Mystery and religion

Given what we have learned from science and philosophy, fundamental aspects of the world are mysterious and verge on contradiction: photons are waves and particles; light from the headlamp on a fast train goes at the same speed relative to the train and relative to the ground; objects persist while changing; we should not murder but we should redirect trolleys; etc. Basically, when we think deeper, things start looking strange, and that’s not a sign of us going right. There are two explanations of this, both of which are likely a part of the truth: reality is strange and our minds are weak.

It seems not unreasonable to expect that if there were a definitive revelation of God, that revelation would also be mysterious and verge on contradiction. Of the three great monotheistic religions, Christianity with the mystery of the Trinity is the one that fits best with this expectation. At the same time, I doubt that this provides much of an argument for Christianity. For while it is not unreasonable to expect that God’s revelation would be paradoxical, it is a priori a serious possibility that God’s revelation might be so limited that what was revealed would not be paradoxical. And it would also be a priori a serious possibility that while creation is paradoxical, God is not, though this last option is a posteriori unlikely given what we learn from the mystical experience traditions found in all the three monotheistic religions.

So, I am not convinced that there is a strong argument for Christianity and against the other two great monotheistic religions on the grounds that Christianity is more mysterious. But at least there is no argument against Christianity on the basis of its embodying mysteries.

Three levels of theological models

There are three kinds of metaphysical models of a theological mystery—say, Trinity, Incarnation or Transubstantiation:

• realistic model: a metaphysical story that is meant to be a true account of what makes the mysterious doctrine be true

• potential model: a metaphysical story that is meant to be an epistemically possible account of what makes the mysterious doctrine be true

• analogical model: a story that is meant to be an epistemically possible account of what makes something analogous to the mysterious doctrine be true.

For instance, Aquinas’s accounts of the Trinity, Incarnation and Transubstantiation are realistic models: they are meant to be accounts of what indeed makes the doctrines true. Van Inwagen’s relative identity account of the Trinity or his body-snatching account of the resurrection, on the other hand, are only potential models: van Inwagen does not affirm they are true. And the history of the Church is filled with analogical models.

A crucial test of any of these models is this: Imagine that you believe the story to be true, and see if the traditional things that one says about the mystery (in the case of a realistic or potential model), or analogues of them (in the case of an analogical model), sound like reasonable things to say given what one believes.

For instance, consider a time-travel model of the Incarnation. Alice, currently a successful ultramarathoner and brilliant geologist, will live a long and fruitful life. Near the end of her life, she has lost most of her physical and mental powers, and all her knowledge of geology. She uses a time machine to go back to 2020 when she is in her prime. If we thought this story was true, it would be reasonable to find ourselves saying things like:

• Alice is a successful ultramarathoner and barely able to walk

• Alice understands continental drift and does not not know what magma is

• Alice is young and old

• Alice is in the pink of health and dying.

These things would sound like a contradiction, but the time-travel story shows they are not. However, these claims are also analogous to claims that constitute an especially mysterious part of the mystery of the Incarnation (and I suppose a mysterious part of a mystery is itself a mystery): Christ suffers and is impassible; Christ is omniscient and does not know everything; Christ is timeless and born around 4 BC.

Of course nobody should think that it’s literally true that the Incarnation is to be accounted for in terms of time travel. But what the analogical model does show is that there are contexts in which it is reasonable to describe a non-contradictory reality in terms that are very similar to the apparently contradictory incarnational claims.

Change, time and contradiction

According to Aristote:

1. Time is the measure of change.

2. The law of non-contradiction says that a thing cannot have and lack the same property in the same respect at the same time.

The law of non-contradiction seems to be the fundamental basis of logic. Yet it presupposes the concept of time, which in turn presupposes that of change. Thus, it seems, for Aristotle, the concept of change is more fundamental than logic itself. That doesn’t seem very plausible to me.

But perhaps there is a different way to understand the “at the same time” qualifier in (2). Sometimes, we give a rule with something we call an exception, but it’s not really an exception. For instance, we could say: “It is an offense to lie to an officer of the law, except unintentionally.” Of course, there is no such thing as an unintentional lie, but it is useful to emphasize that unintentional falsehoods are not forbidden by the rule.

