Greg Cavin on Bayes' Theorem and Miracles

I wrote most of this post several months ago when my friend Calum Miller came to southern California for a semester abroad. Unfortunately, I simply never got around to finishing it up. Hence, this post comes about five or six months late. However, I still think it's worth posting, in case someone watches the video or comes upon the type of fallacy that I suspect goes into the argument. Here's the post:

A couple weeks ago I went to a debate between my friend Calum Miller and philosopher Greg Cavin on the Resurrection of Jesus. The video can be found here. Cavin's opening speech on Bayes starts at (6:00). He gets into his arguments again at (13:40). In this post I'll discuss a small part of Cavin's opening speech.

At the beginning, Cavin claims that he will show that it is "virtually 100% certain that no miracles ever occur."

Greg Cavin formulates the argument in terms of an assessment of a comparison between probabilities. While Cavin goes into a ton of mathematical detail that I suspect could be simplified to get to the main point, a little bit of it is probably necessary. He formulates the argument in terms of the Odds Form of Bayes' Theorem.

In general, the Odds Form of Bayes' Theorem is as follows. For any events A, B, and D:

P(A|D)/P(B|D) = P(D|A)/P(D|B) * P(A)/P(B)

Cavin comes up with a partition of probability space which is exhaustive and exclusive. In other words, at least one of the following hypotheses holds and if one holds then the others do not.

• M: At least one miracle has, had, or will occur in the universe.
• L: The laws of the sciences as these are currently formulated in standard reference works, without any supernatural non-interference proviso, are true and are laws of nature in their restricted domains.
• (¬M & ¬L): Neither M nor L hold. 

With respect to L, what it is saying is that if you have a law of science 'S,' then a statement of the law will just be of the form: "For all times, all places, S," rather than "Except for the intervention of some supernatural force, for all times, all places, S." In other words, laws of science lack the underlined "proviso."

M and L are taken to be incompatible because if a miracle occurs, i.e. if M is true, then that entails the failure of at least one "un-provisoed" law of science at some time and place, whereas L entails all "un-provisoed" laws of science hold at all times and places. Cavin defines the evidence E with respect to which we will evaluate these probabilites as follows (27:00):

• E: The total evidence, which is a combination of T & C, where T and C are understood as follows:
• T: All of the traces (call them Ti) of miracles. These are all of the pieces of evidence people could take to provide evidence for a miracle.
• C: All of the confirmation instances (call them Ci) of the laws of science. These are all of the pieces of evidence people could take to provide evidence for the various scientific laws.

The partitioning of probability space.

Applying Bayes' Theorem to the argument at hand, this is the Ratio of Posterior Probabilities of L vs M:

P(L|E)/P(M|E) = P(E|L)/P(E|M) * P(L)/P(M)

In other words, the left hand side compares the likelihood of L given the evidence with the likelihood of M given the evidence.

Now, a crucial part of Cavin's argument is in calculating the ratio P(E|L)/P(E|M). This is done by calculating probabilities of all of the Ti given L and M and calculating the probabilities of all the Ci given L and M. If these are lower on M than they are on L, then P(E|L) will be higher than P(E|M). His official argument here is from (31:00) to (34:00), but I asked him a question later that gets to the same point.

After the talk, I asked Cavin why he thought M could not explain C and T as well as L could. In other words, why are, say, the confirmation instances of science less likely given that miracles have occurred than if L holds? He said, "Well, if I told you, 'This is a desk,'  what would that explain? Not much. How can you make any predictions from that? So, likewise, how can the proposition that at least one miracle holds explain anything? It could hardly have any predictive or explanatory power." Of course, that seems true. If the only sentence you knew to be true were "At least one miracle occurs," then you wouldn't be able to predict much, just as you couldn't predict much from just knowing "This is a desk." Hence, the argument goes, P(E|M) is very low.

However, it's a little bit misleading to put things this way. P(E|M), strictly speaking, isn't defined in terms of how much you can predict from the single proposition that at least one miracle occurs. This is clear after considering some very basic probability theory.

First, note that we can always define P(M) as P(M∩A) + P(M∩¬A) for any event A. This can clearly be seen by the following diagram:

P(M) = P(M∩A) + P(M∩¬A)

A is marked out in dark blue.

¬A is marked out in light blue.

Suppose that 'A' denotes some hypothesis, maybe the hypothesis 'The laws of nature almost always but not always hold.' Then the probability that some miracle happens is equal to the probability that some miracle happens and A holds plus the probability that some miracle happens and A does not hold. Again, P(M) = P(M∩A) + P(M∩¬A).

From this we can infer: P(E|M) = P(E|M∩A) + P(E|M∩¬A). Now, you might still think that this is lower than P(E|L) for various reasons. But you certainly couldn't infer it from the type of argument I sketched above. That would be much too easy.

Maybe I am misrepresenting what Cavin said. I hope I'm not. But if I am, let's just say that if someone were to argue in the way I represented Cavin as arguing, then they would be committing a fallacy.

There were many other interesting issues that came up during the debate, such as the likelihood of the laws of nature holding most of the time given theism, and these deserve attention. But for now I think it's worth noting that Cavin's argument doesn't go through as easily as it might have seemed.

What God Knew and Abraham Didn't

The traditional story of Abraham and Isaac is one of the most perplexing parts of the Bible, at least for philosophers. There seems to be some sort of implicit contradiction in the idea of God commanding someone to sacrifice a human being, especially an innocent boy. Moreover, it seems like if one were commanded to do this one should not do it. Before thinking about this more we should review the story very quickly.

In the recounting of the story in Genesis 22, God wishes to test Abraham and see whether he "fears God." To this effect, God commands Abraham to go and sacrifice his only son, Isaac. On the third day of their journey Abraham takes Isaac up to a mountain to sacrifice him. Before going up, Abraham tells his servants with him, "We shall worship and come back to you." (Genesis 22:5) Abraham then binds Isaac and prepares to sacrifice him. When Abraham grabs his knife to kill Isaac an angel sent from God stops him by telling him not to kill the boy. God speaks through the angel and says that he now knows that Abraham fears him, and because of his actions God will shower blessings upon Abraham and his descendants.

