G�del's incompleteness theorems are two fundamental theorems of mathematical logic which state inherent limitations of sufficiently powerful axiomatic systems for mathematics.
22.
It's certainly possible to construct axiomatic systems with infinitely many axioms . talk ) 14 : 33, 14 August 2013 ( UTC)
23.
The last paragraph, however, I have to say seems to be confusing the issue between consistency and truth of an axiomatic system.
24.
An " interpretation " of an axiomatic system is some particular way of giving concrete meaning to the primitives of that system.
25.
Someone could very strongly prove the inconsistency of an axiomatic system, and that would kind of be the'last word'on that system, no?
26.
That might be true for a real set of axioms, but not everything that is labelled that way is an axiomatic system.
27.
This is an axiomatic system that uses formal logic to describe the relationship between parts and wholes, and between parts within a whole.
28.
To doubt the LoEM when extended over the completed infinite was to doubt Hilbert's axiomatic system, in particular his " logical ?-axiom ".
29.
You can't count within an axiomatic system; you can only prove things . " True in the system " also doesn't make sense.
30.
A natural axiomatic system for them might look very strange to us . talk ) 15 : 09, 15 October 2011 ( UTC)
