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# Maths and philosophy watch

1. As a potential EPQ topic I'm planning of merging my love for maths and philosophy by finding an interesting question that merges the two together? Does anybody have any ideas or areas to explore? Any help would be greatly appreciated. Thanks very much
2. How about the epistemology of maths? For example: To what degree can mathematics be said to be, in principle, capable of being known?

Discussion involved could cover things such as mathematics' fundamental principles, attempts to prove those fundamental principles (e.g. Whitehead and Russell's Principia Mathematica) and Godel's incompleteness theorems showing how they, in fact, cannot be wholly proven.
3. (Original post by miser)
How about the epistemology of maths? For example: To what degree can mathematics be said to be, in principle, capable of being known?

Discussion involved could cover things such as mathematics' fundamental principles, attempts to prove those fundamental principles (e.g. Whitehead and Russell's Principia Mathematica) and Godel's incompleteness theorems showing how they, in fact, cannot be wholly proven.
That's actually quite an interesting one I'll do some research into it. I was also maybe considering perhaps the concept of infinity?
4. (Original post by sarah.102)
That's actually quite an interesting one I'll do some research into it. I was also maybe considering perhaps the concept of infinity?
Sure, that has a lot of interesting information associated with it - for example, the concept that there may be infinities of different sizes relative to each other, and that each may exist as 'countable' and 'uncountable' respectively.
5. Depending on how strong your interest for maths is (and how deep you're willing to go) you could perhaps consider the debate surrounding the axiom of choice? Maybe go into the Banach-Tarski Paradox?
6. A popular point of discussion is Platonism: do mathematical objects exist independently of our own reality (waiting to be discovered) or do we create them? Perhaps you could consider whether or not the axioms of mathematics are arbitrary and, if they were, whether this would imply that we create mathematical objects (consider things like hyperbolic geometry.)

e.g: does a theory exist if there is no mathematician to discover it? Does proof of the existence of a proof constitute proof? If there was no such thing as life, what of mathematics? Is it pre-existing without life or doe it accompany/enable it? You could consider hexagons in nature (bee hives etc..), the understanding of plant/ tree growth given by fractal geometry etc..

Hope this gives you somewhere to start

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