Does mathematics need a philosophy?
I have a great respect for this author, but I do have to note that the debate of &quot;constructivism&quot; vs. &quot;platonism&quot; doesn&#x27;t really exist in Philosophy per se, because it relies on a kind of basic misunderstanding of Plato in general. At least since Kant, the general consensus in Philosophy about Plato&#x27;s &quot;forms&quot; or ideal objects is that they are conceptual objects, famously Kant argued that while reality in-itself is inscrutable, the means of judgement whereby we organize the world into concepts (beginning with the intuitions of time and space) are not, and by analysis of judgement we can begin to better understand the process of reasoning and therefore more rigorously understand the means by which empirical judgements are made (and thus further our understanding of empirical reality).<p>Of course, many have attempted to answer the question of the psychological&#x2F;biological explanation for how humans have shared concepts like this and shared, intelligible language. The most prominent thinkers of the 20th century, on both &quot;sides&quot; if you will, were Lacan on the &quot;continental&quot; end, and Chomsky on the &quot;analytic&quot; side. (Even though most Anglo-American--i.e. Analytic--philosophers would not accept Chomsky&#x27;s logic as valid, and Lacan often referenced Anglo-American philosophy in his work...the categories are basically meaningless at this point.) But there are many other names, many people asking the above question, and I will not say who&#x27;s thought attracts me the most, but I will say that most people I meet who study math are not familiar with them or the intellectual trends they are a part of, and they do not have a rigorous enough understanding of what philosophy is, really, to make claims about the usefulness of philosophy for their work--or even debate it, for that matter.