Diagonal arguments are typically arguments that place limitations on the extent that a set can “talk about” attributes of elements of . They are related to the paradoxes of old (e.g., the liar paradox, Russell's paradox) that typically involve some degree of self-reference.
Traditional “diagonal arguments” enter the proofs of, for example,
but also the traditional construction of a
due to Haskell Curry.
As explained by Yanofsky (after Lawvere), each of these diagonal arguments can be viewed as instances of the
which places limitations on how a set can self-describe -valued attributes of (a set ) via a function , or via a function . The name comes from a construction that involves the diagonal map .
Cantor used a diagonal argument to show that for the first time here:
But he was anticipated by
Lawvere’s seminal ideas occurred in
For a leisurely account see the discussion in
A discussion of logic and rigor using Lawvere’s ideas about the diagonal argument and Godel theorem
A nice overview is
The necessary assumptions for Lawvere’s account are reduced in various ways in
Last revised on October 7, 2024 at 11:33:41. See the history of this page for a list of all contributions to it.