Logical Necessity Quotes

A tautology's truth is certain, a proposition's possible, a contradiction's impossible.

Everything necessarily is or is not, and will be or will not be; but one cannot divide and say that one or the other is necessary.I mean, for example: it is necessary for there to be or not to be a sea-battle tomorrow; but it is not necessary for a sea-battle to take place tomorrow, or for one not to take place--though it is necessary for one to take place or not to take place.

I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect.

To say that an idea is necessary is simply to affirm that we cannot conceive the contrary; and the fact that we cannot conceive the contrary of any belief may be a presumption, but is certainly no proof, of its truth.

Certainly nothing is unnatural that is not physically impossible.

Philip Kitcher thinks that mathematics is surprisingly like empirical science. Few mathematicians would agree; philosophers too, from Socrates on, have held the opposite opinion.

Algebra reverses the relative importance of the factors in ordinary language. It is essentially a written language, and it endeavors to exemplify in its written structures the patterns which it is its purpose to convey. The pattern of the marks on paper is a particular instance of the pattern to be conveyed to thought. The algebraic method is our best approach to the expression of necessity, by reason of its reduction of accident to the ghostlike character of the real variable.

Around the time of the Terran Caesar Augustus, a Martian artist had been composing a work of art. It could have been called a poem, a musical opus, or a philosophical treatise; it was a series of emotions arranged in tragic, logical necessity. Since it could be experienced by a human only in the sense in which a man blind from birth might have a sunset explained to him, it does not matter which category it be assigned.

Propositions show what they say: tautologies and contradictions show that they say nothing.

The principles of logic and mathematics are true simply because we never allow them to be anything else. And the reason for this is that we cannot abandon them without contradicting ourselves, without sinning against the rules which govern the use of language, and so making our utterances self-stultifying. In other words, the truths of logic and mathematics are analytic propositions or tautologies.

The picture which the philosopher draws of the world is surely not one in which every stroke is necessitated by pure logic.

I think the most important work that is going on has to do with the search for very general and abstract features of what is sometimes called universal grammar: general properties of language that reflect a kind of biological necessity rather than logical necessity; that is, properties of language that are not logically necessary for such a system but which are essential invariant properties of human language and are known without learning. We know these properties but we don't learn them. We simply use our knowledge of these properties as the basis for learning.