You seem stuck on the notion that the only reason anyone would reject the argument is because they don’t like the conclusion and its implications. You consistently accuse materialists of using reason when it supports their views and rejecting it when it does not. You are ignoring two things: modal logic, regardless of its conclusions, is not capable of proving the validity of real world statements such as "god exists, " and the conclusion does not support any of the implications you are drawing from it.
Why do you believe modal logic can determine the validity of a statement like “god exists”? In defense of modal logic you have told us that it is a useful tool in cumputer programming. That hardly seems reason enough to jump to the conclusion that it is the best logical system for determining the existence of god! Being useful in computer programming does not mean that modal logic can accurately determine the validity of statements about the real world. In fact modal logic’s complete inability to express the idea that we do not know if something exists or not, without assuming its existence in a possible world, is reasonable grounds for concluding that modal logic is not suited for dealing with the real world. Your description of possible worlds as sets of statements gives more clues that what is useful in computer programming may not be factually accurate in real life. A given statement in a set containing at least one true statement may be considered possible in a computer program, but to use that same logical device to assume the existence of real things is absurd. All you have to do is imagine a set such as [A = A, God exists] and god is “possible.” But does god actually exist anywhere? Can you point him out?
This is a proof about necessary existence. That you, and apparently some other people, choose to interpret necessary existence as being equivalent to god is not part of the proof. So, given the conclusion “necessary existence exists,” why would you see any religious implications at all? A material world based on everything having a cause would mean that everything is necessary. The conclusion is perfectly compatible with such a world.
If all existence is necessary, then necessary existence exists. That’s it. There are no more metaphysical implications. You are enamored with the idea that we should be forced to conclude that god exists, and is identical to all existence. I disagree. I still believe that there might be a god of my own definition, so I will not let you hijack the word god into meaning “all existence.” I think it is unfortunate that the word god was used in this proof at all, as it is clearly causing you to draw baseless conclusions. Necessary existence does not imply anything about a single being with a consciousness. It is simply existence which is necessary. Such a concept is consistent with virtually any philosophy and any religious conclusions you draw from it are based entirely on faith.
I have a problem with Becker’s postulate, which is used in the argument (as presented in the above website). From the website:
“Becker’s postulate… holds that modal status (except for actuality) is always necessary.”
To me, this postulate, which is really an axiom, is one that I cannot accept. It appears nonsensical to me.
For instance, it implies:
If p is true, then p is true
But in english p translates as:
“‘p is true in all possible worlds’ is true in all possible worlds”
Let’s define q = ‘p is true in all possible worlds’. We then can write the above statement as:
“q is true in all possible worlds”
Let’s fix one of these possible worlds, and call it world W. The statement then implies: q is true in world W. Or ‘p is true in all possible worlds’ is true in world W. But this makes no sense. (Really the proof uses the instance of Becker’s postulate:
~G => ~G
And ~G implies “there is at least one possible world in which G is not true” is true in world W. This makes no sense either.)
What does it mean for a statement about possible worlds to be true or false IN a given world W? To me it means nothing. It is nonsense. It can only be true or false OF a collection of worlds. Within a specific world it is gibberish.
There are multiple ways to interpret the statement that “a given state is possible”. One way is to use the multiple worlds model, so that if something is possible it exists in a possible world. Another way relies on the assumption that there is only one world that exists, and that ‘possibility’ refers to what might be true about that world.
Using the second method, we can see that it might be possible for something to necessarily exist, but that there might not actually be something with that quality.
How can we actually show that something is impossible?
Until we’re willing to explicitly define what it means for something to be possible or impossible, Libertarian’s arguments are meaningless.
But you have yet to demonstrate that all existence is necessary, or even that any existence is necessary.
Your proofs all make the assumption that something exists, then demonstrate that they cannot make the counterassumption. Well, duh.
If you construct a proof that doesn’t take existence for granted, and then show that existence is necessary, then your arguments will hold. Until you do this, you’re not saying anything particularly interesting or meaningful.
Lib, I appreciate your taking the time to address my queries.
As for my own take on all this at this point in the discussion…
I believe in a perfectly deterministic world, with a few epistemic limitations. My attempt to muddle though a proof needs refining at some point, but I think you can see intuitively how for someone who believes in a perfectly deterministic world, “possible” doesn’t mean much to that person. Nighttime has pointed these things out better than I think I can right now, I have too much going on right now to flesh out the idea any better.
I’m willing to accept that Lib is keeping his own personal religious interpretations separate from the argument, he only brought them in because I was curious and asked him. I did this because the conclusion of the proof, standing on its own, is existentially irrelevant. There is nothing religious at all about his argument other than naming the proposition “God.” If he’d named it “Andre Agassi” we wouldn’t be thinking of this as religious.
I find it rather odd for someone with the handle Libertarian to suggest that “there is nothing substantively real about the universe.” That sounds like our old friend Hilary Putnam checking in, and I doubt that postmodern antirealism is much of a platform for libertarian ethics. If there is nothing substantively real about the universe, then statements we make about the universe cannot be true or false, right? I’m gonna presume I’m misunderstanding what you meant there, since you’ve surely been through this debate before and that would have been pointed out.
