Why would omniscience and free will be mutually exclusive?

My point is the event to which the omniscience pertains to is inherently limited so even though X is what happens it doesn't mean there aren't an infinity of Y that could have happened instead since X is inherently limited. I don't mean ad infinitum but infinity.

 

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Yes, I quite agree. You are making very good points.

Regarding ordinary knowledge possessed by ordinary mortal beings: I accept that knowledge entails truth. That is, more precisely, if I ascribe to you the belief that P, then I thereby endorse the truth of P. I can also grant to someone, for the sake of argument, that beliefs about future contingent propositions don't have determinate truth values. It doesn't follow from those two claims that one can't have knowledge of future contingents. It merely follows that the knowledge ascription will itself also become determinately true only after the future contingent becomes determinately true.

That is, suppose I eat ice-cream today, then your justified belief that I would do so, which you held last week, may be a knowledge candidate. Its status as a knowledge state can only be evaluated today. The alternative would be to insist that it must also be apt to be determinately evaluated last week. While this may make ordinary foreknowledge incompatible with free-will (or at least the principle of alternate possibility) it also has the untoward consequence to make it impossible for anyone to know anything about the contingent future. It would thus badly misrepresent our ordinary concept of knowledge, I think.

Now it may seem that one has the basis for a theological argument for the incompatibility of God's foreknowledge and free-will if one insists that, in God's case, knowledge of the truth of P must entail the truth of P, for all P, *and* God's knowledge states must be determinate at all times. I also think this inference is unwarranted. This postulation about God's knowledge seems to me equivalent to denying that his beliefs about future contingent propositions can lack determinate truth values at those earlier times. But I am quite ready to grant this claim (the denial) regarding even the knowledge states of ordinary folks.

You are right to note that it may not be inferred from the impossibility of God being mistaken about anything that when he knows P to be true, where P is a future contingent, then the necessity of P follows. Such a faulty inference could also be premised on mistaken interpretation of the scope of the necessity operator, as I suggested in an earlier post.

That is, if I claim that God knew that P and that it would have been possible for P to be false, I am not thereby implying that God may possibly have been wrong. I am only implying that P might possibly have been false and God thereby would have known it to be false.

If we write GKt1(Pt2) to mean "God foreknows at t1 that the future contingent proposition P is true at t2", where t1 is earlier than t2, then the faulty inference is from

(1) Nec(GKt1(Pt2) -> True(Pt2))
(2) GKt1(Pt2)

to

(3) Nec(Pt2)

which is invalid. But (1) is all that is entailed by the idea of God's knowledge infallibility. One would need the stronger premise (1b) GKt1(Pt2) -> Nec(Pt2), and this isn't entailed by the mere idea of God's infallibility.

 

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You are relying again on the same logically invalid argument form I analysed earlier. At the earlier time God knows that P, where P is a proposition about some future event. That God knows that P entails merely the truth of P. It does not entail its necessity. Lots of things are known to be true that aren't necessary. Incidentally, this entailment would hold even if God's knowledge weren't infallible. That knowledge is fallible only means that it stems from some fallible epistemic power. It does not entail that one may have known that P and yet P would have turned out not to be the case. This would be incoherent. The fallibility of my knowledge only entails that it would have been possible in any particular case for my epistemic faculties to yield a false belief rather than genuine knowledge.

If you known at t that P will be true at some later time t', then I grant that you can say that this fact about you at t (regarding your foreknowledge, as an ordinary scientific predictor, an astronomer, say) logically entails the truth of P at t'. It still does not entail the necessity of the truth of P at t'. It does not entail this even if your knowledge is infallible. Again, if your knowledge faculty is infallible, then it is merely impossible that you believe at t that P will true at t' while it will not turn out that P at t'. It is still possible that P turns out to be false at t'. In that case you would not have known at t that P would be true at t'. And if your knowledge faculty had been infallible, then you would not even have entertained such a false belief in the first place.

What is throwing you away, I think, is the truth of the conditional statement "if P is foreknown then it could not have turned out any other way". But this way of putting it, that you repeatedly seem to rely on, masks an inherent ambiguity in the scope of the necessity operator. You need it to mean : Foreknown(P) -> Nec(P). But all it can plausibly means is : Nec(Foreknown(p) -> P). You must take care to distinguish a necessary conditional from a conditional necessity.

