4 ms·

Whenever this makes top of HN, it remains one of the most contentiously misunderstood pieces of formal logic -- much like some of Gödel's other famous results.

by dvt 7y ago

Whenever this makes top of HN, it remains one of the most contentiously misunderstood pieces of formal logic -- much like some of Gödel's other famous results. The proof is basically a formalizing of Anselm's Ontological Argument[1]. The proof doesn't "prove" there is a God, it just shows that the argument, written in S5[2] (a type of modal logic), is correct -- more specifically, that if the premises are true, then the conclusion follows. Alvin Plantinga also did a lot of work refining these kinds of modal ontological arguments in the 70s and 80s; of note is his famous "victorious" ontological argument[3] -- still hotly cited to this day. Modal logic, for the uninitiated, essentially adds two new operators to the "usual" logical operators we might have seen in college (negation, implication, conjunction, disjunction, quantifiers): Necessity: ◻P -- P is true in all worlds Possibility: ◇Q -- Q is true in some (or no) worlds It's a very fun and surprising type of logic! A very intuitive result (and one of the first you'd learn) is what happens when you negate a necessary proposition. ~◻P -- P cannot be true in any world! What Gödel's proof shows is that God -- as defined by the premises (basically, as maximally "everything positive") -- is necessary; which is why his last line includes a ◻. I don't want to get too bogged down, so this was purposefully a very surface-level comment. If I piqued your interest, I strongly suggest you check out some of the linked resources! The historical context is also very interesting. It was somewhat unknown how valid Anselm's argument was, and it took almost a millennium before we could satisfactorily formalize the ontological argument (although many non-modal and Aristotelian proofs had been written). What does it mean for non-logicians? Well, if you buy the premises (which is key!), it shows that it's not irrational to believe in God (as defined by the argument). Again, it doesn't prove the existence of God, but it does show that the logic of the argument makes sense. [1] https://plato.stanford.edu/entries/ontological-arguments/#StAnsOntArg https://plato.stanford.edu/entries/ontological-arguments/#St... [2] https://plato.stanford.edu/entries/logic-modal-origins/ https://plato.stanford.edu/entries/logic-modal-origins/ [3] https://plato.stanford.edu/entries/ontological-arguments/#PlaOntArg https://plato.stanford.edu/entries/ontological-arguments/#Pl...

shkkmo 7y ago
> What does it mean for non-logicians? Well, if you buy the premises (which is key!), it shows that it's not irrational to believe in God (as defined by the argument). Again, it doesn't prove the existence of God, but it does show that the logic of the argument makes sense. This understates what the proof shows. It shows that if you buy the premises it's not rational to believe God doesn't exist (as defined by the argument).
- dvt 7y ago
  "Rationality" is not a (meta-)logical property. You're right that the proof shows that, logically speaking, if one buys the premises, God must exist. But more colloquially, it shows that by accepting some premises that are reasonable, one reaches the conclusion that God exists. Ergo, there's an argument a rational person would accept whose conclusion is the necessity of God.
  - shkkmo 7y ago
    > But more colloquially, it shows that by accepting some premises that are reasonable, one reaches the conclusion that God exists. Ergo, there's an argument a rational person would accept whose conclusion is the necessity of God. I think that is a very weak conclusion, there are an infinite number of proofs for god that are valid so long as you accept their particular premises. It is the specific plausibility of the premises and definitions implied in St. Anselm’s Ontological Argument that make it of interest. What this shows colloquially is that if you are arguing against god, you must either reject this definition of god or one of the other premises. If you don't your argument is self-contradictory.
    - dvt 7y ago
      > I think that is a very weak conclusion ... That's kind of my point. It's not some knock-down argument, but it's a very nuanced result that achieved a few very neat things: 1) Formalized Anselm's "greatest of which can be conceived of" notion. 2) The concept of "accidental" (contingent) and "non-accidental" (necessary) properties had existed since antiquity, but modal logic essentially formalized the idea. 3) Showed that Anselm's argument was indeed valid. Again, this project took around 1000 years. Plantinga did a lot of work in trying to make the premises more palatable, but of course, the argument for the existence of God still rages on. (As I'm sure it will far after we're gone.)
  - empath75 7y ago
    Seems to me it’s a reductio ad absurdem argument against the premises.
- 7y ago

by dvt 7y ago

shkkmo 7y ago

> What does it mean for non-logicians? Well, if you buy the premises (which is key!), it shows that it's not irrational to believe in God (as defined by the argument). Again, it doesn't prove the existence of God, but it does show that the logic of the argument makes sense. This understates what the proof shows. It shows that if you buy the premises it's not rational to believe God doesn't exist (as defined by the argument).

dvt 7y ago
"Rationality" is not a (meta-)logical property. You're right that the proof shows that, logically speaking, if one buys the premises, God must exist. But more colloquially, it shows that by accepting some premises that are reasonable, one reaches the conclusion that God exists. Ergo, there's an argument a rational person would accept whose conclusion is the necessity of God.
- shkkmo 7y ago
  > But more colloquially, it shows that by accepting some premises that are reasonable, one reaches the conclusion that God exists. Ergo, there's an argument a rational person would accept whose conclusion is the necessity of God. I think that is a very weak conclusion, there are an infinite number of proofs for god that are valid so long as you accept their particular premises. It is the specific plausibility of the premises and definitions implied in St. Anselm’s Ontological Argument that make it of interest. What this shows colloquially is that if you are arguing against god, you must either reject this definition of god or one of the other premises. If you don't your argument is self-contradictory.
  - dvt 7y ago
    > I think that is a very weak conclusion ... That's kind of my point. It's not some knock-down argument, but it's a very nuanced result that achieved a few very neat things: 1) Formalized Anselm's "greatest of which can be conceived of" notion. 2) The concept of "accidental" (contingent) and "non-accidental" (necessary) properties had existed since antiquity, but modal logic essentially formalized the idea. 3) Showed that Anselm's argument was indeed valid. Again, this project took around 1000 years. Plantinga did a lot of work in trying to make the premises more palatable, but of course, the argument for the existence of God still rages on. (As I'm sure it will far after we're gone.)
- empath75 7y ago
  Seems to me it’s a reductio ad absurdem argument against the premises.
7y ago