28 Feb 15
Originally posted by twhiteheadI've asked that question before myself ... didn't get much of a response as I recall.
I suspect that this discussion would get a lot more complicated if we instead asked the question: does God know his own future, in whatever timeline / reality he exists in? If so, then he himself is without decision making ability or free will.
01 Mar 15
Originally posted by twhiteheadDoes the argument for free will and omniscience not still apply? Where earlier we had □(A -> G) with A being some action Alice (or whoever) takes and G being God knows that Alice will do A. So simply change the meaning of A to be God does A. We still cannot form a logical contradiction.
I suspect that this discussion would get a lot more complicated if we instead asked the question: does God know his own future, in whatever timeline / reality he exists in? If so, then he himself is without decision making ability or free will.
02 Mar 15
Originally posted by DeepThoughtYeah, it's the same basic point. There's no contradiction. Here's another way of thinking about it: I know today that tomorrow I will have a cup of coffee in the morning. So, because knowledge is a factive state (if a knowledge claim is true, then it entails the known proposition is true), it's true that I will have a cup of coffee tomorrow morning. But this doesn't entail that it's necessarily true that I'll have a cup of coffee tomorrow morning. Even though I will, there's a possible world where I won't. There's no contradiction in supposing that one knows, even infallibly, what one will freely do in the future.
Does the argument for free will and omniscience not still apply? Where earlier we had □(A -> G) with A being some action Alice (or whoever) takes and G being God knows that Alice will do A. So simply change the meaning of A to be God does A. We still cannot form a logical contradiction.
03 Mar 15
1 edit
Originally posted by bbarrI've been getting quietly confused about this, this post took two hours to write, logic is a lot harder than I always thought. Earlier I wrote a post about predestination (page 2 post 8) which I now think is wrong, but it raises an interesting point. We've got an if and only if relationship here, modifying my notation slightly I'll use K(A) to mean God knows I take action A. So:
Yeah, it's the same basic point. There's no contradiction. Here's another way of thinking about it: I know today that tomorrow I will have a cup of coffee in the morning. So, because knowledge is a factive state (if a knowledge claim is true, then it entails the known proposition is true), it's true that I will have a cup of coffee tomorrow morning. But t ...[text shortened]... ntradiction in supposing that one knows, even infallibly, what one will freely do in the future.
□ (K(A) <-> A)
Of necessity if God knows I do A then I will do A, because his knowledge is infallible, and necessarily if I do A God knows it because of omniscience. This isn't a problem for the argument as, assuming the axiom of distribution, we have:
□ K(A) <-> □ A
and if ¬□A then we have ¬□K(A), which is fine because if I don't necessarily do A then God doesn't necessarily know that I do A. What worries me is that if we replace K(A) with P(A) = I am predestined by God to do A then we have:
□ (P(A) -> A)
If I'm predestined to do A then I'm necessarily going to do it. In the earlier post I had that as if and only if, but that's not necessary as I'm not automatically predestined on every action. Here all that a possible world were I don't do A means is that I'm not necessarily predestined to do A, but that doesn't mean I have free will in the matter. So I'm left wondering if ¬□A adequately expresses free will, as if it does we have predestination and free will being compatible, which is counter-intuitive.
I hope you enjoy tomorrow morning's coffee!
03 Mar 15
Originally posted by DeepThoughtThe coffee was fantastic, thanks!
I've been getting quietly confused about this, this post took two hours to write, logic is a lot harder than I always thought. Earlier I wrote a post about predestination (page 2 post 8) which I now think is wrong, but it raises an interesting point. We've got an if and only if relationship here, modifying my notation slightly I'll use K(A) to mean God ...[text shortened]... ill being compatible, which is counter-intuitive.
I hope you enjoy tomorrow morning's coffee!
Modal logic can get tricky, that's for sure. I agree that given the notion of omniscience and the factivity of knowledge, it follows:
Necessarily, God knows A if and only if A.
As you note, this biconditional is the conjunction of two conditionals:
Necessarily, if God knows A, then A.
And
Necessarily, if A then God knows A.
The first does not follow from God's infallibility, however. It merely follows from the factivity of knowledge; that if a proposition is known by anyone, even fallibly, then that proposition is true. This is built right into the definition of knowledge as justified, true belief with some extra, anti-Gettier stuff. The second conditional, of course, follows from God's omniscience.
Applying the Distributive Axiom to the biconditional yields:
Necessarily, God knows A if and only if necessarily A.
