provability

From the time GL was formulated, researchers wondered whether it was adequate for formal theories like Peano Arithmetic (PA): does GL prove everything about the notion of provability that can be expressed in a propositional modal language and can be proved in Peano Arithmetic, or should more principles be added to GL?

Provability Logic L.C. 2003

Discussions of the consequences of Gödel's incompleteness theorems sometimes involve confusion around the notion of provability, giving rise to claims that humans could beat formal systems in “knowing” theorems (see Davis (1990, 1993) for good discussions of such claims).

Provability Logic L.C. 2003

This will eventually allow Gödel to formalize the Liar paradox (with "provability" in place of "truth") by substituting into the formula which says, ˜the formula, whose code is

Kurt Gödel Kennedy, Juliette 2007

Pre-emptive use of force, the intentional targeting of suspected belligerents, not posing a direct or immediate, threat or involvement in actions that threaten [Human Life], or suspected provability of a future but in the present non-existent threat in any area were warlike or hostile conditions exist of [UN/ISAF] operations is [Forbidden].

Matthew Yglesias » What if Bernanke Isn’t Reconfirmed 2010

Authorizing a pre-emptive use of offensive force, the intentional targeting of suspected belligerents, even when such individuals do not pose a direct threat, that do not pose an immediate threat, but would pose a high provability of a future threat, not involved in belligerent actions, as long as warlike conditions exist in any areas of [UN/NATO] Alliance operations.

Matthew Yglesias » Death at Gitmo 2010

Pre-emptive use of force, the intentional targeting of suspected belligerents, not posing a direct or immediate, threat or involvement in actions that threaten [Human Life], or suspected provability of a future but in the present non-existent threat in any area were warlike or hostile conditions exist of [UN/ISAF] operations is [Forbidden].

Matthew Yglesias » Democratic Presidents’ Base Problem 2010

Upon pondering Godel, Mathematician Hofstadter stated, "truth is greater than provability".

An Argument from Realism Against Naturalism about Human Beings 2008

In your argument, you're pre-supposing that God created the universe (and therefore science), and are using the lack of dis/provability (which makes it an invalid argument, btw) to justify your own assumptions.

Ridiculous Alabama Republican Gubernatorial Candidate Believes in Science | Indecision Forever | Political Humor, 2010 Election, and Satire Blog | Comedy Central 2010

As Hofstadtter stated, truth is greater than provability.

Aiguy's Computer 2008

Upon pondering Godel, Mathematician [sic] Hofstadter stated, "truth is greater than provability".

An Argument from Realism Against Naturalism about Human Beings 2008