“After defining semantical concepts like logical truth and related ones, I proposed to interpret the modalities as those properties of propositions which correspond to certain semantical properties of the sentences expressing the propositions. For example, a proposition is logically necessary if and only if a sentence expressing it is logically true.”

— Rudolf Carnap

Source: Carnap’s intellectual biography (1963), p. 62

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Rudolf Carnap 21

German philosopher 1891–1970

Anatol Rapoport (1911–2007) Russian-born American mathematical psychologist

Anatol Rapoport. " Various meanings of “theory”." http://www.acsu.buffalo.edu/~fczagare/PSC%20504/Rapoport%20(1958).pdf American Political Science Review 52.04 (1958): 972-988.
1950s

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

Principles of Mathematics (1903), Ch. I: Definition of Pure Mathematics, p. 3
1900s

“Logic is not concerned with human behavior in the same sense that physiology, psychology, and social sciences are concerned with it. These sciences formulate laws or universal statements which have as their subject matter human activities as processes in time. Logic, on the contrary, is concerned with relations between factual sentences (or thoughts). If logic ever discusses the truth of factual sentences it does so only conditionally, somewhat as follows: if such-and-such a sentence is true, then such-and-such another sentence is true. Logic itself does not decide whether the first sentence is true, but surrenders that question to one or the other of the empirical sciences.”

Rudolf Carnap (1891–1970) German philosopher

Rudolf Carnap (1937) cited in: Irving J. Lee (1967) The Language of Wisdom and Folly: Background Readings in Semantics. International Society for General Semantics, p. 44

“A classical concept in Hinduism has been that a true proposition has to be consistent with sruti, yukti (reason/logic) and anubhava.”

Rajiv Malhotra book Indra's Net

Source: Indra's Net (2014)

“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 book Sex and Character

Source: Sex and Character (1903), p. 148.

“A proposition is completely logically analyzed if its grammar is made completely clear: no matter what idiom it may be written or expressed in…”

Ludwig Wittgenstein (1889–1951) Austrian-British philosopher

Philosophical Remarks (1930), Part I (1)
1930s-1951

“Because of the "all-or-none" character of nervous activity, events and the relations among them can be treated by means of propositional logic. It is found that the behaviour of every net can be described in these terms, with the addition of more complicated logical means for nets containing cycles; and that for any logical expression satisfying certain conditions, one can find in net behaving ever fashion it describes.”

Warren S. McCulloch (1898–1969) American neuroscientist

Source: A logical calculus of the ideas immanent in nervous activity (1943), p. 115

“The assimilation of tautologies and contradictions with true and false propositions respectively results from the fact that tautologies and contradictions can be taken as truth-functions just like ordinary propositions, and for determining the truth of falsity of the truth-function, tautologies and contradictions among its arguments must be counted as true or false respectively. …Are the propositions of symbolic logic and mathematics tautologies in Mr Wittgenstein's sense?”

Frank P. Ramsey (1903–1930) British mathematician, philosopher

The Foundations of Mathematics (1925)

“From semantics to shipbuilding, from dream theory to propositional logic, any specialist … is invariably astonished to discover that modern knowledge was foreshadowed at the time. … Should we not replace these foreshadowings by the study of the influences of Hellenistic thought on modern thought?”

Lucio Russo (1944) Italian historian and scientist

7.6, "The Figurative Arts, Literature and Music", p. 228
The Forgotten Revolution: How Science Was Born in 300 BC and Why It Had to Be Reborn (2004)

“I cannot get from the nature of the proposition to the individual logical operations!!!”

Ludwig Wittgenstein (1889–1951) Austrian-British philosopher

Journal entries (12 March 1915 and 15 March 1915) p. 41e
1910s, Notebooks 1914-1916
Context: 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.

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Rudolf Carnap 21

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