Has philosophy ever clarified mathematics?
I've recently been reading some standard textbooks on the philosophy of mathematics, and I've become quite frustrated that (surely due to my own limitations) I don't seem to be gleaning any...
View ArticleAnswer by abx for Has philosophy ever clarified mathematics?
From this article in Wikipedia : "La Géométrie was published in 1637 as an appendix to Discours de la méthode (Discourse on Method), written by René Descartes. In the Discourse, he presents his method...
View ArticleAnswer by Joel David Hamkins for Has philosophy ever clarified mathematics?
I find the case of Alan Turing's development of the concept of computatibility to be an example. Before Turing, the logicians had no clear concept of what it means to say that a function is computable....
View ArticleAnswer by djechlin for Has philosophy ever clarified mathematics?
Two points: one, firstly understanding mathematical processes can be of immense pedagogical value. See e.g. Polya's How to Solve It (and he wrote a more academic book with these themes), or...
View ArticleAnswer by Liviu Nicolaescu for Has philosophy ever clarified mathematics?
I am very skeptical of a philosopher talking about Math, given the unavoidable interpretative elasticity of the philosophical discourse and the blunders of some of its practitioners. (Hegel's name...
View ArticleAnswer by Walter Mitty for Has philosophy ever clarified mathematics?
There is a book that gained a cult following in the 1970s, and this book lies at the intersection of philosophy and mathematics. It's Laws of Form by G Spencer Brown. Few serious mathematicians have...
View ArticleAnswer by Waldemar for Has philosophy ever clarified mathematics?
George Berkeley’s „The Analyst” is an example. Berkeley was a philosopher. He had a philosophical motivation. He attacked a mathematical concept of “Infinitesimals”. He clarified that an original...
View ArticleAnswer by Timothy Chow for Has philosophy ever clarified mathematics?
In order to address this question, I think it is important to first take a step back and examine with a critical eye something that we normally take for granted, namely the professionalization and...
View ArticleAnswer by R Hahn for Has philosophy ever clarified mathematics?
Turing has already been mentioned in previous excellent answers as someone whose ideas sit at the boundary of philosophy and mathematics, conventionally understood. I want to mention Ludwig...
View ArticleAnswer by Avshalom for Has philosophy ever clarified mathematics?
Perhaps it has been cited elsewhere in this context, but Hilary Putnam's 1980 short essay "Models and reality" brings together mathematics and philosophy in its discussion of $V = L$ and the...
View ArticleAnswer by Gerhard Paseman for Has philosophy ever clarified mathematics?
I paraphrase with italics from the original post to give my perspective:My naïve expectation would be that metamathematicians * might take a difficult construction or proof, and clarify it by isolating...
View ArticleAnswer by Lennart Meier for Has philosophy ever clarified mathematics?
As already remarked by others: If one tries a narrow interpretation of your question, you are asking a lot. You want someone whose specialty is not mathematics to elucidate a mathematical argument in a...
View ArticleAnswer by user58926 for Has philosophy ever clarified mathematics?
To add to the discussion: the very dichotomy Philosophy x Mathematics didn't make sense to most thinkers of the past. That still holds true for many of today's philosophers - Philosophy is not a...
View ArticleAnswer by Marcin for Has philosophy ever clarified mathematics?
Would you expect to learn much about how to practice science (or any sub-branch thereof) from the philosophy of science? I hope the answer would be no; that falls within the study of science.The...
View ArticleAnswer by Ben McKay for Has philosophy ever clarified mathematics?
Ludwig Wittgenstein invented the truth table, in trying to clarify the structure of propositional logic. Of course, this is now a standard tool in mathematics and computer science. Wittgenstein was...
View ArticleAnswer by Colin for Has philosophy ever clarified mathematics?
Lawvere has evidently applied a philosophical outlook to some effect in his mathematics.This answer by Urs Schreiber on philosophy stack exchange gets at this and...
View ArticleAnswer by Sean for Has philosophy ever clarified mathematics?
I'm not sure that some people would agree... but Popper's work on provability has clarified how things should work in "classical" statistics, that we can only prove something is wrong not that it is...
View ArticleAnswer by Noam Zeilberger for Has philosophy ever clarified mathematics?
Per Martin-Löf has done work spanning mathematics, logic, and philosophy. I am not sure how much his early work on randomness was influenced by philosophical concerns, but his work on type theory in...
View ArticleAnswer by Thomas Klimpel for Has philosophy ever clarified mathematics?
Just like René Descartes'La Géométrie from Discours de la méthode (1637) might have had a profound influence on mathematics, also Immanuel Kant's Transzendentale Ästhetik from Kritik der reinen...
View ArticleAnswer by AlainD for Has philosophy ever clarified mathematics?
Logic (and formal systems) is a contribution of philosophy.The point is that up to recent times (~1800), mathematics was a discipline of philosophy, just as music was a discipline of mathematics at the...
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