Clarification on how we infer the theists intent wrt free-will/omniscience

Originally posted by DeepThought
Ok., it's not April the 1st, so, is this an actual position you're taking?

Its not a joke if that's what you thought. I am questioning a number of assumptions that are being made in this thread. Too often posters are assuming that the future is not fixed, and then using that assumption to prove the future is not fixed. I am crying foul.

Originally posted by twhitehead
Its not a joke if that's what you thought. I am questioning a number of assumptions that are being made in this thread. Too often posters are assuming that the future is not fixed, and then using that assumption to prove the future is not fixed. I am crying foul.

Well, if the future is fixed then we don't have free will, so it's not really worth considering the case. Since we don't know that the future is fixed and want to check that omniscience is not logically incompatible with free will then the assumption that the future is fixed is begging the question. The unfixedness of the future is automatically implied by ¬□A, I do not necessarily do A. Our axiom of infallible knowledge is □(K(A) -> A). Assuming ¬□A we get to ¬□K(A), God does not necessarily know A. Since what we have shown is that the God's knowledge of what we do is contingent on us doing it what we have proved is that:

¬□A & □(K(A) -> A) -> ¬□K(A)

So we are not begging the question as we haven't used ¬□A to prove itself or any statement about the unfixedness of the future.

Originally posted by DeepThought
Well, if the future is fixed then we don't have free will, so it's not really worth considering the case.

What do you mean when you say it is fixed or not fixed? When you say the future is fixed, aren't you essentially saying the future is caused by the past. So the the claim is one of determinism not so much one about the future.
If one can predict the future, then one needs the universe to be deterministic at least as far as the prediction goes. High levels of prediction imply high levels of determinism.

Since what we have shown is that the God's knowledge of what we do is contingent on us doing it what we have proved is that:
¬□A & □(K(A) -> A) -> ¬□K(A)
Can you put that in English. I don't understand the symbols.

Originally posted by twhitehead
What do you mean when you say it is fixed or not fixed? When you say the future is fixed, aren't you essentially saying the future is caused by the past. So the the claim is one of determinism not so much one about the future.
If one can predict the future, then one needs the universe to be deterministic at least as far as the prediction goes. High level ...[text shortened]...
¬□A & □(K(A) -> A) -> ¬□K(A)
Can you put that in English. I don't understand the symbols.[/b]

I'll number the paragraphs if you want to dispute bits as this is a little long.

(1)
The question in the earlier thread was "Is omniscient prescience logically incompatible with libertarian free will?". So, they formulated conditions for omniscient prescience, namely that:

S1) Necessarily, if God knows that I will do A, then I will do A.

(1.1)
If something is said to be known by an agent, in this case God, then it is a requirement that it is true. This is part of the definition of knowledge. So for God to be prescient we require the condition "If God knows I will do A then I will do A.", whatever the action A is. The necessarily at the front ensures infallibility and, more importantly from the point of view of the original argument, ensures that God is omnisciently prescient in all possible worlds.

(2)
For an agent to have libertarian free will then for any action A they could make in the future it must be possible for them not to take it. So I will possibly not do A. This is the same as I will not necessarily do A.

S2) I will not necessarily do A

(3)
Statement (S1) entails (with brackets to highlight the logical structure)

S3) If (necessarily God knows I will do A) then (necessarily I will do A)

this step is based on an uncontroversial axiom of modal logic. It's easy to justify using the semantics of possible worlds, where necessarily X means X is true in all possible worlds.

(3.1)
Necessarily, if P then Q means that in all possible worlds (if P then Q). Suppose P is true in all possible worlds. If we pick any of the possible worlds we have that P is true and (if P then Q) is true in that world. This means that Q is true in that possible world. Since this argument works for all of our possible worlds this means that Q is true in all possible worlds, which means it's necessarily true. But necessarily P was assumed, so necessarily Q is contingent on it and to remove the assumption we combine them in a conditional statement. So Necessarily(if P then Q) entails if (necessarily P) then (necessarily Q).

