Are materialism and logic incompatible?

[Liberal]

In the thread about what contains the universe, Scylla observed:

You can prove whatever you want if you run fast and loose with your axioms and definitions, and their [sic] ain't no reason to camoflage [sic] it with fancy and esoteric forms and equations.

There is presently a flurry of activity in philosophical circles centered around the resurrection of ontological arguments for the existence of God. In particular, the tableaux of S4 and S5 modal logic have changed the ontological argument from vague to valid. Even philosophers and logicians who do not believe the argument to be sound do acknowledge its validity. (In logic, an argument is valid if its inferences follow from one another, and it is sound if it is valid and its axioms are true.)

One of the very latest tableaux has caused a noted British logician and materialist, Trent Dougherty, to change his mind and concede, "I conclude, somewhat reluctantly, that God exists". Of course, Dougherty understands both logic and materialism profoundly — the former is why he concludes what he does, and the latter is why he concludes it reluctantly.

But I think it's fair to say that Dougherty's concession is exceptional. And obviously, he can't be a materialist anymore. But I'd be interested in hearing from the materialists who, like Scylla, take exception to the definition and axiom offered in the tableau in the other thread.

I'd like to reprint it here in full, but that might be interpreted as cross-posting. I hope that I can be allowed to quote from there just the definition and axiom. That's all we need here anyway, because there's no question whether the argument is valid (unless you refuse to accept logic as a whole). The only question is whether it is sound.

I'd like to know why materialists think these two elements "run fast and loose."

Definition

God = necessary existence

What that means is that God is defined as the greatest possible existence, i.e., existence that is necessary. In addressing what you believe to be fast or loose about that, please explain how it might be unreasonable to define God to be that which is the greatest possible. The definition seems cogent to me — whatever is less is hardly God, and nothing greater is possible.

Axiom

It is possible that God exists

Jab apparently didn't like this one, but isn't it reasonable to assert that the greatest POSSIBLE existence is, um, possible?

[Liberal]

Eris posted this in the other thread:

Lib, not to revive this discussion, but it seems clear that if we use "possible" to mean "must exist in some describable world" and "necessary" as "must exist in all worlds" then any being which must exist necessarily if it exists and is described as possible must exist in all worlds. The five following steps add a nice touch, but don't seem necessary to develop the point.

Well, the five steps simply serve to state formally what you just stated informally.

[Tars Tarkas]

Could you explain what you mean by "materialist" please?

Thanx

[Liberal]

Sure, Tars. I mean a person who believes that "physical matter is the only reality and that everything, including thought, feeling, mind, and will, can be explained in terms of matter and physical phenomena." (dictionary.com)

[xenophon41]

What that means is that God is defined as the greatest possible existence, i.e., existence that is necessary. In addressing what you believe to be fast or loose about that, please explain how it might be unreasonable to define God to be that which is the greatest possible. The definition seems cogent to me — whatever is less is hardly God, and nothing greater is possible.

Well, I'm not clear about what "greatest possible existence" means in real terms. How does this reconcile with the common religious definitions of God? If we're simply defining God as "that which necessarily exists", I don't see the difference in this proof and the statement "What must be, is." That statement is philosophically pleasing to me, and frankly, I think it's a reasonable concept, but I don't see that it implies anything about love, salvation, or any of the immutable characteristics we're used to associating with God. Am I just being thick-headed?

[Liberal]

No, Xeno, not at all. In fact, you sound quite level-headed. Ontology can't qualify existence with broader metaphysical attributes, but may only assign attributes of existence itself.

In real terms? It means that you can say things like God has the greatest possible knowledge or the greatest possible power. But you can't say anything (not with any validity anyway) about the metaphysical nature of those.

[Colibri]

Originally posted by Libertarian
definition

God = necessary existence

What that means is that God is defined as the greatest possible existence, i.e., existence that is necessary. In addressing what you believe to be fast or loose about that, please explain how it might be unreasonable to define God to be that which is the greatest possible. The definition seems cogent to me — whatever is less is hardly God, and nothing greater is possible.
[/b]

It's fast and loose, because in normal parlance "possible" does not equal "necessary." (Don't make me go and get the dictionary - but I will if I have to.) You appear here to be using some non-standard definitions of these two words at least.

[ultrafilter]

Replace "God" with "the universe" in the argument, and it's wholly unremarkable. Furthermore, the conclusion of a valid argument may certainly be false; after all, it only must be true if the hypotheses are true as well.

[Phoenix Dragon]

Okay, the statement "It is possible that God exists" is true enough, at least untill someone supplies evidence one way or the other. But it's as true as saying "it's possible that the Loch Ness monster exists" or "it's possible Anubis exists." It's also as true as "it's possible that God doesn't exist." Without any evidence for any of those statements, though, it'd be pretty hard to convince me that any of these things do exist, however.

As for "God = necessary existence" I think you're jumping to conclusions. First off, you're asking us to define something we don't know. It's about as reasonable to ask me to define what a quark looks like; I don't know. Never seen one, after all. Actually, it's probably less reasonable. I can reliably find information on quarks, information that has been reliably proven true. Unlike any gods.

Further, I don't see how "greatest possible existance" equals "existance that is neccessary." The definition assumes a god to be true, while supplying no reasoning to support this. It can be true enough that if the christian god exists (I'm assuming that's the one you're using, due to various elements of your post), then he must be the greatest possible existance, but without anything to support a god's existance it's irrelavant.

And saying something "is necessary" without anything to support it just doesn't work. I could say there are millions of insubstantial creatures that are impossible for us to detect, and there are no laws of physics, merely these little critters going around and making sure things work right (Very thorough critters, aren't they?). They hold people down to the ground just like gravity would, keep the atmosphere in place, make sure things react properly to being touched or pushed, even keeping an eye on bodily functions to make sure people can live. Without them, atoms wouldn't be able to stay bound, and all matter in the universe would rapidly fall appart and disperse into an even density. They even started the universe. "Obviously," they are necessary. No?

[xenophon41]

Oh, OK. Thanks Lib.

I think this argument actually reinforces materialism just as much as any other metaphysic then, but I need to marshall my thoughts about that.

(I'm thinking along the lines:

If God is that which possesses the greatest possible power and knowledge, this implies
God must contain all possible power and knowledge, which means
God is necessarily Omnipresent, which means
God is all that exists.

Materialism considers that all thought, feeling, mind, and will are derived from that which exists materially, which, if we accept the above means...)

I dunno. I have to let this stew.

(You do such intereting threads, Lib.)

[Apos]

---But I think it's fair to say that Dougherty's concession is exceptional. And obviously, he can't be a materialist anymore.---

Why not? You've not yet explained how you get from "greatest possible existence" to "non-physical existence?"

Personally, I've never seen the point of talking about "materialism" or asserting that "physical matter is all that exists," because I'm not even sure what the actual implication of that statement is. Talking about materialism or amaterialism seems, at the least, highly, misleading in such a situation. If you think something has a certain characteristic, specify specify.

And I still don't think that existence (in other possible worlds) is a valid characteristic of a being that exists in any particular possible world, or that a list of negatively defined maximums defines a being.

