December 2008 Archives

Michael Huemer (in his book Skepticism and the Veil of Perception 2001, APQ 2006, PPR 2007) has marshalled interesting and challenging arguments for phenomenal conservatism:

(PC) If it seems to S that p, then, in the absence of defeaters, S thereby has at least some degree of justification for believing that p. (PPR 2007, p. 30)

In his remarks, Huemer seems to imply that the degree of justification depends on the strength of the seemings. Now (PC) entails the following about hearing God's voice:

(PC*) If it seems to S that God is saying X, then, in the absence of defeaters, S thereby has at least some degree of justification for believing that God is saying X.

It’s puzzling how transworld sanctified agents are supposed to pose a problem for Plantinga’s free will defense. I’m happy to grant Hawthorne and Howard-Snyder’s (P).

P. It is possible that, necessarily, some creaturely essence (or other) is transworld sanctified.

So, for all we know, in every possible world some creaturely essence is transworld sanctified. We can conclude immediately that (P1) is also true.

P1. It is possible that, necessarily, not every creaturely essence is transworld depraved.

Perfectly fine with me. Now, what is the problem for Plantinga’s free will defense? Is it supposed to be this conclusion?

Patrick Grim has a well-known argument that there is no set of all true propositions. Suppose that argument is sound. For every set S of true propositions, there is a larger set S’ of true propositions. Since there is no set of all true propositions, it cannot be the case that anything knows every proposition in the set of all truths. Is this a problem for classical versions of omniscience? Here’s Alan Rhoda (see Enigman, too)

This creates a problem for omniscience if that notion is defined set-theoretically, e.g., believing every member of the set of all truths. One can argue along Cantorian lines that there can be no such thing as the set of all truths. That is, for every set of truths, one can construct new truths that are not already members of the set. As Enigman points out, if this is right, then it follows that an essentially epistemically static (EES) God - i.e., a God who cannot either acquire or lose beliefs - cannot be omniscient (in a set-theoretical sense). Such a God cannot know all truths. Moreover, there would have to exist truths that are forever outside the ken of an EES God.

I confess to not quite seeing the problem described here, unless it turns on that specific set-theoretic definition of omniscience. Suppose we constuct a series of sets such that every set S contains only true propositions and is a subset of the succeeding set S’. We begin with what we would ordinarily call a saturated set of propostions (what Plantinga would call a maximal or complete and consistent set of propositions) and let each subsequent and larger set be constructed in the way Grim descibes. There will be infinitely many larger and larger sets and no largest set of true propositions.

Each set S in the sequence is consistent and contains propositions that hold at the actual world. If we define omniscience set-theoretically, could there be a classically omnisicient being in the actual world? Let an omniscient being be the following:

O. N(x)(x is omniscient iff. ~(ES)(S is a set of true propositions & x does not know every member of S).

(O) states that necessarily, for all x, x is omniscient just in case there is no set of true propositions such that x does not know every member of that set. As you move up in the sequence of sets of propositions, it is never the case that you reach some set S such that an omniscient being does not know every member of (that is, every proposition in) S. Since there is no set S such that an omniscient being does not know every member of S, an omniscient being knows every true proposition. That is perfectly possible even if the sequence is infinite. So there is no problem for classical omnisicence defined set theoretically, even if there is no set of all true propositions. So, we arrive at two conclusions.

1. There is no set of all true propositions.

2. God knows every true proposition.

Addendum

O is not equivalent to O1, since the union of sets in S = the set of all sets of true propositions is not in S. We have conceded that the union of all sets in S is not a set, given Grim’s proof. But O1 entails that there is a set of all true propositions.

O1. N(x)(x is omniscient iff (Vp)(p is a true proposition only if x knows p)

This puts a somewhat interesting restriction on the logic of omniscience. There is one counterexample to the principle,

P. (Kp & Kq) only if K(p & q)

God will know each true proposition (and most conjunctions of true propostions), but he will not know the conjunction of all true propositions, since the conjunction of all true propositions (we should argue) is not a proposition at all.

It seems to me that some folks--perhaps not philosophers--think that Open Theism (OT) somehow significantly helps with the Problem of Evil. But I do not think it does. The natural reason to think OT helps is to say that if an omnipotent God foreknows that George will freely do some evil E, then God can prevent George from doing E, and OT means that God can't foreknow it, so we can't blame God for failing to prevent E. But this is confused. For it would be impossible for God to both foreknow--or even forebelieve--E and prevent E. Foreknowledge does let God put plans for an event into effect before the event happens, but for actual prevention of foreknown evils, what would be needed is Middle Knowledge, not foreknowledge.

I am curious if any philosophers have committed the error I criticize here.