As an aside, Lib from one libertarian (small and large L) to presumably another, I’d love to have a discussion sometime about which religious traditions are consistent with libertarian ethics. Christianity strikes me as placing far too high a value on altruism to be consistent, but I don’t know enough about other religions to know which ones are most similiar to the libertarian ideals. Personally, I’m an atheist (this argument aside, i’m still not sure that even if I accept your argument that I want to call that “God” or “theos” or anything similiar) and I find my views very consistent with libertarianism, and found validation and further exploration along those lines with reading Atlas Shrugged. I’m interested in how people fit together their political ideologies with their spiritual beliefs, since I myself have no such beliefs in the way.
No, no, no. I was not in the least accusing you of misquoting me - you quoted me quite correctly. I was accusing me of misquoting myself. (I hope I won’t be banned for that. ;)) As I said, it was my error, and you are entitled to score a debating point on me.
(However, I won’t concede the point itself merely because I was careless. And I think you and erislover missed my real point. My remark wasn’t intended as a challenge to you. It was to point out that, since I am a scientist, you would have to provide scientifically valid evidence for me to accept it. Erislover’s request for a religious proof of physics was a perfectly valid response. I can’t provide such a proof, any more than you can provide a scientific proof of god.)
The problem with your methodology is that, as Scylla says, it’s “Garbage in, garbage out.”
In this case, it’s “abstraction in, abstraction out.” Even if all your logical steps are correct, if you are dealing with abstractions like “possible” and “necessary” - even if you have precisely defined them, they are still abstractions - your result must necessarily be an abstraction. It doesn’t matter how internally consistent the argument is, there will be no guarantee it will have any applicability externally.
An analogy could be drawn to imaginary numbers, based on the square root of negative 1, in mathematics. It is perfectly easy to perform valid logical mathematical operations on such numbers. However, that does not mean that you will produce a result that has any meaning whatsoever in the real world.
Logical operations, of course, are used to obtain results in science. However, they must be used with in reference to actual identifiable and quantifiable entities to yield valid results.
Just posting a funny thing I came up with. Don’t take this to mean I am condoning this sort of reasoning.
Proof that God does NOT exist.
Definition: God is a being with the property G => G
Axiom: It is possible God does not exist. In symbols: <>~G.
Step 1: Axiom <=> ~G (a translation - ok, this could have been the axiom, as they are equivalent.)
Step 2: ~G => ~G (the definition of God, and modus tollens)
I only need 1 axiom, and it isn’t Becker’s postulate!
Ok, kidding over. Libertarian, I am interested in your defense of Becker’s postulate.
I’m impressed, Jab. That is a pertinent and well-thought-out question that does not even hint at derision or summary dismissal. Unfortunately, there appears to be insufficient evidence that there exists a collective consciousness within which a collective intelligence might exist. Rather, there seems to be strong evidence that, for example, I cannot read your thoughts or transmit to you my own. No one seems actually to feel someone else’s pain.
Some men are more intelligent than others. Proving that even the most intelligent man, Cecil Adams, possesses the most possible intellegence is problematic.
Well, of course I’m stuck on that. Inasmuch as there is no rational excuse for rejecting a sound argument, the excuse must be an irrational one.
[…blank stare…]
Because that’s what modal logic does. It examines modality, “[the] classification of propositions on the basis of whether they assert or deny the possibility, impossibility, contingency, or necessity of their content.” (The American Heritage Dictionary)
It has been soundly proved that He exists in every possible world.
Point? Can you point to love? To mercy? To justice? Wherever you point these out, you are pointing out Him. Oh, and that reminds me that I forgot to address another specious protest. Indulge me a moment please, Night.
I can prove there is a greatest possible integer with your proof of God
Um, no. Maybe with some other proof. But if you define “integer” the way “God” is defined here, you merely substitute one syllablism for another. It is irrelevant whether the term used is “God”, “Allah”, or “Toaster Oven”. It is the concept of necessary existence that is the subject of the proof.
[…continuing with Night…]
Who said anything about religion? It is well known that I despise religion, and believe that God does as well. Why, when speaking of God, ought I to contextualize Him within some arbitrary political machination?
No, I don’t intend to get into definding Becker’s Postulate here. I already did that in the other thread and, as I explained there, though I don’t believe it to be universally true (like Peano’s Induction Axiom or Euclid’s Fifth Postulate), I do believe that it was reasonably applied by Tisthammer. Incidentally, postulate and axiom are synonyms.
I notice that a sentence in the above post seems ambiguous. Let me clear that up: I do not believe that either Peano’s Induction Axiom or Euclid’s Fifth Postulate are universally true. For example, the Induction Axiom does not hold in a mathematical statement that contains irrational numbers, and the Fifth Postulate does not hold on curved planes.
They do according to Euclid’s definition of parallel lines, so long as a “straight line” is defined as intersecting two points on a plane. See Proposition I.27 in Eudlid’s Elements.
It isn’t my proof, but rather a proof whose variants have been examined in excruciating detail by eminent logicians for forty years now. You are the first authority to declare the argument invalid. Even its most vociforous critics, while denying its soundness, have never questioned its validity.
