Are materialism and logic incompatible?

[Liberal]

Satasha

It seems to me Libertarian, that you are saying that the universe or the set of all things must exist because all true statements that can be said about it hold true for it.

Well, of course! How can the moon do that thing called “existing” if no concept of existence is ever conceptualized and introduced?

You are substituting the word god for the word universe or the set of all things.

I most certainly am not. I am substituting the word “God” for the word “necessary existence” (or Supreme Being).

But god implies sentience.

Only inasmuch as sentience exists. If there is sentience, then God’s own sentience is the greatest possible.

The set of all things contains sentient creatures but why would the set of all things have an over all sentience and will, much less morals and feelings?

I can’t imagine. As the record shows, I’ve already called the panentheistic viewpoint weak and the pantheistic viewpoint arbitrary.

The set of all things contains all knowledge (information) but why would there be an all percieving entity for this knowlege? The set of all things contains all power, but why would all of that power necissarily be controled by a single entity? I don’t see how your proof leads to these conclusions.

No offense, but didn’t I already spend, like, 3 hours explaining this to Phoenix? Please refer to my post to him about how things that exist have attributes.

I fully admit that this is over my head, but even in my limited understanding, I can see that you have failed to adress many counter points from the first three pages.

Points about what? The argument? I cannot imagine how I could have addressed them any more thoroughly. In fact, if you examine the record, you can see that I have spent hours and hours and hours addressing them — and most of them more than once or twice.

I think that it is fair for me to say that there is abundant evidence that some people are not reading those addresses. I know of no other sensible reason that DrMatrix would have missed my request to repost the proof. I know of no other sensible reason why Eris would have made reference to “the second axiom” when there isn’t a second axiom. And I don’t know why you would think that I haven’t responded unless you skimmed my posts.

If I’ve missed anything, it is simply because I am human, there are hordes of people who are demanding to be addressed, and there is only so much time in a day. In an argument as simple as this — with one definition, one axiom, and five inferences — defending it is trivial. But I am defending the same points over and over and over.

Just look at what Phoenix did. After sulking that I overlooked his post, he proceeded to ignore summarily almost everything I wrote to him (over the course of several hours) and — dagnabbit! — just basically repeated his questions and protests, the same ones that I addressed in incredible detail, as a rebuttal! Why on earth should I be subjected to that?

What am I, gum on your shoe?

Also the appeal to authority is not cool (pit thread and hinted above). Saying that leading philosophers agree with you and that you will take their word over posters here leads me to wonder why you would discuss this here at all.

Appeal to authority a fallacy only when the authority is of questionable credentials with respect to the matter at hand.

See argumentum ad verecundiam.

I think at the least you are in stalemate by agreeing with Xargque.

:eek:

You think I agreed with Xargue? Criminey.

whole argument becomes moot when you concede that “there is no way to judge between the weak and strong views.”

Oh. That. That has nothing to do with the ontological argument. Nothing whatsoever. He and I were playing with our philosophical navels.

[Liberal]

I’m not ignoring you, Eris. That’s fine if you don’t accept the axiom. It simply means that you are a hard atheist. By not accepting <>G, you must accept ~<>G. Both cannot be true.

I’ve already explained, what, half a dozen times now, why I think <>G is reasonable. I have nothing new to say about it.

[erislover]

There there we stand, Lib. Shame. We agree on so many other things, I do not like standing against you. Well, had to happen sooner or later.

[erislover]

Oh, and just because I do not accept <>G doesn’t mean I accept ~<>G. Really, that’s sort of trivial. I thinkg ~<>G would need to be demonstrated, too.

They are not good axioms, IMO. Too powerful and denial doesn’t cause a contradiction. If it does, then we have defined God into existence, which is, of course, begging the question. I don’t think you can have it both ways.

I think <>E. I do not think E->E. So the proof is totally different from my theological beliefs.

[hawthorne]

[continuation of cardinality sideshow] I think I can better phrase what was troubling me, and it smells faintly of Gödel. It seems to me that a being with the greatest possible existence must know at least two things: 1. that it exists and 2. that it knows all there is to know in that world. I don’t see that this can be reduced. I don’t see how such a being can exist in a world with only one true statement. Put another way, a world with a greatest possible existence being and only one truth is paradoxical - the being must know something ouside the system to fulfill its definition.

