Wilde lectures now online

Videos of my 2019 Wilde Lectures in Natural Theology and Comparative Religion at Oxford’s Oriel College are now available online.

Here are the slides:

• Beauty
• Scepticism
• Forms I
• Forms II
• The finite

Why the Five Ways don't prove the existence of five (or more!) deities

Here is a potential problem for Aquinas’ Five Ways. Each of them proves the existence of a very special being. But do they each prove the existence of the same being?

After giving the Five Ways in Summa Theologica I, Aquinas goes on to argue that the being he proved the existence of has the attributes that are needed for it to be the God of Western monotheism. But the problem now is this: What if the attributes are not all the attributes of the same being? What if, say, the being proved with the Fourth Way is good but not simple, while the being proved with the First Way is simple but not good?

I now think I see how Aquinas avoids the multiplicity problem. He does this by not relying on Ways 3–5 in his arguments for the attributes of God, even when doing so would make the argument much simpler. An excellent example is Question 6, Article 1, “Whether God is good?” Since the conclusion of the Fourth Way is that there is a maximally good being, it would have been trivial for Aquinas to just give a back-reference to the Fourth Way. But instead Thomas gives a compressed but complex argument that “the first effective cause of all things” must be desirable and hence good. In doing so, Aquinas is working not with the Fourth Way, but the Second Way, the argument from efficient causes.

Admittedly, at other times, as in his arguments for simplicity, St. Thomas relies on God not having any potentiality, something that comes directly from the First Way’s prime mover argument.

This reduces the specter of the attributes being scattered between five beings, corresponding to the Five Ways, to a worry about the attributes being scattered between two beings, corresponding to the First and Second Ways. But the First and Second Ways are probably too closely logically connected for the latter to be a serious worry. The First Way shows that there is a being that is first in the order of the actualizing of the potentiality for change, an unchanged changer, a prime mover. The Second Way shows that there is a being that is first in the order of efficient causation. But to actualize the potentiality for change is a form of efficient causation. Thus, the first being in the order of efficient causation will also be a prime mover. So there is a simple—so simple that I don’t recall Aquinas stating it in the Summa Theologica—argument from the conclusion of the Second Way to the same being satisfying the conclusion of the First Way.

Consequently, in the arguments for the attributes of God, Aquinas needs to only work with the conclusion of the Second Way, and all the attributes he establishes, he establishes as present in any being of the sort the Second Way talks about.

That still leaves a multiplicity problem within the scope of a single Way. What if there are multiple first efficient causes (one for earth, one for the moon, and so on, say)? Here Thomas has three solutions: any first being has to be utterly simple, and only one being can be that on metaphysical grounds; any being that is pure actuality has to be perfect, and only one being can be that; and the world has a unity and harmony that requires a unified first cause rather than a plurality of first causes.

Finally, when all the attributes of God have been established, we can—though Aquinas apparently does not, perhaps because he thinks it’s too easy?—come back to Ways Three through Five and ask whether the being established by these ways is that same one God? The ultimate orderers of the world in the Fifth Way are surely to be identified with the first cause of the Second Way once that first cause is shown to be one, perfect, intelligent, and cause of all other than himself. Plausibly, the maximally good being of the Fourth Way has to be perfect, and Aquinas has given us an argument that there is only one perfect being. Finally, the being in the conclusion of the Third Way is also a first cause, and hence all that has been said about the conclusion of the Second Way applies there. So, Aquinas has the resources to solve the multiplicity problem.

All this leaves an interesting question. As I read the text, the Second Way is central, and Aquinas’ subsequent natural theology in the Summa Theologica tries to show that every being that can satisfy the conclusion of the Second Way has the standard attributes of God and there is only one such being. But could Aquinas have started with the Third Way, or the Fourth, or the Fifth, instead of the First and Second, in the arguments for the divine attributes? Would doing so be easier or harder?

Wilde Lectures schedule

For the benefit of any readers who will be in Oxford this month, here is a schedule of my Wilde Lectures in Natural and Comparative Religion.

Wilde Lectures

I've been invited to give the Wilde Lectures in Natural and Comparative Religion at Oxford. It will be in the spring of 2018 or 2019, but I haven't decided which. I am tentatively thinking of speaking on underdiscussed--or undiscussed--arguments for the existence of God.

Balancing between theism and atheism

The problem of evil consists of three main parts:

• The problem of suffering.

• The problem of evil choices.

• The problem of hiddenness (which is an evil at most conditionally on God’s existing).

The theist has trouble explaining why there is so much suffering. The atheist, however, has trouble explaining why there is any suffering, given that suffering presupposes consciousness, and the atheist has trouble explaining why there is any consciousness.

