Alanyzer

On a Misguided Application of Excluded Middle

noreply@blogger.com (Alan Rhoda) — Mon, 10 Aug 2009 18:47:00 +0000

Many discussions of logical fatalism and of the compatibility of divine foreknowledge and future contingency turn on the question of whether propositions about future contingents are true in advance. More exactly, they raise questions about whether any 'will' or 'does' propositions about events which have an intermediate chance of occurring (i.e., a current single-case objective probability greater than zero and less than one) are true. One common argument contends that the 'open future' position, which denies that any propositions about future contingents are now true, leads to a denial of the law of excluded middle (LEM). For example, in a recent collection, David Hunt writes (p. 276):

Either I will call my mother tomorrow, or I won't call my mother tomorrow. One or the other of these statements about the future must be true. The principle that either a given statement or its denial is true is called the "Law of Excluded Middle."

According to Hunt, LEM necessitates that some propositions about future contingents are true. But he's simply mistaken if he thinks his example gives us a clear instance of LEM. It doesn't, and it's easy to show this.

LEM states that, for all propositions P, either P or its denial, Not-P, is the case. This can be given either a truth-functional or a supervaluationist reading.

Truth-functional LEM: For all P, either P is true or Not-P is true.
Supervaluationist LEM: For all P, 'either P or Not-P' is true.

In general, though, the point behind LEM (on either reading) is that P and Not-P are mutually exclusive and jointly exhaustive. Between them, they completely exhaust logical space. Every possible scenario is one in which one of those two holds, and no possible scenario is one in which both hold.

But Hunt's example doesn't correspond to either reading of LEM. To show this we need only describe a logically possible scenario in which neither (1) 'Hunt calls his mother tomorrow' nor (2) 'Hunt does not call his mother tomorrow' obtains. Here's one: Hunt doesn't exist. In that case, Hunt isn't around either to call his mother or to refrain from calling his mother. So neither (1) nor (2) is true. (Compare with 'The present king of France is bald' and 'The present king of France is not bald'. Neither of those is true if there is no present king of France.)

Hunt might respond by suggesting that we should read (2) as (2*) 'It is not the case that Hunt calls his mother tomorrow'. On that reading we do indeed have an instance of LEM with (1) and (2*). But a new problem arises: (2*) isn't about a future contingent. It is true right now simply in virtue of the fact that tomorrow hasn't happen yet. Hence its current truth doesn't depend on anything future. What's more, its truth doesn't depend on Hunt's existence, the existence of his mother, or even the existence of any created thing whatsoever. Of course, if tomorrow Hunt should call his mother, (2*) will then have become false. But that in no way licenses the inference that it is now false.

In sum, either we have a choice between propositions about future contingents, but LEM fails to apply, or LEM applies, but we are no longer forced to choose between two propositions about future contingents. Either way, Hunt's argument has zero force against the open future position.

Theism and Truthmaking

noreply@blogger.com (Alan Rhoda) — Wed, 05 Aug 2009 23:55:00 +0000

Trenton Merricks claims that truthmakers must be what truths are "about" in some unarticulated sense of "about". He then argues against truthmaker-type principles by claiming that there are truths of various sorts for which his undefined aboutness criterion cannot be met.

In two of my last three posts I have criticized Merricks for leaving this vital piece of his argument undefined, and in my last post, I sought to rectify matters by presenting a criterion of aboutness for truthmakers:

A truth is "about" one of its truthmakers in the relevant sense if and only if (a) there exists something such that (b) full acquaintance with that thing and only that thing would enable one to know with certainty that the truth in question is true.

Now, I'm pretty sure that Merricks would reject my criterion, but until he shows me why its wrong I'm going to stick by it. What I want to argue in this post is that if one accepts my criterion of aboutness and if one accepts the necessary existence of an essentially omniscient God (as Merricks does), then Merricks' main objection against truthmaker principles (that there are truths which are not about any truthmakers) fails. In particular, I consider negative existentials and truths about the past.

Negative Existentials
It is true that there are no hobbits. In virtue of what could this be true? Merricks considers the suggestion that the entire physical universe might make this true, but he argues against that suggestion. For one thing, it doesn't suffice unless we posit a totality state of affairs, e.g., there being nothing more. Otherwise we could simply add a hobbit (and maybe a few other things) on top of the physical universe. But in that case the physical universe as it stands would not necessitate the truth of 'there are no hobbits' and so would not suffice to make it true. One wonders, though, what this totality state of affairs is supposed to consist in. It seems rather suspicious. Merrick's chief objection, though, is simply to claim that 'there are no hobbits' is not relevantly about the physical universe.

I think Merrick's is right that the physical universe by itself will not suffice without a totality state of affairs. And I agree that such a state of affairs looks unacceptably suspicious. But I don't think he's considered a plausible alternative truthmaker, one the existence of which he himself would seem to be committed to in virtue of being a theist, namely, God's having a hobbit-free experience of creation. No extra totality state is needed here because God's essential omniscience takes care of that. Nor could any theist reasonably dismiss this as unacceptably suspicious. And, moreover, by my aboutness criterion, this is a truthmaker for 'there are no hobbits' - thus, if we were fully acquainted with God's experience of creation, we would be able to know with certainty that that proposition is true.

Truths about the Past
Merricks, like myself, is a presentism, someone who believes that only what exists now exists simpliciter. A common objection against presentism is that it lacks the resources to supply truthmakers for truths about the past. Merricks accepts the objection but denies its force. He claims that truths about the past are relevantly about any presently existing things. And he argues that presentism is more plausible than any truthmaker principles, hence if the two conflict, it is the truthmaker principles that must go.

Against Merricks, I deny that there is any conflict between presentism and truthmaker principles. In a recently published paper, "Presentism, Truthmakers, and God" (available on my website), I argue in detail that God's memories can supply truthmakers for truths about the past. Moreover, God's memories satisfy my aboutness criterion - thus, if we were fully acquainted with God's memories, we would be able to know with certainty that, say, 'Caesar crossed the Rubicon' is true.

I think similar options are available for the other alleged problem-cases that Merricks considers. Moral: If you're a theist, don't bracket your theism when doing metaphysics. If God exists, he should be metaphysically relevant to (nearly) everything else.

More on Merricks on Truthmaking

noreply@blogger.com (Alan Rhoda) — Fri, 03 Jul 2009 19:26:00 +0000

I've now finishing my re-reading of Trenton Merricks' book Truth and Ontology and I'm still quite unconvinced by his contention that what's true does not depend on what exists in any substantive way. A couple posts ago I noted my main reasons for dissatisfaction with Merricks' arguments:

He loads down truthmaker principles, which affirm a substantive dependence of truth on being, with extraneous commitments.

Most significantly, he takes the raison d'etre of such principles to be that of catching all sorts of metaphysical "cheaters"--those who either (a) try to have their truths on the cheap, without paying an appropriate metaphysical price, or (b) invoke "suspicious" properties to do their truthmaking work. I deny that these concerns are fundamental to truthmaker principles. Such principles are merely attempts to articulate the driving intuition behind correspondence theories of truth, namely, that truth depends on being in a substantive way and, therefore, that there must be some being corresponding to any given truth that "makes" that truth true. What properties count as "suspicious" is to be determined not by truthmaker principles but by explanatory considerations (e.g., Are such properties merely "ad hoc", or do we have independent reasons for positing them? Can they plausibly be regarded as primitives, or can they be cashed out in some explanatorily informative way?)

He never carefully defines the crucial notion of "aboutness" upon which his major arguments depend.

Merricks insists that truths can only be made true by what those truths are "about". He then argues that for many types of truths there are no existing things that those truths are "about", from which he concludes that truthmaker principles are false. It is clear that the notion of "aboutness" is crucial to this argumentative strategy, and it is surprising that a philosopher of Merricks' calibre doesn't define it carefully. In fact, he explicitly declines to give an analysis (pp. 33-34) and relies, instead, on a handful of examples (e.g., pp. 28-29) which indicate only that "aboutness" has something to do with relevance. Here's one such example:

[Y]our thumb fails to be a genuine truthmaker for FLT [Fermat's Last Theorem]. . . . Even though your thumb's existence necessitates FLT's truth, FLT is not about your thumb. (p. 27)

I'll grant that a thumb is not a truthmaker for FLT. And I'll grant that a thumb's inadequacy as a truthmaker for FLT can be explained, to a first approximation, by the observation that FLT is not relevantly "about" a thumb. But Merricks needs to go a lot further than that. If he wants to refute truthmaker principles (and he does) then he needs to give an analysis of what the relevant "aboutness" relation is. Were he to provide such an analysis, of course, fans of truthmaker principles could subject it to scrutiny. Leaving the notion nebulous allows Merricks to rest his argument on impressionistic declarations that this or that type of truth isn't relevantly "about" any existing thing. He thus arrives at his conclusions by a certain amount of theft over honest toil.