 

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This is not so much question begging as self contradictory, it seems to me. You seem to suggest that the truth valuation of alethic modalities (necessity and possibility claims) is relative to individual agent's epistemic perspectives. This threatens to collapse possibility into knowledge of possibility. But clearly, I may have open to me options that I don't (yet) know to be open to me and conversely, I may falsely believe to be open to me options that aren't. Further, even if it were true that 'necessity-for-one' reduces to what one knows to be true, then how is the epistemic perspective of the omniscient being of any relevance to my own perspectival notion of necessity? Either you take the truth valuation of necessity claims to be relative to the subject's perspective or you don't. But here you seem to want to have it both ways.

First you claim that necessity is relative to the perspective of the omniscient being, for purpose of collapsing knowledge of truth into necessity. And then you claim that this perspective conditions what is reasonable for ordinary agents to believe regarding modalities conditionally on the merely possible existence of such a being. There seems to me to be steps missing in the argument.

 

Yazata put it very succinctly:

Put a number on it Pierre-Normand. What is the probability of Y happening instead?

 

This is very succinct and point missing. *Conditionally* to God having such determinate foreknowledge, then the probability of Y happening instead is zero, (if X and Y are incompatible). This never was under dispute. I took some care to distinguish the two claims: (1) Necessarily, knowledge that P entails the truth of P, and (2) Knowledge that P entails the necessity of P. I accept necessary conditional (1) and dispute the claim of conditional necessity (2).

Necessarily, if X happens, then God will have predicted that. It does not follow that X could not have happened instead. It only follows that if it had been the case that X would not have happened, then God would not have predicted it either. This is the modus tollens argument that stems from the denial of the consequent of the necessary conditional claim (1).

If the probability of X happening is 0.25, say, then the probability of him having foreknown that X would happen is likewise 0.25. He never fails, so the probabilities are bound to match (under some frequentist intepretation of probabilities, at least). It is both possible that X would happen *and* possible that X would't happen because it is both possible that God would have correlatively predicted both of those occurrences. Nothing about the ordinary concept of knowledge, or infallible knowledge, precludes that it could be both possible for him to know that X will happen and possible for him to know that X would not happen. It just isn't possible for both cases to be actual in conjunction.

 

Good. So because God has foreknowledge of how the universe will unfold, then the probability of it unfolding in any other way is zero. In other words, the universe can only possibly unfold in one way. So I still don't understand how anyone is free to make a decision that isn't in line with that.

It does follow *if* God has already seen how the entire universe will play out in the fullness of time, because every single event shapes the future. In other words, if X happened instead, then we'd be in a different universe. The universe we're actually in is the one where X could never have happened.

 

Now you are saying that the universe necessarily must unfold in one determinate way because it was foreseen by god that it would do so. You are yet again indulging in the same modal-logical fallacy. What can be said is that necessarily the universe will actually unfold in the way God has foreknown conditionally on God having foreseen it to unfold that way. You have provided no ground to detach the consequent of this conditional and append the necessity operator to it.

One isn't free not to do something such that God will have failed to foresee that it would be not be done. But the concept of free-will and the principle of alternate possibility does not require that one should be able to do that. I must just be *possible* that one could have refrained, counterfactually, to do what one actually did, not conditionally on whatever God foreknew, but *simpliciter*. If I performed action A and God has had foreknowledge of that, then it might also have been possible for me to abstain from doing that, in which case God would have foreknown that I would so abstain.

God's foreknowledge isn't a causal determinant of what I will do (unless you want to build determinism as an additional premise into your argument, or argue that the possibility of infallible foreknowledge entails some form of causal determinism). Rather, God's foreknowledge is merely postulated to be a necessary correlate of my future action. Notice that this isn't even queer or esoteric. The same holds of the fallible foreknowledge of an ordinary predictor. If I predict a solar eclipse, then, necessarily, if my prediction constitutes knowledge, the eclipse will occur. (Notice again the wide scope of the necessity operator). Yet, obviously, my cognitive state of knowledge isn't a causal determinant of the eclipse. It is a merely a correlate of the future event where the source of the correlation stems from my having the requisite predictive skills.

I'm not sure what you mean with the phrase "because every single event shapes the future". This seems to build determinism into the argument. But then God's having or failing to have foreknowledge would be irrelevant. Also, the suggestion that if some event had been different, then this would not have been the same (numerically identical) universe is rather contentious. This would seem to entail that anything that occurs in this universe necessarily occurs. Again, this does not seem to me to be entailed by the possibility of there being a God with infallible foreknowledge.

 

Just to be clear, are you saying that this last statement of yours is something that can be legitimately said?

What I was getting at is that if God knows how the universe will unfold, and all events shape the future (because they are causally linked), then X has to be consistent with how it will unfold.

How is it contentious? Isn't it rather obvious that we'd be living in a different universe now if any single past event had been something other than what it was?

