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Philosophy of mathematics asks questions about mathematical theories and practices. It can include questions about the nature or reality of numbers, the ground and limits of formal systems and the nature of the different mathematical disciplines.
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“Without the assumption of the existence of uniformities there can be no knowledge.”
So I am to discuss the question with reference to two areas of knowledge. I chose to talk about mathematics and the arts (including literature, visual arts, music, etc.).
I put a lot of thought into …
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Is Euclid's syllogistic approach to proving mathematical theorems logically insufficient?
I think that deduction used in syllogistic systems, employing axioms and hence inferential conclusions i.e. theorems is rather weak, and cannot suffice for the robustness needed for proving mathematic …