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Propositions are truth-functions of elementary propositions. (An elementary proposition is a truth-function of itself.) (5)

 

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

 

If I cannot say a priori what elementary propositions there are, then the attempt to do so must lead to obvious nonsense. (5.5571)

 

Ludwig Wittgenstein

 

Pure Mathematics is the class of all propositions of the form “p implies q,” where p and q are propositions containing one or more variables, the same in the two propositions, and neither p nor q contains any constants except logical constants. And logical constants are all notions definable in terms of the following: Implication, the relation of a term to a class of which it is a member, the notion of such that, the notion of relation, and such further notions as may be involved in the general notion of propositions of the above form. In addition to these, mathematics uses a notion which is not a constituent of the propositions which it considers, namely the notion of truth.

 

Bertrand Russell

 

Some philosophers fail to distinguish propositions from judgements; ... But in the real world it is more important that a proposition be interesting than that it be true. The importance of truth is that it adds to interest.

 

Alfred North Whitehead

 

You need the "is of identity" to describe conspiracy theories. Korzybski would say that proves that illusions, delusions, and "mental" illnesses require the "is" to perpetuate them. (He often said, "Isness is an illness.")
Korzybski also popularized the idea that most sentences, especially the sentences that people quarrel over or even go to war over, do not rank as propositions in the logical sense, but belong to the category that Bertrand Russell called propositional functions. They do not have one meaning, as a proposition in logic should have; they have several meanings, like an algebraic function.

 

Robert Anton Wilson