|Propositions, philosophy: propositions are defined as the meanings of sentences, whereby a sentence is interpreted as a character string, which must still be interpreted in relation to a situation or a speaker. E.g. “I am hungry” has a different meaning from the mouth of each new speaker. On the other hand, the sentence “I am hungry” from the mouth of the speaker, who first expressed the German sentence, has the same meaning as the German sentence uttered by him. See also meaning, propositional attitudes, identity conditions, opacity, utterances, sentences.|
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Proposition/Russell: is a complex entity with components: E.g. Smith is taller than Brown: Smith, Brown, the relation taller than - E.g. Brown is smaller than Smith: is therefore equivalent, but is different in all three components! - Letter to Frege: the mountain literally appears in the proposition - Cartwright: thoughts/Frege: unequal Russell’s propositions - they do not contain their objects - ((s) anywhere. ...but their sense).
Proposition/Russell/Cartwright: how can a proposition be wrong if it consists of the components and the nature of their connection? - Solution/Russell: another quality - CartwrightVs: which had already been rejected.
Proposition/Principia Mathematica/Russell: φ x (requires function) - Propositional function: φ x^ - not ambiguous - the values are all propositions of the form j x.
I.e. the symbol φ (φx^) must not express a proposition as does indeed, if a is a value for φ x^ - indeed j(jx^) must be a symbol that expresses nothing, it’s pointless - (neither true nor false) - E.g. -the function- is a human is a human.
Proposition/propositional function/Principia Mathematica/Russell: The symbol (x).j x shall always express the proposition φ x, i.e. the proposition that claims all values for φ x^.
This proposition presupposes the function j x^, not just an ambiguous value of the function - the assertion of φ x, where x is not specified, is different from that which claims all values for φ x^, because the former is an ambiguous assertion, and the latter is not ambiguous in any sense.
Proposition/Function/Extensional/Tractatus/Wittgenstein: functions of propositions are always truth functions - a function can only occur in a proposition by means of its values. (see above extensional) - consequence: all functions of functions are extensional. E.g. A believes p is not a function of p - (Tractatus 19-20) - ((s) VsRussell: (see above)> Waverley, functions equivalent, but not identical, because George IV did not want to know if Scott = Scott - ((s) being believed is not a function of the believed object) - ((s)> extrinsic properties, extrinsic) - ((s)> Function of a function of higher level).
B. Russell/A.N. Whitehead
Principia Mathematica Frankfurt 1986
Das ABC der Relativitätstheorie Frankfurt 1989
Probleme der Philosophie Frankfurt 1967
Die Philosophie des logischen Atomismus
Eigennamen, U. Wolf (Hg), Frankfurt 1993
Wahrheit und Falschheit
Wahrheitstheorien, G. Skirbekk (Hg), Frankfurt 1996