Logical Truth Quotes

Mathematics has the completely false reputation of yielding infallible conclusions. Its infallibility is nothing but identity. Two times two is not four, but it is just two times two, and that is what we call four for short. But four is nothing new at all. And thus it goes on and on in its conclusions, except that in the higher formulas the identity fades out of sight.

A priori Logical propositions are such as can be known a priori without study of the actual world.

Truth by definition is exclusive. If truth were all-inclusive, nothing would be false.

The average IQ in America is - and this can be proven mathematically - average.

It is possible--indeed possible even according to the old conception of logic--to give in advance a description of all 'true' logical propositions. Hence there can never be surprises in logic.

There are also two kinds of truths: truth of reasoning and truths of fact.

There are also two kinds of truths: truth of reasoning and truths of fact. Truths of reasoning are necessary and their opposite is impossible; those of fact are contingent and their opposite is possible.

If pressed to supplement Tweedledee's ostensive definition of logic with a discursive definition of the same subject, I would say that logic is the systematic study of the logical truths. Pressed further, I would say that a sentence is logically true if all sentences with its grammatical structure are true. Pressed further still, I would say to read this book.

Now this principle of induction cannot be a purely logical truth like a tautology or an analytic statement. . . .

Almost all thinking people agree that you should not have probability 1 (or 0) for any event, other than one demonstrable by logic, like 2 x 2 = 4.

The fundamental laws are in the long run merely statements that every event is itself and not some different event.

The truth of a proposition has nothing to do with its credibility. And vice versa.