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### 5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic

#### [elements in logical systems to create new objects]

13 ideas
 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]
 10076 The 'range' of a function is the set of elements in the output set created by the function [Smith,P]
 10074 A 'total function' maps every element to one element in another set [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]