A violation of the Principle of Sufficient Reason?

I have a number of times over my career claimed that in the ordinary course of life, we don’t take seriously the hypothesis that something we can’t find an explanation for has no explanation.

Well, I now had an opportunity for observing what happens psychologically to me when I can’t find an explanation.

A couple of days ago, my wife found a significant pool of water in the morning on the top surface of our clothes dryer. When I looked at it, it was like 250ml or more. If it were on the floor or on the washer, I would expect it was from a washer-related leak. If our clothes dryer had a water connection for steaming clothes, a leak would make sense (ChatGPT 3.5 suggested this hypothesis). If the quantity were lower, it could easily be from wet clothes put carelessly on top of the dryer or condensation. If there was wetness in the cabinets above the dryer, it would likely be a leak in one of the many containers of cleaning, photo-developing and other chemicals stored there. If the ceiling showed a discoloration above the dryer, it would be a leak from upstairs. If the liquid smelled, it might be urine from the cat sneaking in.

But none of these apply, to the point where my best four explanations are all hard to believe:

1. a family member sleepwalking with a glass of water, wandering into the laundry room, spilling the water, and walking away,

2. God doing a miracle just to impress on me that there are more things in heaven and earth than are dreamed of in my natural philosophy,

3. a very precisely aimed horizontal leak from one of the faucets in the room, none of which are above the dryer (the next morning, there were slight leaks in two faucets in the room, but the leaks were a non-directional wetness rather than a jet aimed at a precise target).

4. a family member spilling water (from what?) on the dryer and forgetting all about it.

(A plumber called in for the faucet leaks could think of no explanation, except to note that there are many plumbing problems given our current Texas freeze.)

What is my psychology about this? I can’t get myself to believe any of (a)–(d), or even their disjunction. I find myself strongly pulled to just forget the event, to pretend to myself that the event was but a dream, and it now seems to me that that is one way in which we cope with unexplained events. But of course my wife remembers the event, and I can’t get myself to take seriously the idea that we both had the same dream (plus there was no waking up after it—after we cleaned up the spill, I launched into other activities rather than finding myself back in bed).

What about this option?

5. The event has an explanation: it violates the Principle of Sufficient Reason.

I also can’t take (e) seriously. But do I take (e) less seriously than the options in (a)–(d)? Speaking of subjective feelings, I don’t think I feel much more incredulous about (e) than about (a)–(d).

So what do I really think? I guess:

6. There is a mundane explanation and I am not smart enough to think of it.

Comparing the resurrection rate of humans to the resurrection mendacity rate

Hume argues against miracles by means of his balancing principle:

• (HBP) You should believe p on the basis of testimony only if p is at least as probable as the falsity of the testimony.

There are two interpretations of HBP, depending on whether “probable” refers to the prior probabilities (the probabilities before the evidence of the testimony is accounted for) or posterior ones (the probabilities after the evidence has been weighed). On the posterior interpretation, HBP is almost completely obvious (at least if the “should” is that of epistemic normativity). On the prior interpretation, HBP is well-known to be false: the standard counterexample is that it’s reasonable to believe that you won the lottery on the basis of a newspaper report of the winner even if the chance of a newspaper error exceeds your chance of winning the lottery.

I think the prior interpretation fits Hume’s text better, even if it’s bad epistemology.

In this post I want to suggest that there could be reasonable assignments of priors for a theist on which the prior probability of the falsity of the testimony is less than the prior probability of the miracle.

Assume we are theists. Take the resurrection of Jesus. First, let’s say something about the prior probability of the resurrection of a human. Given theism, there is a good God, and it wouldn’t be surprising at all if there were resurrections. In fact, we might expect it from a loving God. But how often would they happen? What is the resurrection rate in human beings? Well, here we need to turn to empirical data. Let’s grant Hume that apart from the case under examination, there are no resurrections. There have been approximately a hundred billion human deaths, so we have an upper bound on the resurrection rate of less than one in 10¹¹. It’s not unreasonable, I think, given the moderate prior probability that someone would be resurrected, and the lack of resurrections in 10¹¹ cases, to suppose the probability of a particular person getting resurrected would be something like (1/2) ⋅ 10⁻¹¹.

But what is the probability of false testimony? Well, as an initial back of the envelope calculation, suppose we have 11 witnesses, and each has an independent 1/20 chance of lying or being mistaken that Jesus was resurrected. So, the chance that they all lied or were mistaken would be (1/20)¹¹ or (1/2048) ⋅ 10⁻¹¹.

With these numbers, the prior probability of Jesus getting resurrected is about 100 times bigger than the prior probability of the 11 witnesses lying that he was resurrected. And so even in its prior probability formulation, HBP doesn’t destroy the testimony to the miracle.

Of course the numbers are made up. Probably the main problem has to do with the assumption of the independence of the witnesses. But that problem is to some degree balanced by the fact that 1/20 is way too high for a probability of lying or being mistaken that they witnessed a resurrection. (What percentage of the people you know testified to witnessing a resurrection?)

