Willard Van Orman Quine Quotes

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.

Aristotle can be regarded as the father of logic. But his logic is too scholastic, full of subtleties, and fundamentally has not been of much value to the human understanding. It is a dialectic and an organon for the art of disputation.

As a science, logic institutes an analysis of the process of the mind in reasoning, and investigating the principles on which argumentation is conducted; as an art, it furnishes such rules as may be derived from those principles, for guarding against erroneous deductions.

Well it was not exactly a dissertation in logic, at least not the kind of logic you would find in Whitehead and Russell's Principia Mathematica for instance. It looked more like mathematics; no formalized language was used.

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

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

I am opposed to looking upon logic as a kind of game. ... One might think that it is a matter of choice or convention which logic one adopts. I disagree with this view.

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

The example of a syllogism that he had studied in Kiesewetter's logic: Caius is a man, men are mortal, therefore Caius is mortal, had throughout his whole life seemed to him right only in relation to Caius, but not to him at all.

Logic is the art of making truth prevail.

Logic is the science of the laws of thought, as thought,--that is of the necessary conditions to which thought considered in itself is a subject.

Aristotelian logic is massive and marmoreal, but every monument accumulates graffiti.

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.

Consequently he who wishes to attain to human perfection, must therefore first study Logic, next the various branches of Mathematics in their proper order, then Physics, and lastly Metaphysics.

Contrariwise, if it was so, it might be; and if it were so, it would be; but as it isn't, it ain't. That's logic.

Logic and mathematics are nothing but specialised linguistic structures.

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

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.

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

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.

Logic must look after itself. In a certain sense, we cannot make mistakes in logic.

Mathematics seems to endow one with something like a new sense.

A mathematical theorem can be true whether or not it is realized in the world.

In practical life we are compelled to follow what is most probable ; in speculative thought we are compelled to follow truth. A man would perish of hunger and thirst, if he refused to eat or drink, till he had obtained positive proof that food and drink would be good for him. But in philosophic reflection this is not so. On the contrary, we must take care not to admit as true anything, which is only probable. For when one falsity has been let in, infinite others follow.