How to interpret the same data in a completely different way. — Realism in regards to mathematical objects claims that they are abstract (i.e. non-concrete and atemporal) and objective (i.e. independent on the subjective impression of a person). There were dozens of gallons of ink spilled over the dispute about the justification for committing oneself to such abstruse objects, and a certain…

Looking for a good reason to help others. — There are at least two notions of altruism: a superficial and a profound one. Superficial altruism could be defined simply as a general willingness to assist others. It views helping people as a form of self-fulfillment. But this understanding of the term is often criticized as too short-sighted, as we…

i.e. a historical case against Platonism in philosophy of mathematics — Almost everybody, I assume, would agree that mathematics, generally understood as a set of definitions, rules and theorems, is an a priori field. Following the Kantian nomenclature, for the last two centuries there was however no consensus if it was analytic or synthetic. Frege, Russell or the Vienna Circle believed…

A brief survey of recent insights from cognitive science — In the recent “ask me anything” streaming, Noam Chomsky pointed to an interesting problem. Darwin and Wallace were very puzzled and debated the fact that all humans have arithmetical capacity. [That] it’s just a part of our nature to understand that there are infinitely many natural numbers; that when you…

The foundational crisis in mathematics along with roughly four decades following it, was likely the most fertile period in the history of logic and studies in the foundations. After discovering the set-theoretic paradoxes, such as the paradox of the set of all sets, together with the logical ones, like Russell’s…

Mathematics is often believed to bring people to madness. We hear many stories like those about Gödel, Cantor, Nash, and Grothendieck, describing geniuses haunted by insanity that is developing along with their mathematics. And there is something to it. A certain psychologist said that A paranoid person is irrationally rational…