I am allowed to use plain English because everybody knows that I could use mathematical logic if I chose.
Logic must no more admit a unicorn than zoology can.
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.
The rules of logic are to mathematics what those of structure are to architecture.
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 supreme maxim in scientific philosophising is this: wherever possible, logical constructions are to be substituted for inferred entities.
A priori Logical propositions are such as can be known a priori without study of the actual world.
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".
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.
Even in the most purely logical realms, it is insight that first arrives at what is new.
Frege has the merit of ... finding a third assertion by recognising the world of logic which is neither mental nor physical.
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.
Only mathematics and mathematical logic can say as little as the physicist means to say.
All exact science is dominated by the idea of approximation.
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.