Nowhere in the definition, axioms, or inferences is the statement “G” to be found. It is not found until the conclusion. With all due respect, you would do well to reconsider your position on the matter.
You have put me to shame with your graciousness. I ought not to have lashed out at you in the manner that I did. I apologize.
It is ironic that you and your cohort have used a saying popularized by computer science as a (weak and flimsy) attack upon the very discipline that underpins analyzing what is garbage and what is not. One man’s garbage is another man’s treasure, I suppose.
All that links me to it are my tenuous senses, themselves tautologically a part of what they tell me is there. What is real is what is absolute. Or necessary.
Jesus is the consumate libertarian, never forcing any man to believe or behave against his will. He pursued His own happiness in His own way peacefully and honestly, while allowing other men to do the same. He never called upon government to make any law, but rather appealed to the reason and sensibilities of men to recognize His compassion and love for them. He visited only where He was welcomed, and did not resist even when men lynched Him for their own political gain.
He gives His love freely and encourages us to do the same, not from any mopey altruistic motivation, but because embracing His love and our salvation is in our own self-interest and offering it is in His. He even exercises His rights libertarianly — holding that they are tied inexorably to His status as Creator and Owner of the heavens and the earth.
You won’t find a more libertarian example than He, nor more libertarian teachings than His.
Let’s return to “Are you saying the greatest possible being can’t possibly exist”? We’re saying that, one, you’ve no reason to conclude that the greatest possible being is god. Two, that there is any similarity between greatest possible beings in modal universes remains outside the scope of this proof. Three, that “possible” doesn’t have the same meaning in modal logic as it does in English.
Point one, revististed; anyone who became convinced that God existed from this proof or any other modal logic proof seems to have been led seriously astray without other, more exhaustive, symbolic treatment. As you agree, this is a pure a priori ontological proof which says nothing about what qualities this greatest possible being possesses. As such, I think you do logic an injustice when you put the heavily disputed “God” in there when there is no clear call to do so.
Now, I do agree that G->G would be one quality a God would possess.
Point two, revisited; actually, I don’t think anyone but be has said that, but I think it is a salient point.
Point three, revisited; I don’t know how else to say this, honestly. I liked my chessboard analogy, did you not feel it was appropriate?
Libertarian has defined and proven an attribute not a thing.
How you get from that attribute to it’s embodiment in all its myriad froms in a single sentient being is something he cannot explain and seems unwilling to address.
Libertarian’s proof exists in a self-defined and internally consistent world whose ground does not mesh with the real world, and he’s unwilling to take a step outside of that self-defining context, because to do so would be to capitulate to the fact that there ain’t nothing special going on here.
Let me deal first with your chessboard analogy. For the purposes of the proof, the chessboards are not God (they can’t be, because they are each a distinct entity). Neither is the “insane” number of possible positions (it can’t be, because every position is contingent on some rule). God is the bird.
Second, I’m flummoxed as to how you can hold that G->G while holding that there’s no reason to conclude that God is the greatest possible Being. It is accepted axiomatically in modal logic that the greatest possible existence is necessary existence since it exists in every possible world, and a being is merely a manifestation of existence (in fact, they may be treated as synonyms).
In my opinion, protesting that the greatest possible being might not be God is absurd because, if you refuse to call it G-O-D, then whatever you call it, say, Ixfum, then it is Ixfum that I worship and that I consider to be uniquely worthy of worship, and Who in fact is the subject of this proof. It doesn’t matter to me if you say I -> I. That’s still God, which is ordinarily understood to be the “Supreme Being”.
As far as “possible” having a specific technical meaning in modal logic, I’m truly surprised to find you lecturing me about that. Clearly, the record shows that I have myself been making that very point again and again and again. By “possible”, we mean true in at least one world. Check it out. You’ll see that I’ve said this more than once here and elsewhere.
Chessboards weren’t meant to be god, they were meant to be “possible universes”, X chessboards wherein all X possible board states were displayed. A king is on every board. But there is nothing suprising in that.
Exactly. I know you’re clear on it, but it is a point that needs to be kept in mind when we’re discussing the proof in English. the English word “possible” does not always mean “<>”. I think this is leading you astray in how powerful this proof is.
The proof does not demonstrate that the greatest possible being is greater than human life, for one example. It also doesn’t really assert existence of a being, at least not obviously. Not to me, anyway.
I would tend to disregard axiom one or axiom two based on the asserted meaning of those symbols. The proof itself stands firm, no doubt about that.
If you were to ask me, “Is God possible?” in English I would respond, “It seems to be so, yes.” If you were to say “<>G?” I would say, “I think that needs to be demonstrated.” It is simple for me to take on faith that Eris exists because, hey, look at how messy my room is. But it is another to say that I can construct a logical world in which Eris has a definite place. For any non-Discordians, “<>E” is quite a load to swallow. It doesn’t sound innoccuous when phrased in English because “possible” in English etc.
Typically, axioms are either accepted as reasonable or rejected as unreasonable. It seems reasonable to me to say “G[sup]1[/sup] -> <>G[sup]2[/sup]”. What, to you, seems unreasonable about it?