Counterpossible Reasoning in Philosophy of Religion (and Elsewhere)
November 19, 2011 — 16:01

Author: Kenny Pearce  Category: Problem of Evil Theological Fatalism  Tags: , , , , ,   Comments: 20

The latest (July 2011) Faith and Philosophy contains an excellent article by Jeff Speaks on some difficulties related to establishing the consistency of certain claims (he uses as examples the existence of human freedom and the existence of evil) with the existence of an Anselmian God. The basic idea is this: since an Anselmian God is, by definition, a necessary being, establishing the possibility of an Anselmian God is tantamount to establishing the necessary, and therefore actual, existence of an Anselmian God. But these compatibility arguments typically, in one way or another, assume the possibility, and so the actuality, of an Anselmian God. If we were allowed to assume this premise, our task would be extremely easy! We could argue as follows:

  1. God (actually) exists
  2. Evil (actually) exists
  3. Therefore,

  4. The existence of God is consistent with the existence of evil.

Piece of cake! Now I, of course, take this argument to be sound. In fact, I even think that some people (depending on their background beliefs) might be rational in allowing this argument to increase their confidence in the truth of (3). But clearly this argument cannot be used to respond to atheist arguments from evil against the existence of God. It is dialectically inadmissible in that context.
In his paper, Speaks argues that Warfield’s argument for the compatibility of necessary omniscience with human freedom and Plantinga’s free will defense are both a lot like this. That is, they both assume that, possibly, an Anselmian God exists. But if that assumption is admissible, then we could just use this simpler argument. But obviously we can’t use this simpler argument, so the premise must be inadmissible. (This isn’t exactly the way Speaks puts his points together; it’s my interpretation of what his arguments actually show.)
Speaks states the “principal conclusion” of his paper as follows:

any argument for the compatibility of two propositions must also be an argument for the possibility of each of those propositions. Hence it is impossible to argue for the compatibility of two propositions, one of which is necessary if possible, without arguing for the truth of that proposition. (p. 291)

In this post, I’m going to push back.


Specifically, I believe that the standard (Lewis-Stalnaker) semantics for subjunctive conditionals is flawed in its treatment of impossible antecedents, and that once we recognize this flaw for what it is, we can save these compatibility arguments (though, for reasons which will emerge, it might be better to call the modified arguments ‘might’ arguments, or some such). I should note that my suggestion is in some ways similar to a suggestion Speaks makes at the end of his paper, namely, that if we had a notion of some sort of asymmetric ‘dependence’ relation which could obtain between necessary truths, we might show that God’s existence and human freedom are, in this sense, independent. But my solution will require only subjunctive conditionals, and not these additional dependence relations.
I’m going to use Plantinga’s Free Will Defense as my example since it’s more familiar to me, and probably to most readers, than Warfield’s argument. I’ll use the following symbols:

□→ The ‘would’ subjunctive, as in ‘If I were to flip this coin, it would land either heads or tails.’
◊→ The ‘might’ subjunctive, as in ‘If I were to flip this coin, it might land heads.’
G The proposition that necessarily, an omnipotent, omniscient, and morally perfect being exists.
E The proposition that evil exists
TWD The proposition that every creaturely essence suffers trans-world depravity (if you don’t know what that means, you should read Plantinga’s The Nature of Necessity, but I think you’ll be able to understand most of what I say without it).

Now, we can think of the argument from evil as going like this:

  1. G □→ ~E
  2. E
  3. Therefore,

  4. ~G

This is clearly valid (subjunctive conditionals support modus tollens). Plantinga’s free will defense is meant to be an argument for the negation of premise (1). Now, if the conditional is truly a ‘would’ conditional (rather than a ‘would probably’ conditional or some such), then (1) is inconsistent with the following claim:

(FWD) G ◊→ E

That is, if it’s really true that if God existed there (definitely) wouldn’t be evil, then it must not be true that if God existed there might be evil. Plantinga’s free will defense can be construed as an argument for this proposition (which is why I’ve labeled the proposition ‘FWD’).
Now, slightly modifying Plantinga, we can run the argument as follows

  1. G ◊→ TWD (“[even] if God existed, all creaturely natures might [still] suffer trans-world depravity”)
  2. (G & TWD) ◊→ E (“if God existed and all creaturely natures suffered transworld depravity, then there might be evil in the world”)
  3. Therefore,

  4. G ◊→ E (“[even] if there was a God, there might [still] be evil in the world”)

Here’s where Speaks’ problem comes up: on the standard semantics p ◊→ q is equivalent to ◊(p & q) which, of course, entails both ◊p and ◊q. So if G is impossible, the argument is unsound. But if G is possible, then G, and we can take the easy way out, as above.
This implication of the standard semantics is, I submit, incorrect. I think the following conditional is true:

If some humans were able to draw round squares, I might be able to draw round squares.

Furthermore, I think that mereological universalism is necessarily false, but I think the following conditional is true:

If mereological universalism were true, then my body might be part of an object which also had an alien space ship as a part.

In fact, as Trenton Merricks points out near the beginning of his Objects and Persons, pointing out the truth of conditionals like this is an important strategy in metaphysical argument; the fact that this conditional is true is one of my reasons for believing that mereological universalism is necessarily false. But if these sorts of ‘might’ conditionals can be true, then it seems that premise (1) in my rendition of Plantinga’s free will defense might very well be accepted (consistently) by an atheist after all.
(cross-posted at blog.kennypearce.net)

Comments:
  • William McDoniel

    Isn’t the problem here just that different senses of “possible” (and “necessary”) are being used at the same time? What I believe I’ve seen y’all on this blog call S5 modal logic collapses statements like “possibly necessarily P” to “necessarily P”, but obviously that only makes sense when we’re talking about the same kinds of possibility and necessity.
    Something can be logically possible but metaphysically impossible (I think). Something can be epistemically possible (is this a real phrase?) but logically impossible. Likewise for conceivability, and maybe even for a kind of possibility which is entirely independent of logical possibility. It’s this last kind which seems to me to be what you’re getting at with “I might be able to draw round squares”. The possible world that you’re talking about there is not a logically possible world, and for me it’s an inconceivable world, but it’s still a possible world drawn from a set of worlds with many different logics or metaphysics. Maybe it’s meta-logically possible.
    If it is metaphysically possible that a being is metaphysically necessary, then the being is actual. But if it is only conceivable or epistemically (that is, in a “to the best of my knowledge” sense) possible that a being is metaphysically necessary, there’s no further implication (it’s perfectly coherent to say that “possibly, a being is necessary” without asserting that the being is actual, and lots of people do this all the time when talking about God). The FWD is about casting doubt on the idea that God and evil are logically or metaphysically incompatible. All of the “might” talk that goes on in the FWD tends to be getting at our potential ignorance of how things work – it’s an epistemic argument. The conclusion is that /for all we know/ God has a good reason for allowing some evil, but that only implies the epistemic possibility of a logical/metaphysical necessity, so it doesn’t allow what you call the easy way out because you can’t collapse that possible necessity into a necessity. It does, however, allow us to say that it is epistemically possible that premise 1 of the argument from evil is false, and therefore we have a reason not to accept that the argument is sound.
    I’ve been using “logical” and “metaphysical” together because I’m not very clear on what the difference is or, if there is one, which one is appropriate for talking about the argument from evil and the possibility/necessity of God. Sorry about that.

    November 19, 2011 — 20:26
  • Kenny Pearce

    So, Speaks suggests that the FWD may be able to be given an interpretation with epistemic possibility, and I think he’s right that that kind of argument can probably be made to work. But in this post I am using metaphysical/broad logical possibility consistently. Was there a particular point where you thought I was trading on an ambiguity of this sort? What I’m claiming is that the truth of p ◊→ q doesn’t imply that either p or q is possible (though it does imply that if p is possible q is possible).

    November 19, 2011 — 20:35
  • William McDoniel

    Maybe I’m just making exactly the same point Speaks (or someone else) is – I haven’t read the paper and it’s not my field – but it just seems to me that p ◊→ q /is/ implying that both are possible in some to-be-specified way, with “to-be-specified” doing a lot of work. I was reading you as rejecting that but also not having something to replace it with. Is p ◊→ q just not explicable in terms of more basic operators? What are its truth conditions? I meant to be suggesting what seemed to me to be an easier way of explaining how p ◊→ q statements can make sense as they’re used in normal speech about metaphysics, and I apologize if I was just rehashing old ideas.

    November 19, 2011 — 20:59
  • Mike Almeida

    Hi Kenny,
    Your argument makes much stronger claims than does Plantinga’s TWD. Plantinga does not claim (1)
    1. G ◊→ TWD
    There might not be any transworld depraved essences in any close worlds. And your (2) is even stronger.
    2. (G & TWD) ◊→ E
    There are many worlds in which God exists and all creaturely essences are TWD, but there is no evil. Take any world where, no matter which essence God were to instantiate, the overall balance of moral good over moral evil would be negative. In such a world, it might be that every essence is twd, but that God instantiates no essences at all. FWD does not commit us to saying that in every world where every essence is TWD it is overall better to instantiate some essence or other rather than none. So, I think what you want to do is weaken the argument a bit. It still makes the kind of point you want.
    1′. ◊(G ◊→ TWD & (G & TWD) ◊→ E)
    And that gets you to (2′)
    2′. ◊(G ◊→ E)
    And from (2′) you get the consistency claim in (3′).
    3′. /:. ◊(G & E)
    Of course, this does not address the sort of argument from evil you begin with. That argument is designed to show that God’s existence is not consistent with the evil we actually find. But FWD was not designed to address that sort of argument from evil.

    November 20, 2011 — 13:53
  • Mike Almeida

    Also a post about non-trivial counterpossibles in philosophy of religion that exploits the fact that God is a necessarily existing being (fi existing at all).
    http://prosblogion.ektopos.com/archives/2010/10/impossibility-a.html

    November 20, 2011 — 14:02
  • Kenny Pearce

    William – You’re right, I don’t have an analysis to replace it with. Marc Lange in his new book ‘Laws and Lawmakers’ takes counterfactuals as primitive and builds possible worlds out of them, rather than vice versa. His approach is compatible with what I am saying here, but I don’t like the idea of counterfactuals as primitive; they seem like the sort of thing that should be analyzable. What I want is an analysis in terms of laws (a la Maudlin) and/or causal powers (a la Aristotelianism) that will support the intuitive (to me) view that some counterpossibles are true and others false. But I don’t have that analysis.
    Mike – I just looked back at Lewis, and you are right. His official definition of the ‘might’ conditional has it requiring that there be a ψ world in the smallest φ-permitting sphere. So my atheist is making weaker claims than Plantinga’s, and I have to make stronger claims in response. That is, I have framed the debate about being about whether G □→ ~E rather than about whether □~(G&E). But note that since modus tollens is valid with the subjunctive conditional, the weaker claim is sufficient to establish the non-existence of God, so we’d better have a reply to it, and I’m not sure we can reply without making these strong claims.
    Your weakened argument does not have as its conclusion the denial of the atheist’s premise. Perhaps we can keep the conditionals as dealing with broad logical possibility and interpret the outermost diamonds as epistemic possibility, and then get the conclusion that the atheist premise might (for all we know) be false. Maybe that’s good enough.

    November 21, 2011 — 9:24
  • Mike Almeida

    Hi Kenny,
    Yes, right, the weaker argument I suggest really aims to show that it is possible that God and evil coexist. That’s a modest claim, and one that does not engage the atheistic argument you describe. But it does provide a basis for replying to your atheist. Suppose the weak argument succeeds in showing that, in worlds where every essence is TWD and it was better overall to instantiate some significantly free essences rather than none, God coexists with moral evil. The next move is one from epistemic possibility: i.e., for all anyone knows, we are in such a world. So, for all anyone knows, (1) (G □→ ~E) in the atheistic argument is false. Of course, you’ll have to generalize to natural evils, maybe in the way Plantinga does.

    November 22, 2011 — 9:08
  • How about solving the problem like this? When I argue that p and q are compatible, what I’m really arguing is that if it were that Mp and Mq, then it would be that M(p and q).
    That said, I actually think that in practice when philosophers claim to have shown some claims to be compatible, often they simply mean that the conjunction of the claims isn’t subject to certain kinds (determined contextually) of logical/metaphysical/conceptual objection.

    November 23, 2011 — 15:19
  • Keith DeRose

    “In his paper, Speaks argues that Warfield’s argument for the compatibility of necessary omniscience with human freedom and Plantinga’s free will defense are both a lot like this. That is, they both assume that, possibly, an Anselmian God exists. But if that assumption is admissible…”
    I don’t think Plantinga should be read as construing God in an Anselmian way in his treatment of the problem of evil. Or at least I *thought* that he shouldn’t be so read back when I wrote a paper on Plantinga’s FWD. Now, over 20 years later, I am just trusting my past self — young & foolish as he was! — on this matter. I haven’t recently re-read the relevant Plantinga with this issue in mind, but in “Plantinga, Presumption, Possibility, and the Problem of Evil” (Canadian JP, 1991; draft available at: http://pantheon.yale.edu/~kd47/PPPPE.doc ), where I was using these abbrev’s:
    (1) God (exists and) is omnipotent, omniscient, and wholly good
    (2) There is evil in the world,
    I wrote:
    *****
    Plantinga’s assessment of his ontological argument is that it shows “that if it is even possible that God, so thought of, exists, then it is true and necessarily true that he does.” And in the ontological argument, God is being thought of in such a way that he exists necessarily, if it is possible that he exists. But Plantinga must not be thinking of God in this way in his treatment of the problem of evil. If God were so thought of in (1), then after having clearly shown the compossibility of (1) and (2), as Plantinga thinks he has done, he would have been only a couple of deductively valid steps away from clearly showing the existence of God. For if (1) and (2) are compossible, then (1) is possible. And if God exists necessarily if it is possible that he exists, then if (1) is possible, God exists (actually and necessarily). If Plantinga were so close to showing so clearly that God exists, it would be strange that he takes such a more cautious attitude toward the power of his ontological argument (see NN, pp. 216-221).
    *****
    I gather from what I wrote that Plantinga doesn’t explicitly address the matter, and I was reading him as I was to exercise charity. But isn’t it a good exercise of charity, if the alternative — taking him to be construing God in an Anselmian way in his treatment of the POE — makes such an awful mess of things?

    November 26, 2011 — 19:56
  • Keith DeRose

    “That is, if it’s really true that if God existed there (definitely) wouldn’t be evil, then it must not be true that if God existed there might be evil.”
    That’s only true on one of the popular theses of the relation between “might” and “would” cf’s: the duality thesis that Lewis championed for a while. (But then, I think, he moved to an ambiguity thesis on which the “might” cf’s are incompatible with the corresponding “would not” cf’s on only one of two readings of the “might” cf’s.) Stalnaker argued that “might” cf’s should instead be understood as expressing the possibility of the corresponding “would” cf’s: On this account, P>–>Q is compatible with P[]–>~Q, and P>–>~Q is compatible with P[]–>Q. I think a Stalnaker-like view is right here, and argued this in a paper in “Can It Be that It Would Have Been Even Though It Might Not Have Been?,” Phil Perspectives; available (I think illegally, given my very insecure grasp of copyright law) here: http://www.calvin.edu/academic/philosophy/virtual_library/articles/derose_keith/can_it_be_that_it_would_have_been.pdf
    Of course, one could just stipulate that one is using P>–>Q to express the dual of P[]–>Q, but then you lose the claim that P>–>Q expresses anything like might-cf’s in ordinary English.

    November 26, 2011 — 20:12
  • Kenny Pearce

    Alex: I think the suggestion in your first paragraph sounds promising, and I might have more to say about it later.
    Keith: Yes, actually Speaks says that Plantinga told him that the argument was meant to be read as assuming that the existence of God is contingent. But of course Plantinga ACTUALLY thinks that God exists necessarily. So in even offering the argument at all Plantinga is (by his lights) engaging in counterpossible reasoning. It is, at any rate, independently interesting to ask whether a Plantingan argument can be made to work on the assumption that God exists necessarily, if at all. I, for my part, don’t think counterpossible reasoning makes a mess of things; I think it’s a normal and useful part of philosophical discourse, and we need to fix our analysis of conditionals to reflect that.
    I’ll have to think more about the might conditionals, but of course if we adopt Alex’s proposal, then we don’t need them after all, and that might make things cleaner.

    November 29, 2011 — 19:52
  • Justin

    I didn’t read all of the comments, so I’m sorry if I’m reproducing content or missing important points.
    “on the standard semantics p ◊→ q is equivalent to ◊(p & q)”
    This isn’t true, is it? It’s true that on the standard seman tics, the former entails the latter. But, the converse isn’t true. You (or, Speaks) only need the claim that the former entails the latter, but I just wanted to make sure I’m not missing something.
    “if it were that Mp and Mq, then it would be that M(p and q)”
    I can’t see how this helps. Doesn’t this conditional entail:
    M((Mp & Mq) & M(p & q))
    which entails:
    M(Mp & Mq) & MM(p & q)
    which entails:
    (MMp & MMq) & MM(p & q)
    given S4 (I think), this entails:
    Mp & Mq
    Doesn’t that give us the easy way out again?

    November 30, 2011 — 10:56
  • Kenny Pearce

    Hi Justin,
    So, when I was talking about the ‘standard semantics’, I meant the theory given in Lewis’s Counterfactuals. However, as Mike Almeida pointed out, I made an error: on Lewis’s theory there, it is required that q be true in at least one world of the innermost p-permitting sphere. Also, as Keith DeRose pointed out, this part of Lewis’s theory is more controversial than some other parts, so it might not be correct to call it ‘standard’. This was my error, not Speaks’.
    As far as Alex’s conditional, the first entailment you draw from it doesn’t hold. On the standard semantics, p □→ q does not imply ◊(p & q). On the contrary, ~◊p implies p □→ q for any q (just as ~p with the material conditional). Now, I think the standard semantics is wrong here, but I don’t find intuitive support for your entailment either: surely there are some true conditionals with impossible antecedents. The standard account is wrong to suppose that they are ALL true, but surely it’s right to suppose that SOME of them can be true.

    November 30, 2011 — 11:34
  • Justin

    Hi Kenny,
    I’m not all that surprised, but I think I lost the train of the discussion. I thought we were wondering how to resolve a certain problem suggested by Speaks. The problem is that when you take premises of certain valid “compatibility arguments” to be true, then we get an objectionably “easy way out” of, for instance, the problem of evil. I guess I was assuming that we (or, Speaks) were ignoring the possibility that the might-counterfactuals that are premises of the compatibility arguments are just trivially true. Otherwise, I don’t see how we get Speaks’ problem.
    There were two version of the compatibility argument on the table:
    Mike’s Argument:
    1′. ◊(G ◊→ TWD & (G & TWD) ◊→ E)
    2′. ◊(G ◊→ E)
    3′. /:. ◊(G & E)
    Suppose we allow that Plantinga is merely asserting that the premises of this argument true (perhaps trivially). Then it is consistent with what Plantinga is asserting that the argument is invalid. If G is false, then the premises are trivially true and the conclusion is false. Presumably Plantinga doesn’t intend that, so – if we are reading Plantinga as giving this argument – he must be assuming that the premises are non-trivially true. That will get him the conclusion and Speaks his problem.
    Your Argument:
    1. G ◊→ TWD (“[even] if God existed, all creaturely natures might [still] suffer trans-world depravity”)
    2. (G & TWD) ◊→ E (“if God existed and all creaturely natures suffered transworld depravity, then there might be evil in the world”)
    3. G ◊→ E (“[even] if there was a God, there might [still] be evil in the world”)
    If we assume that Plantinga is merely asserting that hte premises of this argument are true (perhaps trivially), then the invalidity of the argument is inconsistent with what Plantinga asserts. But, we don’t get the “easy way out”.Unless Plantinga is assuming that at least one of the conditionals in the premises is non-trivially true, then we can’t infer the actual existence of God.
    If there is a problem, it must arise from the fact that Plantinga is asserting the non-trivial truth of the might-conditionals which serve as premises in his argument. If that isn’t a constraint on how we are understanding the problem, I don’t see how the problem arises.