In the rest of this post I'm going to help Merricks out a bit by clarifying the relevant sense in which truthmakers must be what truths are "about".

First, we need to distinguish between connotative and denotative senses of "about". In the connotative sense, to speak "about" (say) FLT is to say something about the content of the theorem. This requires some understanding of what the theorem means. But I can say, "I heard that some dude proved FLT a few years ago" and thereby talk "about" FLT without having any clue what FLT stands for. That's a strictly denotative sense of "about". Now, truthmaker principles are metaphysical, not epistemological in nature. They require that there exists something in virtue of which a truth is true, but they don't require us to know what that something is. Hence, the relevant sense of "aboutness" is denotative, not connotative.

Second, truthmakers must relevantly necessitate their truths. What that means is not simply that it must be impossible that the truthmaker exist and the truth in question fail to be true. Your thumb, after all, necessitates FLT in that sense. No, it must also be the case that the truth in question could be derived from knowledge of the truthmaker. In other words, if (hypothetically) someone were fully acquainted with a putative truthmaker and only that truthmaker, would that person thereby know with certainty that the truth in question is true? Your thumb is not a truthmaker for FLT because someone acquainted only with your thumb (however fully) would not thereby know FLT.

I claim that the above two points are all there is to the relevant "aboutness" relation. A truth is "about" one of its truthmakers in the relevant sense if and only if (a) there exists something such that (b) full acquaintance with that thing and only that thing would enable one to know with certainty that the truth in question is true.

Merricks, undoubtedly would want to insist on further constraints, at which we could have a healthy debate about them. My complaint is that he should have gone at least as far as I have here, and he could easily have done so.

In my next post, I'm going to use my "aboutness" criterion and show that on metaphysical assumptions that Merricks accepts, there are truthmakers for all of the truths for which he says there aren't any.

Gratuitous Evil and Divine Providence

noreply@blogger.com (Alan Rhoda) — Thu, 02 Jul 2009 18:28:00 +0000

I'm really happy right now because a paper of mine ("Gratuitous Evil and Divine Providence") was just accepted at Religious Studies. In my experience, at least, the turnaround at that journal is phenomenally fast. This is the second paper I've submitted there. On both I received an acceptance notice within a week or less.

I'll post a digital version of the paper to my website once I've sent the final version off to the journal. Here's the abstract:

Discussions of the evidential argument from evil generally pay little attention to how different models of divine providence constrain the theist’s options for response. After describing four models of providence and discussing theistic strategies for responding to the evidential argument, I articulate and defend a definition of “gratuitous evil” that renders the theological premise of the argument uncontroversial for theists. This forces theists to focus their fire on the evidential premise, enabling us to compare models of providence with respect to how plausibly they can resist it. I then give an assessment of the four models, concluding that theists are better off vis-à-vis the evidential argument if they reject meticulous providence.

UPDATE (7/20/09): The penultimate draft of the paper is now available on my website.

Merricks on Truthmaking

noreply@blogger.com (Alan Rhoda) — Wed, 01 Jul 2009 19:53:00 +0000

I've recently been rereading Trenton Merrick's book Truth and Ontology (Oxford, 2007) in which he argues against the substantive dependence of truth on being. Thus, he rejects theses like

TM - Every truth has a truthmaker, a parcel of reality the existence of which necessitates, and thereby grounds, that truth.
TSB - Truth supervenes on being. I.e., every possible difference in truth corresponds to a possible difference in reality (i.e., in what things exist and in what properties have and/or what relations they stand in), and vice-versa.
Correspondence theory of truth - A proposition (or truth-bearer) is true iff what it represents is the case (i.e., iff reality is as the proposition depicts).

Merricks' strategy is to saddle the above theses with as much baggage as he can, thereby imposing steep restrictions on what an adequate theory of substantive dependence would have to look like, and then arguing that such theories fail to satisfy those restrictions.

His favorite restrictions are (1) that it is the purpose of theses like TM and TSB to "catch cheaters" by criticizing (a) those who fail to endorse an ontology robust enough to ground or necessitate the truths they feel free to invoke, and (b) those who try to discharge their grounding obligations by positing "suspicious" properties; and (2) that substantive grounds for truths must consists of what those truths are "about", in some rather loosely defined sense of that term.

For example, Merricks argues (ch. 6) that presentism (the theory that whatever exists simpliciter exists now) is true, that it violates TM and TSB, and therefore, that TM and TSB should be rejected. While he discusses some attempts by presentists to satisfy the demands of TM and TSB, Merricks rejects these either because they trade in "suspicious" properties or because they violate the "aboutness" constraint.

I'm not persuaded by Merricks. In part, that's because I think he's wrong that a purpose of TM and TSB is to catch cheaters of the second sort, namely, those who invoke allegedly "suspicious" properties. (All things equal, we ought to try to avoid "suspicious" properties where possible, but it's not TM and TSB's job to say what those properties are.) Also, I don't think he's nearly clear enough on the relevant sense of "aboutness". He admits it has something to do with "relevance", but apart from a handful of examples that he claims to find intuitive, he nowhere defines the notion.

Still, it is a fair question what someone like myself who is partial to TM and TSB should say about the truthmakers or the supervenience base for various kinds of truths. In particular, necessary truths, general truths, modal truths, negative existentials, counterfactuals, and metaphysical theses like presentism, actualism, and nominalism have all been thought to raise serious problems for TM and TSB. In the next few posts, I'm going to look at some of these problem cases and argue that they are less worrisome for theists than they might be for those of different metaphysical persuasions.

I Made the List

noreply@blogger.com (Alan Rhoda) — Wed, 01 Jul 2009 19:51:00 +0000

of 100+ living philosophers of religion.

Back to Blogging

noreply@blogger.com (Alan Rhoda) — Tue, 30 Jun 2009 21:39:00 +0000

I haven't done much in the way of blogging for the past several months. In large part this is because my energies have been focused on being a father to my now 18-month old daughter and on finishing several papers that I've been working on. Now that my desk is starting to clear up, I'm going to resume blogging again.

I don't promise to blog regularly. Blogging is something I do when I have spare time. It's not something I want to get absorbed into. So when I feel like I'm spending too much time at it, I'll back off again for a while. We'll see how it goes.

I'll put up a post sometime tomorrow with thoughts on truthmaking, theism, and modality. Right now, however, I've got to go home and spend time with my wonderful wife and daughter.

Truth Accessibility Relations among Times

noreply@blogger.com (Alan Rhoda) — Mon, 26 Jan 2009 01:07:00 +0000

In my two previous posts, I have explained the notion of 'truth at a time' and argued that for a (contingent) proposition to be true at T it must supervene upon what exists at T. In short, truth at T requires a truthmaker at T.

A question that remains concerns accessibility relations among times. If a proposition is true at some earlier time, is it necessary that it be true at all later times that it was true at that earlier time? And if a proposition is true at some later time, is it necessary that it be true at all earlier times that it will be true at that later time? In common tense logical notation, these questions concern the theses:

p → FPp
p → PFp

(1) says that if p is true at some time, say T, then it will be true at all times subsequent to T that p was true at T. (2) says that if p is true at T, then it has been true at all times prior to T that p will be true at T.

I believe that (1) is true and (2) is false. In other words, I believe that earlier times are accessible to later times, but I don't think that later times are accessible to earlier times. This antisymmetry means that I take S4 and not S5 to be the right system of modal logic as far as times are concerned.

S4 ensures reflexivity and transitivity among times. Reflexivity means that each time is accessible to itself. Hence, if it is true at T that p, then it is true at T that it is true at T that p, etc. Transitivity means that if T1 is accessible to T2, and T2 is accessible to T3, then T1 is accessible to T3. Hence, if it is true at T1 that p, and if it is true at T2 that it is true at T1 that p, then it is true at T3 that it is true at T1 that p.

To reflexivity and transitivity, S5 adds symmetry. This means that if T1 is accessible to T2, then T2 is accessible to T1. Hence, if it is true at T1 that p, then it is true at T2 that it is true at T1 that p, and it is true at T1 that it is true at T2 that it is true at T1 that p, etc.

Now, if S5 is right, then both (1) and (2) have to be accepted - what's true at any time is mirrored at all times. If S4 is right, however, then we cannot accept both (1) and (2), for that would violate antisymmetry. The questions, then, are whether we should accept antisymmetry or not and, if so, whether we should go with (1) or (2).

