28 Aug 10
Originally posted by Conrau KA good example of that kind of ambiguity is the term 'necessity' itself. A libertarian theist (or determinist-incompatibilist atheist, for that matter) may not want to treat logical necessity in the same way as, say, causal or metaphysical necessity, "pancaking" them together into a single framework and insist that the same possible-worlds interpretation apply to them all.
Well, just because they want to reject S5 in one context, does not commit them to a total rejection of S5 (I am not sure if that's what your aiming at here though.) These different modal systems are not completely exclusive. S5 may represent a person's meaning in one utterance but not in another. We have to accept that language is ambiguous. The axioms ther ...[text shortened]... ejection of metaphysical necessity (just ignore this paragraph if that is not what you mean.)
28 Aug 10
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Originally posted by Conrau KSo my question is whether your notion of necessity in this case accurately reflects the usage of the libertarian theist.
[b]We begin with our intuitive commitments regarding logical necessity, metaphysical necessity, or whatever, and use them to justify our axioms. We then construct models in order both to capture and to clarify our commitments, and in order to make sense of notions like truth and validity.
Absolutely. I am not suggesting that anyone commits themselv tion of metaphysical necessity (just ignore this paragraph if that is not what you mean.)[/b]
Speaking just from my experience: bbarr's does; yours doesn't.
I do not think the theist has an S5 notion of necessity, such that the necessity of God's knowledge cuts across all worlds. What they want to say is that the necessity of God's knowledge (that you will do A) is true only in worlds in which you will do A, allowing the possibility of not-A in other worlds.
Again, I have to disagree on the basis of my experience: nearly all the libertarian theists I have debated on this topic hold to S5. What they want to say is that necessarily, if you will A, then God knows you will A. It is the case that if you will A, then God knows you will A, so they would hold, in every possible world (and it is trivial that it should be true in possible worlds where it is not the case that you will A). They get God's knowledge that you will do A in every world where you will do A; and they can still get the possibility you mention of not-A in other worlds. But off the top of my head, I cannot think of any that I have engaged with who talk like this of necessity in one world and yet not in others, and those I do recall off the top of my head would probably consider that nonsense. With respect to bbarr's argument in the other thread, their lines of attack should be brought against Premise 4.
I'm still thinking about your case and alternative readings of necessity. My only point here is that on the basis of my experience (which, of course, is certainly not exhaustive), there's no way I can agree that what you have outlined captures typical usage.
28 Aug 10
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Originally posted by LemonJelloMaybe the libertarian theists you know are considerably more disciplined thinkers than Conrau (assuming he is one) or me. Speaking for myself, I am just learning a lot of this stuff as I go along. (EDIT: I really mean that;I'm not speaking sarcastically. I hadn't heard of S5 or thought about transfer of necessity a few days back.)
So my question is whether your notion of necessity in this case accurately reflects the usage of the libertarian theist.
Speaking just from my experience: bbarr's does; yours doesn't.
I do not think the theist has an S5 notion of necessity, such that the necessity of God's knowledge cuts across all worlds. What they want to say is that the austive), there's no way I can agree that what you have outlined captures typical usage.
That said, what would you say to the Lord Shark-breakfast-hit by a bus example in my last-but-one post?
(I suspect you would deny that such a world is a possible world; possibly along the lines that if he wasn't hit by a bus then it's impossible he was hit by a bus and if it's impossible he was hit by a bus then there is no possible world where he was hit by a bus. The logic would certainly be consistent. But something strikes me as off about saying that a world is impossible yet could have been.)
28 Aug 10
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Originally posted by lucifershammerNo, I rather think both you and Conrau K are both very disciplined thinkers. I really admire both of your minds when it comes to tackling such issues. It's just that, again based on my experience, the intuitions of libertarian theists do lie with S5.
Maybe the libertarian theists you know are considerably more disciplined thinkers than Conrau (assuming he is one) or me. Speaking for myself, I am just learning a lot of this stuff as I go along. (EDIT: I really mean that;I'm not speaking sarcastically. I hadn't heard of S5 or thought about transfer of necessity a few days back.)
That said, what w hing strikes me as off about saying that a world is impossible yet could have been.)