In any case, I think the above shows that it is far from clear that, assuming theism, a reasonable estimate of the resurrection rate of humans would be lower than a reasonable estimate of the resurrection mendacity rate for groups of 11 people.

Now what if we don’t assume theism, but assume, say, a 1/10 chance of theism? Well, that approximately cuts our estimate of the resurrection rate of humans by a factor of 10. But that’s still not enough to make it clear that the resurrection rate of humans is less than the resurrection mendacity rate for groups of 11.

More on Newtonian velocity

Here is a big picture story about Newtonian mechanics: The state of the system at all times t > t₀ is explained by the initial conditions of the system at t₀ and the prevalent forces.

But what are the initial conditions? They include position and velocity. But now here is a problem. The standard definition of velocity is that it is the time-derivative of position. But the time-derivative of position at t₀ logically depends not just on the position at t₀ but also on the position at nearby times earlier and later than t₀. That means that the evolution of the system at times t > t₀ is explained by data that includes information on the state of the system at times later than t₀. This seems explanatorily circular and unacceptable.

There is an easy mathematical fix for this. Instead of defining the velocity as the time-derivative position, we define the velocity as the left time-derivative of position: v(t)=lim_{h → 0−}(x(t + h)−x(t))/h. Now the initial conditions at t₀ logically depend only on what happens at t₀ and at earlier times.

This fixed Newtonian story still has a serious problem. Suppose that the system is created at time t₀ so there are no earlier times. The time-derivative at t₀ is then undefined, there is no velocity at t₀, and Newtonian evolution cannot be explained any more.

Here’s another, more abstruse, problem with the fixed Newtonian story. Suppose I am in a region of space with no forces, and I have been sitting for an hour preceding noon in the same place. Then at noon God teleports me two meters to the right along the x-axis, so that at all times before noon my position is x₀ and at noon it is x₀ + 2. Suppose, further, that the teleportation is the only miracle God does. God doesn’t change any other properties of me besides position, and God lets nature take over at all times after noon.

What will happen to me after noon? Well, on the fixed Newtonian story, my velocity at noon is the left-derivative of position, i.e., lim_{h → 0−}(2 − 0)/(0 − h)= + ∞. Since there are no prevailing forces, my acceleration is zero, and so my velocity stays unchanged. Hence, at all times after noon, I have infinite velocity along the x-axis, and so at all times after noon I end up at distance infinity from where I was—which seems to make no sense at all!

So the left-derivative fix of the Newtonian story doesn’t seem right, either, at least in this miracle case.

My preference to both the original Newtonian story and the fixed story is to take velocity (or perhaps momentum) to be a fundamental physical quantity that is not defined as the derivative, or even left derivative, of position.

The rest is technicalities. Maybe we could now take Newton’s Second Law to be:

1. ∂_t⁺v(t)=F/m,

where ∂_t⁺ is the right (!) time-derivative, and add two new laws of nature:

2. ∂_t⁺x(t)=v(t), and

3. x(t) and v(t) are both left (!) continuous.

Now, (2) is an explicit law of nature about the interaction of velocity and position rather than a definition of velocity. On this picture, here’s what happens in the teleportation case. Before noon, my velocity is zero and my position is x₀. Because I supposed that the only thing that God miraculously affects is my position, my velocity is still zero at noon, even though my position is now x₀ + 2. And I think (by the answer to this), laws (1), (2) and (3) ensure that if there are no further miracles, I remain at x₀ + 2 in the absence of external forces. The miraculous teleportation violates (2) and (3) at noon and at no other times.

But of course this is all on the false premise of Newtonian mechanics.

Causation and Thomism

Assume a Thomistic metaphysics, including the primary/secondary causation model from Aquinas. Thus, whenever a created cause has an effect, it has the effect it does only because God, through primary causation, cooperates with the created cause. If God did not cooperate with the created cause, the creature’s secondary causal power would be impotent to produce the effect. On the other hand, God can directly cause something by primary causation without the secondary causes doing anything.

Suppose that I strike a match, but God doesn’t cooperate in the frictional causing of fire. Then the match is struck, and does everything a struck match does, except that no fire results. Now imagine these two scenarios:

1. I strike a match which, in the ordinary way and with God’s cooperation, causes fire.

2. I strike a match, but God does not cooperate with me; however, God miraculously causes a fire just like the one in (1).

These two scenarios are different. So they must differ in something. They cannot differ in God, since that would violate divine simplicity, a core commitment of Thomistic metaphysics. So they must differ on the side of creatures. If so, they differ in the match striking or in the fire (or, more precisely, in the match and in that which is on fire, given a substance-accident ontology), God’s cooperation or lack thereof making the match-striking or the fire different.

Suppose God’s cooperation makes the match-striking different. Then in scenario (1), created reality includes the event of divinely-cooperated-match-striking. This event surely doesn’t need any further divine cooperation, or else we’d have a regress. But no item in created reality is sufficient on its own to produce an effect witout God’s cooperation being added to it on the primary/secondary causation model.

