But as the work proceeded I was continually reminded of the fable about the elephant and the tortoise. Having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortois
A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science.
All traditional logic habitually assumes that precise symbols are being employed. It is therefore not applicable to this terrestial life but only to an imagined celestial existence... logic takes us nearer to heaven than other studies.
The rules of logic are to mathematics what those of structure are to architecture.
The question of "unreality"is a very important one. Misled by grammar, the great majority of those logicians who have dealt with this question have dealt with it on mistaken lines. They have regarded grammatical form as a surer guide in analysis than, in fact, it is. And they have not known what dif
Inferences of Science and Common Sense differ from those of deductive logic and mathematics in a very important respect, namely, when the premises are true and the reasoning correct, the conclusion is only probable.
Logic must no more admit a unicorn than zoology can.
I am allowed to use plain English because everybody knows that I could use mathematical logic if I chose.
This illustrates an important truth, namely, that the worse your logic, the more interesting the consequences to which it gives rise.
The true function of logic ... as applied to matters of experience ... is analytic rather than constructive; taken a priori, it shows the possibility of hitherto unsuspected alternatives more often than the impossibility of alternatives which seemed prima facie possible. Thus, while it liberates ima
Only mathematics and mathematical logic can say as little as the physicist means to say.
The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists of the analysis of Symbolic Logic itself.
The conception of the necessary unit of all that is resolves itself into the poverty of the imagination, and a freer logic emancipates us from the straitwaistcoated benevolent institution, which idealism palms off as the totality of being.
Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say.
Analytic It is clear that the definition of "logic" or "mathematics" must be sought by trying to give a new definition of the old notion of "analytic" propositions.
Formality Thus the absence of all mention of particular things or properties in logic or pure mathematics is a necessary result of the fact that this study is, as we say, "purely formal".
I am delighted to know that Principia Mathematica can now be done by machinery. . . I am quite willing to believe that anything in deductive logic can be done by machinery.
In the first place a philosophical proposition must be general. It must not deal specially with things on the surface of the earth, or within the solar system, or with any other portion of space and time. . . . This brings us to a second characteristic of philosophical propositions, namely that they
Frege has the merit of ... finding a third assertion by recognising the world of logic which is neither mental nor physical.