Ontological arguments

Great Debates
141

Ah! Now I see why this is the modal modus tollens in question, Newton. (Thought I’d just forget about it just because I was back to not liking the proof, didn’t you? Well I am never satisfied!)

First, let’s state the modus tollens.

(A -> B) & ~B -> ~A
Now apply necessitation
(A -> B) & ~B -> ~A

No problem, right?

Well, look what Peter Suber suggests we read “->” as. (I had to convert his images to type.)

Now the modal modus tollens as given makes perfect sense: it is just the modus tollens cum necessitation.

142

This is a good statement of my problem with this stuff in the first thread (too lazy to look it up right now) - the attempt to assume that G is the Christian god with all the attributes thereof (omniscience, omnipotence, omnibenevolence, etc…). These are mutually contradictory in my view and I see no reason to add these attributes to G. In short, I don’t think the MOA, even if valid, proves anything of any use to a theist.

143

erislover, you are exactly correct. I’ve been exhorting Lib to change his G -> G premise to (G -> G). Suber’s solution works as well, but at the cost of some clarity (to my mind). The only implication in his entire proof that needs to be strict is the one in that first assumption (as well as the first one in the “modal modus tollend”).

The rest of the implications in his proof are not usually given as strict implications (for instance, we usually see P -> P instead of (P -> P). The latter can be obtained from the former by the rule of necessitation. P -> P can’t be obtained so easily from (P -> P) first of all because P -> P is exactly the rule you would want to use). Or else the justification he gives for some of his steps are wrong (the last step, for instance, isn’t classical modus ponens if -> is read as strict implication). And he probably has to add some extra applications of P -> P to get rid of a few extra boxes.

I haven’t entirely forgotten the argument, either. I’ve recently come across a paper in my day job entitled A Symmetric Modal Lambda Calculus for Distributed Computing. It presents a programming language for mobile computation (where programs can “migrate” around a network) based on a natural deduction system for (intuitionistic) S5.

In their interpretation, possible worlds are interpreted as network nodes. A is the type of a computation (producing a value of type A) that can occur at any node (i.e., it is the type of mobile code). <>A is the type of a value of type A that occurs at some node (i.e., it is the type of a handle to a remote resource).

It appears (unless I’ve screwed up) that the term


\f.\g.letd w'.x = g in unbox (fetch [w'] (unbox (fetch [w] f)) x)

(a backslash is an asciification of lambda) has type


[](A -> []A) -> <>A -> A

demonstrating that there is a proof of Lib’s God’s existence in this system (and in particular, one that doesn’t rely on excluded middle or anything else non-constructive). Perhaps more interestingly, it gives a computational interpretation to the search for God. I don’t expect anyone to read the paper, so I’ll describe what the term above does:

It is a function that expects two arguments and returns God. The first is mobile code for a function that can transform God into mobile code for God. The second is a handle to our remote God resource.

First, we check our handle to remote God to determine which world he is local to, then we invoke some code in that remote world. The code in the remote world fetches our conversion function (that can turn God into mobile code) from us, and applies it to God yielding a mobile code for God, which is then sent back to us. On our end, we simply have to unbox the mobile God to get an actual God in our world.

That’s pretty much the structure of the modal proof as given by Lib. We use <>G to place ourself in the world where God exists by hypothesis, we use the necessity of G -> G to discover that God is necessary in that world, and we use a symmetric accessibility relation (which S5 has) to guarantee that we can “get back” to our own world with God in hand.

144

However, since we’re not omniscient, we’re really not in a position to posit <>G, given G.

145

We don’t have to be omniscient to posit <>G, in fact, we might know only that one thing.

But I think you missed the game I was playing, I didn’t posit <>G. If you give me (G -> G) (mobile code for a function that can turn God into mobile code for God) and <>G (a reference to a remote God), I can produce God for you.

If you want to know whether I think it is justified to automatically assume that you can always find a remote referenced to God, <>G, then I think you have to read the thread more carefully.

146

erislover, here is where I first began pointing out that the implication in G -> G is strict implication. Back then, I had never heard of MOP.

147

But given G, which according to Lib implies ~<>~G, knowing <>G is knowing a lot of things that aren’t known!

Anyway, I did understand that you weren’t positing <>G. I was just sayin’…

148

Man, two years we’ve been talking about this thing.

149

Well, I don’t know about you guys, but it’s not the only thing I’ve been talking about for two years.

150

Having fallen behind by two or three days, I’ll offer some sundry observations:

(1) I’ve stated these many times before: (a) I don’t necessarily equate the G of this proof with Christ; (b) the G of this proof is ontologically perfect, nothing more nor less; and © I do not like the label “religious”.