(3.2)
Now, again using possible world semantics I'll justify statement 2. Suppose (I will do A) in the actual world. For libertarian free will to exist it must be the case that there is a possible world where not (I will do A). If there is no possible world where not (I will do A) then I have no choice but to do it. The possible worlds represent the alternatives for this one. Since there is a possible world where not (I will do A), I will possibly not do A, or not (necessarily I will do A).

(4)
So to recap, we have:

S1) Necessarily, If (God knows I will do A) then (I will do A)
S2) Not (necessarily, I will do A)
S3) If (necessarily God knows I will do A) then (necessarily I will do A).

(4.1)
Assume that necessarily (God does know I will do A). We can conclude from S3 that (necessarily I will do A). But S2 says Not (necessarily, I will do A), so our assumption that necessarily (God does know I will do A) is false. In fact, we have that:

not (necessarily, God knows that I will do A).

(4.2)
So what omniscient prescience means is that in possible worlds where I will do A then God knows I will do A and in possible worlds where I will not do A, God does not have what would in that possible world be the false knowledge that I do A. Or put more simply:

God only knows I will do A if I will do A.

(4.3)
Which means there is no possible logical incompatibility between omniscient prescience and free will. That is to say there is nothing in the formal language that shows there is a contradiction.

(5)
Knowledge is justified true belief. What you are worrying about is the justificatory process - how does God know I will do A? This requires that we have some model of the justification of knowledge, which is what LemonJello suggested we started to discuss and what the first of my replies to him was about. Is it possible for an agent to know something in advance without affecting it. Now, if the universe is deterministic, then yes, but then we don't have free will, all relevant possible worlds are the same. If the universe is non-deterministic then how can God know in advance what the outcome of wave-function collapse events are? But this potentially takes in nomological arguments which was kept out of the first discussion. So we need a sufficient condition for infallibility which is more descriptive than the rather blunt instrument that is the necessity operator.

5.1)
LemonJello made a good point that we could include some nomological necessity - he wrote as *necessity*. I suggested "required", "nomologically required" or "requirement" to distinguish it from the modal operator. What you are talking about is this condition.

(6)
The second of my replies to LJ was worrying out loud about possible world semantics and free will. I think I'm right about the equivocation problem (I'm not the first person to point this type of problem out), I'm much less sure about the begging the question problem. It made sense when I thought of it but once I was typing it in it made less and I ended up relying on identity to get me out of a hole. We can solve the former by insisting our possible worlds are identical up until the point the agent is faced with the decision.

Originally posted by DeepThought
Yes, I managed to impose fatalism despite having read bbarr's argument and having had him go through essentially the same point regarding predestination. Insufficient self-criticism of my train of thought while writing the post I'm afraid. Although in my defence it's an internet forum and the medium tends to cause that.

For *necessity* are you think ...[text shortened]... rline impossible. I'm not sure if this possible world exists, but it was helpful for the point.

For *necessity* are you thinking of something nomological? For an alternative word to avoid the name space collision how about required? It's not quite got the same meaning, but it means we can avoid using the same word.

If we look to arguments in the historical literature that pursue this line of thought (there have been many), one of the descriptors they use is necessary per accidens, or some such. In other words, "accidental necessity". So we could use a qualifier like this, but of course, we would need to hash out specifically what 'accidental' intends in our context. I'm not thinking of something nomic or nomological specifically, which is typically understood to refer to necessity of the natural laws. However, there could be overlap here.

Here is an example of this line of thought, to give some general flavor of the idea. It is sometimes argued that there is a modal asymmetry between the past and the future, such that events that are in the past are somehow "accidentally necessary" in some that way that does not, or need not, transfer to future events per se. This could be motivated, for example, by the idea that things in the past are somehow fixed or not causable or some related notion. For example, if it is a fact that event E occurred yesterday; then some would state that this fact is now accidentally necessary, in that there is nothing that can be done now to alter it or some such. So, some try to formulate an argument for fatalism of the following general form.

