Alan Turing Quotes

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

If logic itself is created rather than being inborn, it follows that the first task of education is to form reasoning.

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

The knowledge of the theory of logic has no tendency whatever to make men good reasoners.

Logic obviously is important. You need to be able to figure things out, to go to the end of a particular problem. But intuition is very important because it references things that logic alone cannot.

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

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

Logic can become enormously difficult, and it would undoubtedly be well to produce more assurance in its use.

What I knew was I liked math and science, and I never wanted to memorize everything. I wanted to understand where it came from.

It is by logic we prove. It is by intuition we discover.

Show Holmes a drop of water and he would deduce the existence of the Atlantic. Show it to me and I would look for a tap. That was the difference between us.

The concept of logical thinking is selection and this is brought about by the processes of acceptance and rejection. Rejection is the basis of logical thinking.

Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity. The activity of the intuition consists in making spontaneous judgements which are not the result of conscious trains of reasoning. The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings.

Mathematics is not just a language. Mathematics is a language plus reasoning.

My favourite subjects at school were algebra and logic: making a big problem into something small.

Logic teaches rules for presentation, not thinking.

We may either proceed from principles to facts, or recede from facts to principles.

Bad reasoning as well as good reasoning is possible; and this fact is the foundation of the practical side of logic.

I like solving problems, and science provides a logical way of solving real-life problems.

Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity.

Logic takes care of itself; all we have to do is to look and see how it does it.

Logic is not a body of doctrine, but a mirror-image of the world. Logic is transcendental.

You should carefully study the Art of Reasoning, as it is what most people are very deficient in, and I know few things more disagreeable than to argue, or even converse with a man who has no idea of inductive and deductive philosophy.

I'm not a great student, so I don't know that I would have been a great detective. Part of my brain sort of works that way, like wanting to figure out puzzles and figure out what happened and why people do the things they do and who they are and how it happened.

The main functions of intelligence, that of inventing solutions and that of verifying them, do not necessarily involve one another. The first partakes of imagination; the second alone is properly logical.