Sometimes opponents of Christianity will say that this verse proves an inconsistency in the Christian conception of God. On the one hand, God is supposed to be a perfect being, and a perfect being, it seems, would never command something intrinsically evil such as sacrificing an innocent person to him. On the other hand, the Bible says he does. Let's give a precise argument which captures the force of this more vaguely formulated one.

The Universe is Contingent (And Therefore Needs an Explanation)

One common fallacy is the fallacy of composition, where one argues from the fact that each part of a thing has a certain feature to the conclusion that the whole thing has that feature. For instance, one could argue that every brick of the house is cube-shaped, therefore the house is cube-shaped. Or one could argue that each part of one's brain is unconscious, therefore the whole brain is unconscious. These inferences are fallacious.

However, I think it is worth noting that not all inferences from properties of parts to properties of the whole are invalid. If each part of a wall is made entirely of stone, then the whole wall is made entirely of stone. Similarly, if each part of the ball is entirely red, then the whole ball is entirely red. And so on.

Contingency seems to be like this, at least in this case. So here's an argument that the universe must be contingent:

Thoughts on the Grounding Objection to Molinism

So, I want to get a bit more clear on what the grounding objection to Molinism is saying. As far as I can tell at this moment, the grounding objection seems to go something like this.

The anti-Molinist says that some general statement about the relation between grounding and truth such as the following holds:

(A) If some proposition is true then there is an entity which grounds its truth.

It seems in this context 'grounds the truth of p' just means 'is the truthmaker of p'. The objector to Molinism then proposes:

(B) There could be no entity to ground the truth of CCF's.

Of course from A and B it follows that all CCF's, if they are meaningful, are necessarily false. Hopefully this is all a correct representation of the objection.

Two Inadequate Arguments for a Finite Past

In this post I will consider two arguments which have at times been brought up in connection with the Kalam Cosmological Argument (KCA), which I will call the "subtraction argument" and the "argument from traversing an infinite," the former of which I have heard from Dr. William Lane Craig. The KCA goes as follows:

1. Whatever begins to exist has a cause.
2. The universe began to exist.
3. So the universe has a cause.

The arguments in question are designed to defend the second premise, which is presumably implied by the past's being finite. I should note that I think the second premise is true and there is strong evidence in favor of its truth. Alexander Pruss has given an excellent argument here, to which I have heard no compelling reply. I also think there is very strong scientific indication of the premise's truth, which Craig has adequately demonstrated. I just don't think these two arguments demonstrate its truth.

The "argument from traversing an infinite" goes something like this:

1*. If the past were infinite, one would have to cross an infinite temporal distance to get to the present moment.
2*. If one had to cross an infinite temporal distance to get to the present moment, then one could not get to the present moment.
3*. So if the past were infinite, then one could not get to the present moment.
4*. But we are at the present moment.
5*. So the past is not infinite.

The argument requires some unpacking. First of all, to say the past is finite is to say there was a beginning of time, and to say the past is infinite is to say there was no beginning of time. Second, 'temporal distance' means the length of time between one moment and another. There is a perfectly good way to define finite temporal distance. If we take our measure of time as a second, we can assign the current time the number 0, the time one second ago -1, the time two seconds ago -2, and so forth. To find the temporal distance from one time t1 to another t2, we take the number assigned to t1 and the number assigned to t2, and take the absolute value of the difference between the two. For instance, take the time 1000 seconds ago. To find the temporal distance from that time to the present time you take the absolute value of -1000 minus 0, which is of course 1000 seconds. Pretty simple.

However, problems begin to arise when we start to talk about an "infinite temporal distance." This phrase is ambiguous, and depending on which interpretation of this phrase we take it will either cause problems for premise 1* or for premise 2*. First, the phrase could mean something analogous to the way finite temporal distance has been defined above. However, infinity is not a real number, so you simply cannot define an infinite temporal distance the same way as above. There is no number "-infinity" from which you can subtract, say, -5. So if this is what is meant, then premise 1* appears to be false, since no real sense can be given to an infinite distance in this way.

On the other hand, crossing an infinite temporal distance could just mean that the set of all the numbers assigned to the seconds is infinitely large. This makes perfectly good sense of the phrase, but then in that case it is not clear why premise 2* is true. As Thomas Aquinas points out, there being an "infinite temporal distance" in this sense is perfectly consistent with all the temporal distances from the past to the present being finite, where "temporal distance" is defined as it was earlier:

"Passage is always understood as being from term to term. Whatever bygone day we choose, from it to the present day there is a finite number of days which can be passed through. The objection, however, is founded on the idea that, given two extremes, there is an infinite number of mean terms." [ST Ia q.46 a.2]

So for instance, the distance from the present to one second ago is 1 second, the distance from the present to two seconds ago is 2 seconds, etc. and so on forever and ever back into time. Hence, no matter how far you go back in time, the distance in the way I've defined above from any given past moment to the present will be finite, and thus you will only have to cross a finite number of seconds to get to the present moment. But of course any finite number of seconds can at least in principle be crossed; hence, premise 2* is false.

So much for the "traversing an infinite" argument then. The "subtraction argument" goes something like this:

1'. If the past were infinite, then an actual infinity would be possible.
2'. If an actual infinity were possible, then one could perform subtraction on infinities.
3'. But if one can perform subtraction on infinities, then one will get contradictory results.
4'. So if the past were infinite, then one would get contradictory results.
5'. So the past is not infinite.

This seems to be one of the arguments William Lane Craig gave in his debate against Peter Millican. Let me first point out an ambiguity in the phrase "actual infinity," after which I'll assess the argument under each interpretation. Here are two possible meanings of the phrase "actual infinity":

(ACT1) An actual infinity exists just in case for some time, at that time there exist distinct concrete objects such that the size of the set containing all and only them is infinite.

(ACT2) An actual infinity exists just in case there is some set containing only distinct concrete objects whose size is infinite.

Some elaboration is in order. First off, both definitions presume when speaking of actual infinities that we are dealing with concrete objects. While my understanding is that Craig does not believe there are infinitely many numbers (he is a nominalist), presumably his argument doesn't presuppose this view; Craig only wants to rule out the possibility of infinitely many concrete objects. Now as for the definitions themselves, the difference between (ACT1) and (ACT2) is that in (ACT1) you only have an actual infinity when all the concrete objects exist at the same time. In (ACT2) you could have finitely many objects at t2, finitely many at t1, and so forth, yet if you take a set containing concrete objects from different times, and the times go back to infinity, you will still have an actual infinity. So both of these definitions make fine sense. However, the assessment of the argument will depend on which interpretation we take.

Let's deal with the first definition, (ACT1). Given our definition of actual infinity in (ACT1), premise 1' does not appear to be true, or at least not obviously true. It is consistent with holding that the past is infinite that at each time there are only finitely many concrete objects. And if you believe only objects in the present moment exist, then 1' is definitely not true. The fact that there were objects at each time in the eternal past in no way implies an infinite collection of simultaneously-existing objects.

My main concern is with 2' and 3' though. Take 2', since it is also ambiguous to a certain extent. The problem is it is not immediately clear what is meant by "perform subtraction on infinities." Craig acknowledges that the ordinary operation of subtraction is not defined for "infinity". If he did mean this, i.e. the ordinary operation of subtraction, then clearly 3' would be true but 2' would have no support at all. So it cannot mean the ordinary operation of subtraction.

Now, Craig gives us an example to support 2' and 3', and this may help us understand what he means. Suppose we have an infinite number of coins. Then we can take away all the coins except three of them. And in this sense we can be said to perform subtraction on infinity, i.e. taking away some number of things from an infinitely large collection. This definition of performing subtraction on infinities makes sense.  But then why is 3' true? Craig says, considering our infinite number of coins, that you can take away infinitely many coins and be left with 3 coins, and thus infinity minus infinity = 3; but you can also take away infinitely many coins and be left with 2 coins, and thus infinity minus infinity = 2; hence, 2 = 3, which is our contradiction.

The problem with this argument is that it runs on an equivocation: We agreed that we are not using "performing subtraction" or "minus" in the normal sense of the arithmetical operation, since this just makes no sense. So "infinity minus infinity = 3" must simply be shorthand for saying "taking away infinitely many objects from an infinite collection leaves us with 3", and similarly with "infinity minus infinity = 2." But then if "2 = 3" means that 2 is identical to 3, then it certainly does not follow that 2 = 3; all that follows is that you can take away an infinite number of things and be left with 3, and also take away an infinite number of things and be left with 2, and this is certainly not a contradiction! It only looks like a contradiction when we are illicitly inferring "2 = 3", as if the phrase "infinity minus infinity = 2" were using "minus" and "=" in the same way as "5 minus 3 = 2." It would be like if I had infinitely many pennies and dimes, and I said, "infinity minus infinity = a penny, infinity minus infinity = a dime, so a penny = a dime." Clearly I am making an illicit inference here, and for the same reason Craig's argument makes an illicit inference as well.

Now, this whole time I have been working under the assumption that throughout the argument "actual infinity" is meant in the sense of (ACT1). But under interpretation (ACT2) the situation is even worse, since it is not clear 2' is true. It seems that in order to "subtract" infinitely many coins in the sense defined above, all of them must exist at the same time. But if "actual infinity" is taken in the sense of (ACT2), then it is not required that all of the infinite number of coins exist at the same time, and thus 2' has no support. And of course, with the exception of premise 1', all the same criticisms I have just given apply equally well under (ACT2). So, interpreted charitably, the argument seems to be a failure, with the primary problem being in premise 3'.

I should note one more time that, in spite of all my criticisms of these two arguments, I think there are good reasons for thinking the KCA is sound. I just don't think these are among them.

Minimal Divine Simplicity and the Trinity

Just a note: I will probably be laying kind of low for a while, since I am now moved in at my new school and taking summer courses. I will be kind of busy for the next two months, so please do not be offended if I don't reply to comments quickly on this blog. I will get back to you eventually. Anyway, enjoy the post!

For Catholics, belief in the doctrine of God's simplicity is dogmatically defined to be held by all the faithful just as much as the doctrine of the Trinity (see the Fourth Lateran Council as well as Vatican I). Does the official dogma of divine simplicity contradict the revealed truth about the Holy Trinity? Not necessarily, at least on a certain construal of divine simplicity. Call this the "minimal doctrine of divine simplicity":

(MDS) God has no proper parts, either metaphysical or physical.

This means that God possesses of course no physical parts, but also no properties, ontological constituents, tropes, accidents, immanent universals, distinct intellectual parts (e.g. distinct will and intellect), etc.

Is this what the Church intends to define when it says God is simple? Arguably so. The definition of simplicity must be strong enough to rule out theistic personalist views of God, for this is not found in the teaching of the Fathers and is arguably inconsistent with the other divine attributes which are mentioned in connection with simplicity in these Councils (e.g. God's being immutable, incomprehensible, infinite in will). Hence, it must mean more than that God is simply non-physical; God isn't just simple in the sense that an angel is. On the other hand it must be weaker than simply identifying God's essence with his existence. For if the Church meant to endorse dogmatically the Thomistic teaching on simplicity, this would make anyone who did not hold to this view in substance to be heretical; hence, the teachings of the Cappadocian Fathers as well as St. Maximus the Confessor, and likely even Bl. Duns Scotus, would be heresy. This is why MDS seems to be a likely candidate for the minimal required belief in divine simplicity for orthodoxy.

But given MDS, this is a truth about the Trinity:

(TR) It is not the case that the persons of the Trinity are proper parts, either metaphysical or physical.

For the persons of the Trinity all share fully in the divine essence; the Father is fully God, just as the Son is fully God, just as the Holy Spirit is fully God. To suppose the persons are proper parts of God would mean there is something G which is fully God, and that each person of the Trinity does not fully share in the essence of G (since, after all, G essentially has as proper parts each of the persons of the Trinity, whereas the same does not hold for each of the individual persons). Hence, the persons of the Trinity cannot be understood to be proper parts of God in any sense; hence, the doctrine of the Holy Trinity cannot contradict the minimal doctrine of divine simplicity.

This seems to show that the Church's teaching here is consistent; it is a separate matter whether Aquinas's teaching which includes the doctrine that God's essence = his existence, as well as that God is pure actuality, can be made consistent with the Trinity.

William Lane Craig on God and Analogy

William Lane Craig, as with most contemporary analytic philosophers of religion, objects to the classical Thomistic idea that God cannot be said to be a being in the sense that we can. I aim to argue that at least some of his claims here are unreasonable.

Craig objects: "One of the aspects of Thomas Aquinas’ thought that I find most disturbing is his claim that we can speak of God only in analogical terms. Without univocity of meaning, we are left with agnosticism about the nature of God, able to say only what God is not, not what He is."

This does not follow in the slightest; in fact, I wonder if Craig actually understands what analogy is, since it is one of the main points of Aquinas's theory of analogy to avoid this problem. Aquinas sought to show, in contrast to Maimonides, that though we can't predicate attributes of God in the same sense as us we can still speak meaningfully and make positive predications about him. Craig fails utterly to show how from the semantic analogy of the term 'being' we are left only with negative theology.

Next, Craig says: "When in discussions with atheists I affirm, 'God exists' and they reply, 'God does not exist,' we may need to be sure that we mean the same thing by 'God,' but there is no equivocation on the meaning of 'exists.'"

I guess what Craig is trying to say here is something like this: If the word 'exists' is analogical, then when I affirm God exists and when atheists affirm God does not exist, we are both equivocating past each other. But this is a genuine ontological dispute and so there is no equivocation; hence, 'exists' is not analogical. The problem is that the main premise is simply not true; if analogy is true, then we affirm that God exists in one sense, and the atheist simply denies that God exists in any sense, including the one I am predicating of God.

In the next paragraph, Craig says this: "The problem you pose brings us to the heart of my current work on divine aseity. What makes God more than just one being among many is precisely His aseity: God alone is self-existent; everything else exists contingently. Only God exists of Himself (a se); everything else exists through another (ab alio). That makes God the source of being for everything apart from Himself."

Now, I really like this, and I agree with this completely. The only problem is that Craig himself doesn't; for if what Craig says is literally true then divine simplicity is true, from which it is a small step to the doctrine that talk about God is analogous. Here's why:

(1) Whatever is non-identical to God is created by God. [conceded by Craig]
(2) If God has metaphysical proper parts ('parts' hereafter), then at least one of these parts is not created by God. [prem]
(3) Either God has parts or he doesn't. [LEM]
(4) Suppose he does have parts. [assp]
Then
(5) All of God's parts are created by God. [by 1]
But
(6) One of God's parts is not created by God [by 2,4]
This is a contradiction. Hence, we must reject our assumption. Hence:
(7) God has no parts.

So by 'metaphysical proper parts' here I mean things like ontological constituents, such as a property-instance (or trope or accident or whatever). (1) is just Craig's own thoughts on the matter, and (2) is true because clearly God doesn't create his essential properties; he depends on those for his existence, since if they didn't exist then neither would he. The rest follows by the meanings of the terms and the rules of logic.

Craig says that he considers God to be a substance, presumably in the same manner we are: "Not a physical substance, of course, but a spiritual substance like a mind."

However, the case is even more clear if Craig thinks God's mind and will are distinct; for if he does, granting Craig's doctrine of aseity, then from (1) it follows God's will must be created by God. But it is absurd to suppose God creates his own will; after all, he must have a will to do that! So, either Craig's doctrine of aseity is false (which I agree with Craig it isn't) or God is not distinct from his will (which I think is right, but is really only intelligible given divine simplicity).

Craig thinks getting rid of Platonism will solve the problems concerning God's aseity; but it doesn't, since even if there are no abstract properties in us there are clearly ontological constituents (my brownness, my height, my shape, etc.). Even taking 'parts' in this sense, I think the above argument shows that if he wants to hold on to the strong doctrine of aseity set out in the quote above he needs to get rid of the idea that God has any parts at all. And if God has no parts in the metaphysical sense then it can be shown speech about God is analogical; for in our case, to say I am good is to say the quality of goodness inheres in me as an accident (or is exemplified as a property, or inheres as a trope or whatever). But since God has no parts in any of these senses, to say God is good cannot be to say this about him. And the same with any of the divine attributes. Thus our terms must be said analogically of God.

[Edit: Craig's reply here. My reply here.]

Thomistic vs. Molinist Predestination Part III

In the last post I discussed whether a Thomist could preserve both the efficacy of God's will and the libertarian freedom of our actions, and it seems to me that he can. Hence, the Molinist objection that God's causing a free action is impossible doesn't work, so we are left with the Thomist view which better preserves God's sovereignty.

The problem then, as brought up in the original post, is in how we can reconcile God's ability to cause anyone to freely choose him with the fact that God doesn't do so. For the teaching of Scripture is that God wills that all men be saved. Now, Aquinas distinguishes between God's antecedently willing that all be saved and his consequently willing that only some be saved, which I explained in the original post. The problem with Thomas' example is that God's will, unlike that of the judge example he uses, is intrinsically efficacious, even in the case of free action.