Of course, there are atheist-friendly naturalistic accounts of consciousness. But they all face serious difficulties. This parallels the fact that theists have theodical accounts of why God permits so much suffering, accounts that also face serious difficulties.

So, on the above, considerations of suffering are a net tie between theism and atheism.

The theist does not actually have all that much trouble explaining why there are evil choices. Libertarian free will does the job. Of course, there are some problems with libertarian accounts of free will. These problems are not, I think, nearly as serious as the problems that theists have with explaining why there is so much suffering or atheists have with explaining why there is consciousness. Moreover, there is a parallel problem for the atheist. Evil choices can only exist given free will. Prima facie the most plausible accounts of free will are libertarian agent-causal ones. But those are problematic for the atheist, who will find it difficult to explaining where libertarian agents come from. The atheist probably has to embrace a compatibilist theory, which has at least as many problems as libertarian agent-causalism.

So, considerations of evil choices look at best as a net tie for the atheist.

Finally, there is the problem of hiddenness for the theist. But while the theist has trouble explaining how we don’t all know something so important as the existence of God, the atheist has epistemological trouble of her own: she has trouble explaining how she knows that there is no God. After all, knowledge of the highly abstract facts that enter into arguments regarding the existence of God is not the sort of knowledge that seems to be accessible to evolved natural beings.

So, considerations of knowledge of the existence or non-existence of God look as a net tie.

The problem of evil, however, exhausts the powerful arguments for atheism. But the above considerations far from exhaust the powerful arguments for theism.

The above reasoning no doubt has difficulties. But I want to propose it as a strategy for settling disputes in cases where it's hard to assign probabilities. For even if it's hard to assign probabilities, we can have good intuitions that two considerations are a wash, that they provide equal evidence. And if we can line up arguments in such a way, being more careful with issues of statistical dependence than I was above, then we can come to a view as to which way some bunch of evidence points.

Faith and credence

Alice: I just saw a giraffe in my yard.
Bob: I always trust you about what's in your yard. So I think it's 55% likely there is a giraffe in your yard.

No, Bob doesn't trust Alice. If he trusted her, his credence that she's telling the truth would have been high.

I am not claiming that we always assign high credence in the assertions of someone we trust in a given matter. This dialogue is perfectly sensible.

Alice to Carla: I just saw a giraffe in my yard.
Bob to Dave: I always trust Alice about what's in her yard. I think I might have just overheard her saying that she saw a giraffe in her yard. So now I think it's 25% likely there is a giraffe in her yard.

In the second dialogue, the reason Bob's credence that there is a giraffe in Alice's yard is lowish has little to do with not trusting Alice about these matters. Rather, it is that he doesn't trust his hearing--he's far from sure that he heard her report a giraffe. I assume in the first dialogue, Bob is quite confident that Alice reported a giraffe--if he isn't, there is no problem.

Trust doesn't require high credence in the assertions of the person we trust. But:

1. If one trusts x with regard to p-type propositions, one assigns high credence to non-exclusive disjunctions like: p is true or x did not assert p.

When I started thinking about this, I also thought it required a high conditional probability P(p | Alice asserted p). But it doesn't require that. Suppose I trust Alice about mathematics and I hear her confidently say something that vaguely sounded like "The derivative of a sine function is a tangent." My unconditional probability that the derivative of a sine function is a tangent is very low (I can just see in my mind that the slope of a sine is bounded and a tangent is unbounded), but even my conditional probability on Alice's asserting it is very low. It's not that I actually don't trust Alice. Rather, it's that if she asserted that the derivative of a sine were a tangent, I would lose my trust in her mathematical knowledge. (It might be a bit more complicated. Trust might be compatible with accepting minor occasional slip-ups. So I might think it's one of those. So maybe even if she said this, I would be trusting her in general--but not in this circumstance.) And it's compatible with trust that there be possible circumstances where one would rationally stop trusting.

Now, here is a question that has had some discussion in the literature: Is it rationally possible to have explicit Christian faith (I am using "explicit" to distinguish from the kind of faith that an "anonymous Christian" might have) and assign only a modest (not at all high) credence to the proposition that God exists? I think that given fairly uncontroversial historical evidence, this can't happen. Here is why:

2. One has explicit Christian faith only if one trusts Jesus in central parts of his teaching.
3. The historical evidence clearly shows that Jesus existed and that a central part of his teaching is that God loves us.