[erislover]

I think I'm going to tackle the OP from a different angle than a proof of god and stick, instead, with a logic versus materialism. This is a long post, but I believe it must necessarily be to make the point I want to make.

My first beef with materialism is that it assrets quite plainly that "everything is material", that is, physical or affecting and affected by other physical things. It is nice to note that when everything is [something] we no longer need to define [something] (unfortunately I've found a few critiques of materialism which insist that it can still be defined, or at least should be). The definition is: "look around". Dangerous grounds to stand on.

My second problem with materialism is the problem it presents for discussions of consciousness. I encountered in long-windedly but forcefully in my recent thread on private phenomena (reference private language, Wittgenstein). No one stepped up to offer a motivated discussion of how language can discuss private phenomenon; it either must be irrelevant (rug sweeping), defined as that which cannot be spoken of (rug sweeping), or denied (IMO, prima facie false: I sure as hell experience the sensation of green). I can find no account of consciousness, materialistically speaking. That does not mean I believe in a soul in any mystical or religious sense. But if I cannot account for consciousness, if I cannot recount my personal experience in language, then materialism needs to explain why we cannot form a perfect map between words and all physical things.

Now, ok, it is true that just because those private phenomena cannot be accounted for at all doesn't mean they aren't physical. But then, it seems to me that there should be some reason why they aren't able to be accounted for. I don't know, maybe not, that thread never came to any conclusions. But if the doctrine is that everything is physical, that must include consciousness. So why can't we discuss consciousness in the same way we discuss other things that we can't directly perceive (like, for instance, atoms).

My third problem with materialism is that it leaves no room for free will. At least, let me say, I have not seen a discussion of how free will manifests itself in a world where everything is physical (except for compatibilism, which I think sort of twists the idea of free will but whatever). Metaphysical materialism seems to demand no free will, where "free will" is a force that may manifest itself without cause and may not be acted on by anything other than itself (keep that in mind for discussion where reality is contingent on God's will ). Where would it come from, and what could we do to it or with it (since it is physical)? Again, I understand that just because it can't account for it now doesn't mean it will never be accounted for. And though I am not sure I am a proponent of free will, I am not sure I am a materialist, either.

Materialism seems bound in thisness; which is to say: everything that is may be pointed at (I think that is a regular notion of physicalness). But if a material investigation into the nature of physical things leads us to the point where we demonstrate that individual particles don't have a thisness (they cannot be pointed at) then I think there is a problem with the underlying assumption of thisness or at least our conception of it. In matters of theoretical science, however, it is possible that there are explantions which we may possess later that will restore thisness to reality (say, for instance, string theory).

Materialists, bound in thisness, have a hard time motivating a discussion on universals that isn't immanent realism or nominalism, though no one who is a nominalist can claim to say anything about reality since all words are universals anyway (universals depend on sameness). But we then reach a strange case of literal pointing. Two people see a red ball, albeit from different angles. We may point to the ball and say "ball" and we may point to the ball and say "red". We may also point to their (completely physical) brains' state(s) of electrical and chemical activity and say "ball" and "red" as well. Right? (an epistemological limitation in saying "no", a problem describing the sensation of green in saying "yes" since I've never seen it done).

Logic and materialism are not fundamentally opposed except to note the apparent discrepancy between building a complete and consistent framework of logic with which to study the universe. This is to say, we can never demonstrate that everything is physical through a rigid symbol-set unless everything can be explained by something like first-order predicate logic. Not something we would normally take very far, though I would appreciate any input on the matter (ultrafilter, if you are reading this then you might recognize my response to your research here!). (see if anyone can follow me here in the next paragraph)

I think this last point is especially important WRT free will. If everything is physical, and disregarding a symbol for "physical", then in order to describe the universe we reach a point where we must lay out a symbol set representing classes of things: particles, forces, and so on. If there are no "random" forces in the universe, then the universe seems to be a completely deductive system (no free will). If there are random forces, how can they be described? Are they really physical, then? That is, a random force cannot be acted upon (else it wouldn't be very random: that's fixing the roulette wheel, my friends) but they can act. Is this not the standard conception of a "soul" or "free will"? I am at a loss to resolve this conflict.

Lib, WRT to my quoted comment. I mean to say that you can't expect people to disagree with the proof. You can expect people to disagree with the definition or the axiom. This most recent example defines God as necessary existence period. No one would deny that necessary existence exists; it does so by definition, I would think. For me to be satisfied by a logical proof of God's existence, I would need to see a logical description of God... a symbolic definition, should I say? A "meaningful" definition might not imply that we can simply pop it into a proof, miscible fluids being one such (possibly overused) example.

xenophon, not inly is it that "whatever must be, is" but "whatever must be, is, if it is", except that the axiom of possibiliy asserts it "is" in at least one case, sealing the deal.

Sorry for the long post, and hope it isn't excessively tangential.

[december]

Here's a quick thought, since I'm on my way out. The phrase, "It is possible," could mean at least two different things:

1. It could express ignorance. "For all I know it might be true that..."

2. It might express a definite belief that something could take place. "It is possible to get a non-stop flight from Newark to Anchorage."

Note that the statement "It is possible that God exists" is true under meaning #1, but false under meaning #2. I wonder if the argument makes use of the slipperiness in meaning.

[RexDart]

Originally posted by Libertarian
I'd like to reprint it here in full, but that might be interpreted as cross-posting. I hope that I can be allowed to quote from there just the definition and axiom. That's all we need here anyway, because there's no question whether the argument is valid (unless you refuse to accept logic as a whole). The only question is whether it is sound.

You don't have to "refuse to accept logic as a whole." I deny only modal logic. Modal logic is absolutely worthless, as it represents nothing.

The universe is a certain way and no other ways. Certain things exist with certain attributes. Those things exist with the attributes they do because the preceding state of the universe determined that they do. That preceding state was determined by the state preceding it. You can throw around the "uncertainty principle" all day, but when it comes right down to it the uncertainty principle is a statement about epistemology not metaphysics. What we know and don't know about the universe has nothing to do with how the universe functions. The universe is causal.

The way the world is right now, that's the only way the world could be. It had to be that way because of simple causality. Nothing occurs without sufficient cause, and if there is sufficient cause the event must occur.

So it is meaningless to say "Possibly X". There is no such thing. There is only X or ~X. Any statement regarding "possible worlds" is meaningless as it has no referent in the actual world from which it can derive meaning.

The Correspondence Theory of Truth, espoused even by famed antirealist Hilary Putnam in his younger years, quoted simply here from one of my favorite texts, Searle's Mind, Language, and Society:

Statements are true if they correspond to, or describe, or fit, how things really are in the world, and false if they do not.
------------
...statements are true only if there is something independent of the statement in virtue of which, or because of which, it is true.

Clearly, from this definition, if we accept the Correspondence Theory of Truth then "Possibly X" cannot ever be true. There is nothing in the world to which it relates.

