Holy Cyclops

Here, I argued that whether or not to accept the fatalistic argument really boiled down to a choice to how to view future events—as already fixed or not as already fixed. Propositions about future events might be taken as already having truth-values, or they might be taken as taking on truth-values only at the time of occurrence of those future events.

But if we assume the existence of a foreknowing God, that changes. Propositions about future events must then be taken as already having truth-values, which God already knows (although we don’t). The fatalistic argument I gave there, then, must go through:

1. p v ~p (Premiss, by the Law of the Excluded Middle)
2. p—>O(E) (Premiss: If it is true that E occurs at time t, then E has an occurrence-value)
3. ~p—>O(E) (Premiss: If it is true that E fails to occur at time t, then E has an occurrence-value)
4. O(E) (1, 2 ,3, Constructive Dilemma)

This applies to any future event E of which a foreknowing God has knowledge, whether it’s the result of human choice or not. And although one may still argue that God’s foreknowledge is like his looking through a time-telescope, so that he is not bringing about event E (or not-E) but is simply observing it or aware of it, one can no longer argue that event E’s occurrence-value isn’t yet fixed.  One can no longer argue that future contingent propositions are neither true nor false.

The background for this post appears here and here.

Chad McIntosh (of Doxazo Theos—see links) thinks that the problem with my second argument is that God’s foreknowledge isn’t necessary. He says that I’d be hard-pressed to find a theist who agreed that it was. But I was just reading Alvin Plantinga’s The Nature of Necessity, and he argues for just that point—he thinks that in order for a possibly existing entity to count as God, it can’t be omniscient in one possible world but not in another, or omnipotent in one possible world but not in another, or morally perfect in one possible world but not in another. He thinks that God must be maximally great—i.e., maximally excellent in all possible worlds—necessarily maximally excellent. If foreknowledge is part of omniscience, then at least one prominent theist thinks it’s necessary.

Still, I agree that if it’s not necessary, then the second argument, in its short form, fails, since N(Kx) is a premiss of the short form; and I assume that Chad would say that the third premiss of the second argument in its long form, N(Kx) v N(K(~x)), was false, so that it, too, would fail. Denying the necessity of God’s foreknowledge is indeed a way of rendering the arguments unsound.

But I suspect that Chad has in mind not that God isn’t necessarily foreknowing, but rather that his foreknowledge is contingent rather than necessary—that whether God foreknows x or foreknows not-x depends on the agent S’s choice, and is not “written in metaphysical stone” independent of S’s choosing. It is not God’s foreknowing that is contingent; it is what God foreknows that is contingent. And that’s how N(Kx) is false: it’s not N(K(something)) that’s false, but rather N(K(specifically x)) that’s false. Chad might then agree to the truth of N(Kx v ~Kx) but not to N(Kx) v N(K(~x)).

(Chad also notes that God needn’t be foreknowing because there are possible worlds in which, for example, God has not created time; but I am restricting myself to consideration of all possible worlds in which there are human beings making choices. The notion of necessity involved will then be one of relative necessity—necessity relative to a restricted class of possible worlds. Since the class of possible worlds in which there are human beings making choices is exactly the class in which freedom matters, necessity relative to this class seems strong enough to be opposed to freedom.)

I agree with Chad when he writes, “Were S to refrain from x and performed [sic] y instead, God’s foreknowledge would have been different.” I have, in fact, written a defense of that very view here.

What I don’t yet agree with is the necessity of deriving Nx (or Nx v N(~x)). Looking at the first argument I gave:

1. N(Kx—>x) (Premiss—to know that x will occur at t requires that x will occur at t)
2. Kx—>x (1, modal axiom M [or T], i.e., Np—>p)
3. Kx (Premiss—it is known that x occurs at t [since God has complete foreknowledge])
4. x (2, 3, modus ponens)

It seems clear to me that in every possible world in which God foreknows that agent S will choose to perform x at t, agent S will in fact choose to perform x at t, and in every possible world in which God foreknows that agent S will choose to perform not-x at t, agent S will in fact choose to perform not-x at t; agent S’s choice of whether or not to perform x at t is fixed once God’s foreknowledge of which he will perform is fixed. The argument works just as well the other way, of course: Once S’s choice is fixed, so is God’s foreknowledge; and since the relevance of the argument is usually with respect to human freedom of choice, we naturally want to say that as a causal or compulsory matter, that is the way it really works—that God’s foreknowledge is like his looking through a time-telescope and seeing what will happen, rather than like his reaching out and forcing events to occur as they do; and I agree with that; but I do observe that as a strictly logical matter, God’s foreknowledge seems clearly to fix S’s choice. In no possible world can we have both Kx and ~x, and in no possible world can we have both K(~x) and x; what we have, for any possible world in which freedom is a live issue, is N([Kx^x] v [K(~x)^(~x)]). The two—God’s foreknowledge and S’s choice—logically fix each other. This isn’t causation or compulsion, but once you have one, you also have the other. If freedom is supposed to mean that at any time before the choice, the choice is not yet fixed, then this seems to defeat human freedom.

But the real problem with the view that it is S’s temporally later choice of x at time t that causes God’s temporally earlier foreknowledge that S will choose x at t comes about if one tries to combine it with the view that God can interact with the universe in any way whatsoever. If one allows God, who foreknows that agent S will choose to do x at t, to tell agent S beforehand of his future choice, there seems to be a problem: Why can’t agent S, having been informed of his future choice, now decide to behave contrarily and to do not-x at t? Obviously, he can’t so choose, for to do so would violate God’s foreknowledge; but how is he free if he can’t so choose? This argument has force even though Nx would normally be thought of as false. If choice x is the choice to put on a green shirt, we would normally think of it as entirely within S’s power to put on a green shirt and also entirely within his power to put on a blue shirt instead. Even if God foreknows that S will put on a green shirt, it may still be that what God foreknows is really that S will freely choose to put on a green shirt. But if God foreknows S’s choice and also tells S about it, why can’t S choose instead to put on a blue shirt, if he is still free? It seems that the sort of interaction that might lead to S’s choosing differently than foreknown is denied to a foreknowing God, if S is thought to remain free; and it seems that S loses his freedom if a foreknowing God does take part in such an interaction.