This is clearly right. If God knows A necessarily, then he knows A in every possible world. But that means that A is true in every possible world, which means that A is necessary. Again, this follows from the factivity of knowledge. Similarly, if A is necessary, then it is true in every possible world. Since God is omniscient, he would thus know A in every possible world, so he would know A necessarily.
All good so far, but you have a worry centering around the notion of predestination. It seems clearly right that:
Necessarily, if A is predestined, then A.
Suppose we apply the Distributive Axiom here. We then get:
If, necessarily, A is predestined, then necessarily A.
Since rules out the possibility of ~A; since there is no possible world in which ~A, it conflicts with the libertarian notion of free will, just as would be the case if God necessarily knew A. But your worry is about something else. It's about the following proposition:
If A is predestined, then necessarily A.
But this doesn't follow from 'Necessarily, if A is predestined, then A'. Just as 'If God knows A, then necessarily A' does not follow from 'Necessarily, if God knows A, then A'. It's this inferential move that we were struggling with in our previous conversations about the purported paradox of omniscience and libertarian free will. From 'God knows A' or "A is predestined', it necessarily follows that A. But what doesn't follow is the necessity of A itself.
Let me try to sharpen this point. You claimed that if you're predestined to do A, then you're necessarily going to do it. But is this right? What justifies the use of 'necessarily' here? Why not simply say that if you're predestined to do A, then you will do A? After all, just because you're predestined to A in the actual world, it doesn't follow that you're predestined to A in every possible world.
This is probably unsatisfying. Here you are, in the actual world, predestined to A. So, you will A. Of course, it's logically possible you will not A, but, in fact, you will A. Given that you're predestined to A, to not A is for you, not a live choice. It is certainly an anemic conception of free will that not A-ing is, for you, merely a logical possibility.
But this anemia has nothing to do with predestination. Yesterday I knew I would have coffee this morning. So, it follows that I had coffee this morning. There are possible worlds where I didn't have coffee and, hence, didn't know I was going to yesterday, but I'm not in those worlds. Since I knew yesterday I would have coffee this morning, not having coffee this morning was, although possible, not in the cards. It wasn't a live option for me in fact, despite seeming so introspectively.
03 Mar 15
Originally posted by bbarrI do not understand that at all.
But this doesn't entail that it's necessarily true that I'll have a cup of coffee tomorrow morning. Even though I will, there's a possible world where I won't. There's no contradiction in supposing that one knows, even infallibly, what one will freely do in the future.
Are you saying that there is a possible future in which you do not have coffee but previously knew infallibly that you would have coffee? Seems like a contradiction to me.
I also think that there is a bit too much focus on the claim that 'no logical contradiction could be found' when it isn't a matter of logic that is at question. Its a matter of whether or not there are multiple universes and whether or not the future can be said to 'exist', and whether or not the universe is deterministic in nature.
03 Mar 15
Originally posted by twhiteheadNo, I'm not saying that. There is no possible world in which both of the following propositions are true:
I do not understand that at all.
Are you saying that there is a possible future in which you do not have coffee but previously knew infallibly that you would have coffee? Seems like a contradiction to me.
I also think that there is a bit too much focus on the claim that 'no logical contradiction could be found' when it isn't a matter of logic that is at ...[text shortened]... t the future can be said to 'exist', and whether or not the universe is deterministic in nature.
1) I know that I will have coffee tomorrow.
2) I will not have coffee tomorrow.
These two propositions together entail a contradiction, though infallibility has absolutely nothing to do with the matter. If I know I will have coffee tomorrow, then it follows from the definition of knowledge as factive that I will have coffee tomorrow. So, given the truth of (1), (2) must be false.
What I am saying is that (1) is consistent with the following proposition:
3) It is possible that I will not have coffee tomorrow.
Or, in other words, (1) is consistent with:
4) It is not necessary that I will have coffee tomorrow.
These proposition, (3) and (4), make modal claims. Each is silent about whether, as a matter of fact, I will or will not have coffee tomorrow. Given the truth of (1), all that follows is the contingent truth that I will have coffee tomorrow. (1) does not entail that it is a necessary truth that I will have coffee tomorrow, so (1) is consistent with the proposition that it is possible I will not have coffee tomorrow.
Some of this certainly is a matter of logic and whether there are contradictions between various claims. Those who believe that God's omniscience is incompatible with libertarian free will are committed to there being some contradiction derivable from the conjunction of the following two types of claims:
(5) God knows that S will A.
(6) It is possible that S will not A.
So, suppose that some subject S commits act A in the actual world. If God is omniscient, then it follows that God knows (and presumably has always known) that S will A. (5) is, thus, just a function of God's omniscience. Yet, on the libertarian conception of free will, for S to freely A it must have been possible for S not to A. (6) is, thus, an expression of the commitment to the libertarian conception of free will. Now, can you derive a contradiction from (5) and (6)? I don't see how. From (5) it follows that S will, in fact, A. But it doesn't follow that it is necessary that S will A. God's knowledge (or my knowledge, for that matter) of the fact that S will A doesn't change the modal status of the fact that S will A. It doesn't render it necessary.
For every possible world in which God knows that S will A, in those worlds S will A. But this doesn't change the fact that, in those worlds, it is contingent that S will A. Just because God knows that S will A in the actual world, it doesn't follow that S will A in every possible world.
You're right that these considerations do not settle the issue of whether the libertarian conception of free will is coherent, compatible with what we know about the nomological structure of the actual world, consistent with other things we want out of a conception of free will, etc.
03 Mar 15
Originally posted by twhiteheadI think bbarr's point is that in order for him to claim that his justified belief was knowledge it had to be true, he had to drink the coffee. If something got in the way of that, such as an unexpected coffee deficit, then it wouldn't have been true and therefore not knowledge. bbarr, is as far as I know, not infallible which means that, although he did know that he would have coffee, he did not know that he knew that he'd have the coffee until he did. God on the other hand is claimed to be infallible and does know that he knows.
I do not understand that at all.
Are you saying that there is a possible future in which you do not have coffee but previously knew infallibly that you would have coffee? Seems like a contradiction to me.
I also think that there is a bit too much focus on the claim that 'no logical contradiction could be found' when it isn't a matter of logic that is at ...[text shortened]... t the future can be said to 'exist', and whether or not the universe is deterministic in nature.
A logical disproof of the compatibility of free will and knowledge would be stronger than one based on physics. Since if one could prove a logical contradiction it would be impossible independently of which physics theory is true. One based on a physics theory is only contingently true as the theory could be overturned. That's to say that it may be true in a possible world where that physics theory happens to be true, but not necessarily in the actual world. So we may as well see if it's logically compatible first. Besides, bbarr is a philosopher specialising in ethics and logic so expecting a physics proof is a bit much. I'm was formerly a physicist and know I don't know where to start with that one.
03 Mar 15
4 edits
Originally posted by bbarrI'm still thinking about your post and there's an additional one in response to twhitehead so I may get back again later. Also I have to check up on the anti-Gettier conditions, which ring bells. Part of the problem is that in normal usage "I know X" means something like "I believe X and X is likely to be true" or even just "I believe X", which I think is a source of confusion for people.
The coffee was fantastic, thanks!
Modal logic can get tricky, that's for sure. I agree that given the notion of omniscience and the factivity of knowledge, it follows:
Necessarily, God knows A if and only if A.
As you note, this biconditional is the conjunction of two conditionals:
Necessarily, if God knows A, then A.
And
Necessarily, if A ...[text shortened]... , not in the cards. It wasn't a live option for me in fact, despite seeming so introspectively.
I inadvertently left out a necessarily in my earlier post despite thinking I'd proof read it (I also had were when I should have had where later in the sentence as well 😞), it was a useful mistake because your post clarified some things about possible world semantics. Although I don't think it damages my point that ¬□A can't fully capture libertarian free will. We have:
□P(A) -> □A ⊣⊢¬□A -> ¬□P(A)
So, if there are possible worlds where I do not do A then in those worlds I am not predestined to. If ¬□A is not intended to fully capture libertarian free will, but only to capture a logical consequence of it, then I'm happy. It's just that in the earlier threads I got the impression that that was the form of free will that was being considered.
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03 Mar 15
Originally posted by bbarrIf proposition 1) is infallibly true. Then you will have coffee tomorrow.
No, I'm not saying that. There is no possible world in which both of the following propositions are true:
1) I know that I will have coffee tomorrow.
2) I will not have coffee tomorrow.
These two propositions together entail a contradiction, though infallibility has absolutely nothing to do with the matter. If I know I will have coffee tomorrow, then ...[text shortened]... of the actual world, consistent with other things we want out of a conception of free will, etc.
If you will have coffee tomorrow it cannot be true that it is possible for you to not have coffee tomorrow.
If modal logic says otherwise then modal logic is wrong.
Because the only possible universes where it can be known 'beforehand' infallibly that you will have coffee
tomorrow are deterministic universes where you cannot possibly not-have coffee tomorrow.
Any non-deterministic universe where it is possible for you to ~A instead of A, is one in which it is also not
possible to know [infallibly] that you will do A prior to you doing A.
I think your argument is question-begging because you miss HOW you [or god] knows infallibly that you will
have coffee tomorrow.
That HOW is why 1) conflicts with 3) and 4).
04 Mar 15
Originally posted by DeepThought
I think bbarr's point is that in order for him to claim that his justified belief was knowledge it had to be true, he had to drink the coffee. If something got in the way of that, such as an unexpected coffee deficit, then it wouldn't have been true and therefore not knowledge. bbarr, is as far as I know, not infallible which means that, althoug ...[text shortened]... is a bit much. I'm was formerly a physicist and know I don't know where to start with that one.
bbarr, is as far as I know, not infallible which means that, although he did know that he would have coffee, he did not know that he knew that he'd have the coffee until he did. God on the other hand is claimed to be infallible and does know that he knows.This couple of sentences from the first paragraph of my earlier post are wrong. If bbarr knew he was going to have coffee then we can build a chain of knowing that he knew as long as we like. If he was wrong about having coffee then he didn't know he was going to have coffee in the first place. In other words he knew he knew before he had the coffee.
K(K(A)) -> K(A) -> A
¬K(K(A)) does not prevent K(A) but is no more or less contingent on A than K(A). I think 😕
Originally posted by googlefudgeProposition (1) as originally stated was:
If proposition 1) is infallibly true. Then you will have coffee tomorrow.
If you will have coffee tomorrow it cannot be true that it is possible for you to not have coffee tomorrow.
If modal logic says otherwise then modal logic is wrong.
Because the only possible universes where it can be known 'beforehand' infallibly that you will have coffee ...[text shortened]... infallibly that you will
have coffee tomorrow.
That HOW is why 1) conflicts with 3) and 4).
(1) If I know I will have coffee tomorrow then I will have coffee tomorrow.
This is identical to the statement
(2) In the actual world, if I know I will have coffee tomorrow then I will have coffee tomorrow.
Consider a statement about a possible world where I do not have coffee tomorrow.
(3) In a possible world, I will not have coffee tomorrow. In that world I will not know that I will have coffee tomorrow.
The knowledge is specific to the world we are talking about. Infallibility is not the same as necessity. Consider these two propositions, again about two different worlds:
(4) In the actual world I am fallible.
(5) There is a possible world in which I am infallible.
They do not contradict each other since the truth values apply to different worlds.
The modal operator we are using here is "necessarily", consider this statement:
(6) Necessarily, if I know I have coffee tomorrow then I will have coffee tomorrow.
This means that in all possible worlds if I know I will have coffee tomorrow then I will have coffee tomorrow. This does not entail that I have coffee in all possible worlds, since in those possible worlds where I don't drink the stuff tomorrow I will not know that I will have coffee tomorrow. It also does not entail that in all possible worlds I will know that I have coffee tomorrow even if I do since we can imagine possible worlds where it comes as a surprise.
Determinism has nothing to do with it. It is simply a matter of the meanings of the words "know" and "necessarily". You may be right in your claim that if the actual world is non-deterministic then it is impossible to know that "I will have coffee tomorrow.", but that doesn't alter the point bbarr was making.
04 Mar 15
4 edits
Originally posted by googlefudge
If proposition 1) is infallibly true. Then you will have coffee tomorrow.
If you will have coffee tomorrow it cannot be true that it is possible for you to not have coffee tomorrow.
If modal logic says otherwise then modal logic is wrong.
Because the only possible universes where it can be known 'beforehand' infallibly that you will have coffee ...[text shortened]... infallibly that you will
have coffee tomorrow.
That HOW is why 1) conflicts with 3) and 4).
If proposition 1) is infallibly true. Then you will have coffee tomorrow.
What would it mean for a proposition to be "infallibly true"? A proposition is true or false, that is all. In our context, infallibility is predicated (or not) unto the cognitive process or knowledge or cognizer himself or herself, not unto things like propositions. For example, infallibility could enter into the analysis of knowledge at the justificatory component: e.g., a general infallibility clause could hold that a necessary component for S's infallibly knowing P is that S is justified in believing P and that this justification is such that it is not possible both for S to have it and for P to be false, or some such. Or, generally, an infallibility condition would have to ensure that there is no possibility that S could err in his or her cognitive process or evaluations at issue. For example, an infallibility condition on S's knowledge such as "Necessarily, if P then S knows P" , or some modified variant, seems to accomplish this globally.