I don't believe that it does of course, but by your own admission,

foreknowledge collapses probability. From the perspective of a being who exists outside/beyond time, there's no difference between an event that occurred in our past and an event that will occur in our future. If X had to happen for Y to be true today, then X will have to happen 10 years from now in order for Y to be true 20 years from now.

 

Yes. This the necessary conditional that the concept of knowledge (either fallible or infallible) seems to entail. It is logically invalid to infer from it the claim of conditional necessity you want to endorse (without additional assumptions).

It is a truism that whatever occurs has to be consistent with whatever else will in fact occur. This is true on anyone's view and adds nothing to the discussion so far as I can see.

I would say, if something merely possible but actual counterfactually did not happen then this concerns the actual universe as it would counterfactually have been, not a different universe. Likewise, if I state that I have been late at work but it would have been possible for me to arrive in time, then this possibility concerns me, not another individual merely qualitatively identical with me until the time of the diverging histories. The principle of individuation or 'worlds' is more fine-grained if you think in terms of 'possible-worlds' as those are understood in model-theoretic semantics of modal logic, say. But a different possible world isn't something akin to a parallel universe. It is (numerically identically) the same world just as it would possibly have been had its history diverged from the actual history of the world at some point in time.

Yes, *if* X *had* to happen... But you provide no ground for the claim that X had to happen. If God actually had the foreknowledge that I will do A, it does not follow that God had to have this determinate state of foreknowledge. It could have been that I would have done something else and that God would have foreknown that instead. Again you want to detach the consequent of a conditional claim fully embedded into the scope of necessity operator and attach the operator to the consequent alone. This is a logically invalid move.

If you truly believe that your conclusion validly follows from your premises, then it may help if you would attempt to formalise your argument using 'K' and 'Nec' operators in the way I have done. Then maybe you would see where your logical intuition leads you astray, or alternatively you'd point out an explicit flaw in my own formal argument.

 

I am not simply saying that X had to happen. I am saying that X had to happen in order for Y to happen. Y is some future state that is contingent (at least partly) upon X.

I'm not quite following you here. Are you suggesting that God didn't have foreknowledge of how the universe would unfold even before he created it? Because if he didn't, he's not omniscient. If he is omniscient, then the universe has been destined to unfold in the manner in which he foresaw it since before it even existed.

It seems to me that you are toying with the idea (albeit incidentally or perhaps even accidentally) that there can always be more than one possible future. Is there some as yet undisclosed (by you) logic that allows this to be compatible with the idea that God has already seen the singular future that will actually come to pass?

Again you seem to be hinting that there is always more than one possible future; that God, rather than having already witnessed the universe unfold in the fullness of time, merely has some very awesome predictive powers (and that his predictions can change).

 

I guess what we're talking here is about accidental necessity... i.e. foreknowledge by an omniscient makes what they know necessary per accidens.

The same as for any past event... i.e. that I woke up this morning is now a necessary truth per accidens. It was conditional up to the point that I woke up.

Surely omniscience results in all events foreknown being similarly necessary - albeit by accident?

 

This is the same premise that you are rewording over and over. Saying that X has to happens in order for Y to happen just is to say that, necessarily, if Y happens then X must also happen. This has exactly the same logical form as before: Nec((Y happens) -> (X happens)). The conjunction of this premise with the further premise (Y happens) fails to entail the conclusion you want to draw, namely that Nec(X happens). Substitute (God has foreknowledge of P) to (Y happens) and substitute P to (X happens).

You get that Nec((God has foreknowledge of P) -> (P)). You still fail to get from this premise, and the further premise that God actually has foreknowledge of P, the conclusion that Nec(P).

No. I have been granting you from the very start the premise that he has total foreknowledge of everything that will in fact happen. And I am showing you that you have provided logically insufficient grounds for drawing the conclusion you attempt to draw.

Your "rather than..." introduce a false dichotomy. As far as I can see (and I may be wrong), it can be both true that (1) God has infallible predictive powers, and hence his predictions can't change and they are always correct, and (2) there is any number of events that happen contingently in the universe. I am not simply toying with the idea that those two claims are compatible, as you say. I am merely showing that your attempted demonstration of their incompatibility is logically invalid. You've reworded essentially the same argument in nearly half dozen posts always with the exact same logically invalid form.

 

I don't see that. Even after you woke up, the fact that you indeed woke up at that particular time becomes *known* to you. It remains conditional on God having known that you would wake up at that time. There occurs no objective change to the conditional status of that event, and neither to its modal status. And as I have been at a pain to show, the necessary truth of the conditional statement logically entails nothing about the modal status of the consequent.