Perhaps I need to look around for some characterizations of freedom.

In a comment to my post What’s Wrong with Modal Ontological Arguments, Kenny mentioned the Moorean Shift.  I want to take a few moments to look at it.

The Moorean Shift takes an argument whose form is modus ponens and converts it into one whose form is modus tollens, shifting premiss and conclusion in the process.  Thus, the argument

1.  p—>q
2.  p
Therefore,
3.  q

one of whose premisses is p and whose conclusion is q, becomes the argument

1.  ~q—>~p
2.  ~q
Therefore,
3.  ~p

one of whose premisses is ~q and whose conclusion is ~p.

The idea is that while accepting the premiss p—>q (which is rewritten in its equivalent contrapositive form ~q—>~p), the person making the Moorean Shift finds ~q more likely than he finds p, so instead of arguing from p’s truth to q’s truth, he argues from q’s falsity to p’s falsity. 

I see nothing wrong with this approach.  When evaluating an argument’s soundness, we must evaluate the truth-values of its premisses.  If one finds q more likely to be false than p is to be true, then he will be more inclined to view the second argument as sound than the first one; conversely, if one finds p more likely to be true than q is to be false, then he will be more inclined to view the first argument as sound than the second one.

For example, one might argue

1v.  If tigers are vegetarians, then tigers do not eat meat
2v.  Tigers are vegetarians
Therefore,
3v.  Tigers do not eat meat

But, while accepting premiss (1v), one might think that premiss (2v) is simply not true, and that the argument is therefore unsound; and if he also thinks that the conclusion (3v) is true, he might construct the new argument

1c.  If tigers eat meat, then tigers are not vegetarians
2c.  Tigers eat meat
3c.  Tigers are not vegetarians

Naturally, one finds the second argument sound but the first one unsound.

The difficulty with the Moorean Shift isn’t the Shift itself, which is entirely legitimate, but rather a linguistic problem in Moore’s use of it against philosophical skepticism that has nothing intrinsically to do with the Shift.  The philosophical skeptic thinks that one cannot know that he isn’t dreaming, or hallucinating, or a brain in a vat, or otherwise deluded about what appears to be true.  G.E. Moore argued against philosophical skepticism by holding up his hand and saying, “Here is a hand before me,” and claiming that since he knew his hand was before him, he knew something about empirical reality, and therefore philosophical skepticism was defeated.  He argued, in other words, in the following way (see Wikipedia entry Here Is a Hand):

Let S be an epistemic agent; let p be some skeptical possibility, like S’s dreaming or hallucinating or being a brain in a vat; let q be a knowledge claim about the world, like S’s hand being held before him.  Then the philosophical skeptic argues that

1s.  If S doesn’t know that ~p, then S doesn’t know that q  (If S doesn’t know that he isn’t dreaming, then S doesn’t know putative fact q about the world—in particular, S doesn’t know that his hand is held out before him)
2s.  S doesn’t know that ~p  (S doesn’t know that he isn’t dreaming)
Therefore,
3s.  S doesn’t know that q  (S doesn’t know putative fact q about the world—in particular, S doesn’t know that his hand is held out before him)

and Moore replies

1m.  If S knows that q, then S knows that ~p  (If S knows putative fact q about the world—in particular, that his hand is held out before him—then S knows that he isn’t dreaming)
2m.  S knows that q  (S knows putative fact q about the world—in particular, that his hand is held out before him)
Therefore,
3m.  S knows that ~p  (S knows he isn’t dreaming)

Moore holds out his hand in front of him and says, “Here is a hand.”  Since, he thinks, he knows that there is a hand before him (”S knows that q”), he also knows that philosophical skepticism is false (”S knows that ~p”). 

Put this way, it seems that a simple linguistic or conceptual mistake is being made.  The philosophical skeptic says that if one cannot know that he is not, say, a brain in a vat (or some other skeptical possibility, like being a dreamer or a self-generator of the appearances), then he cannot know any empirical fact; and then claims that one cannot know that he is not, say, a brain in a vat; and therefore one cannot know any empirical fact.  Moore says that one can know an empirical fact, and therefore can know that the skeptical possibility is false; but the philosophical skeptic’s use of the word know and Moore’s use of the word know seem to differ.  The philosophical skeptic’s use of the word seems intended to imply complete and utter certainty, beyond Cartesian doubt.  Moore’s use of the word seems only intended to imply everyday certainty, beyond everyday doubt.  (We don’t, after all, walk around muttering to ourselves, “Is this really my hand before me?”) 

It would be hard to believe that an acknowledged great philosopher like Moore would have missed this, so perhaps we can read his Moorean Shift, as applied to the philosophical skeptic’s argument, differently.  Perhaps all he means is that he finds it more likely that the everyday assertion that there is a hand before him is true than that the pathological assertion that, say, he is a brain in a vat, is true, and that he therefore accepts (1m)-(3m) rather than (1s)-(3s).  Unfortunately, that just seems like another way of saying that his use of the word know doesn’t imply complete and utter certainty, beyond Cartesian doubt, but only implies everyday certainty rather than philosophical certainty.  Lots of philosophical skeptics, I’m sure, would also accept (1m)-(3m), on that same everyday use of the word know—philosophical skeptics don’t go around muttering to themselves, “Gee, I wonder if this is a hand before me,” in everyday life, either.  The philosophical skeptic’s argument is directed at the conceivability of Cartesian doubt—at the conceivability of our being brains in vats, for example—but I imagine that most philosophical skeptics would nevertheless endorse Moore’s argument for the everyday sense of know.  So, it still seems that Moore and the philosophical skeptic are simply not addressing the same point.  Moore seems not to be addressing Cartesian doubt at all. 

