Axiomatics Quotes

“Instead of proving all possible theorems in an axiomatic system (which Kurt Gödel showed is not possible), professional mathematicians continue to use a formal presentation of mathematics to specify and prove many theorems that are amenable to the formalist paradigm. This has generated a vast corpus of formal theory.
Controversies continue unresolved. Some mathematicians continue to insist on giving explicit constructions of mathematical entities, and do not allow proof by contradiction. This is a valid approach in its own right with much to recommend it. In the end, however, the choice that is likely to lead to the greater conquests is the one that offers the greater power and at the moment, it is David Hilbert's formalism that continues to predominate, while steadily being expanded as mathematics expands."

-David Tall (2013, p. 246) thinks though Formalism (mathematics) may have Lost the Battle it Still may Win the War.”
― David Tall, How Humans Learn to Think Mathematically: Exploring The Three Worlds Of Mathematics

“If you understand McCarthy's eval, you understand more than just a stage in the history of languages. These ideas are still the semantic core of Lisp today. So studying McCarthy's original paper shows us, in a sense, what Lisp really is. It's not something that McCarthy designed so much as something he discovered. It's not intrinsically a language for AI or for rapid prototyping, or any other task at that level. It's what you get (or one thing you get) when you try to axiomatize computation.”
― Paul Graham

“You may think God's solution to sin is axiomatic, but if you practice sin you only force others around you into wanting more evidence because your evidence is just words and not evidence of a changed life”
― John M Sheehan