Given the uncontroversial historical evidence, a rational person will accept with very high credence that a central part of Jesus's teaching is that God loves us. By (1) and (2), if she has explicit Christian faith, she will also assign a high credence to the disjunction that God loves us or Jesus didn't centrally teach that God loves us. Since the second disjunction is uncontroversially historically false, the credence will transfer to the first disjunct, and she will assign a fairly high credence to the claim that God loves us. But that God loves us obviously entails that God exists. So she will assign a fairly high credence to that, too. And hence her credence won't be modest (i.e., not at all high).

Interestingly, as far as arguments like this go, it might be possible to have faith in God while only assigning a modest credence to the existence of God. Someone who has faith in God will trust God. So she will assign a high credence to disjunctions like: God loves us or God didn't say God loves us. But while it's uncontroversial that Jesus said God loves us, it's controversial that God said God loves us, since it's controversial whether God exists, but the existence of Jesus is an uncontroversial historical matter (I understand that even the Soviet historians eventually stopped saying that there was no Jesus).

Do theists believe by faith in God that God exists?

Do theists typically believe by faith in God that God exists? Faith is much more than propositional belief. But someone who has faith in a person can believe propositions by faith. What does that mean? I want to start with this necessary condition:

1. x believes that p by faith in y only if x believes that p because x takes y to have assured her specifically that p.

To make the condition sufficient as well as necessary one would at least need to specify something that ensures that the the apparent assurance causes the belief in the right way.

But given (1), how could one believe that y exists by faith in y? One would have to believe that y exists because one took y to assure one specifically to that effect. But that would be rationally odd. Granted, I could hear a voice in the dark assuring "I exist", and I could first believe that The Voice is assuring me that it exists, and conclude from this that The Voice exists. But I wouldn't be concluding that The Voice exists because of the specific content of what was voiced, but simply because something was voiced. The connection between the assurance and the belief that The Voice exists is not a connection in the right way for belief by faith.

Granted, it is possible that the voice sounds so trustworthy that I first form the belief that the content of what was said is true, and then because of that I come to believe that The Voice exists. In that case, I would indeed be believing that The Voice exists and doing so by faith. But I would be ignoring an obvious logical inference from one's data and getting the conclusion of that inference by other means. So what we seem to learn from the case of The Voice is this:

2. Anybody who believes by faith in y that y exists is in a position to believe by obvious logical inference and not by faith that y exists.

And we would expect that often people in that position would go for the obvious logical inference.

But that doesn't quite answer the question I started with, namely whether theists typically believe by faith that God exists. For it could be that (2) is true, and that most people do in fact go for the obvious logical inference, but the voice of God assuring them of his existence is so powerful that in most cases the belief is overdetermined: they believe both by obvious logical inference from God's assurance and by faith.

There is a second complication. One might have faith in y under one description and believe that y exists under another description. For instance, suppose that The Voice in the dark says: "I am the brother you never thought you had." Then you might believe your brother exists by faith in The Voice. This model works well for Christianity. A Christian might well believe that God exists by faith in Christ, even though Christ is in fact God.

Does the model work outside of Christianity, say in Old Testament times? Well, the Voice/brother case suggests that it might work in cases of religious experience. But it seems implausible that most of the theists in Old Testament times were theists because they had a religious experience whose content included an assurance of God's existence. Maybe, though, one can introduce the notion of indirectly believing by faith, where you indirectly believe something by faith provided that you infer it from something that you (directly) believe by faith. To adapt a Plantinga example, God might give you a religious experience that God forgave you your sins; trust in the "inner voice" (i.e., in God, but you don't know that right away) leads you to believe by faith that God forgave you your sins; and then you conclude by logic that God exists.

I don't have an answer to the question I started with, whether theists typically believe by faith in God that God exists. But I have a story that would have to hold for the answer to be affirmative. Typical theists would either have to be in a rational overdetermination scenario or they would have to be in a position where the difference between two different ways of referring to God can be leveraged to make it rationally possible for them to first believe in an assurer, who happens to be God, and then in God as such.

Symmetries in laws

Theists have often noticed that theism provides a nice aesthetically-based explanation for why we have simple laws, namely that such laws are beautiful and this gave God reason to enact them. (One can run this in two ways: (1) such laws are objectively beautiful, and God made them because of their objective beauty; (2) such laws are beautiful to us, and God created a world where the laws are beautiful to the intelligent creatures therein.)

Another interesting question about the fundamental laws is why they exhibit such nice symmetries. This question on its face seems independent of the question of why the laws are simple. You can have simple but asymmetric laws, and complex but symmetric ones. Again, an aesthetic theistic explanation seems to work well here (and again, it comes in two forms: either the symmetries are objectively beautiful or God made a world where the aesthetic properties of the laws fit with the aesthetic sensibilities of the intelligent creatures).

