Consider this dialogue about the modal ontological argument.
T: Surely, you think it's possible that there is a God, surely. I mean, maybe he exists, doncha think. I mean, you aren't one of those dogmatic atheists, are you.
A: Yes, of course, I admit that it's possible that God exists.
T: Gotcha! Gotcha! Gotcha! Since the existence of God is either necessarily true or necessarily false, the S5 axiom says that if a necessary truth claim is possibly true, it must be necessarily true. Since you have admitted that God possibly exists, you must therefore conclude that God necessarily exists!!!
A: Uh, could we maybe restrict the accessibility relation or something?
Bill Vallicella is dealing with an atheist argument on his site with much the same problems.
20 comments:
its just epistemic and logical possiblity being conflated.
To what extent does the epistemic possiblity of God (for me, now) give me reasons to think that God is really logically possible.
hell if I know. Aquinas was probably right on this one.
How would you obtain the premise that "the existence of God is either necessarily true or necessarily false"?
If God is defined as "a necessarily existent being" then if there is a God, God exists necessarily, and also if there is not one, it is necessarily the case that there is not one (just like it is necessarily the case that there is no last prime number)/
I'm very fond of the Ontological Argument. Because you keep thinking that someone's pulling your leg - but can't quite put the finger on it. And in that way, it forces you to think deep and hard about the nature of God. It's valuable not so much as a proof of God (I do believe the inference "God is possible" -> "God is necessary" holds, but that God's possibility or impossibility is an unknown) but as a conceptualization of God.
I like to think of it as stating that in referring to God, we always refer to an actuality. Things in our world, such as apples, may be described as having certain features (round, red, tasty) and subsequently we may wonder if they contingently exist anywhere. Not so with God.
The argument Bill Vallicella treats slily allows the ontological argument and then attacks it with an argument from evil in order to deduce God's impossibility, hence a strong atheism. Which is great (I like my atheists like my coffee. Strong.). But there is a lot that remains unsaid between "God is a necessary being" and "Unjustified evil is impossible". All standard (or nonstandard) defenses against the argument from evil apply.
I think Robert Maydole's ontological argument is the most succesful one yet.
its just epistemic and logical possiblity being conflated.
I'm not sure what the distinction is supposed to be. If something is epistemically possible, ti is broadly logically possible. That is, if something not a priori impossible (which is what epistemic possibility amounts to here) then it is BLP. One might try to generate worries from the distinction between epistemic and metaphysical possibility, but I've never seen that convincingly done in this sort of case.
That aside, the real problem here is the parity argument. On the other side, one is inclined to admit that, possibly, there is no God. But from possibly there is no God, you get necessarily there is no God.
Modality's just a fancy philosophaster term for probable. Doesn't really add anything. Any argument with premises featuring probable situtions/events would seemingly result in only probable conclusions, or cogent perhaps. Really, "modal-logic" easily becomes a Lewis Carroll whimsy-logic:
If X might possibly be a rat, then X is necessarily a cat.
X might possibly be a rat.
Ergo, it's a cat!
(valid, I guess, but the "modal" premises are not true, or even probably true in any confirmable sense, so unsound).
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The original, non-modal onto-argument's wrong too. How do you know? YOu get an excruciating headache trying to understand it, or even refute it (anyways, "existence is not a predicate" seems applicable. Saying "Concept X exists because it's better to exist than not," does not reason make.... )
I took epistemic possibility to be just "for all I know, it could be" So with respect to all sorts of complicated mathematical theorems. They are either necessarily true or necessarily false. But epistemically they are possible for me.
I took epistemic possibility to be just "for all I know, it could be" So with respect to all sorts of complicated mathematical theorems. They are either necessarily true or necessarily false. But epistemically they are possible for me.
I think I see. You want a priori false propositions--mathematical falsehoods--to be epistemically possible, in some cases. I'd rather make propositions that are not a priori false epistemically possible, though perhaps metaphysically impossible. So, in the mathmatics case, I'd say that you don't know whether those are epistemically possible, since for all you know they are a priori false.
Modality's just a fancy philosophaster term for probable. Doesn't really add anything.
That's just dead wrong. Whereas 'it is probable that' is one modality, there are lots of modailities that have nothing to do with probability.
"If X might possibly be a rat, then X is necessarily a cat.
X might possibly be a rat.
Ergo, it's a cat!"
This wouldn't follow in modal logic. You would have to say 'possibly, X is *necessarily* a rat.' The idea is that if it's possible for X to be necessarily true, i.e. that if there's a possible world where X is necessarily true, then (per S5) X is necessarily true, i.e. true in all possible worlds.
Nope, you've just been fed a bunch of Kripkean hype: read Quine on the supposed "modality.
Modality is probability: probability dumbed-down, really. Premises that are not in fact True but merely possible (ie probably true) may be used, but the argument is merely valid, not valid and sound (ie, true).