With your example, I really don't see much problem. If in the actual world Lord Shark has [I've forgotten what it is] for breakfast; and even if there is a possible world where that is not the case (for whatever reason); then yes the proposition that he has whatever for breakfast is possible. But I do not know too many who would typically be bogged down in the types of weird discussions you mention. They would probably just say that his having whatever for breakfast is true in our world, but only contingently so. I'm sure we could immerse ourselves in the weird counter-intuitive types of discussions that you outline (like in the world where he was hit by the bus it is possible that he has whatever for breakfast today). But it's not that hard for me to extract myself from such seeming craziness by reminding myself that a proposition's being possible here just means that it is true in at least one world. It's better, in my opinion, than talking as if things like necessity feature in some world and yet not others, which to me is nonsense that just defeats the whole point of possible world talk to begin with. Now that would seem crazy! (at least to me).
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28 Aug 10
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Originally posted by LemonJelloSpeaking just from my experience: bbarr's does; yours doesn't.
[b]So my question is whether your notion of necessity in this case accurately reflects the usage of the libertarian theist.
Speaking just from my experience: bbarr's does; yours doesn't.
I do not think the theist has an S5 notion of necessity, such that the necessity of God's knowledge cuts across all worlds. What they want to say is that the ...[text shortened]... austive), there's no way I can agree that what you have outlined captures typical usage.[/b]
Just to be clear, I have not put forward any notion of necessity. As I have explained, I see the different modal logics as descriptively useful in capturing different usages of necessity. I am not stipulating any normative definition. Bbar however has said that necessity cuts across all worlds, that this is what necessity means. My objection is not to say that Bbar is wrong, or that his notion isn't intuitive or more common, just that it may not correspond to what the theist means.
Again, I have to disagree on the basis of my experience: nearly all the libertarian theists I have debated on this topic hold to S5.
Well, then, if they accept a strong notion of necessity, I believe that bbar has successfully refuted them. However, I can think of theologians who hold to a weaker notion of necessity. For example, Thomas Aquinas in a letter Ad Bernardum debates the question of whether God's foreknowledge of a man's death means that there is nothing a man can do to quicken or postpone his death. Thomas Aquinas invokes a distinction between absolute necessity and conditional necessity -- which sounds very much like what I have suggested.
They get God's knowledge that you will do A in every world where you will do A; and they can still get the possibility you mention of not-A in other worlds. But off the top of my head, I cannot think of any that I have engaged with who talk like this of necessity in one world and yet not in others, and those I do recall off the top of my head would probably consider that nonsense.
If that is the case, then they do hold (even if not consciously) a weaker notion of necessity. If they admit the possibility of not-A in some world, while maintaining the necessity of A in another, then they have restricted the notion of necessity so that it does not cut across all worlds. Obviously they may not be aware of this and they may not be able to articulate in philosophically clear language (who ever can?) why this is so, but it is still a position they hold.
I guess it is similar to syntax. Native speakers have very strong and consistent intuitions about the grammaticality of any sentence in their language and obviously are very productive in their own use of the language -- yet they may still be completely unable to understand the syntactic representation of this knowledge and quite unable to explain why they hold these intuitions. What you say suggests that they have some weaker notion of necessity, even if they cannot articulate it explicitly.
I'm still thinking about your case and alternative readings of necessity. My only point here is that on the basis of my experience (which, of course, is certainly not exhaustive), there's no way I can agree that what you have outlined captures typical usage.
There are many cases we may want a restricted notion of necessity. On the last page, Luceifershammer suggested a few cases. But I will outline the two major weaker modal systems and suggest an example in which they are useful.
T: LP --> P. This axiom simply means that if something is necessarily true, it is true. It needn't make any consideration of other worlds. Even though weak, it is has some justification. For example a person might say 'The ground is wet. It must be raining." The only counterexample for that is that it is not raining (rather than the fact it is not raining in some world, even related world -- such consideration is irrelevant.) The 'must' here has modal import but not strong like S5.
4: LP --> LLP. This axioms means that if P is necessary, it is necessary in all worlds related to it. This axiom is basically transitive. So if LP in w1 and w1 R w2 and w2 R w3 then LP in w2 and w3. This may be suitable for temporal logic. So for example, we may say, it is necessarily true in 1700 that Shakespeare wrote Hamlet and consequently it is necessarily true in 1701 and 1702 and so on.