One might hope that symmetry considerations would thus allow one to run a teleological argument for the existence of God that escapes from the difficulty of making the notion of simplicity precise. However, while I think there is hope of a symmetry-based theistic argument, I don't think it escapes from the difficulties of theoretical simplicity. Any set of laws of nature that has an infinite space of solutions has an infinite number of symmetries: any bijection of the space of solutions onto itself is a symmetry. When we are excited by a potential symmetry like charge-parity-time invariance, we are excited by the fact that the symmetry can be specified in a simple way with respect to physically natural quantities. And if we can make sense of these twin notions (simplicity and physical naturalness), then we can likewise make sense of the notion of the simplicity of laws. So while a symmetry-based argument may provide additional evidence for the existence of God, it is subject to the same main difficulty as the simplicity of laws argument. (That said, I think this difficulty is not fatal.)

An enthymematic argument for the existence of God

Scepticism and causeless events

Suppose that there is no First Cause. Then there can be uncaused events—the coming into existence of the universe is an example, for instance. Now consider the Ultimate Sceptical Hypothesis (USH): you are a nonmaterial being that is the only thing that ever exists; you came into existence the previous moment for no cause at all; and there is no cause of your having the presnet occurrent mental states you now have; and you have just these occurrent mental states and no other states.

Compare, now, USH to what its main nonsceptical alternative is if there is no First Cause. That main alternative will be SN: scientific naturalism, with the initial state of the universe being a brute, unexplained fact. USH is simpler than SN. It is simpler on the crude criterion of entity counting: USH has only one entity, you, while SN has many atoms, galaxies, houses, geckos, etc. However, if we count only unexplained entities, as I suggested in a previous post, USH has only you and your present occurrent mental states (which there aren't many of!), while PN has the universe and its initial state, so maybe we have a tie. But PN is much more descriptively complex: it includes a number of laws of nature with various constants, for instance, as well as a high-energy extremely low entropy initial state. While you just have whatever occurrent mental states you now have—which is not much at all (how much of a thought can you think in an instant). So USH seems to be preferable to PN on grounds of parsimony.

Thus, rejecting a First Cause leads to scepticism.

This is, of course, a variant of a Rob Koons argument.

48 arguments against naturalism

Consider this argument:

1. A desire to be morally perfect is morally required for humans.
2. If naturalism is correct, a desire to be morally perfect cannot be fulfilled for humans.
3. If a desire cannot be fulfilled for humans, it is not morally required for humans.
4. Therefore, naturalism is not correct.

This argument provides a schema for a family of arguments. One obtains different members of the family by replacing or disambiguating the underlined terms in different ways.

If one disambiguates "naturalism" as physicalism (reductive or not), one gets an argument against physicalism (reductive or not). If one disambiguates "naturalism" in the Plantinga way as the claim that there is no God or anybody like God, one gets an argument for theism or something like it. Below I will assume the first disambiguation, though I think some versions of the schema will have significant plausibility on the Plantingan disambiguation.

One can replace "morally required" by such terms as "normal", "non-abnormal" or "required for moral perfection".

One can replace "to be morally perfect" by "for a perfect friendship", "to be perfectly happy" or "to know with certainty the basic truths about the nature of reality" or "to know with certainty the basic truths about ethics" or "to have virtue that cannot be lost". While (1) as it stands is quite plausible, with some of these replacements the requiredness versions of (1) become less plausible, but the "non-abnormal" version is still plausible.

Probably the hardest decision is how to understand the "cannot". The weaker the sense of "cannot", the easier it is for (2) to hold but the harder it is for (3) to hold. Thus, if we take "cannot" to indicate logical impossibility, (2) becomes fairly implausible, but (3) is very plausible as above.

I would recommend two options. The first is that the "cannot" indicate causal impossibility. In this case, (3) is very plausible. And (2) has some plausibility for "moral perfection" and all its replacements. For instance, it is plausible that if naturalism is true, certain knowledge of the basic truths about the nature of reality or about ethics is just not causally available. If, further, moral perfection requires certainty about the basic truths of ethics (we might read these as at the normative level for this argument), then moral perfection is something we cannot have. And if we cannot have moral perfection, plausibly we cannot have perfect friendship either. Likewise, if naturalism is true, virtue can always be lost due to some quantum blip in the brain, and if moral perfection requires virtue that cannot be lost, then moral perfection is also unattainable. And perfect happiness requires certain knowledge of its not being such as can be lost. Maybe, though, one could try to argue that moral perfection is compatible with the possibility of losing virtue as long as the loss itself is not originated from within one's character. But in fact if naturalism is true, it is always causally possible to have the loss of virtue originate from within one's character, say because misleading evidence could come up that convinces one that torture is beneficial to people, which then leads to one conscientiously striving to become cruel.

