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Full Idea
By a 'propositional function' I mean something which contains a variable x, and expresses a proposition as soon as a value is assigned to x. That is to say, it differs from a proposition solely by the fact that it is ambiguous.
Gist of Idea
'Propositional functions' are ambiguous until the variable is given a value
Source
Bertrand Russell (The Theory of Logical Types [1910], p.216)
Book Ref
Russell,Bertrand: 'Essays in Analysis', ed/tr. Lackey,Douglas [George Braziller 1973], p.216
A Reaction
This is Frege's notion of a 'concept', as an assertion of a predicate which still lacks a subject.
Related Idea
Idea 8488 A concept is a function whose value is always a truth-value [Frege]
| 8490 | First-level functions have objects as arguments; second-level functions take functions as arguments [Frege] |
| 21566 | 'Propositional functions' are ambiguous until the variable is given a value [Russell] |
| 18961 | We can identify functions with certain sets - or identify sets with certain functions [Putnam] |
| 13812 | A 'zero-place' function just has a single value, so it is a name [Bostock] |
| 13811 | A 'total' function ranges over the whole domain, a 'partial' function over appropriate inputs [Bostock] |
| 10074 | A 'total function' maps every element to one element in another set [Smith,P] |
| 10076 | The 'range' of a function is the set of elements in the output set created by the function [Smith,P] |
| 10075 | A 'partial function' maps only some elements to another set [Smith,P] |
| 10605 | Two functions are the same if they have the same extension [Smith,P] |
| 10612 | An argument is a 'fixed point' for a function if it is mapped back to itself [Smith,P] |
| 10209 | A function is just an arbitrary correspondence between collections [Shapiro] |
| 13700 | A 'total' function must always produce an output for a given domain [Sider] |
| 15105 | F(x) walked into a bar. The barman said.. [Sommers,W] |