[jab1]

[quote]Originally posted by Libertarian
(In logic, an argument is valid if its inferences follow from one another, and it is sound if it is valid and its axioms are true.)My emphasis. Once again, you have yet to demonstrate why anyone ought to believe that it is possible for God to exist. Until you have done so, I will not concede that your axiom IS true. (I won't concede that it is false, either. I'm taking the neutral position.)

God is defined as the greatest possible existence, i.e., existence that is necessary.

Why is God necessary? Necessary for what?

In addressing what you believe to be fast or loose about that, please explain how it might be unreasonable to define God to be that which is the greatest possible. The definition seems cogent to me — whatever is less is hardly God, and nothing greater is possible.

My quibble is that you have yet to show how your definition conforms with reality as we know it. You can define God anyway you wish. But why you think it's unnecessary to show how accurate your definition is, I don't know.

To sum up, your argument is the finest example of circular reasoning I've ever seen. You want to show that God exists, and your axiom states that He does; your axiom is the same as your conclusion. If that isn't circular, what is it?

[jab1]

Originally posted by Libertarian
Sure, Tars. I mean a person who believes that "physical matter is the only reality and that everything, including thought, feeling, mind, and will, can be explained in terms of matter and physical phenomena." (dictionary.com)

That describes me perfectly.

[erislover]

Possible can mean "not forbidden" with no implication of "necessity", this is true; however, this is where the logical phrase "possible world" comes into play: the hypothetical construction of all worlds so that a birds eye view shows that everything not forbidden is compulsory (imagine an insane amount of chessboards covering all possible positions). given this description of possible, and the relationship that "necessary" means "exists in all these worlds" or is equated with "compulsory" then there's your discrepancy, december.

But note that the logical meaning of []G is ~<>~G; it is not possible for no G, or that G is necessary. This is what we mean by "necessary" and what we would also mean by "not possible" (in the case of ~G).

BUT, let's rephrase the proof here for kicks. Translate it in your head as you go.

I. G->[]G [erl's note: something that could probably only apply to God]
II. <>G [Ah, agnosticism!]
III. <>G -> G || ~G (|| means "or")
IV. ~G -> ~[]G (though it could still be <>G)
V. ~[]G -> ~(~<>~G) (tautology explained above)
V...which -> <>~G
does <>G -><>~G? To me, yes. That's what "possible" means: may or may not exist(part III). But that isn't what it means in modal logic. "possible" means "is, somewhere". Normally, if something was possible but never happened we wouldn't then conclude that it was impossible (forbidden), only that it just didn't happen (but was still possible). Modal logic eliminates this meaning of possible, however, and thus asserts God's existence in some logical construct. As I said in the other thread, if we are going to assert God's existence then why mess around with logic? Just assert his existence in this world (the actual one) and be done with it.

RexDart, possibility expresses itself in the model of reality, not reality, 'tis true, for the materialist (where something either is or is not, an ontologial law of the excluded middle). If the notion of "possibility" cannot be expressed in your model of reality, then you see that you are saying that everything which is not forbidden is compulsory? Does that sound right to you, metaphysically speaking?

[ultrafilter]

Originally posted by Colibri
It's fast and loose, because in normal parlance "possible" does not equal "necessary." (Don't make me go and get the dictionary - but I will if I have to.) You appear here to be using some non-standard definitions of these two words at least.

What is necessary is always possible; however, not everything that is possible is necessary. These are formal, logical terms, so there's no reason to assume that they should follow standard parlance. The possibility operator <> is undefined, while the necessity operator [] is defined as follows: []P <-> ~<>~P (i.e, P is necessarily true iff it is not possible that P is false).

[erislover]

In fact, hell, my analogy of chess is very appropriate to what I see is the problem with this proof. Consider having enough chessboards and pieces laid out in such a manner as to compose every single possible state of the game. In all boards there will be two kings. The kings are necessary. But that is the rule! Of course they'll be there... we required them to be there before we even laid out the boards!

[erislover]

Ah, er, some of my "implies" arrows should be ,-> not just ->. Still, minor point when the distinction I wanted to make was modal logic's "possible versus English's "possible".

[erislover]

GAH! <-> not just ->

[jab1]

erislover: Free will may be nothing more than a collection of neurons in the prefrontal lobe of the brain that respond to certain inputs. For example, someone reminds you that you didn't feed the cat as you said you would. You feel guilty; guilt feels bad and you want to feel good, so you do what you believe is necessary to feel good again: You go feed the cat.

Why is mysticism required to understand how this works?

[RexDart]

Originally posted by erislover
RexDart, possibility expresses itself in the model of reality, not reality, 'tis true, for the materialist (where something either is or is not, an ontologial law of the excluded middle). If the notion of "possibility" cannot be expressed in your model of reality, then you see that you are saying that everything which is not forbidden is compulsory? Does that sound right to you, metaphysically speaking?

Using words like "forbidden" and "compulsory" seems to confuse things. There is only a way things are, and true statements correspond to that way things are. Everything that occurs had to occur, or else it wouldn't have occured. If that makes everything that occured "compulsory" by your language, then I agree.

The idea that "everything which is not forbidden is compulsory" is not at all problematic as I see it. Commonly we think of something like a pebble falling off a local cliff or overlook as something that isn't forbidden, since we know such things tend to occur. It would indeed be the height of folly to suppose that the pebble must fall just because common laws of physics don't prevent the *isolated* incidence of it falling. This would be to confuse the common notion of forbidden (i.e. not inconsistent with physical laws) with the causal sense of the word (i.e. lacks sufficient cause.)

Take the pebble on the cliff for example. With our general lack of information about the forces at work on the cliffiside, we are tempted to say that such a thing is not "forbidden". However, the pebble will only fall if sufficient cause leads to that event. I will gladly say that it is "forbidden" for an event to occur without sufficient cause.

So under that interpretation of "everything which is not forbidden is compulsory", the interpretation that most fits what I claim about the world, I agree. So if we boil that statement down with some definitions....

1. An event is "forbidden" if it lacks sufficient cause, since that lack will prevent it from occuring.
2. An event is "compulsory" if it has sufficient cause, since that will compel it to occur.
3. An event either has sufficient cause or does not have sufficient cause. (law of excluded middle)
C. All events must be either "forbidden" or "compulsory"

If that's how you're reading what I said, then I agree completely. If you care to deny that argument, than show me either...A) an event that occurs without sufficient cause, noting that I make no claims about the materialistic origin of the cause...or B) demonstrate that the attribute of "being caused" cannot be related to an event.

[erislover]

Then, Rex, I think you should be pretty much compelled to accept modal logic, which also doesn't say how the chess game will be played, it only puts a byunch of boards out and notices a king exists on all of them.

That is, God.

That is,

C. All events must be either "forbidden" or "compulsory"

Though, heh, that should be "4", no? anyway, everything is either forbidden or compulsory allows modal logic to work the way it does here, by saying that
<>G<-> G || ~G
which does not follow the normal use of "possible" in the sense of "Will you make it to the bank today?" ; "It's possible."

Either that or it is senseless to speak of the future, which is an interesting notion in itself (since the future "isn't").

jab

You feel guilty; guilt feels bad and you want to feel good, so you do what you believe is necessary to feel good again: You go feed the cat.