My argument turns on the relation between time and causality and on the falsity of determinism. Earlier events can cause later events, but not vice-versa (or so most of us think). That motivates antisymmetry, but to establish it we have to appeal to the idea that what's true at a time depends upon what exists at that time. Suppose event E1 at T1 indeterministically causes event E2 at T2. It is true, therefore, at T2 that E2 is occurring. Given symmetric accessibility between T1 and T2, it is true at T1 that it is true at T2 that E2 is occurring. But this is false if the causal relation between E1 and E2 is indeterministic, for in that case we do not have a truthmaker at T1 for "E2 is occurring at T2".

If determinism is true, then a unique sequence of later times is implied by earlier times. It can be true at T1, therefore, that "E2 is occurring" will be true at T2. Hence, T2 is implicitly accessible from T1. But if determinism is false, then no unique sequence of later times is implied by earlier times. Let p represent the occurrence of some event that is causally contingent from the perspective of T1 (e.g., "E2 occurs at T2"). From that perspective, it may be that p is true at T2, and it may be that p is false at T2. Moreover, there is nothing at T1 sufficient for making it true either that p will be the case at T2 or that p will not be the case at T2. Since what's true at T1 depends on what exists at T1, it cannot be true at T1 either that p will be true at T2 or that p will not be true at T2. Given indeterminism, therefore, it follows that (2) is false. If, for example, there being a sea battle at T2 is causally contingent at T1, then even if a sea battle does occur at T2, it does not make "A sea battle will occur at T2" true at T1, contrary to (2).

But what about (1)? It would be very counterintuitive if (1) were false. It's falsity would allow, for example, that "Caesar crossed the Rubicon" might be true in, say, 1000 A.D., but not true in 2000 A.D. So I want to insist that (1) is true, but I emphasize that it's truth is not a mere matter of logic. If we accept that truth supervenes on being, then (1) commits us to a substantive metaphysical position. Since what's (contingently) true at T2 depends upon what exists at T2, for it to be true at T2 that some event E occurred at T1, there must be something at T2 sufficient for making that true. E's occurring at T1 is not enough. There must also be something that carries E's occurring at T1 forward in time and that constitutes at T2 E's having occurred at T1. As to what that "something" is, I refer the reader to this forthcoming paper of mine.

In summary, if determinism is false, as I believe, then (2) is false. (1), however, is true - it would be intuitively quite odd (to say the least) if it weren't - though it comes at what some will regard as an unacceptable metaphysical price. Those folks either have to deny that truth supervenes on being or reject (1). I think either is a much bigger price to pay.

Truth at a Time and Truth Simpliciter

noreply@blogger.com (Alan Rhoda) — Mon, 26 Jan 2009 00:42:00 +0000

As a follow-up to my previous post, I'd like to say a bit about how truth at a time and truth at a world relate to truth simpliciter.

Unlike 'truth at a world' and 'truth at a time', truth simpliciter is not evaluated from the perspective of any given time or world, but absolutely. In other words, it is evaluated from the proverbial "God's eye" or absolute perspective, that is, in relation to what exists simpliciter. Consequently, what is true simpliciter depends on the correct metaphysics.

Actualism is the thesis that the only possible world that exists simpliciter is the actual world, whereas possibilism is the thesis that all possible worlds exist simpliciter. Presentism is the thesis that only what exists now exists simpliciter, whereas eternalism is the thesis that all past, present, and future world states exist simpliciter. If actualism and presentism are correct, then what exists simpliciter is coextensive with what exists now. Moreover, truth simpliciter coincides with what is true now. Hence, "Obama is now President" is true simpliciter.

In contrast, if actualism and eternalism are correct, then all instantaneous world states (however foliated into past, present, and future) exist simpliciter. As a result, truth simpliciter and truth at a time can come apart. Omnitemporal truths, which are true at all times, hold distributively across the entire time series and are true simpliciter. So are transtemporal truths, which hold collectively of the entire time series. These can, but arguably need not, be true at all times in the series. For example, "At some time or other, Obama is President" is true simpliciter. It is also true now. But it may not have been true at all earlier times because the fact that makes it true may not be accessible from all earlier times. One way in which this could happen (defended by Peirce, Prior, Hartshorne, and Ryle) is through reference failure. Arguably, before Obama was conceived, there was no such individual for propositions to refer to. Finally, there may be (though this is controversial) atemporal truths, truths about matters that stand in no relation to time whatsoever. These truths, if they exist, are true simpliciter, but fail to be true at any time. (Some people think mathematical truths fall into this category. I doubt this. I say that '2+2=4' is omnitemporally true, not atemporally true. It sounds rather odd to say that it isn't true now.)

Finally, if possibilism and eternalism are correct, then all worlds and all instantaneous world states in all worlds exist simpliciter. As before, truths that hold distibutively over all world-time pairs (i.e., at all times in all worlds) will be true simpliciter. Similarly, anything that is true at all worlds (i.e., necessary truths) will be true simpliciter. Further, truths that hold collectively of the entire world/history ensemble (e.g., "At some time in some world Obama is President") will be true simpliciter. This latter truth is true now in alpha (the actual world), but it need not be true true at all times in all worlds for it may not be accessible from all times in all worlds.

Truth-at-T Depends on What Exists-at-T

noreply@blogger.com (Alan Rhoda) — Sun, 25 Jan 2009 04:21:00 +0000

In my previous post I made the following claim without argument: "for a proposition to be true now, what it represents as being the case must correspond to ... what is the case now." I'm now going to give that argument.

Every argument for any categorical conclusion requires some categorical assumptions which are not defended within the scope of that argument. Here are some of my assumptions:

Truth supervenes on being (TSB). This means that what is true depends on what exists for its being true. Moreover, every difference in truth corresponds to a difference in being, such that if anything that is true had not been true, then there would have been a corresponding difference in reality.
Correspondence theory of truth (CT). A proposition is true if and only if the state of affairs (STOA) that it represents obtains. In other words, a proposition p is true if and only if the STOA that would be posited were p asserted obtains.
It makes sense to speak of a proposition's being true at a time. This notion is compatible with, but does not entail, the idea that truth is temporally invariant.

I won't defend these claims here, though if pressed I might be willing to restrict (1) and (2) to contingent truths.

Now, the key to establishing my claim that what is true at a time depends on what is real or what exists at that time is to understand the notion of 'truth at a time'. I want to suggest that we should think about this notion in a manner analogous to the idea of 'truth at a world'.

In metaphysics, possible worlds are typically distinguished in terms of what is true 'at' them. Thus, worlds W and W* are distinct if and only if something is true at W that is not true at W*, or vice-versa. To consider what is true at a world is essentially to ask what would be true if that world were actual. Alternatively, since each world is actual from its own perspective, we can ask how things stand from the perspective of that world. Finally, what is true at one world may be reflected in what is true at another world. Whether this is so depends upon the accessibility relations that hold among the worlds in question. Thus, if p is true at W, and if W is accessible to W* (that is, if one can "see" W from the perspective of W*), then it is true at W* that p is true at W.

Analogously, 'truth at a time' means truth as judged from the perspective of a given time. By a 'time' I mean a complete time-slice of reality, an instantaneous world state. To determine what is true at a time we ask what would be true if that time were present. Alternatively, since each time is present from its own perspective, we can ask how things stand from the perspective of that time. If T is such that Caesar is ruling in Rome, then "Caesar is ruling in Rome" is true at T. If T* is such that Nero (and not Caesar) is ruling in Rome, then "Caesar is ruling in Rome" is false at T*. As with worlds, what is true at one time may be reflected in what is true at another time. Whether this is so depends upon the accessibility relations that hold among the times in question. Thus, if p is true at T, and if T is accessible to T* (that is, if one can "see" T from the perspective of T*), then it is true at T* that p is true at T. If, in addition, T* is earlier than, simultaneous with, or later than T, then accessibility may be expressed in terms of tense. Thus, if p is true at T, and if T is accessible to T*, and if T is earlier than T*, then it is true at T* that it was the case that p is true at T.

The thesis I set out to defend follows from what I have said above. Just as what is true at a world depends upon what obtains at that world, so also what is true at a time depends upon what obtains at that time. This neither precludes nor entails there being accessibility relations among times such that what is true at one time either has been or will be true at another time. Accordingly, it cannot be true now, for example, that there will be a sea battle tomorrow, unless this truth supervenes upon present reality. Depending on accessibility relations, however, it may be true now that it will (probably) be true tomorrow that there is a sea battle.

A Recent Objection to the Alethic Openness of the Future

noreply@blogger.com (Alan Rhoda) — Fri, 16 Jan 2009 18:41:00 +0000

The future is 'alethically' open at time T with respect to possible state of affairs X and future time T* > T if and only if neither "X will obtain at T*" nor "X will not obtain at T*" is true at T.