But the Moorean Shift remains a perfectly reasonable way of choosing among deductively valid arguments, since what one wants to accept are sound arguments, which involves assigning truth-values, or at least likely truth-values, to a valid argument’s premisses.  And that’s all the Moorean Shift does:  It says, “I find this premiss more likely than that one, and therefore find this argument more likely to be sound than that one.”

In The 70th Philosophers’ Carnival appears The Barefoot Bum’s analysis, here, of what goes wrong with Alvin Plantinga’s “Victorious” ontological argument for the existence of God. Since it’s something I’ve been looking at, I thought I’d take my own shot.

Plantinga’s argument takes differing forms.  For technical reasons, he puts it in terms of the exemplification of properties in possible worlds, rather than in terms of the existence of entities in possible worlds, and in its more detailed form, he puts it in terms of properties that entail other properties.  None of that will really affect my objections to the argument.  I’m going to present the simpler of the forms Plantinga presents in The Nature of Necessity.

Let maximal excellence (ME) be the property of being omniscient, omnipotent, and morally perfect—i.e., Godlike.

Let unsurpassable greatness (UG) be the property of necessary maximal excellence—of being maximally excellent in every possible world—of being Godlike in every possible world. 

Notice that in the widely accepted modal logic S5, which Plantinga uses, any statement that is necessarily true in one possible world is necessarily true in each possible world.  This is because if we had Np in world W[1] but ~Np in world W[2], we would have both P(Np) and P(~Np) (because truth in some possible world is what possibility means, in possible-worlds semantics)—but in S5, P(Np) collapses to Np and P(~Np)=P(P~p)=P~p=~Np, so we wind up with Np and ~Np, a contradiction.  In S5, a necessary truth in one possible world is a necessary truth in all other possible worlds, too.

Let a universal property be one which is instantiated in every possible world or in no possible world.  Note that UG is a universal property.  If UG is instantiated in any possible world, then N(ME) is instantiated in that possible world, so that N(ME) is instantiated in every possible world (because what is necessary is necessary in every possible world), so that UG is instantiated in every possible world.  Hence, either UG is instantiated in every possible world or in none of them.

1)  There is a possible world in which unsurpassable greatness is exemplified.     (Premiss)
2)  The proposition a thing has unsurpassable greatness if and only if it has maximal excellence in every possible world is necessarily true.    (Definition of UG)
3)  The proposition whatever has maximal excellence is omnipotent, omniscient, and morally perfect is necessarily true.      (Definition of ME)
3a)  Unsurpassable greatness is a universal property.  (As noted above)
4)  Possesses unsurpassable greatness is instantiated in every possible world.    (1,3a)
5)  Possesses unsurpassable greatness is instantiated in the actual world.  (4, universal instantiation)

And any being possessing unsurpassable greatness in the actual world is clearly an actually existing God.  Q.E.D. 

What is wrong with the argument?  Well, perhaps nothing is really wrong with it; but it certainly doesn’t give any reason to believe in God.  When one defines UG=N(ME), and then uses the premiss P(UG), he is using the premiss P(N(ME)).  But if he is working in S5, in which P(N(ME))=N(ME), it’s hardly surprising that the assumption of the possibility of the exemplification of universal greatness gets him the existence of God.  Defining UG as N(ME) guarantees, as Plantinga well realizes, that UG is a universal property:  Either UG is exemplified in all possible worlds or in none of them.  P(UG) seems like a tempting premiss, because it’s easy to confuse logical or metaphysical possibility with epistemic possibility.  One might think, “Gee, all I have to assume is that UG’s exemplification is possible?  That’s not much to ask!”  But it is a lot to ask when UG is defined as N(ME).  If one instead assumed the possibility of UG’s non-exemplification, a “proof” of God’s nonexistence would follow:

1)  There is a possible world in which unsurpassable greatness is not exemplified.     (Premiss)
2)  The proposition a thing has unsurpassable greatness if and only if it has maximal excellence in every possible world is necessarily true.    (Definition of UG)
3)  The proposition whatever has maximal excellence is omnipotent, omniscient, and morally perfect is necessarily true.      (Definition of ME)
3a)  Unsurpassable greatness is a universal property.  (As noted above)
4)  Possesses unsurpassable greatness is instantiated in every possible world.    (1,3a)
5)  Possesses unsurpassable greatness is instantiated in the actual world.  (4, universal instantiation)

1.  P(~UG)      (Premiss)
2.  In some possible world, ~UG.   (Definition of possibility in possible-world semantics)
2a.  UG is a universal property.   (As noted above)
3.  In every possible world, ~UG.     (1,2a)
4.  N(~UG).      (Definition of necessity in possible-world semantics)

Therefore, an unsurpassably great being does not exist in any possible world, so there is no God.  (The conclusion that there is no God requires the ascription of unsurpassable greatness to God.  Without it, one simply has P(~N(ME))=P(P(~ME))=P(~ME), so that in some possible world there is no God, but might be one in the actual world.)

