a-triangle
Explanation
The Joke
A math teacher begins a proof with the standard mathematical phrasing: "Suppose there exists a triangle ABC." A student immediately objects: "NO! I will not! Why do we always let mathematicians get away with this stuff?! Have any of you seen an object made of infinitely thin, perfectly straight line segments?" The student is a radical empiricist who refuses to accept abstract mathematical objects. When the teacher tries another hypothetical — "Suppose pixies exist and suppose they all own purple monkeys" — the student identifies them as "a radical empiricist" and calls to seize them. In the final panel, the student is being arrested, and the officer says "You're coming with us, pal," to which the student replies: "You can't be certain of that!"
The Humor
The comic takes the philosophical position of radical empiricism — the view that only things directly observable through experience are real — and applies it literally to a math class. Mathematics is built on abstraction and idealization; no one has ever seen a "perfect" triangle made of infinitely thin lines, yet mathematicians routinely assume such things exist for the purpose of proofs. The student's objection is philosophically consistent but practically absurd, since rejecting mathematical abstractions would make all of mathematics impossible. The final punchline — "You can't be certain of that!" — shows the student applying their radical skepticism even to their own arrest, unable to accept any claim that isn't directly empirically verified. The joke highlights the tension between philosophical rigor and practical reality.
References
Radical empiricism is a philosophical position associated with thinkers like David Hume and William James, holding that knowledge comes only from sensory experience. The comic exaggerates this position to its logical extreme. The phrase "suppose there exists" is standard mathematical language for introducing an abstract object in a proof, which a strict empiricist would indeed find objectionable since mathematical objects are not physical entities.