(2) As an atomic statement, G does not mean “there is a being that exists in all possible worlds”. G means “the greatest possible being exists in the actual world”.

(3) It is not the case that something has been circumvented in the application of the rule of modal modus tollens. All modal rules of inference and formulas are based on the implication of the RN — necessity obtains. For any proposition, p -> q, if q is necessarily false, then so is p. It’s that simple, For modal MT, the necessity of the truth value of the consequent determines the necessity of the truth value of the antecedant.

For the proposition G -> G, G is the antecedant and G is the consequent. Therefore, if the consequent is necessarily false, then so is the antecedant. The modal MT of G -> []G is []~****[]G -> **~**G.

(4) If you’ve just now stumbled onto a paper tying computer science to modal logic, then you’ve just now started studying computer science (or modal logic). Modern model logic (replacing symbols for strict implication with symbols for necessity) was appropriated by computer science in the 1950s, and has been used for decades now particularly in AI applications. In fact, the origins of the MOP are from this. Hartshorne put together work he had seen on modal logic in computer science together with Godel’s ontological proof to produce the first valid MOP. Plantinga, a professional logician, then refined it.

Modal logic was invented by CI Lewis in the early 20th century, when he first proposed the strict implication of modal modus ponens as a biconditional. He emmended that a couple of years later as a simple conditional because the bicontionality destroyed the modality of the system. Godel hooked onto that, and here we are.

(5) Probably most importantly (since Newton seems insistent on making points about it) any material implication can be made into a strict implication simply by making the implication necessary. That is, p -> q is a material implication, while (p -> q) is a strict implication. And voila, we have S3 modal logic. That doesn’t have any mystical meaning. It doesn’t mean that the strict implication is more true than the material one. It just means that the strict implication makes a metaphysical commitment while the material one makes an epistemic commitment. Certain paradoxes can arise from material implications that can be dealt with by strict implications. And modal logic is one of many solutions — relevance logic, entailment logic, and counterfactual logic are three others.

The difference between epistemic and metaphysical commitment is the difference between a single universe of truth value and multiple universes of truth value. In other words, epistemic (material) values of truth can change, while metaphysical (strict) values of truth cannot. For example, the assertion “all people live on the earth” is materially true, while the assertion “all people are mortal” is strictly true. The material assertion can become false if some people start living on Mars. All tautologies are strictly true.

It’s also important to note the difference between epistemic and metaphysical modality. There’s a difference between the statement, “it is possible that it is raining outside for all I know” (epistemic) and “it is possible for it to rain outside” (metaphysical). The modalities of the MOP are all metaphysical. Thus, <>G means that it is possible that God exists in the metaphysical sense; that is, it is possible for Him to exist. It is not a matter of what anyone knows.

In the proposition p -> q, there is no need for any step to make the implication strict. It is already strict by virtue of the fact that q is a necessary consequence of p. And in general, every modal statement is strict. And every modal statement that makes an ontological commitment is metaphysically modal.

151

If G is Christ (more generally, the Christian god) then we must begin with G as Christ. If G is not Christ then it is not appropriate to tack the attributes of Christ (what others here call OM3I) onto G at the end of the proof.

152

“It is possible for it to rain outside” is only reasonable because “it is possible for it to not rain outside” is also reasonable.

~<>~ R (rain) is only valid because R is known to actually exist.
~<>~ G is only valid if we know that the qualities we imagine the greatest possible being would have not only actually exist, but exist in combination in one entity.

<>G->~<>~G, therefore <>G is not valid unless G is something already known to exist, in which case we have to rule out all supernatural qualities.

153

That’s part of why I don’t.

I agree with that. And that’s why I respect the opinions of people who oppose the proof on those grounds. (Though, as I’ve explained, in my opinion, the reasonableness of <>G is greater than the reasonableness of either ~<>G or <>~G.)

Epistemically, yes. But metaphysically, it is valid if and only if it follows from some other truth that itself is necessary. (Note: this allows for a non-technical interpretation of “valid”.)

Epistemically, yes — with the reservation that the only quality open to discussion in an ontological argument is existence. But metaphysically, what we know has nothing to do with it. (Note: this allows for a non-technical interpretation of “valid”.)

Actually, that’s not valid simply because <>G does not imply ~<>~G.

154

OK, then G is not the ‘greatest possible existence’, because ~<>~ holds true for all things known to exist, and is certainly a greater existence then <>~.

155

You can only argue that the reasonableness of <>G is greater than the reasonableness of either ~<>G or <>~G by question begging, which IMO is not so reasonable. :wink: IMO, both are equally reasonable. Which brings us back to the original question, does he or does he not?