Consider the following (non-deductive) line of reasoning in favor of an open future (cf. Rhoda, et al.):

1. (a) Presentism is true, and hence (b) any facts that are true must be made true by present states of affairs. Moreover, (c) it is a cheat to allow such states of affairs as its being five minutes before George freely mows the lawn. (d) Without such cheats, the only way a fact about the future could be made true by a present state of affairs is if the present state of affairs causally necessitates the future fact. Since (e) not all future states of affairs are causally necessitated by present ones, (f) the future is open.

Now, consider the same line of reasoning with a past/present swap and a causal direction swap:

2. (a) Presentism is true, and hence (b) any facts that are true must be made true by present states of affairs. Moreover, (c) it is a cheat to allow such states of affairs as its being five minutes after George freely mows the lawn. (d) Without such cheats, the only way a fact about the past could be made true by a present state of affairs is if the past fact is a necessary cause of the present state of affairs. Since (e) not all past states of affairs are necessary causes of present states of affairs, (f) the past is open.

Now I think 2a-d is precisely as compelling as 1a-d (in my view, neither is very compelling). There may be a difference, however, at step e in both cases. We have good reason to believe 1e, because of libertarian free will and quantum indeterminism. Do we have good reason to believe 2e? If we either believe in essentiality of origins or think that God is in time and his memories are caused by the state of affairs of which they are the memories, then we have some reason to deny 2e. Otherwise, it seems we would need to accept 2e--after all, apart from something like essentiality of origins and the issue of God's memories, it seems like typically the effects produced by one cause, C1, could have been produced by another, C2. Thus, unless we believe in essentiality of origins or think that God is in time and has memories caused by the state of affairs of which they are the memories, if we accept 1a-f, we should likewise accept 2a-f. But 2f is absurd. Hence, we should likewise be very suspicious of argument 1 and its conclusion 1f.

This is an attempt to make precise something I said in the comments to my previous post, and analyze it. Let T(p) be the claim that p is true. Work with epistemic probabilities. Assume the following three principles:

1. p entails T(p)
2. If p entails q, then P(p) is no greater than P(q)
3. P(not-p)=1-P(p)

Let OF be the claim that the future is open, so that no proposition about a future contingent is true (i.e., it either lacks truth value, or it is false, depending on the version of OF). Let q be the claim that tomorrow I will toss a quarter a thousand times and each time it will land tails. Let p be not-q. Intuitively, P(p) is more than 1-2^-1000 (more, because the chance that I will both to do the tossing is very small). Now OF entails not-T(p) (by definition of OF). Hence, P(OF) is no bigger than P(not-T(p)) = 1-P(T(p)) by (3). But P(p) is no bigger than P(T(p)) (by (1) and (2)) and hence 1-P(T(p)) is no bigger than 1-P(p). Thus, P(OF) is no bigger than 1-P(p). But P(p) is more than 1-2^-1000. Hence, P(OF) is less than 2^-1000. Hence, OF is not worthy of belief.

But in writing this argument out rigorously, it became clear that there is a way in which it begs the question against those defenders of OF who deny excluded middle. For (3) implies a probabilified version of the axiom of double negation (the axiom of double negation is: not-not-p entails p), and double negation has to be denied by those who deny excluded middle. So the defender of OF can get out of the argument if she denies the axiom of double negation, and gives a propositional probability theory compatible with that denial. But to deny double negation is to go pretty far down the road of implausibility--all reductio arguments go down the drain at that point. Of course one might maintain double negation for non-future-tensed claims, but that's ad hoc.

The following argument is sound:

1. Tomorrow I will freely eat dinner. (Premise: I have good albeit fallible inductive knowledge of this)
2. God infallibly knows every true proposition that it is (metaphysically) possible to infallibly know. (Premise)
3. If God infallibly knows p and God infallibly knows q, then God infallibly knows everything entailed by the conjunction of p and q. (Premise)
4. Possibly, God infallibly knows that I will eat dinner tomorrow. (Premise)
5. Possibly, God infallibly knows that tomorrow I will eat dinner freely or not eat dinner. (Premise)
6. I will eat dinner tomorrow. (By (1))
7. God infallibly knows (6). (By (2), (4) and (6))
8. Tomorrow I will eat dinner freely or not eat dinner. (By (1))
9. God infallibly knows (8). (By (2), (5) and (8))
10. (6) and (8) entails (1). (Conceptual truth)
11. God infallibly knows (1). (By (3), (7), (9) and (10))
12. If Open Theism is true, God does not infallibly know anything I will freely do. (Premise)
13. Open Theism is false. (By (11) and (12))

Suppose I have a new account of, say, omnipotence. Presumably, I still want to still claim that the attribute that I have given an account of is sufficiently close to the traditional understanding of the attribute that we are talking about the same attribute, and I am not simply denying that God has omnipotence in the traditional understanding, but clarifying. This is going to be a vague matter to some degree. But I do want to propose one necessary condition: My understanding of the attribute should be compatible with what my religious tradition takes to be central, paradigm cases of the exercise of that attribute.

An account of divine justice on which rewarding the just simply was not an option would depart too far from the traditional understanding, since rewarding the just is a paradigm case of the exercise of divine justice according to the tradition. Likewise, creation and miracles are paradigm cases of the exercise of omnipotence. An account of omnipotence on which one of these two was impossible would not be an account of omnipotence. This is true even if the account accepted traditional verbage like: "God can do anything that's logically possible", but added that creation or miracles are logically impossible.

On the other hand, if one departs somewhat from traditional wording, but keeps the paradigm cases, one has more of a hope of maintaining that one is merely clarifying. Thus, even if one is not willing to say that God can do anything that's logically possible, because one says that suicide is logically possible but God cannot do it, instead opting for some view like that God is the first cause in all possible worlds, or that God can do anything that it is logically possible that God can do, vel caetera, as long as one maintains the paradigm cases of omnipotence from the tradition, one might be just clarifying.

But the Christian tradition, I claim, sees two particularly impressive and noteworthy cases of omniscience--knowing what is in the depths of the human heart and knowing future contingents. It is impressive that God knows how many hairs I have. But that is something that creatures can figure out, too. It is impressive that God knows all mathematical theorems. But since a theorem is, by definition, provable, a creature could in principle know it. These kinds of knowledge, while impressive, are not very different from the knowledge that creatures we have. But the tradition, I think, takes knowledge of the contents of our mind, as well as knowledge of future contingents, to be the paradigm impressive examples of omniscience.

If one does not save paradigm cases like these, one has not clarified the traditional understanding of omniscience but one has rejected it. This is so even if one says: "God knows everything that is true", but denies that there are true non-tautological propositions about the future. If one does that, then one is no more a believer in omniscience, than someone who thinks God can do everything logically possible but who denies that creation is possible is a believer in omnipotence.

Many Prosblogion readers will be interested in the following Summer Seminar Opportunities at Calvin College.

Application deadline is January 16, 2009. For more information and application requirements, visit www.calvin.edu/scs

Flame of Love: Social Science and Theology on the Great Commandment July 13-24, 2009, Calvin College, Grand Rapids, MI Stephen Post, SUNY Stony Brook; Margaret Poloma and Matthew Lee, University of Akron How do God’s love and human caring interact? What happens when they do? Stephen Post, who directs the Center for Medical Humanities, Compassionate Care, and Bioethics at Stony Brook University, joins University of Akron sociologists Margaret Poloma and Matthew Lee to lead a review of their research on “Godly Love,” the human attempt to live out the divine vision of radical love.

Deliver Us from Evil: Genocide and the Christian World June 22 - July 10, 2009, Calvin College, Grand Rapids, MI James Waller, University of Vermont Guest Speakers: John Roth and Victoria Barnett What roles do Christian churches play in cultures where killing an entire group of people is seriously considered, or even tried? James Waller, social psychologist and author of Becoming Evil: How Ordinary People Commit Genocide and Mass Killing (Oxford, 2nd ed., 2007), will lead an examination of churches’ roles in times of genocide and the consequences for contemporary Christian thought and practice.

Philosophical Reflections on Liturgy June 22 - July 10, 2009, Calvin College, Grand Rapids, MI Nicholas Wolterstorff, Yale University; and Terence Cuneo, University of Vermont This research and writing seminar aims to turn the conversation in philosophy of religion toward liturgy, the ritual enactment of Christian faith, hope and mission. It also seeks to add philosophical depth to the current scholarship on worship and liturgy. Cuneo is a participant in and student of the Orthodox tradition and Wolterstorff is perhaps the most-published of any current philosopher on liturgy

N.B.: This is being reposted from earlier in the week, thus responses to some previously raised objections appear after the fold.

Pro-lifers who are also classical "closed" theists, (as I assume the majority of Pro-lifers at least in the US to be), face a problem from the following argument:

1) Assume that God is omniscient, omnipotent, and omnibenevolent [classical theism]
2) It follows from (1) that God always brings about the maximally beneficial state of affairs (MBS) for any creature x.
2.1) If God is omnibenevolent, then God always wills the MBS for x
2.2) If God is omniscient, then God always knows how to bring about the MBS
for x.
2.3) if God is omnipotent, then God always has the power to bring about the
MBS for x.
2.4) it is the case that God is omniscient, omnipotent, and omnibenevolent.
2.5) So, God always brings about the MBS for x [2.1 -2.4 MP]
3) Assume God allows abortion to occur
4) In that case either abortion is the MBS for some creature x or either (1) or (2) is false.
5) (1) and (2) are true
6) Therefore, it must be the case that abortion is the MBS for x [4,5 MT]

If this argument is correct then pro-lifers who are also classical theists should not be universally opposed to abortion, since the argument concludes that God would only allow abortion in the case where it is the MBS. However most who are pro-life would find this conclusion counterintuitive or even counter-dogmatic. So how do we account for the wrongness of abortion?