more from this thinker
|
more from this text
Single Idea 10612
[filed under theme 5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
]
Full Idea
If a function f maps the argument a back to a itself, so that f(a) = a, then a is said to be a 'fixed point' for f.
Gist of Idea
An argument is a 'fixed point' for a function if it is mapped back to itself
Source
Peter Smith (Intro to Gödel's Theorems [2007], 20.5)
Book Ref
Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.174
The
13 ideas
with the same theme
[elements in logical systems to create new objects]:
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]
|