So, it is the fire that must be made different by God’s cooperation. In scenario (1), the fire is caused by the match and God while in (2), it is caused by God alone, and that makes the fire different between the scenarios. I would like to say that the esse of the fire is different in the two cases: in the ordinary case its esse is at least in part being caused by the match with God’s cooperation while in the other case the match doesn’t enter into its esse. But the details don’t matter for this post: what matters is that the fire is different between scenarios (1) and (2).

But this has an unfortunate consequence: If the fire must be different in some metaphysical way in cases (1) and (2), it follows that God cannot directly and independently of creation cause the same effect as the match caused. And this violates the Thomistic principle that whatever a finite cause suffices for can be produced by God directly. God cannot directly produce a fire-caused-by-the-match; that would be a contradiction.

So we have a conflict between a number of Thomistic principles:

3. Divine simplicity

4. Divine omnipotence

5. The primary/secondary causation model

6. God can directly cause anything he can cause in cooperation with a creature.

It seems to me that 3-5 are more central to Thomism than 6. So, I am inclined to reject 6, perhaps replacing it with the weaker principle that for any item x that God can cause in cooperation with a creature, God can cause an item x^* which is qualitatively just like x.

Perhaps I was too quick when I said that (1) and (2) must differ in the match or the fire. Perhaps they differ in something “in between” the match and the fire, a token causal relation. I think this is a problematic solution for two reasons. First, it is central to Aristotelianism that all that exists are substances and their accidents. The token causal relation, if it’s not “in” any creature, would violate this. Second, it seems that the match strike plus this “in between” thingy are now sufficient to produce the fire, or else we can run the above argument with the match strike and the “in between” thingy in place of the match strike. But no mere creature is sufficient to produce an effect without God’s cooperation.

Velocity and teleportation

Suppose a rock is flying through the air northward, and God miraculously and instantaneously teleports the rock, without changing any of its intrinsic properties other than perhaps position, one meter to the west. Will the rock continue flying northward due to inertia?

If velocity is defined as the rate of change of position, then no. For the rate of change of position is now westward and the magnitude is one meter divided by zero seconds, i.e., infinite. So we cannot expect inertia to propel the rock northward any more. In fact, at this point physics would break down, since the motion of an object with infinite velocity cannot be predicted.

But if velocity (or perhaps momentum) is an intrinsic feature that is logically independent of position, and it is merely a law of physics that the rate of change of position equals the velocity, then even after the miraculous teleportation, the rock will have a northward velocity, and hence by inertia will continue moving northward.

I find the second option to be the more intuitive one. Here is an argument for it. In the ordinary course of physics, the causal impact of physical events at times prior to t₁ on physical events after t₁ is fully mediated by the physical state of things at t₁. Hence whether an object moves after time t₁ must depend on its state at t₁, and only indirectly on its state prior to t₁. But if velocity is the rate of change of position, then whether an object moves via inertia after t₁ would depend on the position of the object prior to t₁ as well as at t₁. So velocity is not the rate of change of position, but rather a quality that it makes sense to attribute to an object just in virtue of how it is at one time.

This would have the very interesting consequence that it is logically possible for an object to have non-zero velocity while not moving: God could just constantly prevent it from moving without changing its velocity.

Axiom T for physical possibility

Here is an argument for naturalism:

1. Only states that can be described by physics are physically possible.

2. Non-natural states cannot be described by physics.

3. Physical possibility satisfies Axiom T of modal logic: If something is true, then it’s physically possible.

4. So, non-natural states are physically impossible. (1 and 2)

5. So, non-natural states do not occur. (3 and 4)

I am inclined to think (1) is true, though it is something worth pushing back on. I think (2) is close to trivial.

That leaves me a choice: accept naturalism or deny that Axiom T applies to physical possibility.

I want to deny that Axiom T is a good axiom for physical possibility. The reason isn’t just that I think (as I do) that naturalism is actually false. The reason is that I think the axioms of physical possibility should hold as a matter of metaphysical necessity. But if Axiom T for physical possibility held as a matter of metaphysical necessity, then naturalism would be metaphysically necessary. And that is really implausible.

Yet Axiom T is very plausible. What should we do about it? Here is one potential move: Axiom T holds when we restrict our statements to ones formulated in the language of physics. This escapes the implausible conclusion that non-natural states are metaphysically impossible. But holding even this restricted axiom to be an axiom, and hence metaphysically necessary, still rules out the metaphysical possibility of certain kinds of miracles that I think should be metaphysically possible. So I think my best bet is to throw out Axiom T for physical possibility altogether. As a contingent matter of fact, it holds typically for statements formulated in the language of the correct physics. But that’s all.

Lying to prevent great evils

Consider this argument:

1. It is permissible to lie to prevent great evils.

2. Not believing in God is a great evil.

3. So, it is permissible to lie to get people to believe in God (e.g., by offering false testimony to miracles).

But the conclusion is absurd. So we need to reject (1) or (2). I think (2) is secure. Thus we should reject (1).

I suppose one could try to calibrate some great level E of evil such that it is permissible to lie (a) to prevent evils at levels greater than E but (b) not to prevent evils lesser than E. I am sceptical that one can do this in a plausible way, given that not believing in God is indeed a great evil, since it makes it very difficult to achieve the primary goal of human life.

Perhaps a more promising way out of the argument is to formulate some subject-specific principle, such as that it is wrong to lie in religious matters or for religious ends. But it is hard to do this plausibly.

It seems better to me to just deny (1), and be an absolutist about lying: lying is always wrong.

A Thomistic argument for essentiality of origins

Here is a suggestive Thomistic line of thought in favor of the essentiality of origins—i.e., the principle that the causes of things are essential to them.

Consider two possible cases where a seed is produced in the same apple tree T:

1. A seed is produced at t because of the tree’s exercise of seed-producing powers together with God’s cooperative exercise of primary causation.

2. A seed is created directly at t by God and not by the exercise of the tree’s powers.

And suppose that the seeds in the two cases are exactly alike, occur in the same place on the tree, etc.

I will argue that the Thomist should say that these will be numerically different seeds, and the best explanation of their difference is given by essentiality of origins.

For the Thomist is committed to there being a genuine difference between the two cases. Cooperative divine-creaturely causality is metaphysically different from divine primary causality. But where does the difference lie? Well, in (1) the tree’s causal powers are activated, while in (2) they are not. But it is a standard scholastic maxim that the effect is the actuality of the cause qua cause. Thus it seems that the difference between cases (1) and (2) should be found in the effect, namely the seed.

Furthermore, suppose that the difference between the cases is solely located in the cause, namely that in case (1) the tree’s causal powers are activated but not in (2), and that this activation is an accident A of the tree. The difference between cases (1) and (2) then is that in case (1), A occurs in the tree and in case (2) it does not. But for any accident of the tree, God could miraculously suppress any effects of that accident. Thus, there will be a case where A occurs in the tree and no seed results. And we could, further, imagine that:

3. Not only does God suppress the effects of A but he additionally directly miraculously produces an effect exactly like the one that A would have produced.

The difference between (3) and (1) can’t be in the activation of the tree’s causal power, since that is still there in (3). So we really should suppose a difference in the effects between (3) and (1). But a similar difference should exist between (2) and (1).

Note that the Thomist cannot say that there is a difference on the side of the causes lies in God, namely that in case (1), God’s causal power is unactivated but it is activated in (2) and (3). For an intrinsic difference in God between possible worlds would violate divine simplicity.

Thus, it is the effects, namely the seeds, that are numerically different, and they are different precisely because their causes are different. But the seeds are exactly alike. So the difference must be a metaphysical difference between the seeds. And this strongly suggests essentiality of origins. Indeed, it suggests that entities have encoded within them the identity of their cause.

Objection: The argument at most suggests that there has to be a numerical difference when something is produced by a finite cause (with God cooperating) and when something is produced directly by God. But why think there is also a difference when the effect is produced by one finite cause rather than another?

Response: The simplest metaphysical explanation of why it makes a difference whether God produces the effect or it is produced by finite causes is that the effect has metaphysically encoded in it what its cause was. In fact, my own view is that this may be found in the effect’s esse: perhaps an effect’s esse is to be caused by this-and-that.

Moreover, suppose that there need be no numerical difference between effects of different finite causes, but there is a numerical difference between direct effects of divine causation and the effects of finite causes. Then in principle scientists could have directly made the numerically same seed that the tree made in (1), but God couldn’t have directly made the numerically same seed. That seems unacceptable. (Of course, one might rejoin that essentiality of origins is unacceptable as it implies that God couldn’t directly make the numerically same seed that the tree could make. But when, as I suppose, an effect of necessity encodes in itself what its cause is, the impossibility of something’s being made by a different cause does not seem to be a limitation on that cause.)

Thomism, chance and cooperative providence

Thomists have two stories about how God can act providentially in the world. First, God can work simply miraculously, directly producing an effect that transcends the relevant created causal powers. Second, God can work cooperatively: whenever any finite causal agency is exercised, God intentionally cooperates with it through his primary causation, in such a way that it is up to God which of the causal agents natural effects is produced.

I think there is a difficult problem for cooperative divine agency. Suppose Alice is desperate for food for her children. She finds an indeterministic alien device which has the following property. If she presses the big button on it, the machine has probability 1/2 of producing enough food for a month for her family, and probability 1/2 of giving her a mild shock and turning off for a month.

Alice says a quick but sincerely prayer and presses the button. Then, presumably:

1. The probability that the machine will produce food is 1/2 conditionally on God not working miraculously.

But now notice:

2. Necessarily, if God does not work miraculously, the machine will produce food if and only if God intentionally connaturally cooperates with the machine to produce food.

From (1) and (2) we can conclude:

3. The probability that God will intentionally cooperates with the machine to produce food is 1/2 conditionally on God not working miraculously.

But imagine a different machine, where pressing the button has probability 1/2 of producing enough round pizza for a week and probability 1/2 of producing enough square pizza for a week. If Alice pressed the button on that machine, God, in acting cooperatively, would not have any significant reason to make the output of the machine come out one way or another.

In the round-or-square-pizza machine, we would expect the probability that God would cooperate to produce a particular outcome to be 1/2. But in the food-or-nothing machine, God does have a good reason to make the output of the machine be food: namely, God loves Alice and her family. We would expect the statistics for divine intentional cooperation to be different in the case of the two machines. But they are the same. In other words, it seems that God’s cooperative providence cannot depart from the statistics built into the natures of creatures. Yet that providence is fully under God’s voluntary control according to Thomism. This is puzzling.

If the Thomist says that God’s special providence is always exercised miraculously rather than cooperatively, the problem disappears. Absent special providential reasons, God has reason to follow the natural statistics of the machines. But if we allow that God sometimes exercises his special providence cooperatively, that should skew the statistics, and it cannot do that given the argument from (1) and (2) to (3).

Restricting special providence to miracles is a real option, but it destroys one of the advantages that Thomism has over competing theories.

Miracles, visible and hidden

We would expect God intervene a lot in our world to prevent misery. But there are at least three things that could give God reason limit his interventions:

1. The value of our trusting in him without being overwhelmed by the obviousness of his interventions.
2. The danger that we would end up counting on miracles, which would undermine our motivations for helping others.
3. The intrinsic value of the world proceeding according to its natural course.

Notice, however, that considerations (1) and (2) only apply to evident miracles, though (3) applies to all. Thus while God always has general reasons to refrain from miracles, those reasons are stronger when the miracles would be evident. Thus if the reasons God has against evident miracles--namely reasons (1), (2) and (3)--are sometimes overcome, we would expect the reason God has against non-evident miracles--namely reason (3) alone--to be overcome as well. (This is not a conclusive argument, because there are also special benefits to evident miracles, namely that God's message spreads.) Hence if there are evident miracles, we would expect that there would likely be hidden miracles as well. I am imagining here cases like this. Francis has early, undetectable cancer. But God has things for Francis to do, plus God doesn't want Francis to suffer, and so he miraculously stops the cancer before anybody knows about it. (Transsubstantiation is also an invisible miracle, but I am not counting it as hidden, since God has made it known that it occurs.)

Given (1)-(3), we could imagine God doing something like this in response to the misery of the world. First, he draws a rough limit n_v on how many visible miracles can happen without seriously endangering (1), (2) and (3). That number might be relatively small. Second, he draws a rough limit n_h on how many hidden miracles can happen without seriously endangering (3). That number is likely to be much larger. So now we have two questions very relevant to the problem of evil:

4. Do we have reason to think there are fewer than about n_v visible miracles?
5. Do we have reason to think there are fewer than about n_h hidden miracles?

There is significant evidence of visible miracles. Not in great numbers, but it is plausible that if the number was significantly higher, then (1) and/or (2) would be endangered. So the answer to (4) is negative. And I think the answer to (5) may be negative as well. For of course we don't know how many hidden miracles there are! We can't do controlled experiments to see how many people and animals develop cancer in the absence of God. Of course, this isn't an answer to the problem of evil. But it's a step in that direction.

(Some people wouldn't count hidden miracles as "miracles", because miracles must be wondrous--they must speak of God and his ways. That's just a terminological point as far as this post is concerned.)

Evidence that prayer works

There is some evidence that prayer works (PW)—and I mean this in the straightforward naive sense. Here is that evidence: Lots of people believe that prayer works (BPW). It is more likely that lots people would believe that prayer works if it worked than that they would believe that it works if it didn't work, i.e., P(BPW|PW)>P(BPW|~PW), and so BPW is evidence for PW.

There are at least two reasons why people are more likely to believe that prayer works on the hypothesis that it actually works than on the hypothesis that it does not work.

The first reason is that if prayer works for you, then that's likely to increase your degree of belief that prayer works, as well as the degree of belief in this among your friends.

The second reason is that if prayer works, then that's likely to increase the survival of communities that pray, leading to mimetic selection for prayer. And at the community level, prayer typically doesn't come for free. First, there tends to be a dedicated class of people who pray and teach how to pray—say, a clergy. Second, prayer is often attached to material outlays, whether those of sacrificing cattle or of building temples. Third, prayer takes time and maybe mental energy (though the last one is balanced by the fact that it may be restful). Of course, prayer may also have community cohesiveness benefits independent of whether prayer works in the naive sense. These benefits may be balanced by the costs. But these benefits are also available if prayer works in the naive sense, and are themselves accentuated then (it brings a community together if their prayers are fulfilled). So although the existence of such benefits makes P(BPW|~PW) higher than we might otherwise think, nonetheless P(BPW|PW) will be even higher, both due to a greater degree of these benefits, and due to the obvious benefits of prayer working.

Of course it's a hard question to say just how much evidence the widespread belief in the efficacy of prayer provides for that efficacy. But it's clear that it provides some.

Some valid arguments from absurdity

Here are some curious forms of argument that I want to play with. First:

1. Doctrine D is so absurd that no one could believe D while fully realizing its absurdity, except by a miracle.
2. Someone believes D while fully realizing its absurdity.
3. So, a miracle has occurred.

Given the human capacity for believing the unbelievable, it is going to be hard to support (1) for any interesting D (except maybe: p and not p).

