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To say that Godel's proof is essentially Anselm's is somewhat shortsighted. Godel used not only modern notation, but also modal logic (which would not exist unt

by dvt 12y ago

To say that Godel's proof is essentially Anselm's is somewhat shortsighted. Godel used not only modern notation, but also modal logic (which would not exist until the mid-20th century) to prove the necessary existence of God. My biggest point of contention with your claim is that Anselm didn't make a contingent/necessary distinction. Instead, he was caught up in a muddled "exists in understanding/exists in reality" distinction which is decidedly not an analogue of the former. To go a step further, Anselm merely assumed the possibility of God, whereas Godel actually proved it.

lisper 12y ago
> Godel used not only modern notation, but also modal logic (which would not exist until the mid-20th century) Formal modal logic wasn't invented until the 20th century, but Anselm is using modal logic nonetheless. A modal logic is simply a logic that allows operators to be applied to propositions. Necessary-truth and possible-truth are only two possible operators. "Knows" and "believes" are two other classic examples. Anselm's logic uses the operators "actual-truth" and "conceptual-truth". All these proofs have essentially the same structure whether the operators are actual/conceptual or necessary/possible. You could even render the same proof in the modal logic of knowledge and belief. In fact, modern evangelicals often do this. The result renders as something like, "Look at all the martyrs who died. No one makes that kind of sacrifice for false beliefs, therefore their beliefs must be true."
- dvt 12y ago
  Even though you are correct and logicians like Avicenna and Peter of Spain wrote in gory detail about (what we take to be) Medieval Modality[1], this does not make Medieval Logic even remotely as rigorous as its modern incarnation. The issue here is about having a sound, consistent, and complete logic. S5[2] (what Godel used) has those properties, whereas Anselm didn't even have the notion of soundness or completeness, let alone a logical system that would satisfy them. [1] http://plato.stanford.edu/entries/modality-medieval/ http://plato.stanford.edu/entries/modality-medieval/ [2] http://en.wikipedia.org/wiki/S5_%28modal_logic%29 http://en.wikipedia.org/wiki/S5_%28modal_logic%29
  - lisper 12y ago
    Very well, I concede the point.

by dvt 12y ago

lisper 12y ago

> Godel used not only modern notation, but also modal logic (which would not exist until the mid-20th century) Formal modal logic wasn't invented until the 20th century, but Anselm is using modal logic nonetheless. A modal logic is simply a logic that allows operators to be applied to propositions. Necessary-truth and possible-truth are only two possible operators. "Knows" and "believes" are two other classic examples. Anselm's logic uses the operators "actual-truth" and "conceptual-truth". All these proofs have essentially the same structure whether the operators are actual/conceptual or necessary/possible. You could even render the same proof in the modal logic of knowledge and belief. In fact, modern evangelicals often do this. The result renders as something like, "Look at all the martyrs who died. No one makes that kind of sacrifice for false beliefs, therefore their beliefs must be true."

dvt 12y ago
Even though you are correct and logicians like Avicenna and Peter of Spain wrote in gory detail about (what we take to be) Medieval Modality[1], this does not make Medieval Logic even remotely as rigorous as its modern incarnation. The issue here is about having a sound, consistent, and complete logic. S5[2] (what Godel used) has those properties, whereas Anselm didn't even have the notion of soundness or completeness, let alone a logical system that would satisfy them. [1] http://plato.stanford.edu/entries/modality-medieval/ http://plato.stanford.edu/entries/modality-medieval/ [2] http://en.wikipedia.org/wiki/S5_%28modal_logic%29 http://en.wikipedia.org/wiki/S5_%28modal_logic%29
- lisper 12y ago
  Very well, I concede the point.