John White Chadwick Quotes

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

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

Induction for deduction, with a view to construction.

Mathematicians create by acts of insights and intuition. Logic then sanctions the conquests of intuition.

Deduction, which takes us from the general proposition to facts again-teaches us, if I may so say, to anticipate from the ticket what is inside the bundle.

Even the greatest mathematicians, the ones that we would put into our mythology of great mathematicians, had to do a great deal of leg work in order to get to the solution in the end.

It is an old maxim of mine that when you have excluded the impossible, whatever remains, however improbable, must be the truth.

When I was in school, I liked math because all the problems had answers. Everything else seemed very subjective.

When you have eliminated the impossible, whatever remains, however improbable, must be the truth.

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

From a drop of water a logician could infer the possibility of an Atlantic or a Niagara without having seen or heard of one or the other.

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

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

Sometimes one must make extended conclusions from limited data.

Beginning to reason is like stepping onto an escalator that leads upward and out of sight. Once we take the first step, the distance to be traveled is independent of our will and we cannot know in advance where we shall end.

Inference is always an invasion of the unknown, a leap from the known.

Everybody who reasons carefully about anything is making a contribution ... and if you abstract it away and send it to the Department of Mathematics they put it in books.

A universe whose only claim to be believed in rests on the validity of inference must not start telling us the inference is invalid.

What is thinking? It is the activity of searching out what must be true, or cannot be true, in the light of the given facts or assumptions.

Once you've ruled out the impossible then whatever is left, however improbable, must be the truth. The problem lay in working out what was impossible, of course. That was the trick, all right. There was also the curious incident of the orangutan in the night-time.

The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience

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.

It is not really difficult to construct a series of inferences, each dependent upon its predecessor and each simple in itself. If, after doing so, one simply knocks out all the central inferences and presents one's audience with the starting-point and the conclusion, one may produce a startling, though perhaps a meretricious, effect.

The investigation of mathematical truths accustoms the mind to method and correctness in reasoning, and is an employment peculiarly worthy of rational beings.