Pure Logic Could Never Lead

Tolstoi Explains Somewhere In His Writings Why, In His Opinion, “science For Science's Sake” Is An Absurd Conception. We Cannot Know All The Facts, Since They Are Practically Infinite In Number. We Must Make A Selection. Is It Not Better To Be Guided By Utility, By Our Practical, And More Especially Our Moral, Necessities?

Thought Must Never Submit, Neither To A Dogma, Nor To A Party, Nor To A Passion, Nor To An Interest, Nor To A Preconceived Idea, Nor To Whatever It May Be, Save To The Facts Themselves, Because, For Thought, Submission Would Mean Ceasing To Be.

I Then Began To Study Arithmetical Questions Without Any Great Apparent Result, And Without Suspecting That They Could Have The Least Connexion With My Previous Researches. Disgusted At My Want Of Success, I Went Away To Spend A Few Days At The Seaside, And Thought Of Entirely Different Things. One Day, As I Was Walking On The Cliff, The Idea Came To Me, Again With The Same Characteristics Of Conciseness, Suddenness, And Immediate Certainty, That Arithmetical Transformations Of Indefinite Ternary Quadratic Forms Are Identical With Those Of Non-euclidian Geometry.

How Is Error Possible In Mathematics?

Mathematics Is The Art Of Giving The Same Name To Different Things.