Like with this pseudo-premise:
"""if there's a possible world where X is necessarily true"""
Merely to say "there exists a possible world X" is not really saying something true, even in the sense of existential generalization. It's has to be "there exists an X (in some domain, or somewhere) which can be confirmed, or proven to exist in some fashion. Really the adjectivals themselves are arguably not part of predicate logic: the necessity's built into the argument (or the quantifiers). Modality concerns statistical/inductive arguments (tho' it seems that most philo-dweebs have bought the Kripkean line).
Perezoso, whether an argument in ML is sound is another issue altogether: my point is that your formulation wasn't even valid (note, I said *doesn't follow*). You didn't even provide a premise S5 is applicable to (without some adjustment).
Nyet. Read it again: a valid, modus ponens form. Validity's usually trivial.
I'm sort of a busy right now, but Quine notes (correctly, I believe) that modal terms do not refer. Modality is about thinking, not about objects (Quine might not call it thinking, but then he doesn't believe in a "mind" anyway).
Without being able to identify/confirm objects (even say mathematical objects) existential generalizations mean squat.
For that matter, given infinite domains (really most claims about G*d's existence) EG does not work either (there may be a G*d, and he may be in like the Andromeda Galaxy!)
Quine may not go far enough: "possibility" is really conditional probability, in most conceivable cases (or it's merely a problem of verification). The odds involved in Crap shooting do not bring into being "possible worlds."
Necessity on the other hand seems redundant, if not superfluous. When student X gives the right answer (ie True) to an algebra problem, he's given the necessarily true answer. The pythagorean identity is true, so it's necessarily true.
Rational theology (ie trying to prove G*d's existence merely by deductive logic, or ML) seems like a type of advanced soothsaying. Anyway, if God existed, he would have provided obvious evidence of his existence, wouldn't He? Some of the existenz dudes were at least more honest than the scholastics: credo que absurdum seems as good as Aquinas' chestnuts
Perezoso, yet again you've missed the point. Let me put it this way -- show me where you get the following in ML using any modal axioms, theorems or systems: <>P --> []Q (which is, of course, the form of your first premise: posssibly, X is a rat implies that necessarily, X is a cat).
You can make a move like this:
<>P --> []<>P
but I fail to see how you make the move you've made:
<>P --> []Q
You missed the point. Following Quine (and many others) I don't accept "possibility" as an object (except in regards to specific outcomes, ala gambling scenarios, etc), and "necessary" is superfluous, in most conceivable cases; moreover, to say "there exists some possible X" is really, just BS, incapable of being proven true. For that matter, the idea that something's "necessarily possible" seems pretty much BS--indeed it seems like some strange attempt to salvage metaphysical idealism.
The example was merely there to show how ludicrous "modal" arguments are--then metaphysicians often depend on the ludicrous. We'd be better off discussing the lending crisis.
"The example was merely there to show how ludicrous "modal" arguments are"
If you want to show how ridiculous modal arguments are, I'd recommend providing examples of modal arguments that are actually acceptable in modal logic; yours wasn't. That's the point. You can make a position *look* ridiculous by misrepresenting it, but that doesn't accomplish much...
No. you're wrong. There's no modal argument for "God"; in fact there are no valid and sound arguments (non-modal) which would prove the existence of God at all, since the object "G*d" (supposed object) cannot be identified, if even defined. Got it?
For that matter, just in terms of formal logic, the status of ML remains controversial (rightfully so).
Logic can't really deal with events in time: once
time or tense enters the equation, you're doing something like induction, or probability, if not physics. The logicians can make sh**t up (temporality, modality, etc), but it's just another game. There might be a few applications in programming for a temporal logic (AN Prior's system seems a bit more workable than Kripke's), but generally just part of Operation Mindf*ck.
"No. you're wrong. There's no modal argument for "God"; in fact there are no valid and sound arguments (non-modal) which would prove the existence of God at all, since the object "G*d" (supposed object) cannot be identified, if even defined. Got it?"
No, I don't get it, and with good reason: you're addressing a claim I've never made. My posts have been about your poor example -- period. How's this modal proposition:
Possibly, you haven't a clue, so you keep setting up strawmen to avoid admitting that your example either was a complete misrepresentation of ML or evinced a complete misunderstanding of ML?
Possibly, you don't know what the thread concerned. I could care less about the wiki spam on Kripke's modal spam, either. (and Kripke appears to have misread/oversimplified Prior's work, just like he misread Bertrand Russell on descriptions).
Here's another hint: convert modus ponens (p -> q) via material implication (~p v q), and then once again, via de morgan ~(p & ~q). Now try the "modality."
Maybe try like a stats class, before taking on the Great minds of logic. Saying something is possible is more or less meaningless, or vacuous as the philo-bots say.
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