Why is mysticism required to understand how this works?

Well, I'll invite you right out of this thread and into this one, then, where I eagerly await a description of feeling from a materialist perspective.

[Scylla]

Once again, I hate the hocus pocus arguments and 50 cent words that seem to rise up every time someone tries to sell you a load of horse doody.

Since Lib is taking the high esoteric and academic path with the professional philosophers and whatnot (professional philosopher?) I'll take the low road an play the brutalist.

You're palming a card Lib. They game is rigged, and the modal mode just a bit of hinky misdirection, a two dollar parlor trick that even Penn & Teller would be ashamed to pull.

Your definition is false. The God you define isn't the God everybody else is talking about. In fact I say your God isn't even a God at all. At the very best he's a minor league demigod from a minor pantheon. The kind of God Hermes would kick around, the butt-end of all Gods. More likely the God you define is nothing more exciting than a plate of cold beans.

Since when does possible come into the criteria for Godhood?

The way we figure it out here in detention and without the help of no Professional philosophers is that if you can't do something impossible then you ain't no God.

Your miserable, little puny philosopher's God is constrained by the possible. Big whoop. I can blow a quarter out of my nose at 40 mph. I'll bet your God can'e even do that.

The God of your proof can't do half the stuff that it was in the Bible. I therfore say that it ain't God. In fact I know who it is. It's Fred isn't it?

All you proved was Fred. I know about him already, and let me tell you. Fred ain't no big deal.

[RexDart]

erislover let me try to explain why what I argued isn't compatible with modal logic. I use "v" for "or", that's how I was taught. I'll use parentheticals to group to avoid confusion of operating order, and parenthetical notes. This is my first time trying this out, and it's taken me awhile to work through this, I'm out of practice:

1. X -> []X (everything that occurs is compulsory)
2. ~X -> []~X (everything that does not occur is forbidden)
3. X v ~ X (excluded middle)
4. []X v []~X (from 1 and 2)
5. []X v ~[]X (excluded middle)
6. ~[]X <-> []~X (from 4 and 5)

At this point, I've concluded that for any statement about the world, that statement is either necessarily true or necessarily not true. I have also equated "not necessarily X" with "necessarily not X". Now I'll use some modal logic relations:

7. []X -> <>X (if X is necessary, then it must also be possible)
8. []~X -> ~<>X (if it is necessary that ~X, then X is not possible)

Those are basic concepts of the relation between possible and necessary as I understand you use them. Now, for "possible" to have any use at all in philosophy, there must be at least one X for which X is possible but not necessary...so suppose premise 9:

9. (<>X and ~[]X)
10. []~X (from 6)
11. ~<>X (from 8)
12. <>X and ~<>X (a contradiction)

Since premise 9 leads to contradiction, it cannot be the case, therefore:

13. ~(<>X and ~[]X)
14. <>X -> []X
15. []X -> X
16. <>X -> X (from 14 and 15)

Premise 13 is merely "for no statement X can X be possible and not necessary." This flows from my original two premises that represent what I think of the world. Thus, every X that is possible must be necessary. This means that anything that is possible exists. "Possible" as you use it to describe possible worlds means a proposition that could be true, but sometime isn't. From what I've figured in the argument above, that can never happen. So, for someone who adopts my first two premises, possible never describes the situation it purports to. I must conclude it is meaningless. Things that don't exist cannot be thought of as being possible. Possible worlds don't exist, so they cannot in fact be thought of as possible. Possibly true, necessarily true, and true all mean the same thing. There is a way the world is, and only discussions referring to that world and how it really is have any meaning.

As an aside, I suppose this ontological argument for God must do something similiar along the way to arrive at <>G -> G. Obviously I disagree with that, since my attempt to work this modal logic above was simply a way of showing that the conclusions such logic leads to appear meaningless to me.

[The Ryan]

Well, you've presented this argument before, I pointed out quite a few places where the argument is not only unsolid but invalid as well. But in the vain hope that you'll listen this time:

And obviously, he can't be a materialist anymore.

How so?

What that means is that God is defined as the greatest possible existence,

How do you compare two possible existences to see which is "more" possible"? What if there are two that are equally possible.

It is possible that God exists

The word "possible" is ambiguous.

[RexDart]

Oh, and I should have written to followup to 16:

~X -> ~<>X (modus whateverthehell)

That was what I was trying to say at the end anyways.

[Scylla]

~X -> ~<>X

No duh.

Try this:

*^^^>>>*X~~


You know when I first saw this thread title I thought it was "Are Masturbation and logic incompatible?"

Now I'm wondering if they're the same thing.

[ultrafilter]

Originally posted by RexDart
4. []X v []~X (from 1 and 2)
5. []X v ~[]X (excluded middle)
6. ~[]X <-> []~X (from 4 and 5)

Step 6 does not follow from steps 4 and 5. What you're claiming is that ((A v B) & (B v C)) -> (A <-> C), which is obviously false: if B is (D v ~D) and C is ~A, then your hypothesis is true and your conclusion is false. Care to try again?

[Liberal]

Colibri

It's fast and loose, because in normal parlance "possible" does not equal "necessary." (Don't make me go and get the dictionary - but I will if I have to.) You appear here to be using some non-standard definitions of these two words at least.

In "normal parlance", survival of the fittest is natural selection, but biologists, when using the term, don't mean the same thing as armchair science critics who acquired their knowledge of Tennessee v John Scopes from movies like Inherit the Wind.

Here's an introduction to modal logic, hosted by Stanford University. There, you'll see that possible and necessary have strict and formal meanings. And certainly, possible does not equal necessary. So, I am using the standard definition of the two words as they are used in formal logic.

Possibility is truth in at least one world. Necessity is truth in all possible worlds.

[Liberal]

Ultra

Replace "God" with "the universe" in the argument, and it's wholly unremarkable.

That's certainly right. In fact, replace God with "Yiznetsin" and it's equally unremarkable so long as Yiznetsin is defined as the greatest possible existence. That's why symbological systems are so useful — it is impossible to equivocate since your definitions are always carried forward through your tableaux.

Furthermore, the conclusion of a valid argument may certainly be false; after all, it only must be true if the hypotheses are true as well.

Absolutely. Likewise, the conclusion of an invalid argument may be true even if every axiom is false and not one inference follows from another.

What is necessary is always possible; however, not everything that is possible is necessary. These are formal, logical terms, so there's no reason to assume that they should follow standard parlance. The possibility operator <> is undefined, while the necessity operator [] is defined as follows: []P <-> ~<>~P (i.e, P is necessarily true iff it is not possible that P is false).

That's right, except that I wouldn't say that possibility is undefined; it is merely underived. It's defined as truth in at least one world.

[Liberal]

Here's a quick thought, since I'm on my way out. The phrase, "It is possible," could mean at least two different things:

1. It could express ignorance. "For all I know it might be true that..."

2. It might express a definite belief that something could take place. "It is possible to get a non-stop flight from Newark to Anchorage."