    November 30, 2011 — 13:32
  • Kenny Pearce

    So Plantinga’s own formulation is not in terms of might conditionals. Plantinga argues instead as follows:
    1. ◊(G & TWD)
    2. (G & TWD) □→ E
    :. 3. ◊(G & E)
    This inference is clearly valid. The problem is that, given an Anselmian conception of God, which Plantinga elsewhere endorses, ◊G implies G. 1, of course, implies ◊G. That’s what gives rise to the problem. My formulation in terms of might conditionals was an attempt to reformulate the argument in a way that could deal with this problem.

    November 30, 2011 — 13:43
  • Justin

    I see. That’s helpful; thanks.
    But, I’m still trying to see how Alex’s suggestion is supposed to be an advance over yours. It seems to me that they’re in the same boat.
    If the premises might just be trivially true, then the soundness of the argument doesn’t give rise to Speaks’ easy way out(though, the argument might not have much rhetorical force). In particular, this claim will be false:
    “on the standard semantics p ◊→ q is equivalent to ◊(p & q) which, of course, entails both ◊p and ◊q.”
    It will even be false – taking into account Mike’s point – if we modify it by substituting ‘entails’ for ‘is equivalent to’ (which is all you needed).
    If the premises are supposed to be non-trivially true, then Alex’s conditional – just as much as your premises – will need to be read on a theory of counterfactuals according to which those with necessarily false antecedents might be non-trivially true.

    November 30, 2011 — 14:12
  • Kenny Pearce

    Yes, that’s right. I think Alex’s suggestion might be an advance over mine insofar as ‘would’ conditionals are less confusing than ‘might’ conditionals, but they are both instances of the same basic strategy. Also, Alex’s suggestion is closer to Plantinga’s original argument than mine is. (Maybe Alex thinks there are more advantages than this, but those are the two that I see.)

    November 30, 2011 — 14:24
  • Here’s a rough start of a theory of non-triviality of conditionals.
    A material conditional “if p then q” is trivially true provided that (a) the only reason that it is true is that p is false or (b) the only reason that it is true is that q is true or (c) the only reasons that it is true are that p and q are true.
    A subjunctive conditional “p □→ q” is trivially true provided that (a) the only reason that it is true is that p and q are both true or (b) the only reason that it is true is that p is impossible or (c) the only reason that it is true is that q is necessary or (d) the only reasons that it is true are that p is impossible and q is necessary.
    For instance, “If it is now snowing in Anchorage, then it is now snowing in the Sahara” understood as a material conditional is trivially true, because the falsity of the antecedent (I just checked!) is the only reason for the conditional to be true. The contrapositive “If it not now snowing in the Sahara, then it is not now snowing in Anchorage” is trivially true, since it is true only because of the truth of the consequent. On the other hand, “If I am going to meet the Queen for dinner tonight, I will wear a suit” is non-trivially true. It is true not just because its antecedent is false–there is another explanation.
    Likewise, “Were horses reptiles, then Fermat’s Last Theorem would be false” and “Were Fermat’s Last Theorem false, horses would be mammals” are “Were I writing this, it would not be snowing in Anchorage” are trivially true, in virtue of impossibility of antecedent, necessity of consequent and truth of antecedent and consequent, respectively. But “Were horses reptiles, either donkeys would be reptiles or there would no mules” is non-trivally true–there is another explanation of its truth besides the impossibility of antecedent, namely that reptiles can’t breed with mammals and mules are the offspring of horses and donkeys.

