The above proposition is occasionally useful.

 

The above proposition is occasionally useful.
--
Comment after the proof that 1+1=2, completed in Principia Mathematica, Volume II, 1st edition (1912), page 86

 

Bertrand Russell

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To make our position clearer, we may formulate it in another way. Let us call a proposition which records an actual or possible observation an experiential proposition. Then we may say that it is the mark of a genuine factual proposition, not that it should be equivalent to an experiential proposition, or any finite number of experiential propositions, but simply that some experiential propositions can be deduced from it in conjunction with certain other premises without being deducible from those other premises alone.

 

Alfred Jules Ayer

 

Your good friends naturally bring out the best and sometimes the worst sides of you, and you go from there. I'm not a rusher. I'm horribly suspicious at first of people. It's being everyone's friend on the telly - when I meet someone they expect me to instantly be that best mate for them and occasionally you get up with a shit in your pocket and you don't want to talk to anyone. I don't mind a gab but occasionally I really am rude. And occasionally I really enjoy it.

 

Liza Tarbuck

 

I cannot get from the nature of the proposition to the individual logical operations!!!
That is, I cannot bring out how far the proposition is the picture of the situation. I am almost inclined to give up all my efforts. ——

 

Ludwig Wittgenstein

 

Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true ... If our hypothesis is about anything, and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.

 

Bertrand Russell

 

The criterion which we use to test the genuineness of apparent statements of fact is the criterion of verifiability. We say that a sentence is factually significant to any given person, if, and only if, he knows how to verify the proposition which it purports to express — that is, if he knows what observations would lead him, under certain conditions, to accept the proposition as being true, or reject it as being false.

 

Alfred Jules Ayer