Note that the statement "It is possible that God exists" is true under meaning #1, but false under meaning #2. I wonder if the argument makes use of the slipperiness in meaning.

No. It makes use of strict definitions of both possible and necessary. A statement is possible if it is true in at least one world. A statement is necessary if it is true in all possible worlds. Here are a couple of examples:

"A=A" is a necessary statement.

"Parallel lines do not intersect" is a possible statement.

[RexDart]

Originally posted by RexDart
4. []X v []~X (from 1 and 2)
5. []X v ~[]X (excluded middle)
6. ~[]X <-> []~X (from 4 and 5)
--------------------------------------------------------------------------------

Originally posted by ultrafilter


Step 6 does not follow from steps 4 and 5. What you're claiming is that ((A v B) & (B v C)) -> (A <-> C), which is obviously false: if B is (D v ~D) and C is ~A, then your hypothesis is true and your conclusion is false. Care to try again?

You are most certainly in error, sir, for two distinct reasons. First, proposition 5 is most definitely an exclusive "or", for such is the nature of the law of excluded middle. So is proposition 3, "X v ~X", from which proposition 4 follows straight to form, so it is also exclusive. In which case A v B means A -> ~B, since it is an exclusive "or." With exclusive "or", ((A v B) & (B v C)) -> (A <-> C) is in fact true.

Your example makes B a proposition that is always true, that's OK. What's not OK is that it defines C in relation to another element of the statement, so it is not a proper substitution. If we are to apply your form to the elements of my argument that you call into question, then B is the element common to both propositions, namely []X. So the other two elements, A and C, are []~X and ~[]X. You then go on to define C in reference to A, for some arbitrary reason, making it ~A. No matter how you assign the letters, you are making a bad substitution. You are handwavingly assigning C a value of ~A, which is not appropriate to my terms. Are you saying that for some legitimate reason []~X is assigned by you a value of ~(~[]X), or that ~[]X is assigned a value of ~([]~X)?

Let me further illustrate this in case you don't understand why your substitution is bad. If I say:

A -> B
A
_______
B

...that is a valid argument. You can't just reply with...

Oh yeah? Well, let B = ~A, then
A -> ~A
"Hahahahaha, I fooled you, try again!!!!"

It's an improper substitution, plain and simple.

[Liberal]

Scylla and Jab

My emphasis. Once again, you have yet to demonstrate why anyone ought to believe that it is possible for God to exist.

God was defined for the tableau as the greatest possible existence (which itself is the definition of necessary existence). I think it is clearly demonstrated on its face that that which is the greatest possible is possible, unless you would care to show how A = not A.

Until you have done so, I will not concede that your axiom IS true. (I won't concede that it is false, either. I'm taking the neutral position.)

If you mean what you say, then abandon your position; otherwise, show how that which is the greatest possible is not possible.

Why is God necessary? Necessary for what?

For noncontradiction, I reckon. You may define God however you wish (and clearly, you do) and develop whatever tableau you like. For this tableau, however, God is defined as necessary existence. And that means that He exists in all possible worlds.

If you think that some entity other than one that exists in all possible worlds merits the designation "God", then please explain why. And if you think that there is some greater entity than the greatest possible entity, then please describe it.

My quibble is that you have yet to show how your definition conforms with reality as we know it. You can define God anyway you wish. But why you think it's unnecessary to show how accurate your definition is, I don't know.

Once again, I cannot imagine a more accurate definition for God than that entity for which there is none greater. And once again, I wish you would explain what entity might be greater than the greatest one.

Once again, I hate the hocus pocus arguments and 50 cent words that seem to rise up every time someone tries to sell you a load of horse doody.

PT Barnum sold horse doody using widdle biddy words to people who thought Newton's laws were hocus pocus.

Since Lib is taking the high esoteric and academic path with the professional philosophers and whatnot (professional philosopher?) I'll take the low road an play the brutalist.

Do you have another choice?

You're palming a card Lib. They game is rigged, and the modal mode just a bit of hinky misdirection, a two dollar parlor trick that even Penn & Teller would be ashamed to pull.

Said the creationist to the evolutionist. Honestly, Scylla, if you simply said "I don't understand this stuff", I could respect your position. But when you say "I don't understand this stuff, and therefore it is hooey", I can't take you seriously.

Your definition is false [sic]. The God you define isn't the God everybody else is talking about. In fact I say your God isn't even a God at all. At the very best he's a minor league demigod from a minor pantheon. The kind of God Hermes would kick around, the butt-end of all Gods. More likely the God you define is nothing more exciting than a plate of cold beans.

What is superior to that which is the greatest?

Since when does possible come into the criteria for Godhood?

You've got the contingency reversed. It seems reasonable to me to assume that God and truth are compatible. Worlds in which statements may be both true and false (A = not A) are not possible.

The way we figure it out here in detention and without the help of no Professional philosophers is that if you can't do something impossible then you ain't no God.

I see. Well, that would explain right much.

Your miserable, little puny philosopher's God is constrained by the possible. Big whoop. I can blow a quarter out of my nose at 40 mph. I'll bet your God can'e [sic] even do that.

You leave me torn by ambivalence. Should I be delighted that you can form an argument no more compelling than a squint-and-grunt, or should I feel sorry for my materialist friends who must deal with your being on their side?

The God of your proof can't do half the stuff that it was in the Bible. I therfore [sic] say that it ain't God. In fact I know who it is. It's Fred isn't it?

If you prefer to call the greatest possible existence "Fred", I have no problem with that. What matters isn't the word but the meaning that it carries.

All you proved was Fred. I know about him already, and let me tell you. Fred ain't no big deal.

Sadly, I believe you.

Try this:

*^^^>>>*X~~

Okay, Scylla. You can stop staring at me now and eat your checkers.

[Nightime]

Are materialism and logic incompatible, or are materialism and possible worlds theory incompatible? I think you asked the wrong question.

No matter how much faith you have in them, possible worlds are not part of all logic. They are a part of modal logic, but modal logic is particularly unsuited to be used to describe the validity of statements such as "god exists." If you expect anyone to accept this proof, you must first explain why modal logic is the best form of logic to determine the validity of such a statement.

In any case, this proof is both flawed and meaningless.

This thread actually shows the flaws of the proof better than any of the arguments I have seen before. The proof does in fact contradict materialism. It assumes that there are things that are "possible." The question that comes to my mind is: is modal logic incompatible with materialism? It clearly is. Is that not a point against modal logic, rather than against materialism?

RexDart makes the clear case that everything either is, or is not. There is no possible. If all the causes for anything were known, it would be clear that it was inevitable. If there are no random forces, everything that is, is necessarily. The proof would obviously fail. Presumably the followers of modal logic would attempt to bring up examples of random forces. But can they prove that there are completely random forces at work? Even in that highly unlikely case, could they prove that those things which could have happened, but did not, have any implications on the real world? If not, the proof fails. It is logical to conclude that everything has a cause, until it is proven otherwise.

Eris brings up the question of free will. I have gone over this before, but once again, I am baffled by how people think random forces are necessary for free will. Exactly what is your definition of free will, that it relies on chance? If a decision is based on chance, wouldn't that mean that it was not based on free will?

