The Imagined Gods Objection to Pascal's Wager

Blaise Pascal’s famous Wager proposes that prudence requires belief in God. Even if the probability of God’s existence is very small, the potential payoff—eternal salvation—is infinitely large, and so outweighs any finite cost of belief. On this reasoning, to “wager for God” is rationally mandatory.

The Immolation Line: My Best Chess Composition

White to Move

Do Atheists Have Nothing to Say About Morality?

There’s a common refrain—sometimes smug, sometimes sincere—echoed in religious circles: “If you’re an atheist, you have nothing to say about morality.” Popular apologists like Frank Turek echo it; philosophers like William Lane Craig give it academic weight. The claim is simple: if you don’t believe in God, you can’t justify moral claims. But the simplicity of the claim masks a profound confusion—not just about atheism, but about morality itself.

An Introduction to Category Theory

“Category theory is the mathematics of mathematics… Whatever mathematics does for the world, category theory does for mathematics.” - Eugenia Cheng

Cleared for Mate: A Chess Composition

White to Move

The Paradoxes of Implication: Paper Tigers

The goal of logic is to formalize arguments. Arguments take the form of natural language, which subjects them to varying interpretations. On occasion, we encounter provable logical statements that are incongruous with our intuitive reasoning. The paradoxes of implication are just that — a set of provable logical statements whose conclusions do not depend on their premises [2]. These paradoxes are made possible because, in classical logic, a true statement is implied by any statement, and a false statement implies any statement. Consider the following statement. If this paper is wet and this paper is not wet, then the Moon is made out of cheese. Many observers find these statements unsettling; what does the condition of this paper tell you about the Moon? Surprisingly, this statement has a proof in classical logic. If $p$ is the statement that this paper is wet, and $q$ is the statement that the Moon is made out of cheese, then we proceed as follows: