Horwich I 54
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: are not the same as Russell’s propositions - they do not contain their objects - ((s) ."...but their sense").
Horwich I 56
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.
Horwich I 59
Proposition/Principia Mathematica
(2)/Russell: φ x (requires function) - Propositional function: φ x^ - not ambiguous - the values are all propositions of the form j x.
>
Propositional function.
Horwich I 60
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 is pointless - (neither true nor false) - E.g. -the function- is a human is a human.
>
Levels/Order.
Horwich I 60f
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^.
Horwich I 61
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.
(1)
1. R. Cartwright, „A Neglected Theory of Truth“ , Philosophical Essays, Cambridge/MA pp. 71-93 in: Paul Horwich (Ed.) Theories of Truth, Aldershot 1994
2. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press.
- - -
Russell I 125
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).
>
Truth function, >
Extension.
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 are 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).