- The famous logician Kurt Goedel left behind a formalized "proof" for the ontological argument of Anselm of Canterbury.
Anselm gave a "proof" that the term "a being than which none greater can be conceived" must refer to some existing being, i.e., that there must exist a being than which none greater can be conceived.
See the following lecture by the logician Brendel for a formalization of Goedels "proof"
http://wwwmath.uni-muenster.de/logik/Veranstaltungen/cl2010/slides/brendel.pdf
It closes with a critical assessment of what Goedel's formalization proveproves and what it does not prove.
- You may also read Gettier's presentation of the "Gettier example" in
http://www.ditext.com/gettier/gettier.html
The Gettier example is considered a counter-example against a widely hold definition of knowlegde as justified true belief. Gettier's formalization is not so extensive like Goedel's argument.