I believe that the future is alethically open with respect to future contingent states of affairs. Thus, if the present state of the world is indeterministic with respect to whether a sea battle occurs tomorrow (i.e., if that's a future contingent), then on my view neither "A sea battle will occur tomorrow" nor "A sea battle will not occur tomorrow" is now true. Indeed, I submit that both propositions are now false.

There's an interesting challenge to my view that has recently been proposed by Alex Pruss of Baylor Univ. His argument is encumbered with the technical trappings of probability theory, but the basic objection can be stated quite simply as follows:

On the open future view that I espouse, there are no “will” or “will not” truths about future contingents.
But we have excellent (inductive) reasons for believing that there are “will” or “will not” truths about future contingents (e.g., “S will not win the lottery” - assume, e.g., a standard lotto and that S has only one lotto ticket).
Therefore, we have excellent reasons for believing that the open future view is false.

This is a potentially devastating argument against my position. The logic is clearly valid, I'm already committed to (1), and premise (2) looks very plausible. Clearly, I have to deny (2). The challenge is to make it clear why that's a reasonable thing to do.

In the first place, it is essential to get as clear as we can on exactly what proposition is expressed by the sentence "S will not win the lottery". This is important because linguistic expressions do not wear their meaning on the sleeve, so to speak. We have to interpret them as best we can in light of whatever contextual clues are available. Due to factors like vagueness, ambiguity, lack of information about the context, and so forth, interpretation is often difficult and frequently inconclusive.

In the second place, there is an important distinction that we have to make between modally inflected uses of "will" and "will not" and amodal uses. Interpreted in the former sense, "S will not win the lottery" may be read as saying something like "S will probably not win the lottery". Here the word "probably" attributes an objective probability to the event S's not winning the lottery. Different objective probabilities can be captured with different qualifiers (e.g., "will definitely", "will possibly", or, more generally, "will, with probability p"). Interpreted in the amodal sense, "S will not win the lottery" should be read as saying something like "Subsequently, S does not win the lottery". This says nothing about what it's objective probability is, other than implying that it is non-zero. Probabilities applied to this proposition have be read as epistemic probabilities, which qualify the attitude that a subject has toward a proposition without entering in the meaning of the proposition. The contrast, then, is between a modal, objective probability reading "S will probably not win the lottery" and an amodal reading "Subsequently, S does not win the lottery".

In the third place, there is a potential ambiguity in the scope of the word "not" in "S will not win the lottery". Does it apply just to the predicate alone or to the rest of the proposition in its entirety? On the first reading, "S will not win the lottery" means "S will not-(win the lottery)". On the second reading, "S will not win the lottery" means "Not-(S will win the lottery)". These readings are distinct since the former entails the latter, but not vice-versa. It is possible, after all, for "Not-(S will win the lottery)" to be true without "S will not-(win the lottery)" being true - for example, when S does not exist.

Crossing the above distinctions gives us four basic readings of "S will not win the lottery":

S will probably not-(win the lottery).
Not-(S will probably win the lottery).
Subsequently, S does not-(win the lottery).
Not-(subsequently, S does win the lottery).

Now, presumably, we have good (inductive) reasons to believe all of these to be true. (a) and (b), however, pose no difficulty for my position, since I am not committed to saying that "will probably" propositions are false when it comes to future contingents. It comes down, then, to the amodal propositions (c) and (d). To refute me the objector has to show that we have good reason for believing that either (c) or (d) concerns a future contingent and is true now. It is here that I make my stand. I deny that these conditions are satisfied by (c) or (d).

For a proposition to be true, what it represents as being the case must correspond to reality, to what is the case. Likewise, for a proposition to be true now, what it represents as being the case must correspond to present reality, to what is the case now. Now, (c) clearly represents what is, from our present perspective, a future contingent state of affairs. It represents S's not winning the lottery subsequent to a contextually specified index date. I deny, however, that (c) is true now or that we have good reason for believing it to be true now on the grounds that there is no present reality that it corresponds to. We have good reason for believing that it will probably come to be true, but not for believing that it is true. Thus, after the drawing of the lottery, either S will have won subsequently to the index date or not. At that point, assuming S does not win, (c) will be true. But not until then.

With respect to (d), I grant that it is true now and that we have good reason for believing it to be true now, but I deny that it directly concerns the future. It concerns, rather, a present fact, for it says it that it is not (now) the case that subsequently S does not win the lottery. This is provably correct. Future events do not obtain now.

In summary, I reject premise (2) of the objector's argument on the grounds that (i) the sorts of "will not" propositions about future contingents that we have good reasons for believing to be true now are not the sorts of propositions to which the doctrine of alethic openness applies, and (ii) the sorts of "will not" propositions about future contingents to which alethic openness applies are not the sorts of propositions that we have good reason for believing to be true now.

Could God Infallibly Know that He Is Omniscient?

noreply@blogger.com (Alan Rhoda) — Thu, 15 Jan 2009 20:36:00 +0000

I've been reflecting a bit about the following analogy proposed by Enigman:

Given someone who knows that she can move freely anywhere within an infinitely dimensional space, does she know that she has complete freedom of motion? The problem is that such a space is isomorphic to a hyperspace containing such a space as a mere slice.

This analogy is supposed to call into question whether God can be certain that there is no reality beyond his ken. Couldn't the entire space of God's knowledge simply be a mere slice of a larger hyperspace containing things of which not even God is aware?

Traditional theism answers with an emphatic NO. But can that answer be solidly justified, or is it simply a dogmatic prejudice?

One strategy for justifying the traditional answer is to go Thomistic. On Thomas's account, God is defined as ipsum esse subsistens. His essence is identical to his existence. That trait is necessarily unique to God. Hence, in everthing else there must be a real distinction between existence and essence. As such, beings other than God cannot account for their own existence. Hence, they must all owe their existence to God as their creator. And since God has perfect self-knowledge, he knows his own creative activity, and so knows of the existence of whatever else other than himself that there may be.

My problem with that response is that I think Thomistic metaphysics creates more problems than it solves. For one thing, it's hard to see how Thomas can account for real contingency. Identity is a necessary relation (if two things are identical then they are necessarily identical). It follows that God's essence = his existence, across all possible worlds. Now, either there are multiple, distinct possible worlds, or there are not. If not, then everything is necessary, which is counterintuitive in excelsis. If, however, there are multiple possible worlds, then they differ in some respects, which means that there are contingencies. Hence, what God has to know in order to know everything must vary from world to world, which means that the content of God's knowledge must to some extent be contingent. But if God's existence is really identical to God's essence, then everything about God must be essential and thus invariant across possible worlds in which God exists, including the content of God's knowledge, which is inconsistent with the assumptions that there are multiple possible worlds and that God's knowledge is exhaustive. In short, the following three assumptions are mutually inconsistent:

God has exhaustive knowledge of reality.
God's essence is identical with his existence.
Some facts are contingent.

Since 3 is undoubtedly true, either 1 or 2 is false. My preference is to deny 2.

Let me turn now to what I think is a better strategy. The key idea is that actuality is the sole delimiter of real possibility. What this means is that real possibility is always relative to some actuality. For example, what's physically possible depends upon what physical laws are actually in place. Now, suppose we stipulate that God is the sole delimiter of real possibility. If that be accepted, then there are no real possibilities that are not grounded somehow in God. For example, there could be no metaphysically possible world in which God did not exist. Now, if both God and actuality are delimiters of real possibility, then they must be related in some systematic way. Assuming that pantheism is false, that relation can't be identity. A theist, however, could subordinate the one to the other and say that God is the delimiter of possibility in virtue of being the delimiter of actuality. Thus, what's possible is grounded in what's actual, and what's actual is grounded either in God's nature or God's will. If that's right, then in knowing himself, God knows all actualities, and there is no possibility for there to be any actuality that is unrelated to God.

Does that solve the problem? Well, it's a good start at least. One might wonder how God can be sure that he is the sole delimiter of real possibility. If he is, then his perfect self-knowledge guarantees that he knows that he is, and the problem is solved. But if God is not sure, then he can conclude that either he isn't the sole delimiter of possibility or he doesn't have perfect self-knowledge.

Does Moral Realism and Infinite Spacetime Entail Atheism?

noreply@blogger.com (Alan Rhoda) — Sun, 11 Jan 2009 22:25:00 +0000

Vlastimil Vohánka send me an email recently asking for my thoughts on the following reconstruction of an argument recently proposed by Quentin Smith.