Suppose P is the proposition that S will do A at time T2 (T0 is prior to T1 is prior to T2):

(F.1) At time T0, G foreknew that P. [Supposition of foreknowledge]
(F.2) If an event occurred in the past, it is now necessary that the event occurred when it did. [This would invoke some principle of accidental necessity of past events]
(F.3) At T1 it is now necessary that at T0 G foreknew that P. [From F.1 & F.2]
(F.4) Necessarily, if at T0 G foreknew that P, then P. [Follows from the analysis of knowledge]
(F.5) If X is now necessary; and if necessarily, X -> Y; then Y is now necessary. [A transfer of necessity principle]
(F.6) At T1 it is now necessary that P. [From F.3 & F.4 & F.5]
(F.7) If at T1 it is now necessary that P, then S is not free with respect to A at T2.
(F.C) Hence, S is not free with respect to A at T2.

Again, the above would give a general flavor of such arguments. I think such arguments have problems, though, such as the Ockhamist objection. Here is a Plantinga paper I would recommend that gives good background on this:

http://www.andrewmbailey.com/ap/Ockhams_Way_Out.pdf

Regarding the other point -- that of having justificatory conditions that can bridge the gap to infallible foreknowledge of things like future actions -- I do not have a good handle on that part of the discussion yet. Seems like a worthy point to explore, but it may take some time for me to assemble my thoughts on that. (Anyway, some arguments like the general one I outlined above do not seem to invoke infallibility in a material way. Others do, though. )

Originally posted by DeepThought
Something's occurred to me about discussions concerning free will using possible worlds. Suppose I have some decision to make, call it D. In the actual world I go for ¬D. There's some possible world where I do D. Now, if I knew about the other me that did that I might say: "I wouldn't do that, that's not like me". So I'm wondering to what ext ...[text shortened]... potential fallacies, equivocation on the one hand and begging the question on the other.

Yes, very good observations. This is one reason why libertarian constraints on freedom do not seem to make much, or any, sense. Under libertarianism, it is a precondition for freedom that one have available these sorts of alternative possibilities. However, this effectively severs any reasonable relationship between one's free actions and one's reasons and dispositional traits, etc. It leaves me wondering why exactly such putatively "free" actions should be referenced back to the one performing them at all. This seems like a very deep notional problem for libertarian construals.

But, additionally, I would again recommend the Plantinga essay, since it has an appendix at the end where he responds to a particular point of criticism from Nelson Pike. In that section, it has some very interesting discussion on difficulties with explicating one's ability to do otherwise within possible world semantics. See what you think about it. I think it is directly relevant to the concern you raise in your third paragraph. I agree with you that there is something further to be fleshed out here.

Originally posted by LemonJello

For *necessity* are you thinking of something nomological? For an alternative word to avoid the name space collision how about required? It's not quite got the same meaning, but it means we can avoid using the same word.

If we look to arguments in the historical literature that pursue this line of thought (there have been many), one of ...[text shortened]... ne I outlined above do not seem to invoke infallibility in a material way. Others do, though. )

Thanks for the link. I've read the first section, happily Plantinga's a pretty clear writer, but it'll still take me a bit of time to absorb what's there. It's interesting to see that Aquinas was the first to clearly see that the correct formulation is □(K -> P) and not K -> □P. I find the notion of a modal asymmetry between past and future, with the past existing and fixed and the future not necessarily fixed, due to quantum randomness for example, quite natural. Relativity introduces some interesting features to this as what is the past depends on the frame of reference of a given observer, but does assert a space-time so within the theory the past is real.

Originally posted by DeepThought
Which means there is no possible logical incompatibility between omniscient prescience and free will. That is to say there is nothing in the formal language that shows there is a contradiction.

I admit I have struggled (and failed) to follow your post up to here. If I am correct, you are basically saying that:
If A causes B and A causes C, then it doesn't follow that B causes C.
And I say that's a difficult question to deal with and I remain unconvinced.

I dislike your statement that "there is no possible logical incompatibility between omniscient prescience and free will." It seems to be a rather grand claim based on rather narrow definitions of the terms in use and also on a particular formulation of how the universe works.