The second option is that the "cannot" is a loosey-goosey "not really possible", weaker than causal impossibility by not counting as possible things that are so extraordinarily unlikely that we wouldn't expect them to happen over the history of humankind. Thus, in this sense, I "cannot" sprout wings, though it seems to be causally possible for my wavefunction to collapse into a state that contains wings. Premise (2) is now even more plausible, including for all the substituents, while premise (3) still has some plausibility, especially where we stick to the "morally required" or "required for moral perfection", and make the desire be a desire for moral perfection.

If I am counting correctly, if we keep "naturalism" of the non-Plantingan sort, but allow all the other variations in the argument, we get 48 arguments against naturalism, though not all independent. Or we can disjoin the conjunctions of the premises, and get an argument with one premise that is a disjunction of 48 conjunctions of three premises. :-)

First Order Logic and an ontological argument

[I also posted this on prosblogion.]

I want to give this argument in part to provoke a bit of discussion of the role of FOL in philosophy. I don't think the argument carries great weight, in large part because of Objection 2 (see the end).

1. (Premise) The inferences allowed by classical First Order Logic (FOL) combined with a modal logic that includes Necessitation are valid.
2. (Premise) If every being is contingent, then possibly nothing exists. (A material conditional)
3. Necessarily something exists. (By 1)
4. So, there is a necessary being. (By 2 and 3)

The proof of (3) is as follows. Classical logic allows (Ex)(x=x) to be inferred from (x)(x=x). Since (x)(x=x) is a theorem, so is (Ex)(x=x), and hence by the rule of Necessitation, we have: Necessarily (Ex)(x=x). And thus (3) follows. And of course Necessitation is a part of standard modal systems like M, S4 and S5.

I think (2) is intuitively plausible. Here is one way to try to argue for it:
5. (Premise for reductio) Premise (2) is false.
6. (Premise) The non-existence of non-unicorns does not necessitate the existence of unicorns.
7. Every being is contingent and it is necessary that at least one thing exists. (By 5)
8. Necessarily, if no non-unicorns exist, then at least one thing exists. (By 7)
9. Necessarily, if no non-unicorns exist, then at least one unicorn exists. (By 8) 
Since (9) contradicts (6), our reductio argument for premise (2) is complete.

(I am grateful to Josh Rasmussen for simplifying my original argument.)

Now, the weak point in the argument, I think, is premise 1, and specifically the assumption of classical FOL which allows the derivation of (Ex)F(x) from (x)F(x). In a free logic, this wouldn't happen.

But it is still an interesting fact, and a real cost to contingentism (the view that all beings are contingent), that it requires one to abandon classical logic or modify Necessitation. After all, there is some non-negligible prior probability that classical logic and Necessitation license only valid inferences.

Moreover, there is the question of why one should go for a free logic? If one's reason for going for a free logic is precisely that FOL licenses the derivation of (Ex)F(x) from (x)F(x), then one runs the danger of begging the question against the anti-contingentist, in that the derivation is valid (in the sense that necessarily if the premise is true, so is the conclusion) if there is a necessary being.

Objection 1: There is likewise a cost to the non-contingentist who is prevented from adopting those logics on which it is provable that possibly nothing exists.

Response: The non-contingentist who accepts such a logic can still make the move of distinguishing metaphysical and narrowly logical necessity. She can then say that the logic gives an account of narrowly logical necessity. Therefore, all that is shown in such a logic is that it is narrowly logically possible that nothing exists, but not that it is metaphysically possible that nothing exists. On the other hand, it is much harder for the contingentist to make the analogous move of saying that (3) is true in the case of "narrowly logical necessity". For it is widely accepted that if there is a distinction between metaphysical and narrowly logical necessity, the narrowly logical necessity is stronger of the two. Thus, if one accepts (3) with "narrowly logical necessity", one accepts (3) with metaphysical necessity, too.

Objection 2: There are other good reasons to accept free logic, besides the fact that FOL licenses the derivation of (Ex)F(x) from (x)F(x). Specifically, FOL+Necessitation implies that:
10. Necessarily (Ex)(x=a)
is true for every name a.

Response: This objection almost convinces me and is one of the main reasons why I think that while my argument lowers the probability of contingentism, it is not very powerful.

