Is this the basic loophole in Zeno’s paradox?

So, Zeno assumes that, to go from the mark at 1m to the mark at 2m we’ve to do an infinite number of tasks. Like the task of getting to 1.001m, the task of getting to 1.000005m,the task of getting to 1.658m,etc. So, to perform an infinite number of tasks, one must take an infinite … Read more

Is $” \sum_{n = 1}^{\infty} (-1)^n \; \text{is a real number}”$ an invalid statement or a false proposition?

So we’re beginning an introductory logic course and my professor is giving examples for valid statements/ propositions – meaningful statements that are either true or false but not both. So he puts forth this one; $$” \sum_{n = 1}^{\infty} (-1)^n \; \text{is a real number}”$$ I said it was a false proposition. My argument was … Read more

Do all mathematical and logical axiomatic systems implicitly ground natural numbers?

Maybe this question is more suitable for Philsophy SE, but I want to hear mathematicians’ opinions. Suppose that we have an axiomatic system A with axioms A1,A2,A3,…,An,… Notice that this at least implicitly grounds natural numbers, as n∈N is the only reasonable option. (Or is it? I’d love a counterexample to that, if anyone was … Read more

Is there any theorem that can only be proven using the axiom of choice and that is actually used in real-world applications?

I don’t have a strong background in mathematics but I am interested in it from a philosophical perspective and I was wondering: is there any theorem or mathematical tool that is used in real-world applications and that can only be proven or justified by assuming the axiom of choice to be true? Answer That depends … Read more

Does Mathematics exists apart from the mathematician? [closed]

Closed. This question is opinion-based. It is not currently accepting answers. Want to improve this question? Update the question so it can be answered with facts and citations by editing this post. Closed 7 years ago. Improve this question Does Mathematics exists apart from the mathematician? Explain yourself. Mathematics seems to be a projection of … Read more

Are Mathematicians Pluralists About Math?

This has been rangling around my head for awhile. With the death of Hilbert’s program via Gödel’s Incompleteness Theorems (and the prior damage done to Logicism via Russell’s Paradox), have mathematicians become pluralists, of some sort, about their discipline? In ‘Varieties of Logic’, Stewart Shapiro says, “Pluralism about a given subject, such as truth, logic, … Read more