attention conservation notice: Some readers may be a bit puzzled about my previous blog post, so I decided to clear up the confusion once and for all.
Anselm proposed his ontological proof in 1078 and subsequently it was criticized
and rejected e.g. by Thomas Aquinas, David Hume and Immanuel Kant. Bertrand Russell explained that "the argument does not, to a modern mind, seem very convincing, but it is easier to feel convinced that it must be fallacious than it is to find out precisely where the fallacy lies."
The reason it is so difficult to "find out precisely where the fallacy lies" is
that Anselm's argument is actually correct.
Kurt Gödel formalized the proof and in 1991 Paul Oppenheimer and Edward Zalta used Prover9 to check it. Their paper describing it in some detail is available here as pdf.
Since the paper is not exactly easy reading, I thought it would help
to post a precise natural language version [source, see section 8.5]:
1. There is (in the understanding) something than which there is no greater. (Premise)
2. (Hence) There is (in the understanding) a unique thing than which there is no greater. (From (1), assuming that the greater-than relation is connected.)
3. (Hence) There is (in the understanding) something which is the thing than which there is no greater. (From (2), by a theorem about descriptions.)
4. (Hence) There is (in the understanding) nothing which is greater than the thing than which there is no greater. (From (3), by another theorem about descriptions.)
5. If that thing than which there is no greater does not exist (in reality), then there is (in the understanding) something which is greater than that thing
than which there is no greater. (Premise)
6. (Hence) That thing than which there is no greater exists (in reality). (From (4) and (5).)
7. (Hence) God exists. (From (6).)
I assume this clears that up once and for all ...
added later: Alexander Pruss proved the existence of a 'necessary being' in modal logic. It is left as an exercise for the reader to show that the 'necessary being' can be identified with 'that thing than which there is no greater'.
12 comments:
There is (in the understanding) a prime number than which there is no greater. (Premise)
I am afraid that your premise is false.
Btw if you read the paper (p. 18) you will find that the 'greater-than' relationship can be relaxed somewhat.
These arguments only show that our world exists. The whole world is that thing than which there is no greater.
1. The understanding set has an upper bound.
2. And a least upper bound.
3. The LUB is a member of the set, e.g., it is not an open set.
4. Yeah, Yeah, we already said that.
5. Well if there weren't actually an LUB, there would be a greater UB doh!
6.Huh?
7.Huh? Huh? Bullshit!
Hence, proof is topologically unsound and relies on begging the question.
>> The whole world is that thing than which there is no greater.
Consider (in the understanding) our world, including prime numbers, as it is (in reality).
Now add (in the understanding) a pink unicorn.
The result would be (in the understanding) greater than our world (in the understanding)
Thus it follows that our world is not "that thing than which there is nothing greater".
CIP,
I am surprised you have doubts about the proof, because you already believe in The One ...
>> >> proof is topologically unsound
Not many non-trivial theorems have been checked by machines yet.
But this is one of them ...
CIP,
one more thing (pun intended).
It seems that you accept the premise 1)
Well the conclusion follows from that and if you read the natural language version carefully you will actually see it.
What Prover9 shows is that the logic of Anselm's argument is correct. So there is no ??? at 6 or 7.
If there is anything wrong with the argument then it is with the premise (but it seems you accept that, just like many philosophers before you).
wolfgang,
Have you read Yujin Nagasawa's paper concerning the OA? he makes a pretty good case against "greatest possible island" style parodies. However, "deist" style parodies still pose an issue, because they use a parallel argument to show that a God exists, but not the God of Western Theism. (For example, a deist-type God that is not/never will be concerned with Earth and humanity.)
If I were to accept the premise , my first conclusion from it would be that there is a greater understanding beyond that understanding which it refers to.
>> Have you read Yujin Nagasawa's paper
not yet, but thank you for the link.
>> that there is a greater understanding
do you just mean a greater understanding (in the understanding) or actually a greater understanding (in reality) ?
I mean a greater understanding than the understanding can conceive of.
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