What I’m getting at is that the world needs to be sufficiently complicated to allow the existence of a greatest being or entity. And whilst I’m questioning whether this is possible for a world with one true statement, I guess I’m doubtful of it beyond that.

[preguntas_sin_pantalones]

Libertarian writes:
“Dougherty’s argument is much less controversial, eliminating Becker’s Postulate altogether and avoiding the whole mess of arguing by the excluded middle. So his was the argument that I selected for these renewed discussions.”

From the “new” proof Libertarian presented:
“Inference Number 2: (p -> p) -> (<>p -> p)
This inference is a statement of Bouer’s Theorem, and you can find proof of it in any sufficiently advanced text on K logics. It says simply that if an entity is implied to exist necessarily, then the entity’s existence is implied by virtue of its possibility. It is our axiom that allows us to invoke this theorem.”

Prove Bouer’s theorem WITHOUT USING BECKER’s POSTULATE. Folks, look carefully. This is what the old proof showed, and it used Becker’s postulate. Libertarian is throwing up more smoke. I suspect he realizes he can’t defend Becker’s postulate, so he quotes a theorem, hoping no one will call his bluff.

Libertarian writes:
“[Preguntas,] For the reasons that I’ve explained. Put simply, the inferences follow from one another. That is the definition of a valid argument.”

But I have been pointing out that an invalid statement is inserted into the proof: ~G => ~G. The right hand side of the implication is nonsense. It is inserted into the proof, and manipulated as if it made sense. That is INVALID. It is not a soundness issue. Or rather, in the sound interpretation of worlds and possibility, ~G is nonsense. So the proof in this case becomes invalid.

[Liberal]

Eris

Once again, we’re at an impasse. I cannot accept that both A and Not A are true; and I cannot accept that both are false. I consider the Law of Noncontradiction to be the most fundamental principle of logic. God go with you, my friend.

Hawthorne

Maybe if I put it this way (I presume you saw my post to Apos): that world in which one statement is true is not the only world. It can’t be. You touched on that fact yourself with your reference to Godel. Remember that God is composed of all truth (all possible worlds). It makes no difference if there are uncountably many.

[Dryga_Yes]

To be honest, I’ve never even heard of modal logic before reading these threads. A lot of this seems quite confusing. I just want to know if I’ve understood the foundations of modal logic (and this proof) correctly…

If you write out the entire proof, without making my head hurt by talking about possible/necessary existance and assloads of funky symbols, would it look something like this?:

*1. There are infinite possible words… everything that can happen will happen, in one world.
2. There is a maximum to how much power a being can have.
3. Therefore, in some of all these worlds, say 1/10000 of them, there exists a being with maximum possible power.
4. There is a maximum to how much knowledge a being can have.
5. In some of the worlds with a being with maximum possible power, said being will also have maximum knowledge.

etc. for any attribute you can think of *

And thus you’ve proven the existance of a omnipotent and omniscient being, at least in one world.

Anyway, what I still don’t get is how you get from that to this:

*6. There is a maximum to how many worlds you can exist in.
7. Therefore, in some of the worlds with a being with maximum possible power and knowledge, that being will also exist in all other worlds.
*

Please tell me if I’ve misunderstood how the whole system works, but if this really is how the proof goes then it doesn’t sound like much more than the modal logic equivalent of asking if you’ve stopped beating your wife.

[erislover]

I accept non-contradiction, too. That doesn’t compell me to accept ~<>G or <>G, however, only that I don’t accept both of them simultaneously. And I won’t accept them axiomatically.

You say, “If, if, God exists” etc. Yes, if. If <>G. but you never demonstrate <>G.

You are either defining him into existence or asserting his existence. Which destroys what you want the proof to prove.

[Liberal]

Preguntas

Prove Bouer’s theorem WITHOUT USING BECKER’s POSTULATE. Folks, look carefully. This is what the old proof showed, and it used Becker’s postulate. Libertarian is throwing up more smoke. I suspect he realizes he can’t defend Becker’s postulate, so he quotes a theorem, hoping no one will call his bluff.

That’s insane. Let me get this straight. You have yet to accept any proof that I have given of anything, including the common proof that necessary existence exists. And now, you want me to show you the proof for Brouer’s Theorem? (Interesting that you misspelled it identically to the way I did. I submit that you know nothing about it.) Buy a book. Read a clue.