Originally posted by twhitehead
I admit I have struggled (and failed) to follow your post up to here. If I am correct, you are basically saying that:
If A causes B and A causes C, then it doesn't follow that B causes C.
And I say that's a difficult question to deal with and I remain unconvinced.

I dislike your statement that "there is no possible logical incompatibility betw ...[text shortened]... definitions of the terms in use and also on a particular formulation of how the universe works.

It took me a month to get my head around these arguments, I was helped by being able to follow the symbolic argument.

I don't see how you got from what I was saying to if A causes B and A causes C then B does not necessarily cause C. However the latter is correct. If I boil the electric kettle and I put some soup on the cooker, then I cause the water to boil and I cause the soup to be heated. The kettle boiling does not cause the soup to be heated.

The argument hinges on what is meant by necessity. It does not hinge on how the universe works. Necessity simpliciter means true in all possible worlds. That is the form of necessity used in the argument. We are starting to look at weaker forms of necessitation, the necessity of the past, which they call necessity per simpliciter.

Roughly the past has already happened so it can't change (although I'll have some things to say about that in a future post) so it is necessary. But that something happened in the past is contingent on it having happened. We can imagine possible worlds where it did not, so it is not necessary simpliciter.

Try looking at the Plantinga paper LJ referenced in the first of his above posts, he looks at the argument we are using in the first section and is a clear writer.

Originally posted by LemonJello

For *necessity* are you thinking of something nomological? For an alternative word to avoid the name space collision how about required? It's not quite got the same meaning, but it means we can avoid using the same word.

If we look to arguments in the historical literature that pursue this line of thought (there have been many), one of ...[text shortened]... ne I outlined above do not seem to invoke infallibility in a material way. Others do, though. )

I've read most of the Plantinga paper, but not yet the Appendix, I should have finished it by tomorrow and then I'll have to reread it a few times on Saturday and might just have it. I want to check I've got what he's saying with the appropriately numbered condition (42), the single agent condition. I don't really understand the necessity of the multi-agent condition, what it adds relative to the single agent version.

I'll go through the bits of his expression so we can check that my understanding of it tallies with yours.

P(T) - the proposition true at time T.
S(x) - x is an agent.
A(y) - y is an action.

B(x, y) - y is a basic action for x.

He talks about basic actions. A basic action is something an agent can do via an action A* which they can directly do. So I can type this post, the action A, by bashing the keyboard with my fingers, the direct action A*. I'm assuming this is what he means by directly - with some part of my body.

C(x,y,t) - x can do y at time t.

This is important as it is not that x necessarily does y, but that he could do y. If the agent does y then that changes the truth of the past proposition, it is enough that the agent can do y to render the past proposition non-necessary. I don't think that this could be expressed using the possibility operator. There is a possible world where x does y, but that could be due to something contingent to that possible world and not relevant to the actual world - do you agree with that point?

D(x,y,t) - x does y at time t.
□ª = accidental necessity
□ = logical necessity
∀t (t ≥ T) = for all times t such that t is at or after T

In symbols statement 42 is:

□ªP(T) <-> P(T) & ¬∃x ∃y ∀t [(t ≥ T) & S(x) & A(y) & B(x,y) & C(x,y,t) & □(D(x,y,t) -> ¬P(T))]

Provided I've got the existential and universal quantifiers in the right order. I don't quite get the necessity operator at the end.

I'm also wondering why it needs an agent, clearly to relate it to free will we need one, but is that fundamental to accidental necessity, or is it just needed to connect it to the will of an agent. Suppose x is just some event, E(x,t) means an event at time t, which may be a basic action by an agent. Why can't we have:

□ªP(T) <-> P(T) & ¬∃x ∀t [(t ≥ T) & E(x, t) & C(x, t) & □(D(x, t) -> ¬P(T))]

where C(x, t) means x can happen at t, D(x, t) is x does happen at t. I'm wondering if I've missed something in his argument.