As for why the proof is meaningless, you have to go back to the definition. God is necessary existence and he is the greatest possible. Both these terms rely on the concept of "possible", and therefore in order to even be coherent you would first have to disprove materialism before attempting the proof, but aside from that there are other issues. The concept of "greatest" is similar to concepts such as "eternal." You cannot speak of something as the "most eternal." It is dangerous to modify such terms if you wish to make sense. In fact "greatest possible" only makes sense if something is the absolute standard. For example, the greatest possible power can only refer to something that contains all power. The complete scope of existence contains all existing power. Is there any reason to believe there is an entity apart from all of existence that contains all existing power? No. Therefore "god" is indistinguishable from "existence." So, the conclusion is "existence exists." Not a conclusion with many religious implications.

[ultrafilter]

RexDart: My substitution most certainly is valid. If you don't believe so, provide a citation. However, if you're using "v" to mean exclusive or, then you're using non-standard notation without telling us, which isn't nice.

You are correct in that this is true if you're using an exclusive or, but once again, shame on you for not telling us.

Originally posted by RexDart
Let me further illustrate this in case you don't understand why your substitution is bad. If I say:

A -> B
A
_______
B

...that is a valid argument. You can't just reply with...

Oh yeah? Well, let B = ~A, then
A -> ~A
"Hahahahaha, I fooled you, try again!!!!"

It's an improper substitution, plain and simple.

There's nothing wrong with that substitution. Consider the argument you get by that substitution:

A -> ~A
A
_______
~A

Recall that a valid argument is one in which the conclusion is true if all the hypotheses are true. Since the hypothesis of that definition is false, it is vacuously satisfied, and the argument is valid.

[hawthorne]

Question: is there a possible world where the greatest possible existence is none at all? If a barren world is possible, then then the proof can be valid but otiose. What counts as a possible world?

It's close to A and !A, but not. It's A, but A is uninteresting. It's also close to Scylla's ugly anti-intellectual critique. In the other thread I callled the axiom portmanteau and vague. It wasn't just a grumpy drive-by. What counts as a possible world? What doesn't? What counts as existence? The fleeting? The known? If in a possible world the greatest possible existence is that which shuns the light for a millisecond in the company of no sentients - or even life forms - does that count?

But, yeah, given I don't understand what qualifies as a "possible world"; what can qualify as a "God"; nor what "existence" is; the proof looks valid.

That being said, Lib, I do appreciate that you (i) have a serious agenda; and (ii) usefully test some oversure types here.

Smogily,

[Hamish]

I know next to nothing about modal logic, but I did want to address a something I found in this thread.

At least one poster suggested that a proof of the divine necessitates that the material world does not exist. I would take issue with this. My religion teaches that the divine is an inherent quality of the physical world, a hidden aspect of it. I do not see how the divine and material would be mutually exclusive.

As regards the OP, I don't find it surprising at all that two different methods -- modal logic and materialism -- with two different definitions of "truth" should arrive at two different conclusions. I believe both methods are useful in understanding the world but blind if taken in exclusivity. Truth is best understood through a multiplicity of methods, which requires that one accept that these methods will occasionally contradict.

[RexDart]

Originally posted by ultrafilter
RexDart: My substitution most certainly is valid. If you don't believe so, provide a citation. However, if you're using "v" to mean exclusive or, then you're using non-standard notation without telling us, which isn't nice.

You are correct in that this is true if you're using an exclusive or, but once again, shame on you for not telling us.

Fair enough. I admitted it had been awhile since I'd done this sort of formal logic. I figured that an "or" statement founded on the law of excluded middle was obviously exclusive, since ~(A&~A) is always true.

There's nothing wrong with that substitution. Consider the argument you get by that substitution:

A -> ~A
A
_______
~A

Recall that a valid argument is one in which the conclusion is true if all the hypotheses are true. Since the hypothesis of that definition is false, it is vacuously satisfied, and the argument is valid.

If it's still valid after that, then you really didn't defeat my argument with your so-called substitution, did you?

As an aside, I'm curious if an argument in which the premises can never be true could ever be valid. I agree a valid argument is one in which the conclusion is true if all the hypotheses are true, but that can never be tested with the argument above since A -> ~A will never be true for any A.

If an argument form contains three elements labelled A, B, and C, and defines relationships between those elements, it certainly seems like one ought not be able to substitute by defining one of those terms in relation to another term outside the relations already established. A, B, and C represent distinct propositions, if they were meant to be negations of one of the other propositions you'd use that relation in the first place.

Using your methods I can appear to disprove the transitive principle:

A = B
B = C
_____
A = C

Let C = ~A, substitute....

A = ~A

I haven't actually disproven it, since if A=B then B most certainly cannot ever equal ~A. Since B has already been defined as equal to A, how can you call substituting ~A for B a valid substitution? What I've really done above is artificially alter the argument such that one of it's premises can never be true. It's the same handwaving trick you used on my argument. I defined three elements in relation to each other, then you just waved your hand and substituted for one of the elements with a negation of another element.

What you really did wasn't a substitution at all. It was a new line of argument. To take the simple example as above, it's as if you saw A=B, B=C and then added a new line C=~A.

I haven't the first bloody clue where I could find a "cite" for this online. If somebody who knows about this sort of thing can pipe up, I'd appreciate it.

Anyways, it's all moot since with the exclusive "or" my argument is alright anyways, correct?

[xenophon41]

I do not see how the divine and material would be mutually exclusive.

I quite agree.

If a greatest possible existence is necessary (assuming it is possible), then, I think, this implies that necessary existence is not possible outside of the greatest possible existence.

"Nothing exists but God" is the same thing as "God is everything which exists" or "Everything which exists is God". How this conflicts with materialism is beyond me.

[jab1]

Lib, I'm gonna try one more time.

You're defining God before you've found Him. You're saying God exists before you've found Him. You're no different from a biologist saying that it's not impossible for his hypothetical animal to exist, therefore said animal DOES exist, and that he doesn't have to produce a specimen to demonstrate that he's right. His logical proof ought to be enough, he thinks, and he can't understand why he needs to go and find a specimen. He doesn't understand the difference between a hypothesis (which is all he has) and a theory (which his hypothesis would become when and ONLY when he's secured a specimen that fits his criteria).

So as I've stated before, till you have empirical evidence for the existence of God that can withstand close scrutiny, all you have is a lot of pretty words.

[RexDart]

Let me ask a few questions of Libertarian, since he started the thread. These are not merely rhetorical questions despite how they're phrased. (I'm going to abandon the sub-debate about modal logic to address this, that was a sidetrack in the first place, and more important this other seems...)

I hate to sound like an existentialist, but even if the proof is entirely valid and sound, what does that mean to me or my life? If all that has been proven is the proposition G which stand for the proposition that "the greatest possible existence exists necessarily", what does that do for me?

If the universe if finite, then the greatest possible existence could be expressed merely as the summation of all the lesser existences, in which case we really would be saying nothing more than "the universe exists." If the universe is infinite, I doubt that we can meaningfully discuss it.

