand. Sure. So that sort of knowledge could possibly be called a priori. But the fundamental axioms of maths must be a posteriori. They are descriptions of our empirical world.
What do you think, /sci/?