We can state the problem equivalently as follows. God wills that all men be saved, as we know from Scripture and the teaching of the Church. Since God's will is efficacious, it follows that all men are in fact saved. But it is false that all men are saved. So it seems we have a straight contradiction. Hence, we must understand the 'antecedent' will as willing in some other sense--according to Aquinas this would be a willingness rather than a simple willing--since it is clearly God's consequent will which is actually satisfied (some people are not saved and are damned). The problem is that I have difficulty understanding how God could have a "willingness" distinct from a simple willing if he is absolutely and most simple. Let me explain:

God should be construed as lacking any potentiality to be fulfilled. Now, the way I understand this consequent will, being a willingness, is as a sort of "background desire" to have everyone be saved. But a desire is something that can be fulfilled. So God has a potentiality to be fulfilled, which is false. Hence there is no such willingness.

Maybe the problem here is that we should reject this understanding of "willingness." I may simply be misunderstanding Thomas' notion here. This interpretation may be somewhat uncharitable anyway, since Aquinas explicitly argues that the order between antecedent and consequent is in God's effects and not in his absolutely simple will itself. So my question then is how this can be. One way I'm thinking of construing this willingness is as follows: God absolutely wills the existence of human beings; the natural end of each human being is union with God; so in some sense God wills their salvation just by willing their existence. So God wills their salvation in one respect, though by not willing their predestination does not will it in another respect. Hence, no contradiction. Another way might be to say that God gives men sufficient grace to choose him; (sufficient grace on the Thomistic view is grace which gives one the ability to choose God, but which does not entail one actually does); hence God wills that all men have the means to salvation; so in some sense God wills that all are saved. I am not so sure about either of these options, either as to whether they are what Thomas intended or whether they work.

The key then is to find some notion of 'antecedent will', distinct from God's simple and absolute willing. And this is where I'm stuck at. It appears that the Molinist view doesn't work since Thomism can preserve freedom and perfect sovereignty (not even mentioning the other problems with Molinism); the Thomist view seems inadequate insofar as it is not clear what God's antecedent will is, this being a willing apart from God's efficacious, absolute, and simple will. Is there some third way that I'm missing? I don't think Congruism can help here, since there is still the question of why God doesn't elect all people he creates, and from my reading Scotus's doctrine here is not much different from Thomas' or Augustine's. Maybe this is a good theological reason to accept a weaker version of God's sovereignty in favor of Molinism? Any thoughts?

Thomistic vs. Molinist Predestination Part II

In my last post I explained that God does not cause1 our free actions, but only cause2's them; hence, there can be no conflict between God's efficaciously willing that one do an action and our doing it libertarianly freely. I'd argue that one's free actions being caused is only inconsistent if we are using 'caused' in the sense of cause1. This is how I understand physical determinism:

(PD) The past state of the world, together with the laws of nature are sufficient to render necessary one unique future.

Clearly then God doesn't determine my next action A in this sense in cause2ing it, since God could have just as well created everything with the laws of nature and the past state up to my current time and yet cause2ed me to do ~A. It's only the case that I must do A under the supposition that God wills I do A, but it's not absolutely speaking necessary that I do A, since God could have willed otherwise.  In other words, libertarian freedom is possible, since even given the laws of nature + the past state of the world I could have done otherwise if God had so willed.

But maybe God's cause2ing me determines me in some morally relevant sense (where a form of determinism is morally relevant just in case if it were true it would preclude moral responsibility and freedom) since his causing is 'logically prior' to my acting. So we can generalize determinism from physical determinism to 'logical determinism' as follows:

(LD) An event E is logically determined by some state S just in case (a) necessarily the proposition expressing E (i.e. the proposition that E is the case) is true if the proposition p expressing S is true and (b) p is true.

Since necessarily if God wills that I do A then I do A, and God wills I do A, by this definition I'm logically determined to do A. So if this is a genuine morally relevant form of determinism, then God's cause2ing determines our actions and removes freedom. The problem with LD however is that it's not clear that it is a morally relevant form of determinism. After all, necessarily, if I do A then God wills I do A, and I in fact do A, but I don't determine God in any relevant sense to will that I do A. But if LD was a morally relevant form of determinism then I would.

I would simply hold to this: necessarily, God wills I do A if and only f I do A. This is true, but this is only meant to secure the efficacy and dependence of everything else for its existence on God's will.  This is similar to supervenience relations, and just like supervenience relations it only implies a necessary covariance; it does not necessarily imply any causal priority either of God's willing or my acting. To come back to the original point, we are working on different "causal plains" so to speak; I cause only in the sense of cause1, and God causes only in the sense of cause2. There is no causal priority of either of God's willing or my acting to the other.

Hence, I'm not sure this form of determinism, viz. logical "determinism", is a genuine form of determinism. I mean we can call it determinism (nomina significat ad placitum) but the question is whether it is a morally relevant kind, i.e. one which removes free will and moral responsibility. In the next and final post I'll come to the point about whether Aquinas's picture of predestination works.

Thomistic vs. Molinist Predestination Part I

This post comes out of a very large and high-quality discussion on predestination on Facebook. If you don't have Facebook you should really get it, if only because (among other things) we have a thriving Thomism group on there. I will be posting in three parts.

So, I'm kind of agnostic between Thomistic and Molinist views of predestination at the moment (though sympathetic to the Thomistic view). I'm worried about the Thomistic view since if God's will is efficacious then he should be able to bring about the salvation of all, and so the only explanation for why not all are saved is that God does not will it, which is contrary to Scripture. Aquinas replies by distinguishing between God's consequent and antecedent will. So God in general ('antecedently') wills that all men be saved, but taking all things into consideration ('consequently') wills that only some are saved; just as a judge wills that all men should live but taking into consideration particular cases wills that some should die. However, the difference between the two cases is that God's will can never be thwarted or perverted.

The problem with the Molinist view in my book is that I don't think it fits well with God's providence/omnipotence. The Molinist will reply that there's no problem, since it's not contrary to God's omnipotence if God can't bring about something that's impossible, and God's causing someone to freely choose him is impossible, since a free action can't be determined. But here I see no reason why God cannot bring about either of two contraries of a person's choice (i.e. either action A or not-A) and the action still be free--for God and creatures are working on different causal plains so to speak; God creates 'ex nihilo' by giving the whole of existence to particular states of affairs, whereas creatures cause in the sense of interacting with each other. It is only causing in the latter sense of interacting with by coercing or forcing that is incompatible with free will, and this is not the sense in which God is a cause.