Now, Aristotle is, as far as I know, a presentist. On presentism, the only properties a thing has are its present properties, and it lacks precisely those properties it doesn’t presently have. So it’s not really possible for an object to have and lack the same property, since the having and lacking would have to be both present, and hence at the same time. But it is useful to emphasize that having the same property at one time and lacking it another is not forbidden by the law of non-contradiction, and hence the logically unnecessary qualifier “at the same time”. Strictly speaking, I think “in the same respect” isn’t needed, either.

The Incarnation and timelessness

Consider the standard argument against the Incarnation:

1. Everything that is God is F (omnipotent, omniscient, impassible, etc.).

2. Everything that is human is non-F.

3. Christ is God and human.

4. So, Christ is F and non-F.

5. Contradiction!

But it is only a contradiction to be F and non-F at the same time: we’ve known this since Aristotle.
Thus the kenotic theologian gets out of the argument by holding that Christ was F prior to the Incarnation and wasn’t F after the Incarnation. (A difficult question for the kenoticist: is he now F?) But that’s contrary to the teaching of the Councils.

However, the “at the same time” observation does not need to lead to kenoticism. In fact, the Christian who is a classical theist should deny that Christ is F and non-F at the same time. For it is strictly false to say that Christ is F at t for any divine attribute F and any time time t, since God has the divine attributes timelessly rather than at a time.

This is not kenoticism. Rather, the view is that Christ is F timelessly eternally and non-F at t (for any t after the beginning of the Incarnation). Kenoticism on this view is metaphysically absurd, because God cannot cease to be F: one can only cease to be something that one used to be, and there is no “used to be” where there is no temporality.

But we sometimes say things like:

• While he was suffering on the cross, Christ was upholding the existence of the universe.

I think there are two ways of make sense of such statements. First, maybe, things that happen timelessly count honorifically as holding at all times. (Compare David Lewis’s idea that abstract objects count as existing in all his worlds.) Second, the statement can be understood as follows:

• While he was suffering on the cross, the following proposition was true: Christ is upholding the existence of the universe.

So, orthodox Christians do not actually need to talk of natures to get out of (1)-(5). Of course, if we want to allow—as I think we should—for the logical possibility of multiple simultaneous incarnations, then the temporal qualification way out won’t help. (Nor will the kenotic solution help in that case, either.)

Note, by the way, that once we realize that there can be timelessly eternal existence, we need to modify Aristotle’s temporal qualification to the law of non-contradiction:

• it is impossible to be F and non-F in the same respect at the same time or both eternally.

Finitism and mathematics

Finitists say that it is impossible to actually have an infinite number of things. Now, either it is logically contradictory that there is an infinite number of things or not. If it is not logically contradictory, then the finitist's absurdity-based arguments are seriously weakened. If it is logically contradictory, on the other hand, then standard mathematics is contradictory, since standard mathematics can prove that there are infinitely many things (e.g., primes). But from the contradictory everything follows ("explosion", logicians call it). So in standard mathematics everything is true, and standard mathematics breaks down.

I suppose the finitist's best bet is to say that an infinite number of things is not logically contradictory, but metaphysically impossible. That requires a careful toning down of some of the arguments for finitism, though.

Hiddleston's review of Actuality, Possibility, and Worlds

NDPR has a review of my Actuality, Possibility, and Worlds by Eric Hiddleston.  I think it's quite a helpful review--the concerns about my account are powerful and interesting.

This post is a very rough bunch of responses to Hiddleston, and will not be comprehensible without reading his review.

I am inclined to endorse some version of the "externalist" way out that Hiddleston gives.  I think this will damage at least one of my arguments against Platonism, the one that says that opponents of Platonism are "horribly confused" if Platonism is true. But Hiddleston is right that that's a bad argument.

