Alonzo Church Quotes

When I dealt with set theory, I could never make it be the music that I wanted.

Formal logic is mathematics, and there are philosophers like Wittgenstein that are very mathematical, but what they're really doing is mathematics - it's not talking about things that have affected computer science; it's mathematical logic.

Mathematics, in its widest significance, is the development of all types of formal, necessary, deductive reasoning.

Logic and mathematics are nothing but specialised linguistic structures.

I think part of the appeal of mathematical logic is that the formulas look mysterious - You write backward Es!

I have in later years taken to Euclid, Whitehead, Bertrand Russell, in an elemental way.

if you do not appreciate the mathematics, you cannot see, among the great variety of facts, that logic permits you to go from one to the other

An ounce of algebra is worth of a ton of verbal argument.

The one [the logician] studies the science of drawing conclusions, the other [the mathematician] the science which draws necessary conclusions.

Logic is an old subject, and since 1879 it has been a great one.

Mathematics is a language plus reasoning. It's like a language plus logic. Mathematics is a tool for reasoning.

For hundreds of pages the closely-reasoned arguments unroll, axioms and theorems interlock. And what remains with us in the end? A general sense that the world can be expressed in closely-reasoned arguments, in interlocking axioms and theorems.

Logic, n. The art of thinking and reasoning in strict accordance with the limitations and incapacities of the human misunderstanding. The basic of logic is the syllogism, consisting of a major and a minor premise and a conclusion - thus: Major Premise: Sixty men can do a piece of work sixty times as quickly as one man. Minor Premise: One man can dig a post-hole in sixty seconds; Therefore- Conclusion: Sixty men can dig a post-hole in one second. This may be called syllogism arithmetical, in which, by combining logic and mathematics, we obtain a double certainty and are twice blessed.

I am not a mathematician, but I was aware that for centuries, mathematics was considered the queen of the sciences because it claimed certainty. It was grounded on some fundamental certainties - axioms - that led to others.

Here at Wisconsin we didn't get an undergraduate course in mathematical logic until the '60s.

I was a mathematics major and really into math.

I have hardly ever known a mathematician who was capable of reasoning.

I like - I love calculus. I love linear algebra, probability and statistics, that kind of stuff. I just really like that.

Mathematics is a logical method. . . . Mathematical propositions express no thoughts. In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics.

SYLLOGISM, n. A logical formula consisting of a major and a minor assumption and an inconsequent.

One can't proceed from the informal to the formal by formal means.

The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists of the analysis of Symbolic Logic itself.

Mathematical proofs, like diamonds, are hard and clear, and will be touched with nothing but strict reasoning.

Mathematics and logic have been proved to be one; a fact from which it seems to follow that mathematics may successfully deal with non-quantitative problems in a much broader sense than was suspected to be possible.

Mathematical reasoning may be regarded.