The good thing about this is that is not reflexive as well. So simply because it is necessary in 1700 does not mean it is necessary in 1500 (when Hamlet was not yet written). S5 would require that it be necessary in 1500 and 1400 and 1300 and son on. We would eventually end up with the same problem as Aristotle's naumachia.
Now you might be tempted to say that the native speaker in these cases is just wrong or they are using some non-standard definition of necessity. Perhaps in the first case, you may simply say that their utterance is invalid or that their definition an abuse. In natural language semantics, this isn't much fun though. The preference is to recognise these as correct and use different axioms to describe them -- to treat them seriously as they are used not as philosophers want them to be used.
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28 Aug 10
Originally posted by lucifershammerAhh...welcome back to the forum. We were just lamenting your absence on another thread.
A good example of that kind of ambiguity is the term 'necessity' itself. A libertarian theist (or determinist-incompatibilist atheist, for that matter) may not want to treat logical necessity in the same way as, say, causal or metaphysical necessity, "pancaking" them together into a single framework and insist that the same possible-worlds interpretation apply to them all.
http://www.redhotpawn.com/board/showthread.php?threadid=132366&page=2
28 Aug 10
Originally posted by Conrau KI was first introduced to modal logic a decade ago, and haven't thought much of it since. We have little need for it in ethics, epistemology and philosophy of mind; those philosophical sub-disciplines in which I specialize. We do, however, often use locutions like 'in nearby possible worlds' when talking about counterfactuals, tacitly referencing the accessibility relation relevant to the conversational implicature of certain uses of the 'possibility' and 'necessity'. But, interestingly, we don't use locutions like this when dealing with issues of logical, conceptual or metaphysical necessity. The accessibility relation formalized by S5 are just taken for granted when speaking of these forms of necessity. This is no accident. The intuitions that inform the development of modal logic substantively begin with Leibnitz's claim that necessity is truth across possible worlds. S5 is popular precisely because it best formalizes this intuition.
[b]We begin with our intuitive commitments regarding logical necessity, metaphysical necessity, or whatever, and use them to justify our axioms. We then construct models in order both to capture and to clarify our commitments, and in order to make sense of notions like truth and validity.
Absolutely. I am not suggesting that anyone commits themselv ...[text shortened]... tion of metaphysical necessity (just ignore this paragraph if that is not what you mean.)[/b]
Your question is whether such a robust account of necessity captures the intuitions of the libertarian theist. Your suggestion is that S5 may be reasonably rejected on these grounds. But S5 axiomatizes Leibnitz's claim by construing the accessibility relation as symmetric, reflexive and transitive. So, if the libertarian theist thinks that the notion of necessity implicit to S5 is too strong, and fails to do justice to what he intends by 'necessity' as it appears in the sorts of theistic claims at issue in this debate, then he presumably would want to reject either symmetry, reflexivity, or transitivity. Moreover, he presumably would have some reason for this rejection. My claim is that your rejection seems ad hoc, and pretty much empty until a justification or alternative account is given. Merely claiming that other uses of 'necessity' are more appropriately captured by formalizations other than S5 is just hand-waving. The claims we're dealing with here are not tensed, or deontic, or even, really, epistemic in the sense relevant to epistemic logics. Yet it is these domains in particular that have motivated deviations from S5 and the development of different systems.
Now, you claim that the libertarian theist does not have an S5 notion of necessity. Perhaps. It is likely that the run-of-the-mill libertarian theist has no particular formalized notion of necessity in mind when he claims, for instance, that God is necessarily omniscient, or that God necessarily believes only true propositions, or that it is necessary that if a proposition is true, then God knows that proposition. But if a theist rejects S5 in the manner you suggest, then he will be committed to claims like 'there is a world where it is false that God is omniscient', or 'there is a world where God believes a false proposition', or 'there is a world where there is a true proposition that God does not know'. These are just instances of the general schema 'Necessarily P and possibly ~P', which you think the theist can endorse subsequent to the rejection of S5. So, give me some account of God, or necessity, or something that makes these claims plausible! If you can't, the the mere fact that a theist can reject S5 doesn't cut any ice. It is as if I give a theist a proof in FOL and he responds "Sure, but that proof relies on the law of the excluded middle, which I reject". Well, O.K., but (1) do you have any independent reasons to reject that law? and (2) are you prepared for the fallout of rejecting that law?