156

Anduril, changing the hypothesis changes the definition. I don’t see how we can be discussing the same definition if you feel <>~G is warranted. I don’t think it is a matter of question begging at all. If we accept the law of the excluded middle, we’d suggest
<>G V ~<>G
– either G is possible or it is impossible,
not
<>G V <>~G which is not exclusionary, though is it a tautology.

You’re suggesting
<>G V <>~G is “just as reasonable”. But this reads,
<>G V ~G “Either G is possible, or G is not necessary.”

Seriously. Perfection is defined as “the greatest thing that can exist.” You seem to be discussing a form of perfection as “the greatest thing that doesn’t have to exist.” Well, great–God’s speed. :wink: But <>~G is not a neutral substitution. It changes not only the outcome (which, really, is to be expected) of the proof, but what, exactly, we’re proving.

Take Newton’s excellent programming semantics. He suggests, “if you give me mobile code for a function that can turn some G into mobile code for G, and a reference to some G, I can produce G.” You’re suggesting that we give him a reference to something else (to ~G). As you might see, then, the situations aren’t reasonably similar at all, any more than giving you a cheeseburger when you asked for a Whopper is a reasonable substitution.

157

If “doesn’t have to” doesn’t apply here, then perfection is “the greatest thing that must exist”, not “can” exist.

158

It seems at face value that this conclusion must be excluded because of the condition “greatest POSSIBLE being”. Clearly defining a being that cannot exist in order to exist is like inserting a strawman to defeat the argument, right?

As I recall, the problem we ran into was how to differentiate God from a pebble on the ground, or say, a colony of aliens, or the nebulous idea “existence itself”…

So the conversation moved into (probably me first) stating that a perfect being would include a being that was AWARE that it exists, to which the concept of suicide follows… then you ground the perfection of that being to the consent of all possible beings given INFINITE HANDICAPS TO ITSELF and still not being de-selected. My innitial slant was, “Ok, a perfect being is a being that will commit suicide upon any request, every being having instant access to make that request, and NEVER BE CHOSEN by the beings that it procures from oblivion” (clearly I’m adding stuff here, like a “creator God”, but c’mon… what’s really the argument trying to get a foothold on anyways?). Again, just really making a solid claim about infinite handicap and infinite selection being the criteria for “great” — but assenting to that point makes any God concept in history seem downright false and evil, not to mention our own moral code in general, so one would tend to gloss over this as evidence of “perfection”.

But then first cause arguments arose, again, as a means of trying to differentiate this “perfect being” from a pebble, moss, me, you, the next door neighbor, a colony of aliens, or even, ultimately, just a synonym for existence itself. Along this line, it became clear that a God who doesn’t need to exist in order to create existence is the only God who could fill first cause criteria – from this, it was concluded that the argument didn’t have any solid footing unless “greatest possible” was defined, as we always end up with “This perfect being cannot exist in order to exist.”. But when it’s stated that this argument cannot be used, because it violates the “possible” part, the point again comes back

“Ok, so how do you define “greatest possible” as something other than ME, or THEM, IT or just a synonym for existence? Or just me with better technology and less scruples such that I abuse coersion to avoid falsifying my inherent greatness?”

Because, again, you have a meaningless proof, if all you can really state is that “This linguistic token exists” QED

It’s like, ok, we agree that linguistic tokens exist, we’re typing responses to the post, we understand these things… where’s the proof for God though?

We kept asking for terms to be defined and kept being rebuffed by comments like “You don’t define logical symbols” or some such…

And here it is, still going.

This has no bearing on the intricacies of all the arguments about the rules of logic in terms of symbolic semantics or whathaveyou – these were just some of the basic english language arguments that occurred with respect to the proposal of this proof.
The issue that kept coming up over and over was “define greatest”. Because, it’s easy to invert values like this with a valid argument. If you take the tack that it’s relative … then “greatest” would have to conform to every possible definition of greatness, which involves the perspective and consent of every possible being, which involves a mechanism for testing this, which involves the suicide contract.
If the logic discussion isn’t happening for you (which it’s not much for me unfortunately), maybe this might summarize the gist of more native conceptual exchange with regards to the proposal of this proof.

Another thing that came up is that the “greatest posssible being” would at least know the sum total what all of the lesser possible beings know.
Let’s say that a lesser being knows a reason why they think what they are thinking, or rather, you can narow this self referrential knowledge down with the collective knowledge of all beings…

Then you have a being who knows every reason why they think what they think.
If that reason has nothing to do with their own creation ex nihilo (which was already addressed in the “cannot exist in order to exist argument” with respect to first cause), then it follows that they have no reason to think… as all reasons would be external!

