“A theorem is a proposition which is a strict logical consequence of certain definitions and other propositions”

— Anatol Rapoport

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

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "A theorem is a proposition which is a strict logical consequence of certain definitions and other propositions" by Anatol Rapoport?

Anatol Rapoport 45

Russian-born American mathematical psychologist 1911–2007

Rudolf Carnap (1891–1970) German philosopher

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

“There are numerous theorems in economics that rely upon mathematically fallacious propositions.”

Steve Keen (1953) Australian economist

Source: Debunking Economics - The Naked Emperor Of The Social Sciences (2001), Chapter 12, Don't Shoot Me, I'm Only The Piano, p. 259

“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 book Language, Truth, and Logic

Source: Language, Truth, and Logic (1936), p. 20.

“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.”

Carl Friedrich Gauss (1777–1855) German mathematician and physical scientist

A reply to Olbers' 1816 attempt to entice him to work on Fermat's Theorem. As quoted in The World of Mathematics (1956) Edited by J. R. Newman

“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

“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.

“[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)

“A tautology's truth is certain, a proposition's possible, a contradiction's impossible.”

Ludwig Wittgenstein book Tractatus Logico-Philosophicus

Certain, possible, impossible: here we have the first indication of the scale that we need in the theory of probability.
4.464
Original German: Die Wahrheit der Tautologie ist gewiss, des Satzes möglich, der Kontradiktion unmöglich
Source: 1920s, Tractatus Logico-Philosophicus (1922)

“An argument is a connected series of statements intended to establish a definite proposition… A contradiction is just the automatic gainsaying of anything the other person says."

No, it's not…”

Graham Chapman (1941–1989) English comedian, writer and actor

“A physical theory, like an abstract science, consists of definitions and axioms as first principles, and of propositions, their consequences; but with these differences:—first, That in an abstract science, a definition assigns a name to a class of notions derived originally from observation, but not necessarily corresponding to any existing objects of real phenomena, and an axiom states a mutual relation amongst such notions, or the names denoting them; while in a physical science, a definition states properties common to a class of existing objects, or real phenomena, and a physical axiom states a general law as to the relations of phenomena; and, secondly,—That in an abstract science, the propositions first discovered are the most simple; whilst in a physical theory, the propositions first discovered are in general numerous and complex, being formal laws, the immediate results of observation and experiment, from which the definitions and axioms are subsequently arrived at by a process of reasoning differing from that whereby one proposition is deduced from another in an abstract science, partly in being more complex and difficult, and partly in being to a certain extent tentative, that is to say, involving the trial of conjectural principles, and their acceptance or rejection according as their consequences are found to agree or disagree with the formal laws deduced immediately from observation and experiment.”

William John Macquorn Rankine (1820–1872) civil engineer

Source: "Outlines of the Science of Energetics," (1855), p. 121; Second paragraph

“A theorem is a proposition which is a strict logical consequence of certain definitions and other propositions”

Help us to complete the source, original and additional information

Anatol Rapoport 45

Related quotes

Related topics