1. Necessarily, global moral realism is true (everything, or rather, every physical entity, has a positive amount of value). Premise
2. Necessarily, aggregative value theory is true (each physical location has a finite positive amount of value; a location can be a person, any other animal, a plant, a particular of matter or energy, a point of space or time, or some larger complex of particulars of these kinds, for example, a forest, an orchestra or an hour of time; values add up). Premise
2*. Necessarily, the performance of an action is morally indifferent iff the performance of that action neither increases nor decreases the amount of value in the universe. Premise, or from (2)
3. Contingently (and according to contemporary physics), spacetime is infinite, both temporally -- there are infinitely many non-overlapping future hours --, and, more controversially, spatially -- at each time there are infinitely many non-overlapping, equal sized cubes of space. Premise
3*. Necessarily, every human action has only finite effect on the amount of value in the universe. Premise
3**. Necessarily, neither any finite addition to nor any finite detraction from an infinite amount of value neither increases nor decreases the amount of value. Premise
4. Moral nihilism is contingently true (it does not morally matter what humans do, it does not matter what actions humans perform). From (1)-(3**)
5. Humans have no intrinsic dignity (from 1-3**); humans have no rights (from 1-3** or from 4); human life has no meaning (from 1-3** or from 4); every human's life is less valuable than the entire state of his being dead (from 1-3**).
5*. God (at least as traditionally conceived) does not exist. From (4) or (5)

The gist of the argument is that if something exists that is infinitely valuable, if some such thing would exist regardless of what we do, and if our contributions are at best finite, then nothing we do makes any real difference to the aggregate value of what exists (since ∞ + 1 = ∞). Hence, nothing we do really matters.

Now, I think that premise (3) of this argument is particularly questionable. I don't think there are any empirical results from physics that establish or that even could establish the existence of an infinite spacetime. But the argument could be reconstructed without that premise. For example, instead of infinite spacetime, we could start from the assumption that God necessarily exists and has infinite value. The result, if the rest of the argument is sound, would be a reductio ad absurdum of theism.

If there's a fundamental flaw in the argument, it has to do with its assumptions about the nature of value. There are several that I find particularly questionable.

I'm skeptical about (1). If all that ever existed was a diffuse cloud of hydrogen, would it have positive value? I'm inclined to think not. I suggest, rather, that there may be no value that is not value to someone or, more broadly, to some sentient being. This is reflected in the notion of the good as that which is desirable, a notion that has no application apart from beings capable of desiring.

I'm also skeptical about (2). Can values simply be added up? Not if there are incommensurable kind of value. It may well be that there is no common currency in which all values can be "cashed out" and then added up.

Finally, I'm skeptical about (3*). Why think that human actions have only a finite effect on the amount of value in the universe? Suppose, for example, that there is an afterlife and that one of the possibilities is heaven (infinite positive utility). Well, if I by my own choices and the grace of God can enter the kingdom of heaven, then haven't I done something that contributes infinite value? Or if inspire others to lives of virtue and godliness so that they enter the kingdom of heaven, then haven't I done something that contributes infinite value?

Assertibility and Meaning (Take 2)

noreply@blogger.com (Alan Rhoda) — Sat, 20 Dec 2008 21:35:00 +0000

As I note in a comment on my previous post, I have a strong intuition that there should be some sort of systematic connection between assertibility-conditions and truth-conditions. The source of that intuition, I think, stems from the Principle of Charity, which states that, so long as it is contextually plausible to do so, one should try to interpret the statements a person makes in such a way that what they say would be rationally assertible for them. This is, I think, an essential heuristic principle of interpretation, one that connects the meaning that we impute to people's utterances to assertibility-conditions.

But it's not so easy to come up with a generalized statement of how assertibility-conditions bear on truth-conditions. There are several traps to avoid. Here are some:

We don't want assertibility to be a necessary condition for truth, since there can be truths that are not rationally assertible for anyone (except maybe God, but let's leave him out of this). For example, there is, presumably, a truth about how many times the last emperor of China sneezed, but I doubt that anyone is in a position to assert that the number of sneezes is equivalent to any particular number.
We don't want truth to be a necessary condition for assertibility, since there can be rationally assertible propositions that are false. For example, prior to Copernicus and Galileo, heliocentrism was rationally assertible, despite the fact that it turned out to be false.
We don't want to epistemicize truth or to equate it with warranted assertibility, at least not if we want to take a realist approach to metaphysics.

In my previous post, I tried this proposal:

(1) Whatever anyone must believe in order rationally to assert a proposition p is part of the meaning of p.

But as Rafal helpfully pointed out to me, this won't do. The most glaring problem, perhaps, is that there seem to be propositions that simply cannot be rationally denied, whether because they are obvious a priori truths (e.g., 1+1=2) or because denying them would land us in a performative contradiction (e.g., there are true sentences). Consequently, (1) yields the result that these propositions are part of the meaning of every proposition whatsoever. And that's just not plausible. So I went back to the drawing board and came up with a new proposal:

(2) Where q is a proposition that someone could rationally deny, if anyone must believe q in order rationally to assert p, then q is part of the meaning of p.

This gets around the problem by restricting the claim to propositions that someone could rationally deny. Rafal, however, raises two further problems. One concerns cases in which p is a proposition that cannot be rationally affirmed (e.g., 4+1=193). Given the standard semantics for counterfactuals, (2) would seem to imply that every proposition whatsoever is part of the meaning of 4+1=193. Fortunately, there is a simple revision of (2) that blocks these sorts of cases:

(3) Where q is a proposition that someone could rationally deny and p is a proposition that someone could rationally assert, if anyone must believe q in order rationally to assert p, then q is part of the meaning of p.

We're making progress toward a plausible principle, but we're not out of the woods yet, for Rafal has another counterexample, one that might rule out (3). Let p be "2+2=4". This is rationally assertible. Let q be "There are true mathematical statements". This is rationally deniable (or so mathematical fictionalists would have us think). It seems that one cannot rationally assert p without asserting q. Hence, by (3), we should conclude that q is part of the meaning of p. Yet, arguably, this is not so (at least, mathematical fictionalists would argue the point).

Now, I'm not quite sure what to make of this counterexample. I'm sufficiently skeptical of mathematical fictionalism, that I'm tempted to appeal to (3) as a reason for rejecting mathematical fictionalism. On the other hand, I don't know enough about the philosophy of mathematics to feel comfortable being so cavalier. Nor is it clear to me right now how to revise (3) in order to block this and similar counterexamples.

For the moment, then, I'm stuck. I'm not prepared yet to give up (3), but neither do I feel very certain that it's right.

Assertibility and Meaning

noreply@blogger.com (Alan Rhoda) — Thu, 18 Dec 2008 04:11:00 +0000

Thesis: Whatever anyone must believe in order rationally to assert a proposition p is part of the meaning of p.

Obvious case: One cannot rationally assert p unless one believes that p.

If the thesis is right, then it provides a test for whether a given proposition q is part of the meaning of p. In other words, it gives us a test for determining whether p semantically implies q.

Test: If you want to know whether q is part of the meaning of p, suppose that someone S does not believe q (or even believes not-q), and consider whether S could rationally assert p.

If "no", then q is part of the meaning of p.
If "yes", then q is not part of the meaning of p.

Example: Let's test whether the Peircean semantics for the future tense is correct. According to the Peircean, the future tense is intrinsically modal, and to assert that an event E "will" happen implies that the world is now tending strongly (probability > 0.5) toward E's happening.

Suppose, then, that S does not believe that the world is strongly tending toward E's happening. Indeed, suppose that S believes that E's happening is highly improbable. Could S believe that and, at the same time, rationally assert "E will happen"?

It seems clear to me that the correct answer is "no". Hence, it follows that the Peircean semantics for the future tense is correct.

To resist this argument, a proponent of an Ockhamist semantics for the future tense must reject my thesis. The Ockhamist believes that the future tense is not intrinsically modal. On his view, to say that E "will" happen implies nothing about its probability, save that it is non-zero. Rather, to say that E "will" happen is simply to say "E does happen subsequently", nothing more. Since I think my thesis is pretty plausible, I think it gives us a good reason for rejecting Ockhamism.

I wonder if anyone out there has an plausible counterexamples for my thesis.

A Cantorian Argument for Open Theism?

noreply@blogger.com (Alan Rhoda) — Thu, 11 Dec 2008 19:07:00 +0000

I'v just read an interesting paper on Enigman's website entitled "Omniscience and the Odyssey Theodicy". At one point in the paper, he employs Patrick Grim's well-known Cantorian argument against omniscience to argue for open theism over against an essentially epistemically static (EES) deity (my term, not his). The argument is intriguing.

According to set theory, anything can be a member of a set, including other sets. Hence, there can be no such thing as the set of all sets, for reasons pointed out by Cantor. Take any non-empty set (e.g., {1,2}) and form the set of all subsets (the power set) of the original (e.g., {{∅}, {1}, {2}, {1,2}}). That set will always have more members than the original set. And since this operation can be carried out for any set, there can be no such thing as the set of all sets.

