Charles Sanders Peirce quote: “To "postulate" a proposition is no more than to hope it is true.”

“Some philosophers fail to distinguish propositions from judgments; … But in the real world it is more important that a proposition be interesting than that it be true.”

Alfred North Whitehead (1861–1947) English mathematician and philosopher

Source: 1920s, Process and Reality: An Essay in Cosmology (1929), 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 occasion 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 Adventures of Ideas (1933), Pt. 4, Ch. 16.
Context: Some philosophers fail to distinguish propositions from judgments; … 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.

“[Relativist] Rel. There is a well-known proposition of Euclid which states that "Any two sides of a triangle are together greater than the third side." Can either of you tell me whether nowadays there is good reason to believe that this proposition is true?
[Pure Mathematician] Math. For my part, I am quite unable to say whether the proposition is true or not. I can deduce it by trustworthy reasoning from certain other propositions or axioms, which are supposed to be still more elementary. If these axioms are true, the proposition is true; if the axioms are not true, the proposition is not true universally. Whether the axioms are true or not I cannot say, and it is outside my province to consider.”

Arthur Stanley Eddington (1882–1944) British astrophysicist

Space, Time and Gravitation (1920)

“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.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

Recent Work on the Principles of Mathematics, published in International Monthly, Vol. 4 (1901), later published as "Mathematics and the Metaphysicians" in Mysticism and Logic and Other Essays (1917)
1900s
Context: 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. Both these points would belong to applied mathematics. We start, in pure mathematics, from certain rules of inference, by which we can infer that if one proposition is true, then so is some other proposition. These rules of inference constitute the major part of the principles of formal logic. We then take any hypothesis that seems amusing, and deduce its consequences. 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.

“When I have asked thinking men what reason they had to believe that every fact in the universe is precisely determined by law, the first answer has usually been that the proposition is a "presupposition " or postulate of scientific reasoning. Well, if that is the best that can be said for it, the belief is doomed. Suppose it be " postulated " : that does not make it true, nor so much as afford the slightest rational motive for yielding it any credence.”

Charles Sanders Peirce (1839–1914) American philosopher, logician, mathematician, and scientist

The Doctrine of Necessity Examined (1892)
Context: When I have asked thinking men what reason they had to believe that every fact in the universe is precisely determined by law, the first answer has usually been that the proposition is a "presupposition " or postulate of scientific reasoning. Well, if that is the best that can be said for it, the belief is doomed. Suppose it be " postulated " : that does not make it true, nor so much as afford the slightest rational motive for yielding it any credence. It is as if a man should come to borrow money, and when asked for his security, should reply he "postulated " the loan. To "postulate" a proposition is no more than to hope it is true. There are, indeed, practical emergencies in which we act upon assumptions of certain propositions as true, because if they are not so, it can make no difference how we act. But all such propositions I take to be hypotheses of individual facts. For it is manifest that no universal principle can in its universality be compromised in a special case or can be requisite for the validity of any ordinary inference.

“It is quite impossible for a proposition to state that it itself is true.”

Ludwig Wittgenstein (1889–1951) Austrian-British philosopher

4.442
Original German: Ein Satz kann unmöglich von sich selbst aussagen, dass er wahr ist.
1920s, Tractatus Logico-Philosophicus (1922)

“There is no hope, as far as I can see, of pushing the postulates of economic theory back to a set of irreducible axioms.”

Richard Stone (1913–1991) British economist, Nobel Memorial Prize winner

Source: The Role of Measurement in Economics. 1951, p. 15

“If we can advance any propositions that are both true and new, these are indisputably our own, by right of discovery; and if we can repeat what is old more briefly and brightly than others, this also becomes our own, by right of conquest.”

Charles Caleb Colton (1777–1832) British priest and writer

Preface
Lacon (1820)

“Let x represent an act of the mind by which we fix our regard upon that portion of time for which the proposition X is true; and let this meaning be understood when it is asserted that x denote the time for which the proposition X is true. (...) We shall term x the representative symbol of the proposition X.”

George Boole (1815–1864) English mathematician, philosopher and logician

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 165; As cited in: James Joseph Sylvester, ‎James Whitbread Lee Glaisher (1910) The Quarterly Journal of Pure and Applied Mathematics. p. 350

“From a rational standpoint, it might be expected that man should be far more willing to express financial confidence in his skills rather than risking his earnings on the mindless meanderings of chance. Experience, however, has strongly indicated the reverse proposition to hold true.”

Richard Arnold Epstein (1927) American physicist

Source: The Theory of Gambling and Statistical Logic (Revised Edition) 1977, Chapter Ten, Games Of Pure Skill And Competitive Computers, p. 337

“After that, work and hope. But never hope more than you work”

Beryl Markham book West with the Night

Source: West with the Night

“To "postulate" a proposition is no more than to hope it is true.”

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