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28 Aug 10
Originally posted by Conrau KI think I see what you mean. You want to capture 'necessary' as a competent speaker would use the term in a phrase like 'necessarily, god knows you will A'. Is that right?
[b]I agree, you could specify a set of possible worlds and an accessibility relation in such a way as to capture some other notion of necessity. I just don't think it will capture the relevant one.
I disagree. I think that a proper restriction of necessity is exactly what the libertarian theist wants. He wants to say that in the worlds in whic ...[text shortened]... s very dubious consequences (for example, if something is possibly necessary, it is necessary.)[/b]
What I wonder though, if this is the case, whether you are attempting to build a modal scope fallacy into the formalism? Isn't the above phrase expressing something more like:
@(p ->Kc(p)) (omniscience condition)
Where:
@ = necessity operator
p = any proposition
Kc(p) = agent C knows that p
Now, to try to conclude that @Kc(p) is just our old friend the modal scope fallacy isn't it?
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28 Aug 10
Originally posted by lucifershammerI think you have a point about intuitions here. My response is that logical necessity is itself counter intuitive but nonetheless is the correct way to approach the question of the compatibility of god's omniscience and libertarian free will. These are both concepts which also have counter intuitive ramifications against which we must be on guard. I think the stringency of S5 helps us do this.
It seems to me that all of our discussions so far have invoked 'necessity-lite' rather than absolute necessity.
Let's look at the example you gave in your OP - coffee and toast for breakfast. In this world, let's say you did actually have coffee and toast this morning. Therefore, it must be possible that you had coffee and toast for breakfas ...[text shortened]... sing it all along - does seem to have something to do with that discussion.)
In the possible world where I was knocked down last night it is possible that I had coffee and toast this morning. Although this is counter intuitive, if you think about logical necessity for long enough this starts to look perfectly reasonable. That's my experience anyway. If you can't get your intuition to line up with this, then it follows that your intuition is that all facts are necessary. For example compare this scenario with me actually having coffee and toast this morning. It is possible I had waffles, it just happens not to be the case.
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28 Aug 10
Originally posted by bbarrThanks, I appreciate that and feel the same, great contributions from you all.
Also, I want to take a moment to say that I deeply appreciate the conversations I have had with the four of you. Your criticisms and suggestions and arguments are just great. Thanks.
28 Aug 10
Originally posted by Conrau KWell, then, if they accept a strong notion of necessity, I believe that bbar has successfully refuted them.
[b]Speaking just from my experience: bbarr's does; yours doesn't.
Just to be clear, I have not put forward any notion of necessity. As I have explained, I see the different modal logics as descriptively useful in capturing different usages of necessity. I am not stipulating any normative definition. Bbar however has said that necessity cuts across al ...[text shortened]... o treat them seriously as they are used not as philosophers want them to be used.[/b]
I disagree. Again, the libertarian theist I described can (and should) reject Premise 4 of bbarr's argument in the other thread.
If that is the case, then they do hold (even if not consciously) a weaker notion of necessity. If they admit the possibility of not-A in some world, while maintaining the necessity of A in another, then they have restricted the notion of necessity so that it does not cut across all worlds.
No. Please state exactly where I implied this libertarian theist maintains the necessity of A. Again, what he maintains is the necessity that if you will A, then God knows you will A. In no way does that imply or is that the same as maintaining the necessity of A. As I mentioned, he gets that God knows you A in every possible world where you do A; and he gets the possibility of not-A. He doesn't have to as you say weaken his notion of necessity in any way to get what he wants.
What you say suggests that they have some weaker notion of necessity, even if they cannot articulate it explicitly.
Again, no, I do not agree.
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At any rate, if your outlinings captured typical usage, I should expect to see people talking like you suggest, but I have not seen that.
But I do really appreciate your offerings here, and I will need to think more about them. Thanks,
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29 Aug 10
1 edit
Originally posted by Lord Shark@(p ->Kc(p)) (omniscience condition)
I think I see what you mean. You want to capture 'necessary' as a competent speaker would use the term in a phrase like 'necessarily, god knows you will A'. Is that right?
What I wonder though, if this is the case, whether you are attempting to build a modal scope fallacy into the formalism? Isn't the above phrase expressing something more like:
@(p ...[text shortened]... w, to try to conclude that @Kc(p) is just our old friend the modal scope fallacy isn't it?