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. In contrast, according to open theism God is not epistemically static. He can acquire new beliefs. Indeed, his knowledge is, as Enigman puts it, "indefinitely extensible". As a result, there are no higher-order set-theoretical truths that God cannot eventually come to know. And this constitutes an advantage for open theism. On neither account can God know all truths, but, unlike EES theism, open theism is compatible with the idea that there are no truths that God cannot come to know.

Now, I think this is a very interesting argument for open theism, one that I have not heard of or considered before. I'm not sure that it's sound in its present formulation, though, because I'm not sure that omniscience is best understood in a set-theoretical fashion.

I would suggest that omniscience, in its primary sense, is best construed as a kind of knowledge by acquaintance. On this view, "omniscient" means being fully acquainted with all that is, where "all that is" need not be conceived as a set of discrete constituents, but rather as a continuous field. Here's an analogy. Consider a continuous plane surface. On that surface one may analytically isolate or pick out individual points and lines. In so doing, one brings those points or lines to the foreground, so to speak, but only over against a background, the continuous surface. Since the surface is continuous, no analysis of it can bring all of it into the foreground. There are always more points one could identify, more lines one could draw, etc. If this is right, then an omniscient God's knowledge doesn't come in presliced propositional packets; rather, it exists as a plenum of intelligibility. (I take the term "plenum" from Richard Creel's book Divine Impassibility.) Any part of that plenum can be analyzed out of it as a proposition, but no set of propositions can exhaust the plenum.

Now, even if that way of thinking about omniscience is on the right track, it may still be possible for an Enigman-style argument in favor of open theism to get off the ground. For if the plenum cannot be exhaustively analyzed in propositional terms, then no deity can have exhaustive propositional knowledge. However, an EES deity, on the one hand, is permanently stuck with whatever propositional knowledge he starts out with, whereas an open theist deity's propositional knowledge is indefinitely extensible. There is no point at which he can bring the entirety of the plenum into the foreground, but at the same time there is no part of the plenum that cannot be brought into the foreground. Hence, even on this analysis of omniscience an open theist God turns out to have a higher-quality sort of omniscience than an EES God.

By the way, while I don't endorse Enigman's "Odyssey theodicy" I think that's a really cool name. Kudos to Enigman for a stimulating paper.

Tom Wolfe on Political Correctness

noreply@blogger.com (Alan Rhoda) — Wed, 19 Nov 2008 16:32:00 +0000

This is an insightful interview with author and sociologist Tom Wolfe. He discusses a variety of topics including political correctness, coed dorms, and feminism. The general theme is that many people and institutions today are too concerned with ephemeral goods like social status, and for the sake of them sacrifice timeless goods like courage, temperance, and intellectual integrity.

Concluding paragraph:

People in academia should start insisting on objective scholarship, insisting on it, relentlessly, driving the point home, ramming it down the gullets of the politically correct, making noise! naming names! citing egregious examples! showing contempt to the brink of brutality! The idea that a discipline should be devoted to “social justice” is ludicrous. The fashionable deconstructionist doctrine that there is no such thing as truth, only the self-serving manipulation of language, is worse than ludicrous. It is casuistry, laziness, and childishness in equal parts. Sociology in this country didn’t start with Max Weber. It started with an act of pious charity on the part of Protestants concerned about life in the slums. Today the discipline, if it can still be called that, has returned to sheer sentiment. Only this time the pious are from the puritanical order of political correctness, preying with the rhetoric of Rococo Marxism, which means steering clear of the by-now totally discredited “vulgar Marxism,” all that tired old business of the proletariat, the peasants, the capitalists, the bourgeois elements, the infantile leftists, since all they really care about is preserving Marxism’s greatest joy: the Manichaeistic take on life. Everything is light or darkness! Black or white! No irksome middle grounds or shades of grey! How much simpler the taxing stone-hard task of analysis becomes! He good! He bad! That’s the right idea!

(HT: Uncommon Descent)

Versions of Incompatibilism

noreply@blogger.com (Alan Rhoda) — Wed, 10 Sep 2008 23:59:00 +0000

In philosophical discussions, and especially in philosophy of religion, the term "incompatibilism" comes up in wide variety of contexts. I've discerned five different types of incompatibilism.

Moral incompatibilism: The thesis that human moral responsibility is incompatible with thoroughgoing causal determinism.
Ontic incompatibilism: The thesis that foreexistence is incompatible with future contingency. More precisely, the thesis that if a unique and complete sequence of future world states were to (tenselessly) exist, then the future would be causally determined.
Alethic incompatibilism: The thesis that foretruth is incompatible with future contingency. More precisely, the thesis that if the future could be fully and accurately described in terms of what either 'will' or 'will not' happen, then the future would be causally determined.
Epistemic incompatibilism: The thesis that infallible foreknowledge is incompatible with future contingency. More precisely, the thesis that if a perfect knower (like God) could exhaustively and infallibly know the future in terms of what either 'will' or 'will not' happen, then the future would be causally determined.
Providential incompatibilism: The thesis that foreordination is incompatible with future contingency. More precisely, the thesis that if a perfectly provident being (like God) were to efficaciously foreordain all of the details of the future, then the future would be causally determined.

There are, of course, complex debates surrounding each of these. I happen to be an incompatibilist in all five senses, but regardless of how these debates turn out, it is important to keep these issues distinct. Many thinkers are incompatibilists in some of these senses but compatibilists in others.

Incidentally, if moral incompatibilism (1) is true, then, given how I've defined (2)-(5), it follows that moral responsibility is incompatible with foreexistence, foretruth, foreknowledge, and foreordination.

Open Theism and the Test for a Prophet

noreply@blogger.com (Alan Rhoda) — Sun, 24 Aug 2008 23:29:00 +0000

During my year at Notre Dame's Center for Philosophy of Religion, I'm going to be working on a book-length research project on open theism, a relatively new proposal for understanding divine providence that has gotten a lot of discussion over the last 15 years, especially in philosophy of religion and evangelical theology circles.

Roughly stated, open theism holds that divine providence is neither wholly meticulous (as it is in Calivinism, Thomism, or Molinism) nor wholly general (as it is in process theism). In other words, God has not efficaciously decreed every particular thing that happens (contra Calvinism, etc.) but has efficaciously decreed some particulars (contra process theism).

The current debate about open theism centers on four key issues: (1) its fidelity to Scripture, (2) the significance of its differences from the mainstream theological tradition, (3) its ramifications for religious practice, and (4) its core philosophical presuppositions, esp. creation ex nihilo, creaturely libertarian freedom, and the incompatibility of meticulous providence with creaturely libertarian freedom.

In this post I want to briefly comment on one challenge, nicely posed by philosopher Francis Beckwith in an article entitled "Limited Omniscience and the Test for a Prophet". Beckwith charges that open theism, which he inaccurately supposes to entail the idea that God has "limited omniscience", is incompatible with the Biblical test for prophecy given in Deuteronomy 18:22:

If what a prophet proclaims in the name of the LORD does not take place or come true, that is a message the LORD has not spoken. That prophet has spoken presumptuously. Do not be afraid of him.

Based on this verse, Beckwith develops an argument that runs, in its essentials, thus:

Necessarily, if X speaks for God about the future, then X is correct.
If open theism is correct, then it is possible that X speak for God about the future and be mistaken.
Therefore, open theism is false.

This argument is clearly valid (that is, if the premises are both true, then the conclusion must also be true), but not, I think, sound (since it is not the case that both premises are true). The premise that I wish to challenge is the second one.

The rationale for premise (2) runs something like this: Proponents of open theism hold that creaturely free decisions cannot be infallibly known in advance. It is possible that the outcome of a prophecy depends upon creaturely free decisions. Therefore, it is possible that the outcome of a prophecy cannot be infallibly known in advance. Therefore, it is possible that God could inspire a prophet to declare categorically that some future event will happen and that event not happen.

This reasoning overlooks something, however. It overlooks the possibility that there might be some other necessary factor that would prevent God from inspiring any categorical prophecy that he couldn't be infallibly certain about. Plausibly, there is such a factor in God's essential nature, namely, God's concern for his own integrity. If so, then it is consistent with open theism to deny the possibility that a prophet might speak for God about the future and be mistaken on the grounds that, necessarily, if God couldn't be absolutely certain about the prophecy's coming true then he wouldn't have given the prophecy in the first place. With that, premise (2) fails.

All that I'm arguing right now is that the quick knock-down attempted by Beckwith is too quick. There is, of course, a lot more to be said on this issue, and it is not yet fully clear that open theism is consistent with everything the Bible has to say regarding prophecy. Further reflections, however, will have to wait for another time.