Edit: I see why he wants the necessity operator at the end. It protects the omniscience condition. If God knows that D(x, y, t) he can arrange for ¬P(T). In other words the logical condition is set up to allow the omniscient being to change the past when there's a potential conflict between omniscience and past actions (putting a million dollars in a box). I'm wondering if this begs the question.

[WORD TOO LONG]

Plantinga doesn't talk about this, but I'm starting to worry about what we mean by time. The time in general relativity is a coordinate, and contingent on the coordinate system chosen. In fact it is not wrong to say that time doesn't really exist in GR. It is necessary for quantum mechanics. So in Physics there is a problem of time. The Wikipedia page on that talks about some new developments where yet another interpretation of quantum mechanics has time as an emergent phenomenon. Something that makes sense for observers inside the universe, but for external observers time does not exist which is making the atemporal picture of a God outside time look meaningful. The problem is the relevant part of the page is really badly written and it's Wikipedia so the person writing it may simply have not understood what they were talking about.

I'll need to do some reading about this and think about it to check it doesn't change the argument. But I'm thinking of a working definition along the lines of event 1 being before event 2 means event 1 can cause event 2 (is in the backward light cone of) and event 3 not being able to cause event 2 means it does not have a well defined time ordering with respect to it (is outside either light cone - no physical signal can pass between them). There's a danger of begging the question, but a God outside time would

Originally posted by DeepThought
I've read most of the Plantinga paper, but not yet the Appendix, I should have finished it by tomorrow and then I'll have to reread it a few times on Saturday and might just have it. I want to check I've got what he's saying with the appropriately numbered condition (42), the single agent condition. I don't really understand the necessity of the multi- ...[text shortened]... can pass between them). There's a danger of begging the question, but a God outside time would

A God who isn't limited by time would be able to see all things at once at
all times. I'm assuming outside of time is what than means.

Originally posted by KellyJay
A God who isn't limited by time would be able to see all things at once at
all times. I'm assuming outside of time is what than means.

If you had been following the thread you would know that if a God who isn't limited by time exists, then the future exists and there can be no free will.

Originally posted by KellyJay
A God who isn't limited by time would be able to see all things at once at
all times. I'm assuming outside of time is what than means.

An observer outside the universe (if that's a meaningful statement) observing the universe would see it all at once. They would be outside of time. So yes, that particular interpretation is consistent with God not being limited by time. But be a bit wary of it, I got that from a Wikipedia page and the writer didn't necessarily understand the theory. It was a fairly badly copy edited page and those pages tend to be unreliable. I'll have to check some of the references to check they're a) credible and b) actually do say that. Also the interpretation they were using may be completely inconsistent with libertarian free will.

Originally posted by twhitehead
If you had been following the thread you would know that if a God who isn't limited by time exists, then the future exists and there can be no free will.

I just noticed, in the post where I replied to you about 5 posts ago I inadvertently used necessity per simpliciter when I was talking about the necessity of the past. It should have said:

We are starting to look at weaker forms of necessitation, the necessity of the past, which they call necessity per accidens.

Originally posted by DeepThought
The argument hinges on what is meant by necessity. It does not hinge on how the universe works.

But 'what is mean by necessity' apparently does hinge on how the universe works. The talk of 'possible worlds' has to do with how the universe works. That is why I am saying that trying to throw out causation and keep it strictly in logic is a mistake as all you are doing is hiding what you really want to say in definitions.

If I boil the electric kettle and I put some soup on the cooker, then I cause the water to boil and I cause the soup to be heated. The kettle boiling does not cause the soup to be heated.
Not quite what I said. Suppose You put the soup on the cooker. The soup will be cooked, and the germs in the soup will be killed. My point was that the soup being cooked does not cause the germs to be killed.
How are you defining 'cause'?
1. In all possible universes in which you put the soup on the cooker, the soup will be cooked.
2. In all possible universes where you put the soup on the cooker the germs will be killed.
3. In all possible universes where the soup was cooked, the germs were killed.
4. Why can we not say that the soup getting cooked caused the germs to be killed?