The use of unsurpassable greatness, defined as necessary maximal excellence, is a trick.  One might use it to “prove” the existence of unicorns.  Let maximal unicornness (MU) be the property of being one-horned, white, equine, and so on; let unsurpassable unicornness (UU) be the property of necessary maximal unicornness (UU=N(MU)).  Notice that UU, just like UG, is a universal property.  Then

1)  There is a possible world in which unsurpassable unicornness is exemplified.     (Premiss)
2)  The proposition a thing has unsurpassable unicornness if and only if it has maximal unicornness in every possible world is necessarily true.    (Definition of UU)
3)  The proposition whatever has maximal unicornness is one-horned, white, equine (and so on) is necessarily true.      (Definition of MU)
3a)  Unsurpassable unicornness is a universal property.  (As noted above)
4)  Possesses unsurpassable unicornness is instantiated in every possible world.    (1,3a)
5)  Possesses unsurpassable unicornness is instantiated in the actual world.  (4, universal instantiation)

And, therefore, unicorns exist. 

Well, obviously not.  The point is that one must have some reason, in Plantinga’s “proof,” to prefer P(UG) to P(~UG).  The two are jointly inconsistent, so you can’t have both.  But one cannot give any reason to prefer P(UG) that is independent of the conclusion that God exists.   So, even if the argument is valid—and the making of St. Anselm’s argument into a valid one is the reason for Plantinga’s labeling it “victorious”—we have no reason to think it is sound.  But more than that, we have no reason to accept its crucial premiss:  P(UG).  Plantinga seems to think that it is rational to accept that premiss, and therefore rational to accept the conclusion that God exists.  But since P(UG)<—>N(UG), it is precisely as rational to accept P(UG) as it is to accept N(UG); how rational can it be to accept N(UG) without reason?  I am not claiming that it is more rational to accept P(~UG); only that I can see no rational reason for accepting either P(UG) or P(~UG).

I was reading Alvin Plantinga’s The Nature of Necessity yesterday, and he quoted and analyzed, in great detail, a couple of passages, one from William Kneale and one from W.V.O. Quine, whose quotation and analysis reminded me once again that professional philosophers sometimes make silly mistakes.

The discussion was about essential and accidental (necessary and contingent) properties.  Kneale’s anti-essentialist argument was, in my reconstruction from memory, that one couldn’t say that the number twelve was essentially composite, because surely it is only a contingent fact that the number of apostles was twelve, so the number of apostles couldn’t be essentially composite; but since the number of apostles and the number twelve are the same number, twelve can’t be essentially composite.

I’ve rendered it in more detail than he did in the quoted passage.  But one can easily see the mistake:  An equivocation on the meaning of “The number of apostles.”  Does “the number of apostles” mean “the actual number of apostles (i.e., twelve),” or does “the number of apostles” mean “the possible number of apostles (i.e., twelve or eleven or thirteen or…)”?  “The number of apostles” and “twelve” denote the same number only if “the number of apostles” is intended as “the actual number of apostles (i.e., twelve)”; if one intends “the number of apostles” as “the possible number of apostles (i.e., twelve or eleven or thirteen or…),” then one can no longer equate twelve with the number of apostles.  One may either say

1. Twelve is a composite number.
2. The (actual) number of apostles is twelve.
3. Therefore, the (actual) number of apostles is composite.

or

1. Twelve is a composite number.
2. The (possible) number of apostles might be twelve but might be some other number, like eleven or thirteen.
3. Therefore, the (possible) number of apostles might be composite but might not be.

In the first case, “the (actual) number of apostles” is a Kripkean “rigid designator,” if I’m remembering his terminology correctly, always equalling twelve and therefore always composite, just like twelve—rendering the argument against essentialism toothless.  In the second case, “the (possible) number of apostles” is a non-rigid designator, not always composite but also not always equalling twelve—again rendering the argument against essentialism toothless.  Only if one could argue that the number twelve had the kind of fluidity of designation that “the (possible) number of apostles” has could one go on to argue that twelve is not necessarily composite—but, of course, that can’t be done.

Quine’s argument, again in my reconstruction of it, was that whether or not a property is thought to be necessary depends on how we describe the property-bearer—that properties of objects are not essentially necessary or non-necessary but are, rather, only necessary or non-necessary relative to our descriptions of those objects.  His example is as follows:  We might normally say that, in some sense, mathematicians are necessarily rational but are not necessarily bipedal, and that cyclists are not necessarily rational but are necessarily bipedal.  (Let’s set aside any question about either the rationality of all mathematicians or the bipedality of all cyclists.)  But suppose a mathematician is also a cyclist.  Then are we to say that he is both necessarily rational and not necessarily bipedal and also not necessarily rational but necessarily bipedal—a contradiction (a pair of them, really)?  Our assessment changes with our change in description:  We say that the mathematician-cyclist is both necessarily rational and necessarily bipedal.

I’m sure I’m not rendering his argument as persuasively as he did, but its main point is the contradiction given.  Two points can be made about this:  First, it may be that saying that mathematicians are not necessarily bipedal, and that cyclists are not necessarily rational, is saying something too strong.  We do not know of all mathematicians that they are not necessarily bipedal; perhaps some of them (like the mathematician-cyclist) are necessarily bipedal, while others aren’t.  (Similarly for cyclists and the non-necessity of their being rational.)  What we can justifiably say is that mathematicians are necessarily rational and possibly bipedal (and similarly that cyclists are possibly rational and necessarily bipedal).  But then the contradiction vanishes:  The mathematician-cyclist is necessarily rational and possibly bipedal, and he is possibly rational and necessarily bipedal, and that doesn’t contradict his being necessarily rational and necessarily bipedal.  Second—and, in my view, the more important point, and the one that qualifies Quine’s argument for inclusion in a post entitled “Silly Philosophical Mistakes”—is that while it is true that we make our descriptions on the basis of what we know, or on the basis of our present interests or purposes, rather than on the basis of what is true, and that for that reason our ascriptions of modal status with respect to different properties will seem to vary according to our present interests and purposes—in contradiction to the essentialist view that necessary properties, at least, are essential to entities—it is nevertheless also true, in opposition to Quine, that while what we know of an object may change (so that we realize, when we learn that a mathematician is a cyclist, that he is not only necessarily rational, as we had thought, but that he is also necessarily bipedal), and that while our choice of description may vary according to our interests or purposes (so that we may know very well that a mathematician is also a cyclist but may or may not choose to ignore it for the moment, resulting in our sometimes describing the mathematician-cyclist as necessarily rational and possibly bipedal and in our sometimes describing the mathematician-cyclist as both necessarily rational and necessarily bipedal), neither our knowledge change nor our choice of description implies that what is true of the object changes or is somehow malleable.  At best, Quine’s is an argument for description-relativism; it isn’t, as he appears to want it to be, an argument for fact-relativism (or for relativism of modal facts to description).  (Even if Quine thinks that we know the facts about objects, that simply means that a description of the object that expresses those facts must be complete in order to capture all of those facts—an incomplete description, chosen for our own reasons, might fail to capture all of those facts.)   