Can There Be a Self-Mover? Aquinas on Act and Potency

noreply@blogger.com (Alan Rhoda) — Sat, 16 Aug 2008 21:57:00 +0000

My family and I are now living in South Bend, Indiana. We survived the move well enough, though unfortunately some of our furniture didn't. (The movers wrecked the baby's crib, broke all four of our floor lamps, and lost a box containing three of wall pictures. Next time we go U-Haul.)

Anyway, my first blog post in a long time concerns Aquinas' distinction between act and potency. More specifically, I'm concerned with Aquinas' claim, central to the first two of his "Five Ways" of proving God's existence, that

(1) Whatever is moved is moved by something else.

If this is right, then there can be no self-movers. In the Summa Contra Gentiles Aquinas presents three arguments for (1). None of these strike me as particularly convincing, but I want to focus for a bit on the third argument, which appeals to the act/potency distinction. Basically, Aquinas argues as follows:

(2) Nothing can be both in act and in potency in the same respect at the same time.
(3) If there were a self-mover, then something would be both in act and in potency in the same respect at the same time.
Therefore,
(4) There cannot be a self-mover.
Therefore,
(1) Whatever is moved is moved by something else.

While I accept the validity of this argument, I am doubtful of its soundness because I find it very hard to come up with interpretations of 'act' and 'potency' that make both (2) and (3) true.

My first thought was that 'act' means actuality and 'potency' possibility, such that for something to be in potency with respect to property F is for it to be possibly F. On that reading, however, premise (2) is false. Since actuality implies possibility, it is perfectly possible - indeed necessary - that if X is actually F at time T then X is possibly F at time T.

My next thought was to make premise (2) true by defining 'potency' as possibly but not actually. The problem is that now (3) is false. To see this imagine a hypothetical situation in which a self-mover M can move either to the left or to the right. Initially, M is in 'potency' (as we have defined it) with respect to both options. That is, both options are possible for M, but neither is at yet actual for M. Now suppose that M moves itself to the left. In that case, M ceases to be in 'potency' with respect to either option and is in 'act' with respect with to going to the left. All this seems perfectly consistent, which falsifies (3). Why? Because the shift from being in 'potency' w.r.t. going to the left and being in 'act' w.r.t. going to the left is diachronic. M is never in 'act' and in 'potency' in the same respect at the same time. This indicates that it is possible for the antecedent of (3) to be true while its consequent is false, which is sufficient to show that (3) is not a necessary truth.

My final thought was to interpret 'act' and 'potency' in a causal sense of active and passive, respectively. This plausibly renders (2) true, though the proponent of self-motion might object that it begs the question. But my main worry again is that (3) is false. Why can't self-motion be understood in terms of acting at T1 so that M's future self is F at T2? Aquinas' argument against self-motion only works if a self-mover would have to be both in 'act' and in 'potency' in the same respect at the same time. But I just don't see why the 'act' / 'potency' relation can't be understood diachronically rather than synchronically. Indeed, shouldn't the very act of self-motion shift the temporal index forward? If so, then (3) is false and with it falls one of Aquinas' arguments in favor of (1).

Blogging to Resume in Mid-August

noreply@blogger.com (Alan Rhoda) — Thu, 17 Jul 2008 23:15:00 +0000

Some of my readers may be wondering why I haven't posted much lately. It's because for the past month and for the next few weeks to come, my wife and I have been swamped with the details of selling our house in Las Vegas, moving to South Bend, Indiana, and working to finalize the adoption of our daughter, Janelle.

Things are coming together. The movers arrive on 7/22 to get our stuff. Escrow signing and adoption finalization take place on 7/23. On the morning of the 24th, my dad, myself, and the two cats will embark on a long 1800-mile drive to South Bend. We're going to try to make it in two days. Once our stuff is moved in, we'll fly back to Vegas. After saying goodbyes to family and friends, my wife, my daughter, and myself will then be leaving Las Vegas for good on 8/4. We should arrive in South Bend as a family around 8/10.

Recent Discussion of Open Theism and Intelligent Design

noreply@blogger.com (Alan Rhoda) — Thu, 17 Jul 2008 23:06:00 +0000

Over at Bill Dembski's blog, Uncommon Descent, I recently got into an extended discussion on the relation of intelligent design and open theism (short answer - neither entails anything regarding the other). For those who might be interested, here's the link. (The initial comment on open theism that prompted my reply occurs near the end of the original post.)

More on Trumping: Reply to an Objection

noreply@blogger.com (Alan Rhoda) — Tue, 20 May 2008 23:08:00 +0000

A blogger named Brandon has criticized the argument of my previous post as follows:

What Rhoda calls "Trumping" is in fact simply a tendentious way of saying "correcting one's own reasoning on the basis of authority"; and the Trumper Rhoda particularly has in mind is someone who says that on matters where Scripture speaks plainly and "indubitably opposes our understanding" we should, in fact, correct our own reasoning on the basis of that authority.

Based on this interpretation of my position, Brandon then offers a counterexample:

Suppose that I am reasoning about quantum physics. The argument looks flawless to me. And someone I recognize as an authority on quantum physics hears me out and tells me that my argument, however clever, is wrong, and simply overlooks some key features of quantum physics, or confuses some key features with other things entirely, or what have you. We would normally say that it would be irrational for me not to correct my reasoning light of that authority, unless we had clear, positive reason for doing so -- i.e., clear, positive reason for thinking that either our authority has misunderstood our argument, or has put forward a view that we know to be rejected by many authorities on quantum physics, or some such.

In response, I would simply point out that the claim Brandon thinks I'm making (that one should never "correct one's reasoning on the basis of authority") is not what I argued for. When I called 'Trumping' is the practice of seizing upon some particular authority or claim, one that is not itself a deliverance of human reason or understanding, and refusing to submit that authority or claim to rational critique. In other words, the Trumper has a cherished theory or dogma of which he says, "I don't care where the evidence and the argument may go from here on out, I'm going to stick to my theory no matter what."

Perhaps it will help if I give a couple examples. First, here's a famous quote from Richard Lewontin:

We take the side of science in spite of the patent absurdity of some of its constructs, in spite of its failure to fulfill many of its extravagant promises of health and life, in spite of the tolerance of the scientific community for unsubstantiated just-so stories, because we have a prior commitment, a commitment to materialism. It is not that the methods and institutions of science somehow compel us to accept a material explanation of the phenomenal world, but, on the contrary, that we are forced by our a priori adherence to material causes to create an apparatus of investigation and a set of concepts that produce material explanations, no matter how counter-intuitive, no matter how mystifying to the uninitiated. Moreover, that materialism is absolute, for we cannot allow a Divine Foot in the door.

What Lewontin is saying here, basically, is that for him materialism is a Trump. So long as evidence and argument support materialism he'll consider it. But he refuses to allow any arguments to count against materialism.

Here's another example, one time from David Hume's famous essay on miracles:

There surely never was a greater number of miracles ascribed to one person than those that were recently said to have been performed in France on the tomb of Abbé Paris . . . . The curing of the sick, giving hearing to the deaf and sight to the blind, were everywhere talked of as the usual effects of that holy tomb. But what is more extraordinary is this: many of the miracles were immediately proved on the spot, before judges of unquestioned integrity, attested by witnesses of credit and distinction, at a time when learning flourished and on the most eminent platform in the world. Nor is this all. An account of them was published and dispersed everywhere; and the Jesuits, though a learned body supported by the civil magistrate, and determined enemies to the opinions in whose favour the miracles were said to have been performed, were never able clearly to refute or expose them. Where shall we find such a number of circumstances converging in the corroboration of one fact? And what have we to oppose to such a cloud of witnesses but the absolute impossibility or miraculous nature of the events that they relate?

In the context Hume has been considering the possibility that a miracle might be sufficiently well-attested to justify belief that it had occurred. Here he relates a "best-case scenario" from history. But Hume doesn't want to admit that any miracle could be sufficiently well-attested and so he summarily brushes aside the evidence he has just presented against his position by whipping out a Trump - in this case, his commitment to the "absolute impossibility" of the miraculous.

In summary, I do not deny that authority may correct our thinking. What I reject as a fallacy is the practice of treating an authority or claim as though it were absolutely immune to rational critique.

In addition, it seems to me that Brandon is falsely opposing "authority" and "reason". When I reason, I do on the basis of evidence, of which there different types - empirical, intuitive, and testimonial. An authority is simply a good source of evidence. Thus, in Brandon's example, the physicist is an authority for me because he is, presumably, a very good source of testimonial evidence regarding matters physical. In correcting my thinking he's not giving me evidence over and against my reason. Rather, he's helping me to reason things out more adequately by improving my pool of evidence.