I do think there are two speculative responses to the objection, which is why I think my argument still has some weight.

i. The truth of (10) for every "name" a shows that FOL's "names" do not correspond in function to names in natural languages. In particular, they show that when translating natural language sentences into FOL, one can only employ FOL's "names" for necessary beings. This shows a significant limitation of FOL--namely, that FOL has no way of translating sentences like "Socrates is mortal." However, the fact that a logic has no way of translating a sentence does not mean that the logic's inferences are invalid. There is probably no standard formal logic that can translate all sentences of natural language.

ii. Another move in defense of FOL+Necessitation is that we should see the inclusion of non-dummy names in a language L as embodying existential assumptions about the referents of these names. Consequently, when we give the Tarskian semantics for a modal logic built on top of FOL, the recursive clauses for "Necessarily s" and "Possibly s" in a language L under an interpretation J should respectively read:
- Necessarily: If e(L,J), then s.
- Possibly: e(L,J) and s.
Here, e(J,L) is the conjunction of all metalanguage claims of the form "a* exists" where "a*" is a metalanguage name for the entity that the L-name "a" refers to under J, if L contains any names, and is any tautology otherwise. Then my initial argument needs to be run in a language with no names.

The Weak Weak Principle of Sufficient Reason

Richard Gale and I have shown that once you grant:

• WPSR: for all contingent truths p, it is possible that p has an explanation,

the existence of a necessary and causally efficacious being necessarily follows (given some plausible necessary truths as premises). WPSR is the weak PSR. The strong PSR claims that every contingent truth has an explanation. The WPSR merely claims that every contingent truth can be explained, i.e., that there is some possible world where it is explained, though it prima facie leaves open the possibility that some contingent truth actually lacks an explanation, though it could have had one. One might worry about the WPSR because one might think that our world contains some in principle inexplicable processes. If that is one's worry, one might be attracted to:

• WWPSR: possibly WPSR is true.

WWPSR says that WPSR, while perhaps not true at the actual world, is true at some world. But here is something that occurred to me after talking with Richard Gale, because he mentioned that a strength of our argument is that it works in every world: WWPSR is enough to show the existence of a necessary being that is necessarily explanatorily efficacious over at least one contingent proposition. For we can just run our argument in the world, w₁, in which WPSR holds. And then we get that in that world there is a necessary being that explains all contingent truths there. Call that being Nec. By S5, that being exists in all worlds. So far the argument is pretty rigorous. The rest will be a bit handwavy.

Nec explains at least one contingent truth in every world. For Nec explains at least one contingent truth at w₁ (as it explains them all there). So suppose for a reductio that it is a contingent proposition that Nec explains at least one contingent truth. Call that proposition e. Since it is contingent, and it is true at w₁, Nec must explain e at w₁. But arguably it would be circular for an exercise of explanatory efficacy to explain why there is at least one piece of explanatory efficacy.

Moreover, since Nec exists in every world, what could prevent his activity from having explanatory efficacy in some world w₂? Whatever that is, it is something that he must have squelched in w₁. So in w₂, presumably he did not squelch that thing or event, and that seems to be a contingent truth at w₂ that he had explanatory efficacy over.

A simple design argument

1. P(the universe has low entropy | naturalism) is extremely tiny.
2. P(the universe has low entropy | theism) is not very small.
3. The universe has low entropy.
4. Therefore, the low entropy of the universe strongly confirms theism over naturalism.

Low-entropy states have low probability. So, (1) is true. The universe, at the Big Bang, had a very surprisingly low entropy. It still has a low entropy, though the entropy has gone up. So, (3) is true. What about (2)? This follows from the fact that there is significant value in a world that has low entropy and given theism God is not unlikely to produce what is significantly valuable. At least locally low entropy is needed for the existence of life, and we need uniformity between our local area and the rest of the universe if we are to have scientific knowledge of the universe, and such knowledge is valuable. So (2) is true. The rest is Bayes.

When I gave him the argument, Dan Johnson made the point to me that this appears to be a species of fine-tuning argument and that a good way to explore the argument is to see how standard objections to standard fine-tuning arguments fare against this one. So let's do that.

I. "There is a multiverse, and because it's so big, it's likely that in one of its universes there is life. That kind of a universe is going to be fine-tuned, and we only observe universes like that, since only universes like that have an observer." This doesn't apply to the entropy argument, however, because globally low entropy isn't needed for the existence of an observer like me. All that's needed is locally low entropy. What we'd expect to see, on the multiverse hypothesis, is a locally low entropy universe with a big mess outside a very small area--like the size of my brain. (This is the Boltzmann brain problem>)

II. "You can't use as evidence anything that is entailed by the existence of observers." While this sort of a principle has been argued for, surely it's false. If we're choosing between two evolutionary theories, both of them fitting the data, both equally simple, but one of them making it likely that observers would evolve and the other making it unlikely, we should choose the one that makes it likely. But I can grant the principle, because my evidence--the low entropy of the universe--is not entailed by the existence of observers. All that the existence of observers implies (and even that isn't perhaps an entailment) is locally low entropy. Notice that my responses to Objections I and II show a way in which the argument differs from typical fine-tuning arguments, because while we expect constants in the laws of nature to stay, well, constant throughout a universe, not so for entropy.