By way of introduction (possibly at too-great length):

Here, I wrote, in part,

“The simple argument for the incompatibility of God’s foreknowledge with human freedom of the will, using ‘Np’ to represent ‘metaphysically necessarily p,’ ‘Pp’ to represent ‘metaphysically possibly p,’ ‘x’ to represent ‘x occurs at time t,’ and ‘Kx’ to represent ‘it is known that x occurs at time t,’ is

1.  N(Kx—>x)    (Premiss—to know that x will occur at t requires that x will occur at t)
2.  Kx—>x          (1, modal axiom M [or T], i.e., Np—>p)
3.  Kx                (Premiss—it is known that x occurs at t [since God has complete foreknowledge])
4.  x                   (2, 3, modus ponens)

Hence, if we assume that event x at t is foreknown, we know that event x at t occurs—and, therefore, not event not-x at t.  But where is human freedom if what is foreknown dictates what occurs?”  I then proceeded to argue that while this argument did not actually imperil human freedom of the will, God’s foreknowledge combined with God’s telling a purportedly free agent what he would do—or, more broadly, God’s initiating any chain of events leading a free agent to choose to do otherwise than God foreknew—would pose a problem:  If God says to person S, “You, person S, will choose to do x at t,” why couldn’t S be contrary and choose to do not-x at t instead?  If he can’t, where’s his freedom?

Chad McIntosh replied, “The simple solution for the defender of divine foreknowledge to the argument as you outlined it is to point out how, even if sound, the argument doesn’t negate creaturely freedom. This is because the necessity in (1) does not carry over to the conclusion, (4). But carrying necessity to x, at least in the argument as you’ve outlined, would be guilty of an invalid modal operator shift. As it stands, all that follows is x, not Nx. In other words, (4) still allows for possibly ~x, which is entirely consistent with creaturely freedom. What you need is an argument that establishes Nx.”

To which I replied, “It seems to me that although Nx is not established, it is also not needed. In every possible world, we have Kx—>x and K(~x)—>~x, so whether x or ~x is foreknown (in particular, which is foreknown by God) fixes whether it is x or ~x that occurs.

“As long as neither Nx nor N(~x) has been established, one may say, as I suggested, that the foreknower’s knowledge is the result of the agent’s freely choosing x or, alternatively, freely choosing ~x, even though there is no escaping the complete correlation between what is foreknown and what is chosen; one may say that although the agent’s choice is temporally fixed before he makes it, it is ultimately metaphysically fixed by his own choice, which in turn makes the foreknower foreknow what he foreknows. But a problem does arise if the foreknower (in particular, God) tells the agent which choice he is going to make. Why can’t the agent, upon being told which choice he’ll make, simply be contrary and choose the opposite? That’s where the problem arises.”

End of introduction.

While I still agree with what I wrote, it has occurred to me that one can rather easily get the conclusion that Chad McIntosh claims I need, with only slightly different premisses:

1.  N(Kx—>x)    (Premiss—to know that x will occur at t requires that x will occur at t)
2.  N(Kx)          (Premiss—it is necessarily foreknown that x will occur at t)
3.  Nx               (1, 2, modal modus ponens)

(Modal modus ponens states that from N[p—>q] and Np, one can conclude Nq.)

Anyone who thinks that God necessarily foreknows all events, including the outcomes of all human choices, will have to endorse the argument.  Of course, we, not knowing whether x or not-x will occur at t, would have to fill in the second premiss as “N(Kx) or N(K(~x)),” but a foreknowing God would know which one he foreknew.  If he foreknew not-x, then we’d simply rewrite the argument with “~x” replacing “x.”  Anyone not happy with thinking of it that way would instead write

1.  N(Kx—>x)             (Premiss—to know that x will occur at t requires that x will occur at t)
2.  N(K(~x)—> ~x)       (Premiss—to know that not-x will occur at t requires that not-x will occur at t)
3.  N(Kx) v N(K(~x))     (Premiss—either it is necessarily foreknown that x will occur at t or it is necessarily foreknown that not-x will occur at t (a consequence of God’s necessary foreknowledge))
4.  N(Kx)—>Nx             (1, Modal Distribution)
5.  N(K(~x))—>N(~x)   (2, Modal Distribution)
6.  Nx v N(~x)             (4, 5, 3, Constructive Dilemma)

Whether Nx or N(~x) is the case will, of course, depend on whether God foreknows that x will occur at t or that not-x will occur at t. 

Naturally, I, not being a believer in God, do not endorse the claim of God’s necessary foreknowledge; but it seems to me that those who do will have to live with human beings’ lack of metaphysical freedom (even though we may very well choose how to act on the basis of conscious deliberation and of evaluation of possible consequences of our actions).

In Paul Boghossian’s Fear of Knowledge:  Against Relativism and Constructivism, a book I’ve recently started reading and am enjoying, he presents an argument against what he calls “cookie-cutter fact-constructivism.”  He is arguing against the sort of view advocated by Nelson Goodman and Hilary Putnam, and illustrated by Goodman’s “constellation” example:  We draw the lines around groups of stars and call them “constellations”; the groups of stars aren’t constellations until we notice them as such.  There is no such fact as “The Big Dipper is a constellation” until we say there is.  That fact is socially constructed.  Moreover, all such facts are socially constructed:  We use our concepts to “carve up” reality, just as a cookie cutter cuts up dough into shaped pieces, and since this “carving up” isn’t done until we do it, we construct the facts about reality; moreover, no way of conceptually “carving up” reality is closer to the way things really are than any other, for there is no way things really are.

Boghossian argues that this “cookie-cutter” view contradicts itself, because even if one says that constellations are delineated by human concepts, and that their constituent stars are similarly delineated by human concepts, and that their molecules (well, plasma, but I don’t think that’s important here) are similarly delineated by human concepts, and so on, one still requires, at some basic level, a “dough” which our concepts can operate on, and there has to be a way that that “dough” really is, unless one wants to insist that the “carving up” goes on infinitely, level after level, which clearly seems absurd.

The problem I see is that this argument only works on the reality-objectivist fact-constructivist—the one who says that there really is an objectively existing reality, and whose fact-constructivism consists of applying human concepts to that reality.  That is to say, his argument only works to establish the reality of an underlying objectively real “dough” against those fact-constructivists who already agree that there is one.  (Such fact-constructivists might then have to agree that there is a way things are at the fundamental level—the level of the “dough”—and simply reserve their fact-constructivism for all higher levels of fact; they might also adopt the view I’m about to describe for everything except the “dough.”)  The reality-subjectivist fact-constructivist, on the other hand, may simply insist that concepts do not apply to objectively existing reality (or to elements of it), but instead apply to one’s own mental life (or to elements of it)—that, for example, my concept of stripedness is not applicable to objectively real tigers but is instead applicable to my ideas of tigers.  (He might or might not agree that if there happened to actually be objectively existing tigers, then my application of the concept of stripedness to my ideas of tigers could be extended, so that the concept of stripedness would then be applicable to actual tigers.)  As long as it is not agreed that there are actual tigers, and as long as it is maintained that the concept of stripedness applies to my ideas of tigers rather than to actual tigers, the only “dough” the reality-nonobjectivist fact-constructivist is committed to is the “dough” of his own ideas—his own thoughts and mental images and the like. 

Perhaps Boghossian will address that sort of position later in his book.  I’ll find out.  

When we think about past events, we normally think of them as “written in metaphysical stone.”  Nothing we could do could make an event E that has already happened at time t fail to happen at time t, and nothing we could do could make an event E that has already failed to happen at time t happen at time t.  I express this by saying that E has an occurrence-value O(E).  Even if one countenances time travel to the past, it seems as though one cannot make an event E which has already happened unhappen, or make an event E which has already failed to occur happen; all one can do is to create a second time-stream in which E’s occurrence-value is different than it was in the first time-stream.  E’s occurrence or non-occurrence at t—O(E)—is fixed for any particular time-stream.  And most of us do not countenance time travel to the past, and therefore take O(E) to be fixed, for any past event E.

By contrast, we tend to think of the future as open.  A future event E might happen or might not happen in this time-stream; its occurrence-value O(E) is not fixed, even in this time-stream.  We take there to be a fundamental disanalogy, in this regard, between past events and future events.  The fatalist argument attempts to undercut this disanalogy.  Reiterating that “O(E)” means “E has an occurrence-value,” and taking p to be the proposition “E occurs at time t,” I give a simple version here:

1.  p v ~p      (Premiss, by the Law of the Excluded Middle)
2.  p—>O(E)    (Premiss:  If it is true that E occurs at time t, then E has an occurrence-value)
3.  ~p—>O(E)   (Premiss:  If it is true that E fails to occur at time t, then E has an occurrence-value)
4.  O(E)        (1, 2 ,3, Constructive Dilemma)

Note that this argument seems to hold both for past events and for future events.  Also note that it says nothing about human freedom.  If p is now true, it may very well be via human choice that E occurs, and that the present truth of p is attributable to a freely made choice; and similarly if p is now false.  The argument ascribes to E a present occurrence-value, but it does not say why E has that present occurrence-value.

However….

The argument rests on the Law of the Excluded Middle, so one may deny that the Law of the Excluded Middle applies to future events; this seems to be Steven Cahn’s suggestion in Fate, Logic, and Time.  One might claim that for future events, neither p nor ~p is true.  And this seems reasonable to me.  I have written premisses (2) and (3) as conditionals, but the biconditionals p<—>O(E) and ~p<—>O(E) really hold, if one holds any sort of correspondence theory of truth.  To say that the proposition “E occurs at time t” is true is just to say that E occurs at time t, and to say that E occurs at time t is to say that the proposition “E occurs at time t” is true.  Thus, to say p v ~p is to say that either E occurs at time t or else E does not occur at time t, and to take p v ~p as saying that either “E will occur at time t” is now true or else “E will not occur at time t” is now true is to take it as saying that either E’s occurrence at time t is now the case or else  E’s nonoccurrence at time t is now the case.  But this, it can reasonably be claimed, is to assume the truth of the fatalistic doctrine itself, for what the non-fatalist wants to say is that neither E’s occurrence at future time t nor E’s nonoccurrence at future time t is “written in metaphysical stone”—that future event E’s occurrence or nonoccurrence won’t be decided, not only epistemically but also metaphysically, until future time t, and therefore that it is not now true that E will happen and it is also not now true that E will not happen. 

The non-fatalist would want to read the argument, for future events, as

1.  p will be true or p will be false
2.  If p will be true, then E will have occurrence-value.
3.  If p will be false, then E will have occurrence-value.
4.  Therefore, E will have occurrence-value.

Such a reading, taking p to have a future truth-value but not a present truth-value, doesn’t imply that E already has an occurrence-value; only that it will have one.  Alternatively, the non-fatalist could construct an anti-fatalist argument, for future events:

1.  p is not now true and p is not now false.     (Anti-fatalist premiss)
2.  E now has occurrence-value if and only if either p is now true or p is now false.  (Premiss)
3.  It is not the case that either p is now true or p is now false.   (1, de Morgan’s Law)
4.  Therefore, it is not the case that E now has occurrence-value.  (2, 3, Modus Tollens)

Of course, the anti-fatalist argument assumes its conclusion just as much as the fatalist argument assumes its conclusion.  Where the fatalist argument assumes that propositions about the occurrence of future events already have truth values and therefore, via the correspondence of a proposition’s truth and the content expressed by the proposition’s being the case, assumes that future events have occurrence-values, the anti-fatalist argument assumes that propositions about the occurrence of future events now lack truth-values and therefore, again via the correspondence between truth and content, assumes that future events lack occurrence-values.  Both the fatalist and the anti-fatalist argument really fail to be arguments at all, but are simply choices of how to view the metaphysical nature of future events.  And that may very well depend on one’s view of time.  One who models spacetime according to Einstein’s “block universe,” for example, might very well make the fatalist choice.  But it looks to me as though the difference between the fatalist and the anti-fatalist is simply one of differing intuitions.

God is sometimes characterized as omniscient, and his omniscience is sometimes taken to include knowledge of the future–of all future events.  But his foreknowledge of events, it is sometimes argued, is logically inconsistent with human beings’ having freedom of the will.  After all, if God already knows what will happen, how can we have any real choice in the matter?  We must choose exactly in accordance with God’s foreknowledge.   

The simple argument for the incompatibility of God’s foreknowledge with human freedom of the will, using “Np” to represent “metaphysically necessarily p,” “Pp” to represent “metaphysically possibly p,” “x” to represent “x occurs at time t,” and “Kx” to represent “it is known that x occurs at time t,” is

1.  N(Kx—>x)  (Premiss—to know that x will occur at t requires that x will occur at t)
2.  Kx—>x        (1, modal axiom M [or T], i.e., Np—>p)
3.  Kx                  (Premiss—it is known that x occurs at t [since God has complete foreknowledge])
4.  x                     (2, 3, modus ponens)

Hence, if we assume that event x at t is foreknown, we know that event x at t occurs—and, therefore, not event not-x at t.  But where is human freedom if what is foreknown dictates what occurs?

The problem with this can be shown if we simply take “Kx” to denote postknowledge instead of foreknowledge.  The same argument works just as well, and yet we don’t think that postknowledge dictates the event x’s occurrence at t.  Rather, we think that event x’s occurrence at t dictates which of “x occurs at t” and “not-x occurs at t” is known.  For an omniscient postknowing being, x dictates Kx, and not-x dictates K(not-x).  We might similarly say that for an omniscient foreknowing being, x dictates Kx, and not-x dictates K(not-x)—i.e., that whether x or not-x happens at time t determines whether x is known or not-x is known, even if the knowledge is foreknowledge instead of postknowledge.

Yet, there’s a clear asymmetry between the cases of foreknowledge and postknowledge.  If a person A makes the choice between x and not-x at time t, and if, at some later time, a postknower tells person A which choice he made, we see nothing strange about it, and it certainly doesn’t affect how we think of person A’s freedom to choose.  On the other hand, if a foreknower tells person A which choice he will make, there is a problem:  Why can’t person A just be contrary and choose to act otherwise than he has been told he will?  If he can do so, then he has the power to render foreknowledge false, which surely can’t be done; if he cannot do so, then he doesn’t seem to be choosing freely. 

It seems that if foreknowledge is to be compatible with freedom of the will, any foreknower is limited in what he can do between the moment of his first attaining foreknowledge and the time t when x is chosen.  In particular, he cannot initiate a chain of events that might lead person A to do what he otherwise would not do.  The simplest way to ensure this would be for the foreknower to remain passive.

Do we, then, limit God, so that although his omniscience extends to complete foreknowledge of events, he does not exercise any power he might have over the course of human events?  (While this might be a stronger restriction than really necessary, it seems like an aesthetically pleasing choice.)  Do we instead say that God’s omniscience does not extend to knowledge of future events? 

I normally try to show what’s wrong with subjectivism, but let me try to think of what a subjectivist might say in response to criticisms.  (I’ll note that there are what one might call “hard subjectivists,” who deny that there is an objectively existing reality, and “soft subjectivists,” who merely don’t commit themselves one way or the other.)  I do want to note that subjectivism is not the same thing as perspectivalism.  We objectivists agree that different human beings perceive the world differently (some have sharper vision than others, some experience synesthesia, some see the world from a greater height than others) and interpret what they perceive differently.  We agree that our experiences affect how we think of what we perceive—that our conceptualizations of the world differ.  Each of us has his own perspective.  That’s not what the objectivist opposes.  The objectivist opposes the notion that nothing exists independently of his own mind.

1)  How does one explain the patterns and regularities of his personal experience? 

The objectivist explains them by saying that there is an objectively existing reality that has a certain structure, and that the structure of that reality causes events to occur in a lawlike way, and that we human beings perceive the lawlike occurrences of that reality (albeit indirectly), and that it therefore makes sense that our sensory qualia also occur in a lawlike way.  I never see objects fall up because my visual qualia reflect the gravitational aspect of objectively existing reality.

