Life is hard
Life is a riddle the answer to which is ineffable.
There is an abyss as unfathomable as the heights of faith and joy.
Love is the answer but one that we have to believe in. Without this faith it’s useless. But if we believe, we will die, we will…
And we’ve killed it.
In an airplane interview released in 2009, Bobby Fischer, arguably the most talented chess player of all time, exclaimed
I hate chess!
He argued that the game is irredeemably broken due to the influence of engines. The reason for this is that now, less and less depends on originality, creativity…
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…
Canadian mathematician Simon Kochen recalled in his tribute to Kurt Gödel how during his PhD exam, he was asked to name five of Gödel’s theorems. The essence of the question was that each of the theorems either gave birth to a new branch of, or revolutionized, modern mathematical logic. “Proof…
On August 2. 2020 Cantor’s Paradise published Bruno Campello’s brief critique of Cantor’s approach in transfinite mathematics. The author raises some doubts about Cantor’s debunking Euclid’s 5th principle stating that the whole is greater than the part. Campello gives an interesting argument against Cantor’s reasoning, but it itself raises a…
