Ontological arguments

Great Debates
41

All this talk of possible worlds and modal logic serves to obscure the utter beauty and truth of your proof, Libertarian.

Thankfully, a simple observation will allow us to cut away all the machinery (and confusion) of possible worlds.

The proof shows, from the premises (G -> G) and <>G that we can conclude G. In fact, careful inspection of the proof shows that it contains a stronger conclusion, namely, G.

That means, from the single premise (G -> G), we can conclude <>G -> G. If God exists in one possible world, he exists in all possible worlds.

Obviously, the contrapositive is also true: ~G -> ~<>G. Or, shifting the negation inward on both sides: <>~G -> ~G. That is, if God does not exist in even one possible world, he does not exist in any possible world.

Thus, all possible worlds agree on the truth value of G. And since G is the only atomic proposition in the entire proof, we don’t need to speak of possible worlds at all; we can just choose a representative world, say this one.

Then all the modal quantifiers can be eliminated by noticing that P (P is necessary, where P is a proposition containing G as the only atomic proposition) will have the same truth value as P, and also that <>P is the same as P.

Thus, the first assumption, (G -> G) is really just G -> G, which is really just G -> G.

And the second assumption <>G is really just G.

Not only have we simplified the assumptions (to “if God exists then God exists” and “God exists”), but we’ve simplified the proof too because we don’t have to have a bunch of extra steps to juggle those meaningless boxes and diamonds:

  1. G -> G Assumption
  2. G Assumption
  3. G Modus ponens, 1 and 2

In fact, even the simplified proof contains a couple of extra steps.

42

Just for S&Gs, let’s suppose we have proved that God exists. What is the nature of this thing we are calling God?

43

I like your reduction of the argument to Proof by Blatant Assertion, Newton meter.

The notion that defining something as being possible necessitates there being something to fill that definition is what makes the argument an example of begging the question. Or either that or it’s a case of equivocation pivoting on two defintions of ‘possible’.

44

Oh sure, Newton. I agree. So long as everything you said is considered, the entire argument can simply be G. Of course, I can also reduce Peano’s proof that 1 + 1 = 2 by explaining all his axioms and definitions and saying that the whole my his reasoning may be represented by X. Then, the proof that 1 + 1 = 2 is X.

45

Or? :smiley: Yeah, I guess there must be something wrong because the conclusion just isn’t acceptable.

46

Or, it must be valid because it proves what you set out to prove.

This is just saying that you have defined it as being possible therefore it must be possible. Petitio principii pure and simple.

47

Boy, that reduction by N*m really shed light on this logical statement… I knew it before, but now I truly understand why it is a beautiful, brilliant crock of crap.

48

One might even say, the greatest possible beautiful, brilliant crock of crap.

49

Everytime I see this proof, I find something else fishy about it.

This time, it’s about “<>G”.

Although this is often interpreted as “It is possible that god exists”, I don’t think this is a proper interpretation. Why not? Because when we discuss modal logic like this, things don’t just “exist” or “not exist”. They either exist necessarily, or contingently, or not at all. (Someone correct me if I’m wrong here.) That is, there is no such thing as “possible” existence, only necessary or contingent existence. (Plus nonexistence.)

So what <>G means is “god exists contingently”. This appears to be at odds with the definition of G.

Does anyone else see it this way?

50

And the precise reason why I visit these boards… whatever you learn to be true makes you stronger, and whatever you learn to be truly nonsense makes you even stronger.

It’s not necessarily wrong, but it is possibly not right, and thus necessarily not right. But, who am I to judge ontology… I don’t even exist.

51

Sure, but in order to be sound, the metaphysical reality the Prime World conforms to needs to conform to bivalent logic. Certainly, a God such as one exemplified by indescribable love would transcend mere boolean algebra. Otherwise, our philosophers certainly would have cracked the secret by now.

52

The reason there is no difference between Newton’s post and the proof itself is because what Newton did was make a narrative of (a version of) the proof. Example:

If we are talking about a natural number system, then we are talking about a system that inherently is ordinal. If we say that Ax(Sx):Ey(y=x’), then inherent in every x is a y such that x is ordinally unique from y.

People use the system to count, and so there is no need to prove that every number has a successor since we can assume that whatever people count, they could count one more if one more was there.

Since the system is ordinal, we can assume that it starts somewhere. And since the system is cardinal as well, we can assume that where it starts is a quantity. It makes sense that the lowest quantity is a unit.

Ordinally, the number that precedes the unit must have no quantity since the unit is the lowest quantity. We can call this number 0, and assume that it is a part of the number system.

In general, we can assume that for any x, there is an ordinally unique number that is cardinally larger. That’s because we have no basis for establishing a ceiling. If x -> y(y = x’), then by modus tollens ~(y(y = x’)) -> ~x. That would mean that there are no numbers at all.

And if y = x, then y’ = x’ because if x’ did not equal y’ then x would not equal y.

Finally, we can say that 0, having no cardinality and being ordinally first is not the successor of any x.

So we do not need any of those meaningless squiggles and marks because all the steps that we’ve just described, we can represent with, say, X. Who needs the five axioms from Peano?

X -> X (Assumption)
X (Assumption)
1 + 1 = 2 (Conclusion)

Russell and Whitehead, therefore, developed a system from Peano that was a beautiful, brilliant crock of crap. And Godel was merely fingering his navel when he differentiated X from “This statement is provable in X”. We can call the latter X as well.