III. "It's a law of nature that the value of the constants--or in this case of the universe's entropy--is exactly as it is." The law of nature suggestion is more plausible in the case of some fundamental constant like the mass of the electron than it is in the case of a continually changing non-fundamental quantity like total entropy which is a function of more fundamental microphysical properties. Nonetheless, the suggestion that the initial low entropy of the universe is a law of nature has been made in the philosophy of sceince literature. Suppose the suggestion is true. Now consider this point. There is a large number--indeed, an infinite number--of possible laws about the initial values of non-fundamental quantities, many of which are incompatible with the low initial entropy. The law that the initial entropy is low is only one among many competing incompatible laws. The probability given naturalism of initially low entropy being the law is going to be low, too. (Note that this response can also be given in the case of standard fine-tuning arguments.)

IV. "The values of the constant--or the initially low entropy--does not require an explanation." That suggestion has also been made in the philosophy of science literature in the entropy case. But the suggestion is irrelevant to the argument, since none of the premises in the argument say anything about explanation. The point is purely Bayesian.

Forgiveness

1. (Premise) If one has done a wrong, one ought to ask someone for forgiveness of it.
2. (Premise) If God does not exist, there are some wrongs (e.g., the murder of someone who has no friends or relatives) that one cannot appropriately ask anyone for forgiveness of.
3. (Premise) If one ought to do something, then one can appropriately do it.
4. Therefore, if God does not exist, there are some things one ought to do but cannot appropriately do. (By 1 and 2)
5. Therefore, God exists. (By 3 and 4)

Collimating a collimator

Collimating a Newtonian telescope basically means aligning the optical axis of the primary mirror with the optical axis of the eyepiece.  An easy way to do this is to use a collimator, e.g., a laser collimator.  The collimator is basically a tube that contains a laser that you put in place of the eyepiece.  You adjust the angle of the secondary mirror in the telescope so the beam hits the center of the primary mirror, and then you adjust the angle of the primary mirror so that the beam comes back on itself.  But it is crucial for this procedure with a laser collimator that the collimator be itself collimated, i.e., that the laser's axis be aligned with the tubing that the laser is in.

Now, if we were writing a philosophy paper, at this point it would be very tempting to say: "And a vicious infinite regress ensues."  But that would too quick.  For a laser-collimator collimator is very simple: a block of wood with two pairs of nails, where each pair makes an approximate vee shape.  You then lay the laser collimator on the two vees, aim it at a fairly distant wall, and spin it.  Then you adjust the adjustments screws on the laser collimator until the beam doesn't move as you spin the collimator on its axis, at which point the laser is collimated to its housing.  Moreover, because of how the geometry works, the vees don't need to be very exactly parallel--all the work is done by spinning.  So, it seems, the regress is arrested: the laser-collimator collimator does not itself need collimation.

Potential lesson: Perhaps sometimes we philosophers are too quick after one or two steps in a regress to say that the regress is vicious and infinite.  For sometimes after two steps, the regress may be stopped with a bit of cleverness.

Well, actually, that's not quite right.  For the double-vee collimator depends on the laser collimator's housing being a cylinder.  And one might argue that manufacturing an exact cylinder requires a procedure like collimation.  For suppose that we manufacture the cylinder by taking a block of aluminum, spinning it in a lathe and applying a lathe tool.  But to get an exact cylinder, the lathe tool needs to remain, at the end, at an equal distance to the lathe's rotational axis.  So that's another alignment procedure that's needed.  I don't know how that's done, being foggy on the subject of lathes, but I bet it involves aligning some sort of a guide parallel to the lathe's rotational axis or by moving the workpiece parallel to the rotational axis.  So another collimation step will then be needed when manufacturing the lathe.

And so the regress does continue.  But still only finitely.  At some point, parallelism can be achieved, within desired tolerance, by comparing distances, e.g., with calipers.  There is still a collimation issue for the calipers, but while previous collimations involved the spatial dimensions, the collimation of calipers uses spatial and temporal dimensions: in other words, the calipers must keep their geometrical properties over time.  For instance, if one sets the calipers to one distance, and then compares another, the caliper spacing had better not change over the amount of time it takes the calipers to move from one place to another.  So calipers allow one to transfer uniformity over time into uniformity over space.