To elaborate on the Thomistic point about how God can cause free actions we must distinguish different senses of the word 'cause.' First there is the sense of 'cause' in terms of interacting. Let's call this 'cause1'. So, for instance, this is what it means when I push you and 'cause' you to fall down, or when neurons cause arms to move, or if Cartesianism is true what happens when the soul causes the body to move. God does not cause in this sense; God does not cause1.

There is another sense of cause which means to create ex nihilo at evey moment, to 'sustain' or give being to things (although I have some reservations about the word 'sustain' since I think it can be misleading, since God isn't in time). We can call this cause2. God causes in this sense by being the cause of all being other than himself. He gives existence or 'esse' to everything. This is a very central doctrine to Thomism. God is the only person who causes in this sense; God is the only person who can cause2. God can cause2 anything that is possible. And on libertarian free will either of two contraries--i.e. either of action A or ~A--is possible, so God can cause2 either. Though I would agree he can't cause1 them, since that would entail determinism.

Now, maybe one can argue that even in the sense of cause2, this counts as a form of determinism which limits moral responsibility, and hence we should revert to the Molinist response. In Part II I'll respond to this point.

All Perfections are Possibly Instantiated

My logic teacher and I were reflecting on the ontological argument and we came up with this. Forgive the cheap operators. A perfection is a property which it is better to have than to lack. Let A be any perfection (say, being perfect) and let B be any non-perfection (like being imperfect) and let 'PA' mean 'A is a perfection' and 'PB' mean 'B is a perfection'. Then let PP be the principle that perfections only imply perfections:

(PP) For any property J and any property K, [PJ & [](x)(Jx --> Kx)] --> PK

Since A is a perfection and B is a non perfection:

[Prem] PA & ~PB

Now, assume for reductio that ~<>(Ex)(Ax). This is equivalent to []~(Ex)(Ax) which is equivalent to [](x)~(Ax). Since necessarily A is not exemplified by anything, then trivially [](x)(Ax --> Bx). So by our premise, [PA & [](x)(Ax --> Bx)] But by (PP) [PA & [](x)(Ax --> Bx)] --> PB. It follows that PB. But by our premise, ~PB. This is a contradiction. So we must reject our assumption. So ~~<>(Ex)(Ax). So <>(Ex)(Ax).

Remarks on "Divine Hiddenness"

[Originally posted at the Rational Gang. Please direct any comments there.]

A lot of atheists say that if God were to perform a miracle in front of their eyes, then they would believe. So then, if God is all good, and "wills all men to be saved," then why doesn't he provide such obvious evidence for his existence? Since an all-loving God is expected to reveal himself to all, and there are atheists that have reasonable nonbelief, this is evidence that God does not exist.

1. Coercion and Moral Responsibility:
A first thing to note is that God wants to preserve our moral responsibility and freedom. Now, almost all accept that it is possible to coerce someone into doing something. This can be done, most obviously, by physical force, as when kidnappers pick up a hostage and put him into a van against his will. Clearly in this context the person is not responsible for this event. Another, more interesting case, is where a mother is forced by a cruel killer to choose between her two sons being shot, or else they will both be tortured to death. The mother is not morally responsible, or at least very responsible, if she ultimately chooses one child in order to save at least one; the ultimate responsibility goes to the wicked sadist who is forcing the "choice" upon her. The point here though is that the mother is not literally coerced by force; rather, she is coerced by reasons. She knows that if she doesn't pick one, they will both be lost. In cases of coercion, one loses moral responsibility for one's actions.

But then it's straightforward applying this to the case of God. God wants us to have the freedom to choose him. He doesn't want to coerce us and ultimately remove our responsibility. But if one can be coerced by reasons, and incontrovertible proof would coerce some people into belief, then it's easy to see why God would not provide incontrovertible proof to absolutely everyone in order that they might all have absolute certainty: It removes responsibility on our part.

2. Divine Obviousness:
A reply inspired by the Thomistic tradition is to say that, as a matter of fact, God isn't hidden at all. Rather, God, as the ultimate source of all being, completely and totally permeates throughout nature. This is how God is omni-present, not in the sense that the universe is God (a la pantheism), but rather that the very existence of things is just one step away from God himself. However, being creatures of habit, and being familiar with the world, we take the awful mystery of existence for granted, and fail to see the divinity which sustains it all. But this is no failure on God's part. It's a failure of us to appreciate God's creation.

3. They're Wrong:
While atheists say they know that if God were to provide them a clear sign such as a miracle then they would convert, that might, for all we (or they) know, not be the case. In fact, this is what we find from the Christian perspective in John 11, where the Pharisees, even upon hearing and accepting that Christ performed miracles, refused to acknowledge him: "So the chief priests and the Pharisees gathered the council, and said, 'What are we to do? For this man performs many signs. If we let him go on thus, every one will believe in him, and the Romans will come and destroy both our holy place and our nation.'" So for these people, even the greatest of miracles would not convince them. How would this apply in the case of others?

According to one theory of the relationship between God's foreknowledge and our freedom, Molinism, God knows infallibly what we would freely do in any given circumstance. Supposing this view is coherent, we can apply it in the case of atheists: God does not give incontrovertible evidence to people who he knows that, in any circumstance where they are given incontrovertible evidence, would not convert. This means that atheists cannot say, "Well, if only God had given me more evidence, then I would have converted." Not necessarily.

If this is too strong, we can even weaken the principle: God does not give reasonable evidence to people who he knows that, in any circumstance where they are given reasonable evidence, would not convert. This seems more plausible anyway. For one, it doesn't seem necessary for God to give everyone incontrovertible evidence. If we are given reasonable evidence and fail to see it, then that is our fault. Moreover, this widens the group of people we are dealing with because, though some may accept God given incontrovertible evidence, fewer will accept God given only reasonable and sufficient evidence, which may explain a large number of unbelievers.