And this again circles back to the meaningfulness of defining “greatest possible being” as a being that doesn’t think, or is not aware that they exist, or even further, cannot exist in order to exist.

So, in summary, when greatness isn’t defined, this is basically a proof that states “This linguistic token exists because you think it’s possible that you are reading it.”.

In the case of the latter, this isn’t so much a proof as it is the statement “existence exists”. or “these linguistic tokens exist, because by the rules of logic, you are reading them”.

Then again, maybe this doesn’t make sense either.

159

It seems at face value that this conclusion must be excluded because of the condition “greatest POSSIBLE being”. Clearly defining a being that cannot exist in order to exist is like inserting a strawman to defeat the argument, right?

As I recall, the problem we ran into was how to differentiate God from a pebble on the ground, or say, a colony of aliens, or the nebulous idea “existence itself”…

So the conversation moved into (probably me first) stating that a perfect being would include a being that was AWARE that it exists, to which the concept of suicide follows… then you ground the perfection of that being to the consent of all possible beings given INFINITE HANDICAPS TO ITSELF and still not being de-selected. (which is what the greatest possible argument would be too =)). My innitial slant was, “Ok, a perfect being is a being that will commit suicide upon any request, every being having instant access to make that request, and NEVER BE CHOSEN by the beings that it procures from oblivion” (clearly I’m adding stuff here, like a “creator God”, but c’mon… what’s really the argument trying to get a foothold on anyways?). Again, just really making a solid claim about infinite handicap and infinite selection being the criteria for “great” — but assenting to that point makes any God concept in history seem downright false and evil, not to mention our own moral code in general, so one would tend to gloss over this as evidence of “perfection”.

But then first cause arguments arose, again, as a means of trying to differentiate this “perfect being” from a pebble, moss, me, you, the next door neighbor, a colony of aliens, or even, ultimately, just a synonym for existence itself. Along this line, it became clear that a God who doesn’t need to exist in order to create existence is the only God who could fill first cause criteria – from this, it was concluded that the argument didn’t have any solid footing unless “greatest possible” was defined, as we always end up with “This perfect being cannot exist in order to exist.”. But when it’s stated that this argument cannot be used, because it violates the “possible” part, the point again comes back

“Ok, so how do you define “greatest possible” as something other than ME, or THEM, IT or just a synonym for existence? Or just me with better technology and less scruples such that I abuse coersion to avoid falsifying my inherent greatness?”

Because, again, you have a meaningless proof, if all you can really state is that “This linguistic token exists” QED

It’s like, ok, we agree that linguistic tokens exist, we’re typing responses to the post, we understand these things… where’s the proof for God though?

We kept asking for terms to be defined and kept being rebuffed by comments like “You don’t define logical symbols” or some such…

And here it is, still going.

This has no bearing on the intricacies of all the arguments about the rules of logic in terms of symbolic semantics or whathaveyou – these were just some of the basic english language arguments that occurred with respect to the proposal of this proof.
The issue that kept coming up over and over was “define greatest”. Because, it’s easy to invert values like this with a valid argument. If you take the tack that it’s relative … then “greatest” would have to conform to every possible definition of greatness, which involves the perspective and consent of every possible being, which involves a mechanism for testing this, which involves the suicide contract.
If the logic discussion isn’t happening for you (which it’s not much for me unfortunately), maybe this might summarize the gist of more native conceptual exchange with regards to the proposal of this proof.

Another thing that came up is that the “greatest posssible being” would at least know the sum total what all of the lesser possible beings know.
Let’s say that a lesser being knows a reason why they think what they are thinking, or rather, you can narow this self referrential knowledge down with the collective knowledge of all beings…

Then you have a being who knows every reason why they think what they think.
If that reason has nothing to do with their own creation ex nihilo (which was already addressed in the “cannot exist in order to exist argument” with respect to first cause), then it follows that they have no reason to think… as all reasons would be external!

And this again circles back to the meaningfulness of defining “greatest possible being” as a being that doesn’t think, or is not aware that they exist, or even further, cannot exist in order to exist.

So, in summary, when greatness isn’t defined, this is basically a proof that states “This linguistic token exists because you think it’s possible that you are reading it.”.

In the case of the latter, this isn’t so much a proof as it is the statement “existence exists”. or “these linguistic tokens exist, because by the rules of logic, you are reading them”.

Then again, maybe this doesn’t make sense either.

160

Yes, “can” exist.

<>a = can
a = does
a = must