Ok. Now I see what the problem is. Obviously we cannot conclude L Kc(p).
L (p --> Kc(p) ) entails L p --> L Kc(p) but then the assertion of p does not lead to L Kc(p).
This certainly captures my initial feelings. It seemed to me to be a clever conjurer's trick to suddenly conclude p is necessary simply because p is true (i.e. the fact that you will A then entails you necessarily will A because God's knowledge is necessary.) I see how premise 4 then is problematic once the omniscience condition is explicitly described.
What I wonder though, if this is the case, whether you are attempting to build a modal scope fallacy into the formalism?
No. I jumped over premise (4) straight to (7), overlooking the fallacy. My criticism, I believe, still stands. We only get a contradiction between (7) and (8) because possibility and necessity are not clearly defined. A theist might have a very broad notion of possibility (as in, 'I can imagine a world where you could not-A'😉 or a very weak notion of necessity ('the necessity of A means only that you will A in a restricted set of worlds.) In that case, there could be several readings of (7) and (8) which avoid a contradiction. So I am not trying to build a formalism around a fallacy. I guess I just focused on one premise rather than another.
In the end, the difference between our objections is very subtle. We would have a similar set of worlds, w1 in which you will A and w2 in which you will not-A. We would capture the necessity of God's knowledge by w1: Kg(A) and w2: Kg(not-A) -- where g is God. The only difference is this: in your world, A and not-A are contingent; in mine, they are, weakly, necessary (but only in the trivial sense that you will A in the worlds in which you will A.) We would appropriately represent this difference in your world with the relations w1 R w2 and w2 R w1, which I would perhaps be required to reject.
I think both our objections are based on a similar intuition and they are not substantially different (both Lucifershammer and Lord Shark) said they were pretty much the same. The question then is whether my objection to (7) has any motivation. Why should we restrict the relations across worlds? I haven't at all suggested an answer. I believe that there are often grounds for a weaker notion of necessity -- such as in temporal logic. We want to say that it is necessarily case that Shakespeare wrote Hamlet (that it is necessarily true now, tomorrow and all future time) without endorsing the claim that it was necessary in the 1400s.
Perhaps it is just ad hoc for a theist to use a different notion of necessity in this case. I hadn't really considered it from that perspective. My assumption was simply 'if that is what the theist means, then fine.' I didn't want to justify why a libertarian theist might want to use a weaker notion of necessity. Obviously if he rejects (4) then there is really no need to get muddled in debates about S5 and so on.
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29 Aug 10
2 edits
Originally posted by bbarrMoreover, he presumably would have some reason for this rejection. My claim is that your rejection seems ad hoc, and pretty much empty until a justification or alternative account is given. Merely claiming that other uses of 'necessity' are more appropriately captured by formalizations other than S5 is just hand-waving.
I was first introduced to modal logic a decade ago, and haven't thought much of it since. We have little need for it in ethics, epistemology and philosophy of mind; those philosophical sub-disciplines in which I specialize. We do, however, often use locutions like 'in nearby possible worlds' when talking about counterfactuals, tacitly referencing the accessib law? and (2) are you prepared for the fallout of rejecting that law?
Ok. I really have no answer to this. Perhaps it is just ad hoc. It reminds me of a similar criticism of paraconsistent logics. I know in recent times there has been a trend to use modal logic as way to solve fallacies like 'P & not-P, therefore I am a flower.' A paraconsistent logician might create a world w1 where the principle of non-contradiction does not apply and then, since the premise can then be false, have a counterexample to this argument. Obviously the major criticism is, like yours, that it is a bit ad hoc. On what basis can we just create a world where basic logic axioms do not apply?
But if a theist rejects S5 in the manner you suggest, then he will be committed to claims like 'there is a world where it is false that God is omniscient', or 'there is a world where God believes a false proposition', or 'there is a world where there is a true proposition that God does not know'. These are just instances of the general schema 'Necessarily P and possibly ~P', which you think the theist can endorse subsequent to the rejection of S5.
I don't accept that. The theist may at least accept the possibility of those claims but even then, perhaps the theist may wish to describe God's omniscience as S5 but not the content of that knowledge. But yes, I get your point that it becomes very ad hoc. Then the libertarian theist would have to hold multiple notions of necessity at the same time and I really have no idea how that would be represented in possible world semantics.