What this ultimately shows is that, even if some atheists are not actually given incontrovertible, or even reasonable, evidence, this doesn't make it the case that God is doing something evil, the reason being that they would not accept the evidence in other feasible circumstances anyhow. It would be for God to cast pearls to swine.

4. Rationality and Reasonableness:
This leads to a further question: are atheists, in fact, given reasonable evidence? Their whole argument may be begging the question here. After all, theists believe that there is reasonable evidence for the existence of God. But then if God has provided everyone with reasonable evidence, the argument fails, because this is precisely what is in question, i.e. whether belief in God is reasonable.

The atheist finds himself in a bit of a pickle. In proposing that there is not enough evidence for Christian belief, he must give us a criterion of reasonable belief that is strong enough such that it supports the reasonableness of atheism, but is not so strong that it begs the question against the theist. To put it another way, there is a tension in the claim that "the reasonableness of atheism entails the unreasonableness of theism," because it is possible that, given the atheist's criterion of reasonableness, the theist can turn right around and say, "Well, it is reasonable to believe that God might not reveal himself to everyone with absolutely convincing evidence."

5. Five points.
To sum up, I think there are five reasons we can give as to why God's existence is not incompatible with "divine hiddenness."
(a) Reasons can coerce. So if one were given incontrovertible reasons to believe in God, then one would be coerced into belief in God. But since coercion is incompatible with significant moral responsibility, and God wants to leave us morally responsible, God does not want to coerce us. Therefore, God does not give incontrovertible evidence.
(b) God is not in fact hidden; rather, God is obvious. However, humans fail to recognize the mystery of their own existence and the creation before them, and fail to see the divine in nature.
(c) For all we know, God does not give those who have a reasonable non-belief in God incontrovertible evidence, because he knows that in all circumstances, they will not believe in God.
(e) For all we know, God does not give those who have a reasonable non-belief in God reasonable evidence, because he knows that in all reasonable circumstances, they will not believe in God.
(e) The atheist begs the question against the theist in two ways: first, by saying that his nonbelief in God is reasonable, since the theist believes there are reasonable grounds for belief, and second, by saying that his reasonable nonbelief implies God's nonexistence, since the the theist can say that, by the atheist's own criteria, it is reasonable to believe that God has reasons to stay hidden.

All in all, this provides a strong cumulative case for believing that the argument from divine hiddenness doesn't work, and that theism is left unharmed.

False Senses of God's Goodness

Introduction:
What does God's omnibenevolence consist in? I think that we need to do a little more work on fully explaining what we mean by this. In fact I'm somewhat distraught, because it seems that if we affirm God's all-goodness we should already know what we're talking about. I think that some of the notions which are typically bound up with omnibenevolence really don't make sense.

In a post a while back I presented the Prussian Free Will Defense. I think the argument is sound. The conclusion that we end up drawing from it is the following. It will be important in determining what omnibenevolence can be and what it cannot be:

(C1) It is not the case that there is some moral principle in the nature of an omnibenevolent and omnipotent being which prevents him from creating a creature who does something immoral.

"Actualizing all possible goods":
I think it's relatively easy to understand omnipotence and omniscience. Omnipotence is just the ability to do all that is possible. Omniscience is just the knowing of all things. So does omnibenevolence consist in the actualizing of all good things?

I'm convinced that this notion is incoherent. (C1) shows that God's omnibenevolence is compatible with God's not actualizing worlds which he could have actualized in which all moral agents always freely choose to do the right thing. And that is certainly incompatible with God's omnibenevolence meaning that he actualizes all possible goods.

The idea that omnibenevolence means "actualizing every possible good" is probably in contradiction with the idea of omnipotence anyhow. One could think of two goods which are mutually exclusive but are both within the range of God's power. For example, my marrying Lucy and my marrying Edith are both goods which are mutually exclusive and possible for God to actualize. However, God can only bring about one of these. Hence, if God is omnipotent, he can't be omnibenevolent if that means that he actualizes every possible good; there are some goods which God could actualize but doesn't.

"Preventing all unnecessary evil":
It seems that the existence of an all-good being must preclude the existence of unnecessary evil. Responses to the problem of evil like Plantinga's Free Will Defense say that some evils which take place are justified by greater goods. But the atheist objects that there are some evils which are probably not justified by greater goods, and in general, the theist agrees that if this were true then an omnibenevolent God would not exist. The typical attempt to solve the problem is to claim that no evils are unnecessary.

But what if the theist were to take a different route and say that even if there were evils which could have been prevented that this doesn't rule out the existence of an all-good God? In fact, I think (C1) shows that this is true. For take again the possible world W1 in which all agents always freely choose to do what is good. (C1) shows that there is no moral principle in the nature of an omnibenevolent being which prevents him from actualizing a world W2 where an evil is committed even though he could have actualized W1 instead. But in that case, some of the evils which take place are unnecessary; they could have been prevented by God's actualizing W1.

A Problem:
So we see that, based on (C1), omnibenevolence cannot imply the actualizing of all possible goods. Neither does it imply the preventing of all unnecessary evils. Yet this seems to sap omnibenevolence of any real content. How could we call something "all-good" which allows needless suffering and withholds a great many good things from us?

To me this is a big problem. I want to find some possible ways in which we can understand omnibenevolence in light of these objections. Any thoughts?

What Does It Take to Be An Atheist?

Consider some valid theistic arguments and what an atheist must do to deny their soundness.

Argument A - A Necessary Concrete Entity:
(1) Possibly a necessary concrete being exists implies a necessary concrete being exists.
(2) Possibly, a necessary concrete being exists.
(3) Therefore, a necessary concrete being exists.

Assume further that it can be shown that the necessary being is God.

What must the atheist do to deny this argument? (1) is just axiom S5. Therefore they must deny (2). This implies that (a) possibly nothing exists or (b) necessarily, there exists at least one contingent entity. This also implies that all concrete entities are contingent.