But I have been pointing out that an invalid statement is inserted into the proof: ~G => ~G. The right hand side of the implication is nonsense. It is inserted into the proof, and manipulated as if it made sense. That is INVALID. It is not a soundness issue. Or rather, in the sound interpretation of worlds and possibility, ~G is nonsense. So the proof in this case becomes invalid.

In WHAT proof? Criminey, man. Not only can you not find a fault in the argument, you go so far as to make up inferences and find fault in those. Where the hell did I say, what is it, “~G => ~G”?

If a moderator doesn’t call you down on that, there is no justice at the SDMB. Sir or madam, you’re dishonest. And THAT is proven. My last word to you is this

[Liberal]

Eris

I accept non-contradiction, too. That doesn’t compell me to accept ~<>G or <>G, however, only that I don’t accept both of them simultaneously. And I won’t accept them axiomatically.

Let A = <>G. Are you saying that both A and Not A are true? That neither is true? That one is true sometimes, and the other sometimes? What, exactly?

You say, “If, if, God exists” etc. Yes, if. If <>G. but you never demonstrate <>G.

Well, for heaven’s sake! <>G doesn’t mean “if God exists”. What on earth are you talking about? <>G is my axiom. Since you like bold, let me give you some bold: It is the only modal status that does not contradict the definition.

You are either defining him into existence or asserting his existence. Which destroys what you want the proof to prove.

That’s just nonsense. “G = G” is the definition, and it most certainly does not prove that God exists. Neither does “<>G”, the only axiom. God exists is expressed by “G”. You know that. So why are you doing this?

[Liberal]

Dryga_Yes

I just want to know if I’ve understood the foundations of modal logic (and this proof) correctly…

Good for you! You are to be commended for your intellectual search.

1. There are infinite possible words… everything that can happen will happen, in one world.

No, that’s not accurate. The correct paraphrase would be “There are as many worlds as are possible… everything that can be possible in every world is possible in every world.” (Note that possibility does not imply either eventuality or actuality.)

2. There is a maximum to how much power a being can have.

Well, yes, but that’s a bit too vague. I would say, “The maximum power that a being can have is the greatest power possible.”

3. Therefore, in some of all these worlds, say 1/10000 of them, there exists a being with maximum possible power.

Sorry, that’s way off base. The Being exists in all possible worlds, not just some of them.

4. There is a maximum to how much knowledge a being can have.

Again, sort of. The Being has as much knowledge as is possible.

5. In some of the worlds with a being with maximum possible power, said being will also have maximum knowledge.

Imprecise, sorry. The Being will have all possible power and all possible knowledge in all worlds where power and knowledge are possible.

6. There is a maximum to how many worlds you can exist in.

The Being exists in all possible worlds.

7. Therefore, in some of the worlds with a being with maximum possible power and knowledge, that being will also exist in all other worlds.

I can’t comment on that; I’m not sure what it means.

Please tell me if I’ve misunderstood how the whole system works, but if this really is how the proof goes then it doesn’t sound like much more than the modal logic equivalent of asking if you’ve stopped beating your wife.

That would be a logical fallacy called “complex question”. At any rate, I hope I’ve assuaged your apprehensions about how the system works.

[preguntas_sin_pantalones]

Libertarian:
“That’s insane. Let me get this straight. You have yet to accept any proof that I have given of anything, including the common proof that necessary existence exists. And now, you want me to show you the proof for Brouer’s Theorem?”

Mock indignation will not remove your responsibilty to prove Brouer’s theorem. You are trying to make me appear less intelligent than you as a rhetorical device, perhaps so you can avoid proving Brouer’s theorem.

Libertarian":
“(Interesting that you misspelled it identically to the way I did. I submit that you know nothing about it.) Buy a book. Read a clue.”

Again, insulting my intelligence gets you nowhere (at least nowhere good).

I know YOUR statement of it:
“Inference Number 2: (p -> p) -> (<>p -> p)
This inference is a statement of Bouer’s Theorem…”
And I know that was what was proven in THE PROOF.

Libertarian writes:
“In WHAT proof?”