I think Hiddleston doesn't give enough credit to my dogs argument against Platonism.  There, I am imagining that the Platonist heaven is augmented with the necessity of there being no dogs, but all earthly stuff is unchanged.  I claim in the book that nonetheless dogs would remain possible.  My line of thought behind that was that dogs would remain possible, because they would remain actual, and the actual is possible, no matter what the Platonist heaven says.  I think Hiddleston's Little-P = Big-P position doesn't help here.

(It occurs to me, by the way, that the Platonist could have a theory that escapes my dogs argument as it stands in the book. Here's the theory. The primitive property is mere possibility. Possibility is then defined in terms of mere possibility: a proposition is possible provided that it is either true or merely possible. But I think this version still has a problem. The original Platonic version has the puzzle of why it is that actuality implies possibility. This version doesn't have that problem. Instead it has the problem of why it is that that mere possibility implies non-actuality.)

Hiddleston also worries a lot about Euthyphro-type questions, like:

• (E1) Why should God be incapable of bringing about really impossible propositions, such as contradictory ones?
• (E2) Why should God be capable of bringing about really possible propositions?

I think there is a neat counter to the "contradictory ones" part of E1 that favors my view over other views. The following seems true to me:

1. If, per impossibile, God or any other agent were capable of bringing about a contradictory proposition, that proposition would be possible.

This suggests to me that what agents can bring about is actually more fundamental than what is contradictory. Notice that the plausibility of (1) highlights a difference between my view and divine command theory. In the case of divine command theory, the following seems false:

2. If, per impossibile, God were to command a horrendous deed, that horrendous deed would be obligatory.

(But see this paper of mine for a more detailed discussion of whether (2) is a good objection to divine command theory.)

I do think Hiddleston's question about what explains why God can do contradictory things is a good and difficult question, but I don't think they're quite species of the Euthyphro problem. I think I can say that there just does not exist any being with the power to bring about contradictory propositions. This is in need of no more grounding than the fact that there are no unicorns--it's just a negative existential. Is it in need of an explanation? My official line on the PSR restricts it to contingent truths. But maybe there still is an explanation of it in terms of some deep facts about the divine nature (maybe its beauty, say). Maybe Hiddleston's best bet here would be to push me in a way that Josh Rasmussen has done: I can't explain why God can't create square circles, just as the Platonist can't explain why everything that's actual is also possible, and so I don't have an advantage over the Platonist here. I don't know exactly what to say here, but I think one difference is with regard to per impossibile counterfactuals.

3. If dogs existed but the Platonic heaven didn't say that they were possible, dogs would still be possible.
4. If God were capable of creating a square circle, square circles would be possible.

I think (4) favors my view and (3) disfavors Platonism. But I am not happy to hang too much on per impossibile counterfactuals.

As for (E2), I don't feel the force of that. First of all, the primary view doesn't mention God: it's quantified over all agents. So the modified question is:

• (E2b) Why should every really possible proposition be such that there is an agent who can bring it about (or, more precisely, bring about a chain of causes leading to it)?

I don't feel much intuitive force to this question. Maybe I've just been thinking along the lines of my view for too long. I am tempted to say that the question is exactly like: "Why should every sample of water contain hydrogen atoms?" That's what Hiddleston labels the externalist way out, so I guess I am with him on that, and I wish I was explicit about that in the book.

"p and I don't believe that p"

A number of folks seem to think that there is some innate "pragmatic contradiction" in assertions of the form: "p and I don't believe that p". Certainly, whenever I've heard these Moorean sentences mentioned, the mentioner assumed this. Yet, there are counterexamples to the "pragmatic contradiction" thesis. And this fact seems to be pretty well-known to people in the relevant field. I mentioned that I had some counterexamples to an ethicist and he found it surprising and interesting. But I then mentioned it to some epistemologists, and they were quite unimpressed. So, here, we have a case where inter-area communication in philosophy has failed: the people in the relevant area know that a thesis is false, while folks in other areas act as if the thesis were uncontroversially true.

