Logic is justly considered the basis of all other sciences, even if only for the reason that in every argument we employ concepts taken from the field of logic, and that ever correct inference proceeds in accordance with its laws.

However the machine would permit us to test the hypothesis for any special value of n. We could carry out such tests for a sequence of consecutive values n=2,3,.. up to, say, n=100. If the result of at least one test were negative, the hypothesis would prove to be false; otherwise our confidence in the hypothesis would increase, and we should feel encouraged to attempt establishing the hypothesis, instead of trying to construct a counterexample.

If a mathematician wishes to disparage the work of one of his colleagues, say, A, the most effective method he finds for doing this is to ask where the results can be applied. The hard pressed man, with his back against the wall, finally unearths the researches of another mathematician B as the locus of the application of his own results. If next B is plagued with a similar question, he will refer to another mathematician C. After a few steps of this kind we find ourselves referred back to the researches of A, and in this way the chain closes.

It may be unpopular and out-of-date to say-but I do not think that a scientific result which gives us a better understanding of the world and makes it more harmonious in our eyes should be held in lower esteem than, say, an invention which reduces the cost of paving roads, or improves household plumbing.

The sentence 'snow is white' is true if, and only if, snow is white.

... semantics ... is a sober and modest discipline which has no pretensions of being a universal patent-medicine for all the ills and diseases of mankind, whether imaginary or real. You will not find in semantics any remedy for decayed teeth or illusions of grandeur or class conflict. Nor is semantics a device for establishing that everyone except the speaker and his friends is speaking nonsense

There can be no doubt that the knowledge of logic is of considerable practical importance for everyone who desires to think and to infer correctly.