Atheist Theorem 1 (AT1): It is not possible that a necessary concrete being exists.
Atheist Theorem 2 (AT2): Either (a) possibly nothing exists or (b) necessarily there exists at least one contingent entity.
Atheist Theorem 3 (AT3): For any concrete entity x, x is contingent.

Disproving AT1, AT2 or AT3 is sufficient for refuting atheism.

Argument B - The Scotistic Cosmological Argument:
(1') Whatever is possible is contingent or necessary.
(2') A first cause is possible.
(3') Therefore, a first cause is contingent or necessary.
(4') Any contingent substance is possibly actualized by another substance.
(5') A first cause is not possibly actualized by another substance.
(6') Therefore a first cause is not contingent.
(7') Therefore, a first a cause is necessary.

What must the atheist do to deny this argument? The atheist can only really deny either (2) or (4).

Atheist Theorem 4 (AT4): Either (a) a first cause is impossible or (b) some contingent substance is not possibly actualized by another.

Hence, disproving this disjunction AT4 is sufficient for refuting atheism. Saying that (b) is false also leads to some interesting consequences about infinite regresses.

Argument C – A Modal Cosmological Argument:
(1*) Every contingent entity possibly has an external cause.
(2*) If the sum total of contingent concrete entities C has an external cause, that cause is necessary.
(3*) C is a contingent concrete entity.
(4*) Possibly, C has an external cause.
(5*) Therefore, possibly there is a necessary cause of C.
(6*) Therefore, there is a necessary cause of C.

What must the atheist deny? All premises seem quite strong. He must then deny (1*).

Atheist Theorem 5 (AT5): For some concrete contingent entity x it is impossible that x is caused.

Disproving AT5 is sufficient for disproving atheism.

Thus far we have Atheist Theorems 1-5:

AT1: It is not possible that a necessary concrete being exists.
AT2: Either (a) possibly nothing exists or (b) necessarily at least one contingent entity exists.
AT3: For any concrete entity x, x is contingent.
AT4: Either (a) a first cause is impossible or (b) some contingent substance is not possibly actualized by another.
AT5: For some concrete contingent entity x it is impossible that x is caused.

Disproving one of these theorems is sufficient for disproving atheism. Showing a contradiction between these beliefs and other atheist beliefs is sufficient for showing atheism as such to be incoherent. To me all of these propositions seem quite implausible in their own right.

Aristotelianism and the Christian Worldview

Originally posted here.

Introduction:
Throughout the centuries the Christian tradition has had a love-hate relationship with Aristotle. His logic and metaphysical categories provided strong tools for developing and formalizing such classic doctrines as the Incarnation and the Holy Trinity. On the other hand, he famously held that the universe was eternal and that there was no first man such as Adam, putting him at odds with Christian belief. Yet in the midst of this conflict, there is much to be gathered and adopted by the Christian. Here I’d like to examine a few of Aristotle’s ideas about the essences of things and see how they relate to the Christian view of man.

Essences:
The first thing to note is that humans, along with every other kind of thing, have “essences” or “natures”. An essence is simply that in virtue of which a thing is what it is. It’s what makes the definition of a thing true. It’s also the grounding of a thing’s essential properties, i.e. those properties which are intrinsic to that type of thing. Without essences we could not form inductive laws, we could not differentiate between kinds of things, and we couldn’t even properly define our concepts.

Essences entail that things have natural ends or functions (what Aristotle calls the “telos”). It would be incorrect to understand “function” in terms of the functions of human artifacts such as wheels or fishing rods. Rather, things have functions in the sense that they function in a certain natural way. So we can see clearly that by their very essences things like dogs or snakes have natural functions, including sensory perception, reproduction, self-change, and sustenance. This is what makes it good for them to pursue certain goals, like eating food or reproducing. To generalize, it is good for them to fulfill their functions.

This may seem irrelevant, but it has truly significant consequences for us as well. It gives medicine a normative structure, making sense of the strong and reasonable intuition that things such as broken bones or tumors are defects, while other things such as firmness of muscle or thorough digestion are indicators of health. It means that we all have certain functions which it is objectively good for us to fulfill. This can provide a foundation for objective morality and a guide to living our lives. Thus understood, essences are both indispensable and significant.

The Christian Picture:
So what is essential to humanity? Well, recall that essences are what differentiate things from entities of other kinds. In attempting to discover our essence then, it would be useful to see how we differ from other things. We share some characteristics with non-living things because we too are made of matter and have mass. But we are different from them precisely in virtue of the fact that we are alive. We are different from some living things like plants due to our sensory capabilities which we have in common with other animals. Yet we humans can be distinguished even from these creatures by our rationality. Unlike other animals, we can abstract from concrete particulars to general universal truths. Thus, humans are by their very essence rational animals.

How well does this fit into the Christian view of things? Consider the idea that God is a being with infinite knowledge, and thus an intellect. In Romans 11:33 for instance, Paul the Apostle praises God’s omniscience: ” O the depth of the riches of the wisdom and of the knowledge of God!” Aristotle’s view confirms precisely what the believer says, that is, that humans are by their very essence endowed with an intellect and will like God’s. As Genesis 1:27 says: “God created man to his own image: to the image of God he created him: male and female he created them.” Every human, male and female, is essentially made in God’s image.

We can also conclude from Aristotle’s view that, because humans have an essence with natural ends, there are some things that are objectively good for all of us, and that these objective moral truths are available to anyone who uses his or her reason and conscience. This confirms what we find in Romans 2:14-15: “For when the Gentiles, who have not the law, do by nature those things that are of the law; these, having not the law, are a law to themselves. Who show the work of the law written in their hearts, their conscience bearing witness to them.”

Much more could be said about all of these ideas. Yet it becomes clear how strongly these Aristotelian theses can be used to support what the Christian affirms. Hence, there is much fruit to be found by the Christian in the Aristotelian tradition, making the ancients very worthy of our attention.