But how do we ensure uniformity over time?  By using a rigid material, like hardened steel.  And how do we ensure the rigidity of a material?  This line of questioning pretty quickly leads to something that we don't ensure: laws of nature, uniform over space and time, that make the existence of fairly rigid materials possible.  And if we then ask about the source of these laws and their uniformity, the only plausible answer is God.  So, we may add to God's list of attributes: ultimate collimator.

There are, of course, other ways of manufacturing cylinders than by using a lathe.  One might cast a cylinder in a cylindrical mould--but that just adds an extra step in the regress, since the mould has to be manufactured.  Or one might extrude a cylinder by pushing or pulling the material for it through a circular die.  In the latter case, one still has to make a circular die, perhaps with a spinning cutter at right angles to a flat piece, and one has to ensure that the material is moved at right angles to the die.  So one has changed the problem of parallelism into the very similar problem of aligning at right angles.  And I suspect we eventually get back to something like rigid materials anyway.

So the lesson that sometimes regresses stop after one or two steps is not aptly illustrated with the case of the collimator.  That regress is still, perhaps, finite--but it goes further back, and eventually to God.

Quam Dilecta

Oddly, I had never read Peter van Inwagen's wonderful "Quam Dilecta" until today. Mark Murphy reminded me of it, and that reminded me that he earlier advised me to read it. I was particularly struck by one paragraph, which I couldn't have said as well, but which I can nonetheless reiterate (and it's rather relevant to my motivational defense of the ontological argument):

There are Christians I know, however, who are very impressive people, and their impressiveness is of a distinctively Christian sort. A common thread runs through their very diverse lives, and it is a Christian thread. I have never been able to discern an "Enlightenment" thread that runs through the lives of the admirable atheists of my acquaintance. There are five or six Christians I know who, for all the rich individuality of their lives and personalities, are like lamps, each shining with the same, dearly familiar, uncreated light that shines in the pages of the New Testament. I can no more doubt this judgment than I can doubt many of my much more everyday sorts of judgment to the effect that this or that person is kind or generous or honest or loving. When one is in the presence of this light--when one so much as listens to one of these people speak--it is very difficult indeed to believe that one is not in the presence of a living reality that transcends their individual lives.

Bioethics without God

It is considered in bad taste to bring God into contemporary bioethics discussions. Why? Well, one reason is that if one does so, one's argument will be irrelevant to atheists and agnostics. But note that in the American public, the percentage of people who accept the existence of God is significantly greater than the percentage who are Kantians, or utilitarians, or virtue ethicists, etc. Thus, say, an argument in favor of cloning based mainly on the premise that God exists (I don't know of any such argument off-hand) will be relevant to a much greater percentage of people than an argument for the same conclusion based on Kantianism. Moreover, while among academics there are significantly more atheists and agnostics, it still may be that the claim that God exists is at least as widespread as a belief in Kantianism, or in utilitarianism, or in virtue ethics.

Another reason it's in bad taste is that it allegedly brings faith into what should be a reasoned discussion. But this presupposes that the existence of God cannot be argued for rationally, a claim that is false (clearly false if we use as our standard of rationality the level of compellingness of arguments in applied ethics). Now one might with greater plausibility claim that no argument for the existence of God will be compelling to all, or even to a majority, of intellectuals. But it is in perfectly good taste to give serious bioethics arguments based on premises that are not compelling to the majority of intellectuals. Thus, one can give Kantian, utilitarian or virtue ethics arguments.

A third, though very pragmatic (but so is the first), reason is contingencies involving legal issues about church and state in the U.S., and cultural hangups connected with this. For better or worse, it is likely that the Supreme Court would see a law grounded in the existence of God, even if the law included a preamble giving a very powerful rational argument for the existence of God, as violating the separation of church and state.

I have theistic friends whom I respect highly and who try very hard to avoid making use of the existence of God in their work in applied ethics. While I think such work is very important both intellectually and practically, I also think there is a danger of distortion in bioethics if one confines oneself to working in this way. When one does have to do non-theistic work in bioethics, one should think of it as a way of tying one hand behind one's back, because that's what the rules of the game call for, not because that's what is appropriate to the enterprise of truth-seeking. For when we are talking about appropriate treatment of the beginning and end of life, it is plausible that the question of the relation between life and God is highly relevant. Some people think that the way science can explain all kinds of facts without invoking God is an argument against the existence of God. That's a bad argument. But if ethics, especially the ethics that deals with the beginning and end of life, could do without God, that should be quite surprising to a theist.

In the above, I talked of mere theism. I have a strong suspicion that, at least in our fallen state, more than mere theism is relevant. John Paul II somewhere said that we can only understand man through Christ. If that's right, then non-Christian bioethics is doomed to incompleteness. And incompleteness in a philosophical enterprise runs the danger of leading to distortion, through onesidedness.