Science
[is] knowledge of the truth of **Propositions** and how things are
called.

— 1650 Human Nature, ch.6.

Closely related to the problem of the parallel postulate is the problem of whether physical space is infinite. Euclid assumes in Postulate 2 that a straight-line segment can be extended as far as necessary; he uses this fact, but only to find a larger finite length for example in Book I, **Propositions** 11, 16, and 20. For these proofs Heron gave new proofs that avoided extending the lines, in order to meet the objection of anyone who would deny that the space was available for the extension.

— Morris Kline,

**Propositions** show what they say: tautologies and contradictions show that they say nothing.

— Ludwig Wittgenstein, in Joachim Schulte

The central **Propositions** [of Descartes]?are these: There is a path
that leads to the truth so surely that any one who will follow
it must needs reach the goal? And there is one
guiding rule by which a man mayalways find this path?give
unqualified assent to no **Propositions** but those the truth
of which is so clear and distinct that they cannot be
doubted.

— 1870 Lay Sermons, Addresses, and Reviews.

The principles of logic and mathematics are true simply because we never allow them to be anything else. And the reason for this is that we cannot abandon them without contradicting ourselves, without sinning against the rules which govern the use of language, and so making our utterances self-stultifying. In other words, the truths of logic and mathematics are analytic **Propositions** or tautologies.

— p. 77 (Language, Truth, and Logic (1936))

No doubt, there are those who believe that judges-and particularly dissenting judges-write to hear themselves say, as it were, I I I. And no doubt, there are also those who believe that judges are, like Joan Didion, primarily engaged in the writing of fiction. I cannot agree with either of those **Propositions**.

—

The cabinet has no **Propositions** to make, but orders to give.

—

— in

I confess that Fermat's Theorem as an isolated proposition has very little interest for me, because I could easily lay down a multitude of such **Propositions**, which one could neither prove nor dispose of.

— A reply to Olbers' 1816 attempt to entice him to work on Fermat's Theorem. As quoted in

A great part of its theories derives an additional charm from the peculiarity that important **Propositions**, with the impress of simplicity on them, are often easily discovered by induction, and yet are of so profound a character that we cannot find the demonstrations till after many vain attempts; and even then, when we do succeed, it is often by some tedious and artificial process, while the simple methods may long remain concealed.

— On higher arithmetic.

Notwithstanding their attacks on the basic conception of rationalism, on synthetic a priori judgments, that is, material **Propositions** that cannot be contradicted by any experience, the empiricist posits the forms of being as constant.

— p. 146 ("The Latest Attack on Metaphysics" (1937))

Leibniz’s theory on the subject as substantia ideans in the sense of a causative agent of decision and acts stands much closer to a materialist interpretation of history than does a philosophy which reduces the thinking subject to the role of subsuming protocol sentences under general **Propositions** and deducing other sentences from them.

— p. 149 ("The Latest Attack on Metaphysics" (1937))

Wherever Mathematics is mixed up with anything, which is outside its field, you will find attempts to demonstrate these merely conventional **Propositions** a priori, and it will be your task to find out the false deduction in each case.

—

The progressive historical role of capitalism may be summed up in two brief **Propositions**: increase in the productive forces of social labour, and the socialisation of that labour. But both these facts manifest themselves in extremely diverse processes in different branches of the national economy.

— Lenin, Vladimir Ilich, "The Development of Capitalism in Russia, “The Mission of Capitalism” (1899)", Marxists .

Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity . The activity of the intuition consists in making spontaneous judgements which are not the result of conscious trains of reasoning... The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of **Propositions**, and perhaps geometrical figures or drawings.

— "Systems of Logic Based on Ordinals," section 11: The purpose of ordinal logics (1938), published in

In a footnote to the first sentence, Turing added: "We are leaving out of account that most important faculty which distinguishes topics of interest from others; in fact, we are regarding the function of the mathematician as simply to determine the truth or falsity of propositions."

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.

— p. 259

Variant : It is more important that a proposition be interesting than that it be true. This statement is almost a tautology. For the energy of operation of a proposition in an occassion of experience is its interest, and its importance. But of course a true proposition is more apt to be interesting than a false one.As extended upon in

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.

— Language as Conspiracy, p. 277

There are numerous theorems in economics that rely upon mathematically fallacious **Propositions**.

— Chapter 12, Don't Shoot Me, I'm Only The Piano, p. 259

No doubt, there are those who believe that judges-and particularly dissenting judges-write to hear themselves say, as it were, I I I. And no doubt, there are also those who believe that judges are, like Joan Didion, primarily engaged in the writing of fiction. I cannot agree with either of those **Propositions**.

— William J. Brennan, Jr.,

Intuitive cognition is such that when some things are cognized, of which one inheres in the other, or one is spatially distant from the other, or exists in some relation to the other, immediately in virtue of that non-propositional cognition of those things, it is known if the thing inheres or does not inhere, if it is spatially distant or not, and the same for other true contingent **Propositions**, unless that cognition is flawed or there is some impediment.

—

No doubt, there are those who believe that judges-and particularly dissenting judges-write to hear themselves say, as it were, I I I. And no doubt, there are also those who believe that judges are, like Joan Didion, primarily engaged in the writing of fiction. I cannot agree with either of those **Propositions**.

—

The treatises are, without exception, monuments of mathematical exposition; the gradual revelation of the plan of attack, the masterly ordering of the **Propositions**, the stern elimination of everything not immediately relevant to the purpose , the finish of the whole, are so impressive in their perfection as to create a feeling akin to awe in the mind of the reader.

— T. L. Heath,

Comparatively few of the **Propositions** and proofs in the Elements are his [Euclid's] own discoveries. In fact, the proof of the "Theorem of Pythagoras" is the only one directly ascribed to him.

— Florian Cajori,