Neither of those possibilities appears to negate materialism in the slightest. Does the greatest possible existence have to be anything other than material? If the universe defines the upper boundary on the magnitude of possible existence, then clearly not. How can any existence be possible that exceeds the scope of the universe? The materialist can easily answer these queries under his way of thinking. In fact, as a bonus to we materialists, the argument if true would appear to show that the universe necessarily exists, so we need no longer worry about it's origins, why there's "something rather than nothing." I could throw away 10 long years of using the anthropic principle and start using this equally mystifying argument that people will also accuse of being circular in reasoning (note I said accuse.)

Does this existence possess any attributes at all, other than simply being the greatest possible existence? If it has other attributes, are they the kind that can described with terms like "greater" and "lesser"? Are you really going to fight tooth and nail over each attribute, turning that attribute into a scalar variable, aligning the scalar with "greater" and "lesser" poles, defining the upper boundary of the scale, and assigning that as an attribute? I really don't see where this argument is supposed to go from there, what it's supposed to accomplish, or how it impacts the life of anybody in the slightest. Anyone got an idea about that?

[ultrafilter]

RexDart: Anytime you see a predicate letter, you may substitute any statement you like for it. Check Elliot Mendelson's Introduction to Mathematical Logic, 4th edition.

I also think you're playing fast and loose with your quantifiers in your argument. It looks like you're using existential instantiation on line 9 and trying to use universal generalization on line 13. Would you mind writing out the quantifiers, to see if you're using them correctly?

[ultrafilter]

Originally posted by Libertarian
That's right, except that I wouldn't say that possibility is undefined; it is merely underived. It's defined as truth in at least one world.

Possibly. Just for reference, the universal quantifier is undefined. However, the truth of a universally quantified statement is. It's probably that sort of difference.

[TVAA]

Libertarian's real problem is that he doesn't understand the difference between possibility and existence. It's probably all that thinking about alternate universes that's warped his mind.

If something exists, it must be possible, but it doesn't follow that if something is possible it must exist.

Additionally, differences in probability don't equate to greater existence. Things and events which have a probability of one don't exist to any greater degree than anything else (even assuming it's possible for the probability of an event to equal one).

[Scylla]

Lib:

You asked me if I had a choice, besides choosing the brutalist, as my role here.

Of course I do, but the brutalist is the best way of exposing the shuck and jive, and that is what your exercise in logic is.

It's a magic trick with a stacked deck.

I know nothing about modal logic, and I don't need to. The fix is in before you even start the fancy flourishes.

I find it especially onerous, because logic and rational thinking are difficult enough on their own.

If one is making a rational case one should try to do it in the simplest and most understandable way possible.

Unnecessary complexity is a sin among engineers, rational thinkers, and those who seek clarity and honest exchange.

Your exercise in modal logic is wholly unnecessary to the debate at hand.

"Garbage in, garbage out," is a saying well known among computer programmers and other logicians.


As I put brutally before and as you completely and totally ignored in your response, your logic is flawed as your definition of God is flawed.


The God of your definition is limited by the possible, and is only qualified by what is best (if I am to understand your explanation of "necessary existance," which doesn't sound to me like best possible, but I'll take your word for it.)

"Best possible" is a new definition of God, and quite at variance to what is commonly meant by the term.

"Best possible" is what car companies say their financing terms are.

I am playing the brutalist to contrast the shuck and jive.


Your flaw is simple, basic, and readily apparent.

"Best possible" does not define God. It is an attribute of God, as it is also an attribute of financing terms at Crazy Jim's used car lot.

You are simple using an attribute of a thing to define the thing.


It is a basic logical fallacy. The classic example of this fallacy is the square rectangle conundrum.

A rectangle is a four sided figure where the opposite sides are parellel and of equal length, and all intersections are right angles.

A square is a four sided figure where all sides are of equal length and meet at right angles.

A square is a rectangle, by definition.

A rectangle however is not a square.

On the face of it, this would seem a case where a=b, but b does not equal a, which would be logically fallacious.

It is not becase rectangleness is only an attribute of squareness when applied to squares. It does not define the thing.

Similarly you use an attribute of Godhood in lieu of a proper definition. You have not proved God, you have only proved rectangleness. You have proved a part of the thing, but not the thing itself.

Your logic is flawed by definition before it begins. The deck is stacked and all the hocus pocus that occurs after the intitial stacking is simply misdirection and stage effect. It might be flashy and sophisiticated, but in logic that is a drawback not a positive.

That is why I say you have only proved Fred. Fred is my idiot cousin who has seldom done a thing well in his entire life.

However, he is the only cousin Fred of mine in existence, and his Fredness is unique unto him and nobody could do it as well.

This of course makes him the best possible Fred he can be.


But that ain't saying much.

God deserves a better proof than Fred, and I don't think God's requires a stacked deck or unnecessary flourishes.

[The Ryan]

Yet another problem with is defining a term in terms of itself. "Possible" means exists in some possible world... but how do we know whether a world is possible? By this definition, a possible world is a world which exists in a possible world. But that doesn't tell us anything.

[Liberal]

I apologize for breaking off abruptly yesterday, but our daughter came to visit us!

It is always a treat when we see her. We watched three movies: Sling Blade, Overboard, and The Exorcist. The first two were thoroughly enjoyable. I love the great moral question that Sling Blade leaves with its viewers — can an evil action come out of a good heart? And Overboard is a wonderful light comedy, with Goldie Hawn conducting an acting tour de force, convincingly playing three very different roles: the hated and dreaded rich bitch, the sweet and nurturing poor woman, and the reformed wealthy matron. On the other hand, the producers of the DVD have ruined a classic and important movie, The Exorcist, with gratuitous overuse of subliminal images that are unnecessary and hokey. There is, however, a very cool new scene not to be found in the original that, to avoid spoiling, I'll just say involves Regan MacNeil coming down the stairs in a most unique and startling way.

With respect to the topic at hand, there is considerable overlap in some of the objections of materialists, so I think I'll consolidate those and respond to them:

What does "possible" mean?

In modal logic, possible means truth in at least one world. Thus, the statement "parallel lines do not intersect" is possible because it is true in worlds with flat planes. But it is not true in all worlds, say, worlds without flat planes. Lines on spheres and lines on saddles, for example, may be both parallel and intersecting.

What does "necessary" mean?

Necessary means truth in every world. The statement "A is A" is true in every world. Why? Because of what "world" means.

What is a "world"?

A world is a set of statements. Thus, a world consisting of no true statements is not possible. A world consisting of at least one true statement is possible. A world consisting of only true statements is necessary.

Is modal logic some kind of smoke and mirror thing?

I suppose that's up to each person to decide for himself. Maybe a bit of history can put it in perspective. If nothing else, this should make for an interesting read if you like learning about the history of things.

Curiously, modal logic was the invention of a materialist, C. I. Lewis (not to be confused with atheist turned theist apologist, C. S. Lewis) in the early 20th century. He developed it to advance his Conceptual Pragmatism philosophy, which required dispensing with a seeming paradox in the first order logic truth table. Those of you familiar with elementary logic know that a false proposition implies any proposition (If A is false, and B is true, then A implies B is true.)