Let's try this:

4. Doctrine D is so absurd that no one could reasonably believe D while fully realizing its absurdity, except by a miracle.
5. Someone reasonably believes D while fully realizing its absurdity.
6. So, a miracle has occurred.

In arguments of this sort, the difficulty has shifted to (5). But we might try the following. Start by observing that a person doesn't become unreasonable simply by having a trivial belief that isn't reasonable. But to center one's life one a belief that isn't reasonable might be enough to render one unreasonable:

7. If at least one of the beliefs central to x's life is not reasonable, then x is an unreasonable person.
8. x is not unreasonable.
9. One of the beliefs central to x's life is D.
10. x fully realizes the absurdity of D while believing D.
11. So someone reaosnably believes D while fully realizing its absurdity.

The conclusions of the above arguments were that a miracle has occurred. Can we conclude that D is true? Well, we would have to look at our best explanation of the miracle. If it involves God, then we have reason to think D is true. Here's an argument that avoids the detour through miracles.

12. Doctrine D is so absurd that no reasonable person would hold D as a belief central to her life while fully realizing D's absurdity unless she knew D to be true.
13. Some reasonable person held D as a belief central to her life while fully realizing D's absurdity.
14. So, somebody knew D to be true.
15. So, D is true.

I think the big difficulty with arguments of this form in the cases most familiar to me, namely with D a doctrine from the Christian tradition, is that people who are paradigm examples of rationality, like Thomas Aquinas, do not take the doctrine to be really absurd.

Compatibilism on the cheap

Could creatures be free in a world with deterministic laws? Yes, because God could work a miracle each time that it is time for a creature to make a decision, a miracle that exempts the choice from the deterministic laws. So, cheaply, free will and deterministic laws are compatible.

This is obviously too cheap, so probably we had better not define compatibilism as the possibility of creaturely freedom in a world with deterministic laws.

Though, maybe, we could stick to that definition of compatibilism (at least in respect of this problem—there are other problems with it), but insist that if God exists, no law can count as deterministic, because God can override every law.

McGrew's SEP entry on miracles

Tim McGrew emailed me that his SEP entry on miracles is up.

Christian apologetics

A correspondent sent me a link to this really nice apologetics site with links to articles by good people (like John Earman and Fred Freddoso) on topics like miracles.

Miracles

I think it would be valuable if a good philosopher of religion were to carefully look at some of the most carefully checked contemporary miracle reports—namely those involved in Catholic beatification and canonization proceedings. I think it would lend some reality to a largely theoretical discussion. These reports are very well documented, I understand.

Here is a story that I was recently sent that is currently under investigation—it is a story of a man dying from flesh-eating bacteria, healed allegedly by the prayers of Blessed Columba Marmion.

A Kierkegaardian argument for miracles

Here is a valid, and perhaps even sound, argument. Kierkegaard would worry that 4 begs the question.

1. (Premise) If something is naturally impossible and it occurs, it occurs by miracle.
2. (Premise) If a proposition is incredible, it is naturally impossible to believe it.
3. (Premise) Christian doctrine is incredible.
4. (Premise) Someone believes Christian doctrine.
5. Therefore, there is at least one miracle.

Some remarks on Hume on miracles

1. Let's suppose for simplicity that miracles would violate of laws of nature. Consider then a "modernized" version of Hume's argument against miracles: The laws of nature have always been scientifically observed to hold. Whatever the merits of Hume's original argument, this version is really weak. It is, in fact, not uncommon for scientists to get data that does not fit what is predicted from the laws. When this data can be reproduced, it is taken seriously. But when the data cannot be reproduced, unless it is in some way spectacular, it will, I think, be dismissed as experimental error, an artifact of the particular experimental setup, etc. If only one scientist saw something on one occasion, and repeats do not show it, and no one else sees it, then it will not be taken seriously. The one scientist who saw the effect might investigate and try to find the source of the deviation, estimate to see whether the deviation falls within experimental error. But sooner or earlier, I think, the problem will be put aside, unless the data point was spectacular. However, miracles are not supposed to follow any rule—God is not a vending machine who produces a miracle when the right coins are put in. (God does answer prayers; however, he does not always answer them in the way expected; I think when we sincerely pray in Jesus' name, we will either get what we asked for, or we will get something as good or better.) So bringing science in does not help Hume's case.

2. Much of my knowledge of the sorts of regularities that miracles would go against is in fact through testimony. For instance, take the case that interests Hume most: the observation that dead people stay dead. I have never actually seen anyone die. I am sure Hume did. But unless one is a medical professional, a soldier or a witness to tragedy, one is unlikely to have seen very many people die. Moreover, one typically personally only observes a particular dead body for a fairly short time. Observe that once a body is buried, one no longer has direct observational data for the claim that the person stays dead. It could be, for all that one has directly observed, that the person came back to life, clawed at the coffin, and then asphyxiated again. Thus, one has very little direct observational data for the claim that dead people stay dead. But the bulk of our data for the claim that dead people stay dead comes from putting together the testimony of others.