I'll close with a quote from Bill Vallicella:

Someone who plays a trump card is not "correcting his understanding" but seeking to put a stop to inquiry.

Suppose I don't know much about a certain subject-matter and so consult an expert about it. Then it is reasonable for me to accept his authority and "correct my understanding" assuming it needs correcting. And it is unreasonable for me to "argue with" the expert when he is speaking from his expertise. But when I accept the authority of a medical doctor, say, I don't accept the authority on the basis of his mere say-so, but on the basis of the fact that in principle it is possible for me to follow the rational and empirical considerations that ultimately warrant his dictum.

But it is different in the case of one who plays a trump card by, say, pointing to a Bible passage. "Look! Right here it says that Eve was created from a rib of Adam! That settles the question." Well, no it doesn't. For it is reasonable to ask: how is the Bible to be interpreted, and by whom? A Catholic might say: the magisterium decides. But then surely it is reasonable to ask: whence its authority? Inspired by the Holy Spirit? Could be, but how do you know? Are the Eastern Orthodox and the Protestants also sometimes so inspired? Or never? And if never, why not? And so on.

The Theologian's Fallacy

noreply@blogger.com (Alan Rhoda) — Fri, 16 May 2008 23:06:00 +0000

In his contribution to a recent book, Perspectives on the Doctrine of God (Bruce A. Ware, ed.), Paul Helm leads off with an epigraph from Anselm (the exact source is not given):

But if Scripture indubitably opposes our understanding, even though our reasoning appears to us to be impregnable, still it ought not to be believed to be substantiated by any truth at all. It is when Sacred Scripture either clearly affirms or in no way denies it, that it gives support to the authority of any reasoned conclusion.

In other words, what Anselm is saying is that the authority of the Bible always trumps human reason when the two come into conflict. Helm clearly approves of this sentiment, as do many other theologians who want to defend cherished doctrines (in Helm's case, theological determinism) against external critique. My concerns, however, are broader than the question of Biblical authority. I'm interested here in the general practice of appealing to some allegedly absolute authority - whether that be the Bible, the Koran, the Vedas, the Magisterium of the Roman Catholic Church, the Mormon's revelation knowledge (i.e., "burning in the bosom"), or what have you - as a "trump card" for defeating rational objections.

It is my view that this practice, which I will dub the "Theologian's Fallacy", is rationally indefensible. (I give it that name because, in my experience at least, theologians seem to like to whip out these sorts of trump cards with considerable frequency, especially when they feel that what they regard as their intellectual turf is under external challenge from science, philosophy, or even common sense.)

What's wrong with this practice? I'll answer that by addressing some questions to a generic practitioner of this fallacy whom I'll call a "Trumper".

Question #1: Do you place ultimate value on the truth?

The typical Trumper will confidently answer 'yes' to this question. Why? Because the Trumper believes that his favorite Trump (the Bible, the Koran, etc.) is or contains absolute and infallible Truth (with a capital 'T') of a vitally important sort. Moreover, the Trumper is prepared to submit to that Trump over and against, if necessary, the most secure deliverances of human reason. This he takes as evidence of his intellectual humility and sincerity, of his preparedness to sacrifice all for the Truth. Conversely, the Trumper sees external critics of the Trump either as ignorant children who need to be taught or as malicious rebels vainly raging against the admantine Truth with the feeble sticks of human reason.

Question #2: Do you place ultimate value on your Trump?

Again, the typical Trumper will answer with a confident 'yes'. After all, in the Trumper's mind, the Trump is or contains absolute and infallible Truth of a vitally important sort.

Question #3: Is it possible that you could be mistaken about your Trump, concerning its status as a source of absolute and infallible Truth?

At this point the Trumper is caught in a bind. On the one hand, his own aspirations to intellectual humility encourage him to answer with a 'yes'. Human fallibility is too familiar for us to dismiss such possibilities out of hand. On the other hand, the Trumper's preparedness to use his Trump as a Trump, if necessary against even the best that human reason and inquiry can muster, requires him to say 'no'. After all, once a person genuinely admits that it is possible for him to be mistaken about a Trump, it ceases to function for him as a Trump. But how could one honestly answer 'no' to this question without committing the sin of intellectual pride? There is a way - the Trump must be self-authenticating in the highest possible degree, such that its status as Truth is at least as obvious (to those who are sufficiently prepared) than the most secure deliverances of human reason and inquiry. This leads us to our final question:

Question #4: Can you honestly maintain that your Trump is self-authenticating in the highest possible degree?

Unless one's Trump is something on the level of the Cartesian cogito, like a simple conceptual truth (e.g., "All triangles have 3 sides") or a simple introspective report (e.g., "I am in pain right now"), to answer with anything other than a blunt 'no' would seem a breathtaking display of nerve. Furthermore, if one's Trump is self-authenticating in the highest possible degree, then one would expect it should be accessible to human reason and inquiry, just like the cogito and simple conceptual truths are. In that case, of course, it can no longer be used as a Trump over and against human reason and inquiry. Still, some incorrigible Trumpers will have the temerity to answer 'yes' to this question. Such people are, I think, beyond hope of rational engagement. But those who still have a robust sense of reality, of their own finitude and fallibility, will look at their prospective Trump (the Bible, say) and realize that they are not in fact more or even equally confident of its Trump-worthiness than they are certain of the best deliverances of human reason. And if they realize that, then they should realize that they are no longer in a position to use it as a Trump.

In closing, I say to any of my readers who are inclined to commit the Theologian's Fallacy and appeal to the Bible, Koran, Vedas, Book of Mormon, Communist Manifesto, Magic 8-ball, or what have you, as a Trump to defeat external criticisms to your pet theories, knock it off! If you really have the Truth that you think you do, then you can and should be able to meet the criticisms head on without whipping out a Trump card.

Conference Highlights

noreply@blogger.com (Alan Rhoda) — Mon, 14 Apr 2008 23:11:00 +0000

Just got back from the Open Theology and Science conference held April 10-12, 2008 at Asuza Pacific University.

It was quite a fun conference. My wife and baby daughter accompanied me, and we all had a good time. Baby Janelle was a big hit with the other participants. Unfortunately, one of the presenters, Bill Hasker, was not able to make the conference due to the whole airline grounding fiasco.

The conference opened with a plenary session by Francis Collins, head of the human genome project. He had a lot of good things to say about the integration of religion and science and even closed his talk by whipping out his acoustic guitar and leading the audience (about 300 people) in signing a hymn, "God of Faith and Learning".

I have two points of critique regarding what Collins said. First, he conflates the notion of common descent (for which he gave some rather impressive evidence) with naturalistic evolution, the idea that the historical process of descent that has given rise to the "tree of life" has involved no non-natural causes. The evidence for the latter thesis is scant and much less impressive. Second, his criticism of Intelligent Design invoked the standard “cooption” response to Behe's irreducible complexity argument. What Collins does not seem to realize is that this response in not even close to being a refutation of ID. That the bacterial flagellum “might” have been cobbled together from existing molecular components does not show that such a scenario is even remotely plausible.

The following morning, things got underway with a devotional from local pastor T. Scott Daniels of the Pasadena Nazarene Church (he called it "Paz Naz" for short). His talk was entitled "Waiting for the Church to Open". He told of a homeless woman who, despite the assistance they've tried to give her, always waits outside for the doors of the church to open so. When they do, she partakes of the free coffee and refreshments inside and attends the service. Daniels related this to the position of many open theists, who often feel rather "homeless" in the modern American church scene. Often suspected (wrongly, I submit) of heresy, some have found themselves booted out of or ostracized from the fellowship of other Christians. The analogy certainly resonated with a number of people at the conference, myself included.

I'll spare a detailed recounting of each of the presentations I heard. All of them were interesting, and everyone at the conference was exceeding nice. One thing I particularly enjoyed was the opportunity to hang out with the likes of Robin Collins, Dean Zimmerman, Greg Boyd, and Patrick Todd (a grad student at UC Riverside whom I've interacted with by email but had never met face-to-face).

My own presentation on "The Fourfold Openness of the Future" went quite well. I had a good discussion with the above-mentioned folks, as well as Alan Padgett. I've still got to iron out some kinks in my argument. When I get in polished a bit, I'll post it here.

The final evening all of us involved with the conference went over to Karen Winslow's house (she's an Old Testament scholar at Azusa Pacific) where we ate dinner and hung out discussing things like the problem of evil, the metaphysics of time, and South Park until late in the evening. Sunday morning, my wife and I went to the Winslow's church (Karen's husband, Dale, pastors a Free Methodist church a couple blocks from Azusa Pacific). I had never been to a Free Methodist service before. It was nice. The people there were very friendly.