Godel’s theorem proves arithmetic systems cannot be complete.
Evidence
Now Godel has effectively established the existence in the arithmetic system of a proposition that is neither demonstrable nor refutable within that system; this entails that the arithmetic system fails to satisfy the condition of completeness. — Jean-François Lyotard, The Postmodern Condition, 321
Categorization
- QUESTION: Lyotard’s use of Godel is controversial; is it a sound analogy or a misreading? Worth checking against a proper treatment of Godel’s theorem.
- XREF: Godel’s incompleteness as the mathematical warrant for delegitimation parallels Jameson’s claims about the loss of cognitive mapping. — connects to: In any consistent formal system within which a certain amount of arithmetic can be carried out, there are statements which can neither be proved nor disproved. — Gödel’s Incompleteness Theorems (Stanford Encyclopedia of Philosophy); Any sufficiently powerful mathematical system must contain true statements that cannot be proven within that system. — Gödel’s incompleteness theorems; There will always be true mathematical statements that cannot be proved from any finite set of axioms. — What Do Gödel’s Incompleteness Theorems Truly Mean? (+1 more)