For what it's worth, here are some of my counterexamples to the thesis. These counterexamples provide cases where one quite sincerely and unproblematically utters an instance of "p and I don't believe that p". Nobody I've met finds all the examples compelling. In all the examples below, "p" is a sentence and the quotation marks are meant to be right-angle quotes so one can substitute within them.

1. An expert tells me "p" and adds that ordinary people like me don't believe that p. But "p" is a sentence so replete with technical vocabulary that not only do I not know what all the words mean, I cannot even parse its grammar. I sincerely tell someone else: "p and I don't believe that p". In this case, I believe that "p" is true, but I don't believe that p. There are two responses I hear to cases like this. Some people say that the distinction between believing that p and believing that "p" is true is specious, and hence the sentence embodies a pragmatic contradiction. These people have a very low bar for what counts as belief and assertion. They will have to accept the next counterexample. Others say that the sentence is not an assertion if I don't understand it. I worry that this sets the bar for assertions too high. These folks may reject the next example for the same reason, but some of the others might still work for them.

2. An expert tells me: "p and you don't believe that p. Work out the consequences for yourself." I'm not very good at logic, so I have to do this step by step. I thus say: "p and I don't believe that p. By conjunction elimination, p. Hey, that's cool! I didn't know that p, and now I do."

3. Suppose I believe that one has no beliefs when one is in the afterlife, because the afterlife is an undifferentiated beliefless mist of joy. I write you a letter to be opened after my death. In the letter I say: "p. And I don't believe that p. I don't believe it, because right now I am an undifferentiated beliefless mist of joy. Therefore: p and I don't believe that p."

4. I write a paper. I think everything in the paper is true. I present the paper at a conference. When I present it, I am really tired. I am reading the sentences outloud, and sincerely, but I cannot parse all of them, nor do I believe their content. Some of the sentences are intermediate steps in the argument, and I've completely forgotten them (or I never believed them in the first place, though I believed them to be true; sometimes, I write down things in the course of a proof by copying and pasting an existing sentence and transforming it by rules of inference—that's just a matter of syntactic manipulation—without bothering to figure out what the new sentence means). But I still believe that whatever I am saying is true. One of the sentences is "p". So I read the sentence: "p". I then add, surprised at myself: "You know: p and I don't believe that p. I don't believe it because it's too complex to parse, and I remember that this is one of those steps that I've forgotten completely."

5. I program a robot to bring you a drink whenever I say to you: "I don't believe that the robot will bring you the drink, and the robot will bring you the drink" (this example works better with the Moore sentence re-ordered in this way). Now, you keep on interrupting me, never letting me say a whole sentence. I say the sentence sincerely; I don't believe that I will finish the sentence, and hence I don't believe the robot will bring you the drink, but the sentence is so constructed that if I do manage to say it, it'll be true, and that's all that sincerity requires.

6. I'm deaf and have been learning out how to vocalize. I do not believe I can do so yet. I know you're standing somewhere where you can't see my lips and I can't see your reactions. I say to you: "I can speak and I don't believe I can speak." I can say this sincerely, because although it's true that I don't believe I can speak, I also know that if I do succeed in saying it, it is true.

7. I have a mental inertia on which once I form the intention to do an action such as saying a sentence, often I am unable to stop even if I change my mind prior to beginning the action. (Unlike in #6, this is actually the case for me.) So, while the sentence is proceeding from my mouth, it need no longer be true that I have any intention of saying it—though I had to have had that intention. Suppose that I know that as soon as I fully form the intention to speak, Fred will (e.g., by neural manipulation) bring it about that I do not believe that p. So, right now I believe that p, but I know that at the time of utterance I won't. I say: "p but I do not believe that p." This example rests on taking the present tense in a sentence to refer to the time of utterance, not the time of deliberating whether to speak. I think this is correct: think of sentences like "It's 12 o'clock", which you utter while watching the clock—you time yourself to begin to speak so that the clock strikes 12 while you're speaking (or maybe at the very end; Richard Gale has an argument that "now" refers to the time at the end of a sentence, by reference to sports announcers who say things like "He's got the ball, no Jones has now taken it from him, but, wait, no, now he's got it back!")