Because the only possible universes where it can be known 'beforehand' infallibly that you will have coffee
tomorrow are deterministic universes where you cannot possibly not-have coffee tomorrow.
Any non-deterministic universe where it is possible for you to ~A instead of A, is one in which it is also not
possible to know [infallibly] that you will do A prior to you doing A.
What you say here implies that one could only infallibly know P if P is necessary. This implies that if P is only contingently true and S believes P, there must be some possibility that S is mistaken about the truth value of P. But what justifies this claim? That P is contingent entails that there is some possible world wherein ~P. How does it also implicate some possible world wherein S is mistaken about the truth value of P? I don't see the connection, so perhaps you can clarify. What we would need is an actual argument that connects these dots. Your statements here just beg the question with respect to theological fatalist arguments. You would actually need to explain in some non-ersatz fashion why in the absence of P being necessary it cannot be that S infallibly knows P.
I think your claims here employ a notional error, or at least a heretofore unwarranted leap. You seem to be asserting, or otherwise taking it as granted, that infallibility regarding S's knowing P requires that it is not possible that ~P. But, actually, what it directly requires is something more like roughly that it is not possible both that S believes P and that ~P, which is something quite different. What exactly justifies your move from this to the necessity of P itself? I'm not saying that there is no argument that can connect these dots. To be honest, I would not be that surprised if there is a sound argument that shows that in the absence of P itself being necessary there can be no knowledge of P without some mere possibility of epistemic error, perhaps for want of justificatory conditions that could satisfy. However, your post doesn't provide such argument.
04 Mar 15
4 edits
Originally posted by LemonJelloIf proposition 1) is infallibly true. Then you will have coffee tomorrow.
What would it mean for a proposition to be "infallibly true"? A proposition is true or false, that is all. In our context, infallibility is predicated (or not) unto the cognitive process or knowledge or cognizer himself or herself, not unto things like propositio ...[text shortened]... justificatory conditions that could satisfy. However, your post doesn't provide such argument.
For example, an infallibility condition on S's knowledge such as "Necessarily, if P then S knows P" , or some modified variant, seems to accomplish this globally.This implies omniscience rather than infallibility. Someone can be infallible, but not know everything.
I think we agree that, since knowledge is factive, to say that I know something already implies the something is true. So the adjective infallible doesn't add anything in a sentence fragment like "God's infallible knowledge ...". So I feel that it must apply to an agent making assertions or as an adverb to the making of the assertions.
Consider a real world example. The Pythia, the priestesses at the Oracle at Delphi who made the predictions, were reputed to be infallible. When they made their predictions they were sat over a crack through which volcanic fumes containing significant amounts of benzene which meant they were whacked out on the stuff and typically couldn't remember what they had said or anything that had happened when communing with Apollo. In this case infallible refers to an agent making assertions. One cannot really assign any high quality to their cognition processes because of the benzene. So it must simply be a consequence of always being right.
I do not think that modal operators add much here. Suppose Alice makes predictions and she is guessing each time. We can imagine a possible world where just through sheer luck all her predictions come to fruition. Since each time she makes a prediction there is at least one possible world where she is right and at least one where she is wrong, there is a possible world where all the predictions she ever makes are true. In that possible world Alice is infallible. This does not mean she knows anything, since she is guessing and there is no meaningful justification, and it doesn't say anything about her cognitive process. She is infallible in that world solely because all the predictive statements she ever makes are true. It also does not mean that in any other possible worlds she is infallible, since we have vast numbers of possible worlds where she is wrong.
There is no particular reason to restrict infallibility to statements about the future, someone who only ever makes definite statements about things that they know and are therefore true would count as infallible.
So to encode infallibility we need some predicates. Alice is a named object a. S means is a statement, B(x,y) x belongs to y, T(x) would be x is true. F(a) would be Alice is fallible, so ¬F(a) denotes Alice's infalliblity. Then Alice's infallibility would be encoded as:
∀x (S(x)&B(x,a) -> T(x)) <-> ¬F(a)
for all x, if x is a statement and x belongs to Alice then x is true if and only if Alice is infallible. This does not involve modal operators. We only need modal operators to rule out vacuous infallibility. We only add necessarily if Alice is infallible because she is a goddess and not just a lucky guesser.