 

I'm aware of that, and I've done it on purpose. To be honest I just don't think that your logic is applicable as a "proof" of the invalidity of my own arguments in this case, otherwise the objection I have raised here (which has also been raised by many people before me, including some philosophers) would have been definitively put to bed many many years ago.

If modal logic is so fundamental as tool for discerning truth, why aren't you a theist? Didn't Gödel formulate a proof of the existence of God using it?

 

Here, let's work with this:

The above is a cut and paste from: http://plato.stanford.edu/entries/free-will-foreknowledge/

It might be more interesting and/or useful to raise objections to this formulation and discuss them one at a time.

 

If you aren't satisfied that I have displayed the logical invalidity of your argument then tell me where I went wrong. How come my logic isn't applicable? This is not 'my' logic, incidentally. If you want to question some principle of modal logic you thing I am relying on, you are free to do so. There is no use in merely repeating the same argument while ignoring my objections regarding its logical form.

The fact that the issue wasn't put to rest does nothing in showing you particular argument to be valid. There might be better arguments towards the same conclusion out there. I said nothing about modal logic being fundamental for anything. I just pointed out that you misused it. It's possible Gödel's proof was logically valid but unsound. It may have rested on questionable premises. I haven't look at it yet.

In any case, you seem to be consistently ignoring my main objection about the specific form of the argument you relied on.

 

X must happen in order for Y to happen because Y (being a future state) is contingent upon X. My justification for this is simply that events in the past are part of the causal chain that leads to events in the future.

So if Y, then X must have happened, since if X didn't happen then Y would not be Y.

If Y represents every single choice that every single human is ever going to make throughout the fullness of time (which is what God has foreknowledge of, among other things, if he is omniscient), and X is a particular decision that you are going to make, then X has to happen, or Y would not be Y.

In opposition to this, you make the argument that it is indeed possible for X to be something else, in which case Y would also be something else (but still represent foreknowledge on God's part). In this way Y is always still contingent upon X, but X is not predetermined. Correct me if I am wrong here.

But consider the fact physics tells us that the universe is not deterministic. This means that even if we didn't have free will, our actions still would not be determinate by virtue of external influences that are indeterminate. Yet in spite of this, omniscience (at least as it is typically defined by the theist) demands that God has infallible knowledge of the future. As an attempt to resolve this problem, it is usually suggested that God is outside of time and effectively views every moment as if it were the present. But I don't see how this changes anything. If the future (Y) is already known, regardless of how it can be known, then it is predetermined (and therefore so is X). To me, this is self-evident. So much so that you're going to need to do a better job of explaining to me why it's not before I will concede the point. This is the basic premise upon which my argument is built, and if it's true (which I believe it is) I can't see how it doesn't hold.

 

No it doesn't - as if God hadn't known then he would not, by definition, be omniscient.
The fact that an event happened means that God (as omniscient) DID know... there is no longer any conditional aspect to it... there is no longer any chance that it did not happen. Is this not the very definition of "necessary".

Do you at least accept that a past event is necessary?

And perhaps that is where the issue lies... as I would contest that there is a change, such that a future act might be conditional but a past act necessarily becomes necessary.

 

That's a theological issue and as such, basically a matter of definition for religious believers to sort out in-house. It might be possible to argue that God is omniscient about everything that exists to be known. But since the future is still open and hasn't yet come to be, God's omniscience doesn't extend to future events. Implying that God can be surprised by what happens, just as human beings are. It even seems to suggest that God is capable of learning (which in turn might have implications for God's supposed perfection). I believe that some Christian theologians have tried to float that kind of 'open theism' theory.

Actually, I did suggest that. The denial is your argument.

If God believes that P is going to occur and if it's impossible for God to be mistaken about P occurring, then it would seem that P's occurance is not only true, but logically necessary as well. The necessity comes from the impossiblity that the event could turn out to be anything other than P. If God had instead known that P is false, then P would have been necessarily false.

Wouldn't that symbolism translate to 'It's necessary that God has foreknowledge of Pt2'? That's may indeed be something that the theists want to argue, based on their definitions of 'omniscience'. They obviously want to suggest that there's nothing that God doesn't know, so it's presumably necessary that he knows this P as well.

But my point is rather different.

The 'Nec' seems to already be implicit in the theological concept of 'Gk'. If God knows P, then there's no logical possibility that P could be anything other than what God knows it to be, hence Nec(P).

So Gk(P) would indeed imply Nec(P)

That's because if there was even a logical possibility that what God believes to be P might actually be Q or R, then that possibility would simultaneously represent the possibility that God is fallible, which supposedly is impossible.