Materialists were its greatest champions for decades. Wittgenstein protege, Georg Henrik von Wright, for example, used it to become the founder of deontic logic. Similar branches of logic were spawned throughout the 1900s as philosophical activity, stuck in a rut for almost a century, suddenly began to flourish once again.

Perhaps the most famous and directly influential application of modal logic, however, has been in the field of computer science. As you can see here, modal logics have made it possible to model and address such concepts as "the train might be late" or "Tom thinks he's smart".

Specifically, propositional modal logics have found critical applications in artificial intelligence, reasoning systems, database systems, software engineering, and program behavior theories (algorithms, processes, etc). Modal logic dealing with temporal necessity is indispensible in modeling "the specification, derivation, and verification of programs as programs may be viewed as progressing through a sequence of states, a new state after each event in the system."

Modal logic was moving along quite rapidly throughout the latter part of the 20th century. Materialists were delighted that they had figured out how to model reality. Who needs God now that truth has been determined to be either contingent on possiblity or else born of necessity?

But the shit hit the fan when, in the late 20th century, Charles Hartshorne, one of the most influential philosophers then alive (he died in 2000), suddenly resurrected one of Anselm's nearly thousand-year-old ontological arguments (his second one) for the existence of God, and framed it as a modal tableau. His original argument was this:

1. g -> N(g)
2. N(g) v ~N(g)
3. ~N(g) -> N(~N(g))
4. N(g) v N(~N(g))
5. N(~N(g)) -> N(~g)
6. N(g) v N(~g)
7. ~N(~g)
8. N(g)
9. N(g) -> g
10. g

QED

Horrors! What was once summarily dismissed as an argument that was invalid on so many levels (even today, many otherwise intelligent people, ignorant of these advances in modal logic use the old arguments against ontological proofs) was suddenly clearly valid. You will find that each inference in Hartshorne's proof follows perfectly from the previous inference. Even the staunchest critics, like Stuber and Stoebenau, were forced to acknowledge the argument's validity, even as they desperately worked to show its unsoundness.

Soon, Plantinga and others began developing new tableaux, some more controversial than others. Eventually, as the new millenium dawned, this became one of the most active and fertile areas of philosophy as big names battle very publicly, no longer over validity, but now over soundness.

On a highly subjective note, I find it amusing and ironic that the very tool that was developed primarily to render God irrelevant is now the tool that holds the most promise of rendering Him as not only relevant but necessary.

What I seem to be seeing is that materialists who understand philosophy (and in particular the branch of philosophy called logic) are finding it more and more difficult to defend their position as the modal argument continues to simplify, but they certainly are not resorting to declaring modal logic to be smoke and mirrors. It's simply too essential to modern technology and science.

Only people who are quite unfamiliar with the discipline are rejecting modal logic out of hand. And it appears to me that they are doing so, not because they have found some hidden flaw that has escaped the world's greatest minds for nearly a hundred years, but because they don't like the implication of the ontological proof. In other words, they seem to be saying, "It was a good thing when it worked for me, but now that it works for you, it is nonsense." Thus, the question in the title of this thread.

What's the difference between "valid" and "sound"?

An argument is valid if its propositions follow from one another by strict rules of inference. There is not one philosopher who says that Hartshorne's proof is invalid. No one can say that because he would lose all credibility. If you will not allow a modus ponens to fall through to the next inference, then you simply dismiss the whole of logic altogether. A materialist who does that has "bought the farm", so to speak, and now has nothing other than mystical fuzziness with which to model his material world.

An argument is sound if it is both valid and it's axioms (or base premises) are true. An honest person is forced, when confronted with a sound argument, to accept its conclusion. Rejection of a sound argument is the very hallmark of intellectual dishonesty.

Therefore, many materialists, while unable to attack the argument's validity, have attacked its soundness. This or that premise that serves as the basis of the argument is not true, they say. In its earliest forms, there were certainly eminently attackable premises, like Becker's postulate, for example. No one was forced to accept the proposition that modal status, except for actuality, is always necessary.

But now, arguments have been developed that use far less controversial premises and even do away with the excluded middle approach altogether (like the one under discussion here). So it is becoming increasingly difficult to hold a straight face while attacking the soundness of modern arguments.

What is truth?

There are many theories of truth, some of which were discussed in great detail in the other ontology thread. Someone here mentioned one of them (actually a variant). But this argument holds without respect to any particular theory of truth. The interpretation of God's nature is left wide open by ontology; thus, holders of the Correspondence Theory of Truth may rightfully interpret God from the argument pantheistically.

But what they may not do is make the sweeping assertion that "Modal logic is absolutely worthless, as it represents nothing." Certainly, that assertion represents desperate ignorance. A computerized society without modal logic is like an industrial society without mechanical theory.

The questions remain unanswered

No one has yet satisfactorily addressed the questions from the Opening Post.

1. What existence can possibly be greater than the greatest possible existence?

and

2. How can the greatest possible existence be impossible?

The hedging and protests are not, in my opinion, earning you any points. If you attack the argument's validity you merely look silly. But if you intend to attack the argument's soundness, you must address its only two axioms and show why they are false. Flail all you like; it won't matter. Tease and cajole a la Scylla as much as you want; it means nothing. Evade, and you lose. Misdirect, and you raise suspicion. Hedge, and you waste everybody's time.

Stop being like Creationists attacking evolution, and answer the damn questions.

[Liberal]

Colbri (from the other thread)

Nice try, Lib, but no go. Here you are quoting my partial rephrasing of my own original statement, rather than the original statement itself. Admittedly it was careless of me not to include every significant phrase of the original statement in my restatement. But such are the perils of GD.

Careless, indeed. I quoted what you wrote. Misquoting is a bannable offense, and I resent any implication that I attributed your quote wrongly. Don't blame me for your squirming.

I quote my original statement here:

Once you guys are able to demonstrate the existence of "god" based on physical evidence and mathematical analysis to the same degree of rigor that physicists have used to characterize conditions near the time of the Big Bang, let me know.

I react to this the way Popper reacted to Adler.

Once, in 1919, I reported to him a case which to me did not seem particularly Adlerian, but which he found no difficulty in analyzing in terms of his theory of inferiority feelings, Although he had not even seen the child. Slightly shocked, I asked him how he could be so sure. "Because of my thousandfold experience," he replied; whereupon I could not help saying: "And with this new case, I suppose, your experience has become thousand-and-one-fold." — Karl Popper, Conjectures and Refutations (1963)

There's obviously no point in addressing your concerns, as they might morph again.

Note I originally said "physical evidence and mathematical analysis" (and should have included the same phrase in my restatement - my error). Does your "proof" happen to be based on some physical data?

A neanderthal question. It is a good thing that you did not make the same requirement of Peano.

Your "proof" merely demonstrates that logical rules can be used to "prove" almost anything, if you use arbitrary definitions to start with. As far as I can see, your "proof" can equally well be used to demonstrate the existence of the Perfect Glass of Beer.

Really? Show me.