Arithmetic, then, is just smoke and mirrors.

53

I don’t know what you mean by reality being sound. An argument can be sound (or not). But what does it mean for a reality to be sound? In any event, we agree that God transcends algebra. That’s why the MOP is merely one of many testaments to Him.

54

By “shed light”, I meant it exposed the statement for what it really was, taking out the distractors. I understood it before, for the most part, but after the N*m post, it’s clear that it is somewhat “circular”, or “useful of itself”. I’m sure you know this?

I am not sure why you seem to think that you can create information (conclusion that God exists) from no information, but rather a definition and an assumption? No matter how much you deny this, it is truly what you are doing here… but by all means carry on. With a brain as big as yours, you are bound to stumble upon something substantial sooner or later. Just don’t make someone else’s gimmick your foundation.

55

I have studied philosophy formally, including the old and tired ontological argument for the existence of god. This argument contends that ‘existence’ is a property which something can have or not have, like an animal can either have or not have stripes and a computer can either have or not have a Pentium processor. It goes on to say that since a god who has the property of existence would be somehow ‘more perfect’ or closer to perfection than one which lacked this property, it follows that god (being defined as perfect) must have, as opposed to not have, the property of existence.

This argument fails on at least two point, and probably many more. (1) Existence is not a property that a thing has or does not have. It is the fact of having properties. The notion of ‘existence’ is the label we use to distinguish between thngs that are and things that are not, and one of the distinguishing factors is that things that are (things that exist) must have at least one property, whereas things that are not (things that don’t exist) do not have any.

(2) Even if existence were a property, there is no way to show that ‘perfection’ implies the having or not having of any given property. One could argue that perfection requires red hair just as well as one could argue that perfection requires not having red hair. Any argument used to support the former contention would apply equally well to the latter contention.

56

I’ve been thinking more on this proof. I think some of you really are short-changing it. It is a little deeper than Newton Meter suggests.

The definition is “the greatest possible being.” This seems circular, but consider it like this: “The greatest being not logically forbidden.” In modal logic, this is what we’re talking about. Contained in this definition is: <>G. It must be possible, or else it is logically forbidden and not the entity we’re concerned with. Maybe there is a god who can make a rock so heavy he can’t lift it or something, but we’re not discussing that here: we’re discussing the greatest being not logically forbidden. This makes <>G no problem, because all the possible worlds contain all logically permissible entities, and that’s just what we’re talking about here: a being not forbidden.

So, yes, we’re defining G into existence, in a way. But this is innocuous. The rejection of <>G indicates that the definition is improper in some way. Specifically the part of the definition that states, “The… being that can exist.”

I ommitted “greatest” from the above sentence, because it is not the second assumption that deals with “greatest” but the first assumption, which concerns itself with “The greatest… being…” Now we are suggesting that the best kind of existence is necessary existence. Unlike ianzin might suggest, we’re leaving Anselm behind: because modal logic already deals with this being existing, we are not contrasting non-existence with existence, but possible existence with necessary existence. So what the first assumption indicates is this preference: that necessary existence is greater than possible existence. Hence, G->G, because the greatest being would be one that necessarily existed rather than is just not logically forbidden (if we accept that necessary existence is “better” than possible or actual existence).

I think I have a deeper respect for the proof now, but my first post to this thread still largely stands (for me) because of the extreme ambiguities involved in the meaning we wish to put into the symbols. While Russell and Whitehead may have proven 1+1=2 in their symbology, it is altogether another matter to suggest that their work proves that one mole of carbon combined with one mole of carbon yields two moles of carbon.

57

I want to reemphasize how I’m breaking down the definition.

The definition is, “The greatest possible being,” otherwise known as, “The greatest being that can exist.”

So the first assumption, G->G, comes only from, “The greatest… being…”

The second assumption, <>G, comes only from, “The… being that can exist.”

Seen in this light, it is much more difficult to justify a <>~G substitution. In fact, I’d have to say it is impossible to justify that substitution.

58

One thing that’s been bugging me about this whole thing…

What we are offered is a proof in S5, not of G, but of (G -> G) -> G. Now, unless S5 is very different from traditional propositional calculus, there’s a problem here. If G is true, clearly (G -> G) -> G is true, as it’s an implication with a true conclusion. But if G is false, G -> G is still true, but (G -> G) -> G is false: it has a true hypothesis and a false conclusion.

Does S5 have theorems that are not tautologies? If so, on what grounds can we call it a good system?

59

The other thing I don’t like is that no one has said exactly what they mean by “greatest”. Is that an undefined term? If not, in what sense is the being whose existence is claimed in the statemen G greater than all other beings?

60

A being that has necessary existence is not real… it is a figment of your extravagant imaginations. Sure, the proof “proves” that a necessary being exists, but only the realm of thought. The necessary being does not actually have distinguishing qualities (physical or extra-physical), it can’t alter our existence in any way, it cannot be touched or communicated with, it cannot do anything worthwhile on it’s own. It’s only an intellectual phenomenon. Do you not see this?

Don’t get me wrong, I have respect for the proof too, but it has absolutely no relevance. I respect it as a clever product of our beautiful minds, nothing more. Aside, from all this, it has not created any new information either, which is the most simple way of debunking it to the level of respect it deserves.