    December 1, 2011 — 9:16
  • Dianelos Georgoudis

    The argument from evil is an attack on theism from within. This argument in effect says: If you believe in theism (a cognitive position which entails the basic ontological and epistemological commitments of theism) then you should change your mind because according to XYZ there is an internal incoherence there. Theistic defenses, such as Plantinga´s free will defense, in effect respond: I don’t have to change my mind because there is an error in your XYZ syllogism and thus your intent to demonstrate an internal incoherence in my cognitive position fails. The point here is that both the argument from evil and the respective defenses take as given the existence of God (or, more exactly, that reality in its ontological and epistemic dimensions is God-based). The way I understand it then, it is not the case that the defense posits the existence of God as a premise (nor posits the possibility of the existence of God as a premise). Rather the defense responds to the argument from evil within the same cognitive order in which the argument from evil operates, namely from within theism.
    In the current context I’d like to broaden the discussion and express the following opinion: Concepts and formalisms strike me as being mere tools. They are there to serve us in our quest for understanding. It is thus understanding which expresses itself in concepts and formalisms, and not the other way around. Those who are inclined to do analytic philosophy should be careful not to put the cart before the horse. They are useful in testing our understanding, but cannot by themselves lead us to better understanding. Concepts and formalisms have not a life of their own, and are useful only if one uses them properly. Philosophy is not a business of formal/mechanical discovery. Not even math, which is understood by many as being the paradigmatic case of a business of formal/mechanical discovery, is ultimately so.
    Perhaps a new argument for theism lurks in this neighborhood, which would or might go like this: Cognition is an intrinsic part of reality. If we find that all cognition is ultimately not one of mechanical discovery, and that on the contrary all knowledge is ultimately the result of personal acquaintance, then the foundations of reality must be of a personal and not of a mechanical nature.

    December 1, 2011 — 9:32
  • Chris Menzel

    It seems to me that there is a fairly obvious way to understand the claim that the proposition

    If mereological universalism were true, then my body might be part of an object which also had an alien space ship as a part.

    is true without finding fault with the Lewis/Stalnaker analysis of counterfactuals. Note first that (as we all know) counterfactuals with necessarily false antecedents are commonplace in informal presentations of well-known logical theorems:

    If there were a universal set, the Russell set would exist.

    If the Halting Problem were solvable, first-order logic would be decidable.

    Of course, these are just homey ways of saying that, properly expressed as axioms in an appropriate theory (ZF set theory, say), the consequent in each case is a logical consequence of the antecedent.
    Now, granted, unlike Kenny’s proposition, these are examples of □→ rather than ◇→ and it is difficult to think of plausible examples of the latter out of logic. However — and I’m going out on a limb here because reasoning about counterfactuals makes my brain hurt so I usually avoid it — it seems to me that the grammatical form of his proposition is somewhat misleading and that it is better expressed as a □→ conditional. I think the reason for this is that the “might” in the consequent has nothing to do with the possibilities raised by the presumed truth of mereological universalism, but only with our ignorance regarding the actual existence of alien spaceships (and hence regarding their existence in nearby possible worlds). Because of this, it seems to me that we are able to rephrase the proposition without any loss of meaning as a □→ conditional:

    If there were alien spaceships, then if mereological universalism were true, my body would be part of an object which also had an alien spaceship as a part.

    Compare this with a “genuine” ◇→ conditional, e.g.,

    If Herman were to cheat on his wife, it might cost him his marriage.

    The anaphoric “it” here inextricably connects the possibility of the end of Herman’s marriage to his infidelity in some close (perhaps VERY close!) possible world; no analogous paraphrase in terms of □→ is possible.
    So it seems to me that Kenny’s proposition is after all of a piece with the logical examples above. More specifically, ignoring the complications engendered by the inessential reference to alien spaceships, the proposition is simply a homey way of expressing that mereological universalism logically implies a class of intuitively false propositions — viz., that my body is a part of an object of which an X is a part, where an X is any kind of thing that is wildly and remotely distinct from a human body. More specifically, “logically implies” here means that, given a clear expression of the principles of mereological universalism (ideally, as axioms in a first-order language), the proposition (expressed by a sentence in the same language) that my body is a part of an object of which an X is a part follows from those principles (as a semantic consequence and, hence, if we’re in first-order logic, as a theorem). That and that alone, I think, is what grounds our willingness to say that Kenny’s counterfactual is true.
    Note if we want pretty much exactly Kenny’s proposition, then we can express the axioms of mereological universalism in a modal language and express the implication in question as a necessary truth. Mereological universalism together with the proposition that it is possible that both alien spaceships and my body exist will then logically imply that my body could be part of an object which also has an alien spaceship as a part. This would of course be a modal implication, but one that is entirely orthogonal to the semantic analysis of counterfactuals.
    I have reached my cognitive capacity for dealing with counterfactuals so I have no clear idea how any of this affects Kenny’s argument. 🙂

    December 4, 2011 — 11:22