Granted, we may have some indirect observational data. I have never seen graves opening when I visited a graveyard, nor have I driven by a funeral parlor and seen staff running out and screaming, with a formerly dead person walking out after them. However, in the case of most graves in a graveyard, it is through testimony that we know that there is someone in fact buried there. The indirect observational data depends on testimony, too, then.

Our knowledge of the regularity that dead people tend to stay dead depends largely on testimony. However, we only get the universal claim which Hume needs, the claim that all dead people always stay dead, when we dismiss some of the testimony available to us, namely the testimony for cases of resurrection. But it is no surprise that if we dismiss the testimony to the deviations from a regularity, what remains is testimony to the universality of the regularity.

3. In fact, miracle reports are very common, across many cultures. This should undercut one's confidence in any kind of Humean argument that miracles are apparent violations of universally holding regularities. For the sheer volume of miracle reports is strong evidence against the claim that the regularities always hold.

4. Hume himself thought that the ubiquity of miracle reports was evidence against their truth, because he thought that miracles should be confined to the true religion, and at most one of the religions could be true. However, I think we can now have a more ecumenical view of miracles. Moreover, I think we can distinguish between miracles that bear witness to a particular proposition and miracles that do not. A healing can simply be an act of divine love for the person healed and her friends/family, and there is no reason to deny that such miracles might hold quite universally.

But some miracles very clearly bear witness to a particular proposition. Thus, in the fifth century, apparently about sixty Catholics had their right hands and tongues cut out at the roots by an Arian heretic for espousing the doctrine of Nicaea. But these Catholics continued to speak, and presumably to preach the Nicaean doctrine. This seems to be a miracle that is a witness to a particular doctrine. Bishop Victor, writing two years after the alleged event, says:

If however any one will be incredulous, let him now go to Constantinople, and there he will find one of them, a sub-deacon, by name Reparatus, speaking like an educated man without any impediment. On which account he is regarded with exceeding veneration in the court of the Emperor Zeno, and especially by the Empress.

In the case of miracles that bear witness to a particular doctrine, when the doctrines conflict, one has a harder time making the ecumenical move. However, I do not know that there really are that many cases of reliable miracle reports that bear witness to incompatible doctrines. The case of the tongueless sub-deacon is very remarkable, and I do not know of any similar miracles reported on the part of the Arians. It is an interesting bit of religious history that at the time of the Protestant Reformation, one of the arguments adduced by the Catholic side was that claims as sweeping as those of the Reformers should be backed up by miracles—but none, the Catholic apologists alleged, were offered.

So Hume cannot dismiss ubiquitous miracle reports that are not tied to a particular doctrine. He could say something about mutual cancelation in the case of miracles that bear witness to a particular doctrine, but it is not clear that there is actually all that much in the way of reports of such miracles, of equal reliability, bearing witness to incompatible doctrines. And even if there were, it seems to me that the hypothesis that both reports are unreliable is less probable on its face than the hypothesis that only one of the reports is unreliable.

Demonic miracles?

Some of the Church Fathers take quite seriously historical reports of marvelous events associated with pagan temples and pagan sorcerers, and attribute these events to demons. The non-occurrence of such events in their own time they then take to be evidence of the power of Christ, who vanquished the devil by dying on the cross and rising again.

My natural tendency is to dismiss reports of magical and like phenomena. But on reflection, if I accept Christianity, shouldn't I take the hypothesis offered by these Fathers to be at least as probable as a sceptical hypothesis about such marvels? After all, if one accepts this hypothesis one needs to dismiss fewer reports by historians, which seems a good thing. Shouldn't I take it to be at least as likely as not that ancient sorcerers really were able to do strange things on occasion by the power of demons and that marvels happened in pagan temples? If I accept Christianity, this isn't an arbitrary hypothesis, like that of someone who thinks that Relativity Theory was false before 438 BC (a randomly chosen date), since as a Christian I independently (a) take Christ's death and resurrection to have been an event of cosmic significance, the great victory over the forces of darkness, and (b) believe that demons do exist.

Does evolutionary theory exclude miraculous divine intervention?

I shall argue that current evolutionary theory (ET) is compatible with the Intervention Claim (IC) that some biological facts about the development of species are explained by one or more miraculous divine interventions at some point in evolutionary history. This implies that evolution is compatible with at least some of the controversial conclusions of interventionist ID.

Now the argument. We can take "evolutionary theory" to have two parts: a concrete and a general part. The concrete part consists of a constantly growing number of specific evolutionary histories explaining the development of particular features of particular organisms, of their geographical distribution, etc., each history having a particular template, in which natural selection tends to play a prominent, but not exclusive, role. The general part will be discussed below.

Two independent arguments now show that IC is compatible with the concrete part of current ET. First, IC merely claims that some biological facts are explained by divine intervention. But the concrete part of current ET does not give evolutionary histories for all features of all organisms. Thus, even if all of the evolutionary histories that form the concrete part of current ET are correct, nonetheless IC might be true, because it could be that an organism or feature for which an evolutionary history is not given by the concrete part of current ET in fact developed through divine intervention. (By the way, in case it is tempting to run an inductive argument from the concrete part of current ET for the claim that every biological feature can be explained without divine intervention, that temptation should abate after thinking about my duct tape parable.)

