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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. ——
--
Journal entries (12 March 1915 and 15 March 1915) p. 41e

 

Ludwig Wittgenstein

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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

 

The necessity of faith as an ingredient in our mental attitude is strongly insisted on by the scientific philosophers of the present day; but by a singularly arbitrary caprice they say that it is only legitimate when used in the interests of one particular proposition, — the proposition, namely, that the course of nature is uniform. That nature will follow to-morrow the same laws that she follows to-day is, they all admit, a truth which no man can know; but in the interests of cognition as well as of action we must postulate or assume it.

 

William James

 

If the whole of natural theology, as some people seem to maintain, resolves itself into one simple, though somewhat ambiguous, at least undefined proposition, that the cause or causes of order in the universe probably bear some remote analogy to human intelligence: If this proposition be not capable of extension, variation, or more particular explication: If it affords no inference that affects human life, or can be the source of any action or forbearance: And if the analogy, imperfect as it is, can be carried no farther than to the human intelligence, and cannot be transferred, with any appearance of probability, to the other qualities of the mind; if this really be the case, what can the most inquisitive, contemplative, and religious man do more than give a plain, philosophical assent to the proposition, as often as it occurs, and believe that the arguments on which it is established exceed the objections which lie against it?

 

David Hume

 

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

 

Memory, then, is a necessary part of the logical faculty. ... The proposition A = A must have a psychological relation to time, otherwise it would be At1 = At2.

 

Otto Weininger