Your very first post in this thread:
http://boards.straightdope.com/sdmb/showthread.php?s=&threadid=114967&perpage=50&pagenumber=1

Libertarian writes:
“If a moderator doesn’t call you down on that, there is no justice at the SDMB. Sir or madam, you’re dishonest. And THAT is proven. My last word to you is this”

No, YOU are dishonest.

[preguntas_sin_pantalones]

Libertarian writes:
“Where the hell did I say, what is it, “~G => ~G”?”

See your first post in the thread I gave the link to above. Pretending I am misquoting you is DISHONEST.

[preguntas_sin_pantalones]

Libertarian writes:
“Where the hell did I say, what is it, “~G => ~G”?”

See your first post in the thread:
http://boards.straightdope.com/sdmb/showthread.php?s=&threadid=114967&perpage=50&pagenumber=1
I actually never said you said this. It is in the proof you quoted though, and which I am discussing. Pretending I am misquoting you is DISHONEST. Trying to bring moderators down on me for it is… well I won’t say what I think of that.

[hawthorne]

In passing, can I suggest erislover’s post would be improved by inserting “either of” between accept and them. It’s a good point - whilst one of them is true and one false, my reluctance to wholeheartedly embrace one of them does not necesitate that I must accept the other. It’s reasonable to say I don’t know and I may never know.

That response of yours to me Lib has really lost me. Maybe I’m not following, but

that world in which one statement is true is not the only world. It can’t be. […]Remember that God is composed of all truth (all possible worlds).

freaks me out. I can’t accept that even the greatest being in any possible world knows more truths than there are.

[Liberal]

Preguntas

I shouldn’t respond to you, but I’m a sucker for persistence.

You’ve confused Tisthammer’s proof (in the other thread) with my arrangement of Dougherty’s proof (in this thread). Tisthammer’s proof does not use Brouer’s Theorem and my arrangement of Dougherty’s proof does not use Becker’s Postulate. Brouer’s Theorem is not proved (at least I’ve never seen it proved) with Becker’s Postulate. It is proved with the K Axiom — ([symbol]f[/symbol] -> [symbol]y[/symbol]) -> ([symbol]f[/symbol] -> [symbol]y[/symbol]) — and 5 Axiom, which I’ve cited earlier. The proof is trivial.

I don’t know whether you’re less intelligent than me or not. I doubt it. That’s what’s scary. And don’t worry about the mods. I cannot recall an instance when one has ever come down on my side.

[erislover]

Are you saying that both A and Not A are true?

Nope. Either <>G or ~<>G is true. I just don’t know which.

Well, for heaven’s sake! <>G doesn’t mean “if God exists”.

I’m sorry, but that is bullshit. That is exactly what <>G means… that he exists in some possible world. G means he exists in this world. That would be the conclusion. You reach that conclusion by asserting that he exists in a possible world.

This needs to be proved. If you can’t prove it, I can reject it. Period. Rejecting it doesn’t mean I must accept ~<>G, which, logically, I would also reject without proof. I believe rejection A and ~A would consitute the English phrase, “I don’t know.”

It is the only modal status that does not contradict the definition.

Then please demonstrate that using modal logic. I don’t see it, frankly. When you say “possible” in modal logic, you mean “exists in a logically descriptive world.” Note the ontological assertion?

[telechus]

I’ve been watching this thread with interest. At this point, I’m hoping to confirm the formal definitions of some the terms used in modal logic so I can better access the argument presented by Lib.

In modal logic, here is the terms and their meaning as I understand them:

world: a set of statements in modal logic where at least one of them is true

possible: belonging to at least one world

neccessary: belonging to all worlds

Are these the meanings that you using in your proof Lib?

[preguntas_sin_pantalones]

Libertarian writes:
“You’ve confused Tisthammer’s proof (in the other thread) with my arrangement of Dougherty’s proof (in this thread). Tisthammer’s proof does not use Brouer’s Theorem and my arrangement of Dougherty’s proof does not use Becker’s Postulate.”

Tisthammer’s proof IS a proof of Brouer’s theorem!!!

Brouer’s theorem:
(p -> p) -> (<>p -> p)

Assumptions of Tisthammer’s proof:
G -> G
<>G
Conclusion of Tisthammer’s proof:
G

Substitute p for G. THEY ARE SAYING THE SAME THING!!!