Secondly, the evolutionary histories involve mutation and recombination, but are mostly agnostic about the precise causes of mutation and of particular recombinations. ET is compatible with determinism, so the histories do not include the claim that mutation and recombination was random or unexplainable. We now know some of the sources of mutation and some of the causal processes involved in recombination, but we would not be so rash as to say that we know all of these sources and processes, and neither would ET be falsified by finding new ones, nor do particular evolutionary histories identify particular causes of mutation or recombination (this particular molecule was hit by this particular cosmic ray, which was emitted by this star, etc.) Therefore, the evolutionary histories are compatible with miracles being involved in the explanation of a particular mutation or recombination event, miracles such as God shifting a molecule around. Certainly, even if some very rare evolutionary history identifies the cause of, say, a mutation event as, say, the impact of a cosmic ray, the history is surely not going to say anything about the particular source of this cosmic ray, and hence will be logically compatible with the claim that, say, God miraculously redirected a cosmic ray to hit this particular molecule at this particular angle.

So we have two arguments for the compatibility of the concrete parts of ET with IC. What about the general part of ET? This makes some sweeping claims, such as that all living things on earth have developed from a single ancestor organism. Now this general claim is compatible with IC, which simply claims that some aspects of the development involved miracles. Now, if ET claimed that all of the biological development from the ancestor organism can be explained in terms of natural selection, then ET would be incompatible with IC. But ET makes no such claim. Indeed, opponents of evolutionary theory are sometimes accused of conflating evolution with natural selection. In modern evolutionary theory, adaptive explanation plays a prominent role, but not an exclusive one. There are other mechanisms involved. To give just one example, one might explain something's arising as a spandrel.

The general part of current ET does not claim to list all of the kinds of processes that were involved in the development from the single ancestor organism to the present biological population on earth. It probably does claim that natural selection was one of the most explanatorily prominent, or maybe even the most prominent one, of these processes. But that claim does not conflict logically with IC, since IC does not claim that miraculous divine intervention was the most important force in biological history. IC does not claim that there was miraculous divine intervention in every organism's history, but even if it were to claim that, this would be compatible with the claim that it is not the explanatorily most prominent part of the development. (Consider a view: God had a plan, and he occasionally made minor tweaks so that things would come out as he wanted.) Thus, IC is not incompatible with the general claims of current ET, if we read these charitably as not including an exhaustive list of the explanatory mechanisms involved.

Objection 1: The general part of ET does include a restriction on the mechanisms involved--it says that these processes are naturalistic.

Response: ET is a scientific theory. It is not a part of a scientific theory to say things like:
(*) "Event E happened by means of some natural cause or other."
It is the part of a scientific theory to say things like:
(**) "Event E happened by means of at least one of the following natural causes: C1, C2, C3."
We can see what kind of evidence is relevant to (**) (e.g., evidence that a random sampling of events like E had them all caused by C1, C2 and/or C3). We cannot see what sort of evidence would be relevant to (*), apart from the bare fact that E happened. Scientific theories have some specificity--they do not simply say that something happened due to some cause or other, and neither do they simply say that something happened due to some natural cause or other. In fact, it seems to me that a decisive argument against calling Intelligent Design in general a scientific theory lies in its lack of specificity:
(***) "An intelligent agent (of some sort or other) intervened (somewhere) in the history of the world (on account of some set of motives or other) to bring about event E."
But (*) is worse than (***) in respect of specificity. We should not, thus, take claims like (*) to be a part of ET.

Objection 2: An axiom in evolutionary theory is that there is no positive correlation between the occurrence of a mutation and the resulting fitness of an organism. This implies that IC is false, since if IC were true, then mutations more likely to make the organism more fit would be more probable, since God would be more likely to miraculously produce them.

Response: Intuitively, there will be more mutations that decrease fitness than those that increase it. (Think of a computer program, and changing a bit of code randomly. Most of the time, it'll either have no effect or the program will crash.) The number of mutations in the history of the world is very, very large. I could estimate this with some data about mutation rates per basepair per generation, but rather than tracking down that data, let's just say it's 10¹⁵--it's going to be much higher than that. IC only claims that there are some miraculous interventions. Let's say there are seven (I am only arguing for logical compatibility of IC and contemporary ET, so I can make up a number here). That is going to be such a tiny fraction of the mutations in the biological history of our planet, that it will still be true that the majority of mutations that make a difference make a negative difference to fitness, and hence it will still be true that there is no positive correlation between fitness and mutation.

Moreover, this will be such a tiny fraction of the number of mutations in the history of the world that any effect it has on overall statistics of mutations is going to be well within very narrow error bounds, so any statistical claims about mutations will still be true. I take it we make no statistical claims of the form "exactly x percent of mutations have property P", but rather ones like "approximately x percent of mutations have property P", and variation of seven out of, say, 10¹⁵ mutations, given that the total is so great, is not going to affect the truth of such claims.