The subjectivist may explain them by saying that his internal world, his phenomenal reality, has a certain structure, and that the structure of that phenomenal reality causes his sensory qualia to occur in a lawlike way.

2)  How does one explain intersubjectivity? 

The objectivist’s explanation is that there really are other people who are on an existential par with himself, and that, having subjectivity himself, he assumes that other people, who seem similar to him in biological construction and physical behavior, and with whom he seems able to communicate, are not mindless robots but do also have mental lives.

It seems a bit tougher for the subjectivist.  If he claims that other people do have subjectivity, then he seems to be saying that the appearances of people in his mind have subjectivity.  They then seem to be portions of his own mind that are inaccessible to him directly, and that are only indirectly accessible to him, via the appearance of communication.  Moreover, if he thinks that their subjectivity includes the appearance of him, the subjectivist himself, then it seems as though we get a vicious loop:  Another person’s subjectivity is a hidden part of the subjectivist’s own mind, but the subjectivist’s own subjectivity is then a hidden part of that other person’s subjectivity, which is in turn a hidden part of the subjectivist’s own subjectivity; which is contained in which?  Intersubjectivity is, then, hard for the subjectivist to explain.

What the subjectivist can  say is something different:  Not that other people really do have subjectivity, but rather that the appearances of other people in his mind appear to talk and appear to act as though  they were subjective; he can treat those appearances as though they were subjective without actually claiming subjectivity for them.  (Notice that this has implications for ethics:  In circumstances in which the subjectivist has no expectation that his actions with respect to another person will have any consequences for himself beyond the action itself, why should he be kind or concern himself with the other person’s feelings?  It’s not as though the other person actually *had* feelings, after all.)  He may, in so doing, say that he is doing no more than is justified by the appearances—and the objectivist must agree that he doesn’t have direct knowledge of other people’s mental lives, and must agree that he only assumes that they have them by ostension.  But does the subjectivist really want to claim that other people don’t have thoughts or feelings?

3)  How is empirical error possible? 

The objectivist who says, “I was mistaken about X,” can say that there was an objective fact of the matter about X and that he misperceived that fact.

The subjectivist has a harder time of it.  He can hardly be mistaken about his own appearances!  What he might say is that he thought that X was so (X appeared to be so), but that various appearances of people appear to be telling him that he’s mistaken, and that on that basis he agrees to use the words, “I was mistaken about X,” even though he couldn’t have been mistaken about the appearance of X; or he might say that he thought that X was so (X appeared to be so), but that now X isn’t so (X no longer appears to be so), and that on that basis he uses the words, “I was mistaken about X,” instead of, “The appearances about X have changed.”  But in neither case is he really reporting an instance of being mistaken; nor could he be.  One can’t be mistaken about one’s own appearances.

The subjectivist’s best course might be to deny that there is such a thing as empirical error—to say that empirical error would require objective facts of matters, and that in the absence of such objective facts of matters, there simply is no empirical error. 

4)  How does one explain the existence of facts or knowledge that he himself is personally unaware of? 

The objectivist says that there is an objectively existing reality comprising a great many facts, and that he himself only knows a few of them—but the ones he doesn’t know are still facts, by virtue of their objective existence, and other objectively existing people may very well know some of those facts that he himself doesn’t know.

The subjectivist denies that there are any facts outside of his awareness, and unless he comes up with a subjectivist account of intersubjectivity, denies that there is any knowledge outside of himself.    He is then committed to denying that scientific research has discovered any facts that he has not himself heard about or read about; he is committed to denying that those people of whose existence he is unaware do not exist.  (There remains the question of whether his being vaguely aware of scientific research, without being aware of its specifics, suffices for him to accept that there are specific facts that he has not himself heard about or read about; there remains the question of whether individuals of whom he is not personally aware may nevertheless exist as part of a class of which he is aware—whether he may admit that individual Chinese people exist, on the basis of knowing that a Chinese population exists, without being aware of particular individuals.)  It seems as though the subjectivist is committed to claiming that all that exists is what he personally is aware of.

5)  How does one account for past events and knowledge of past events beyond his own personal experience? 

The objectivist thinks that temporality is part of objectively existing reality (whether he thinks that past and future objectively exist or not), and that past events really happened and that we can garner objectively existing evidence of what has really happened.

The subjectivist can accommodate talk about a past beyond his personal experience by allowing that the appearances of people appear to talk about a long-gone past and that appearances of people appear to identify various objects as being very old, and so on, and by saying that he simply agrees to talk in conformity with the conventions of those appearances; but, as in (4), it seems difficult for the subjectivist to go beyond that and to discuss an actual remote past.  Any time when he was not conscious seems to be nonexistent, for the subjectivist—including last night, when he was asleep.  

 6)  How does one account for technological progress?

The objectivist thinks that objectively existing people have made real scientific and technological advances, resulting in our having refrigerators and cell phones and laptop computers.

The subjectivist seems to be in a bit tougher spot.  He may say that it is part of the structure of his subjective reality that the appearances will alter over time in the direction of the appearance of technological progress, but otherwise, it’s hard to see how he explains it.  Unless he personally works in the factory where cell phones are made, he can’t appeal to the workings of people and machines to make them (because those people’s actions and those machines’ actions aren’t part of his personal subjective reality), and he must say that the appearances of technological goodies in the appearances of stores just appear, without explanation.

He might say that he has the idea of people’s and machines’ acting to make cell phones, and that he has the idea of people’s making scientific and technological breakthroughs, and that those ideas are part of his subjective reality; but it’s unclear how his having those ideas accounts for the appearance of a cell phone in his subjective reality, unless he again makes appeal to the structure of his internal, subjective reality.

It seems to me that the idea of an objectively existing reality serves to explain a lot, while the subjectivist view is beset with difficulties.