I just posted the paper here. Forthcoming in Oxford Studies in Metaphysics.
Abstract: I shall argue that considerations about frequency-to-chance inferences make very plausible some a localized version of the Principle of Sufficient Reason (PSR). But a localized version isn’t enough, and so we should accept a full PSR.
If God exists, the Axiom of Choice is true. For given any set of nonempty sets, surely God could choose a member of each of the nonempty sets. (This argument is by Meyer, Nous 21 (1987), 345-361.) But if the Axiom of Choice is true, then any set can be well-ordered. And any well-ordered set has the same cardinality as some ordinal. Ordinals are essentially numbers, albeit some of them are infinite. So, indeed, God has disposed all things by number, and necessarily so. (Wisdom 11:20 also says that God has disposed things by size and weight. Perhaps this indicates that the quantifiers in text are restricted to material things. Or perhaps immaterial things count as having zero size and zero weight.)
I actually find the necessity in the above argument quite surprising. Ordinals are pure sets: sets built up out of the empty set, not out of concrete ur-elements. I find it surprising that any infinite set of concrete objects that God could create can still be numbered with a pure set.
Plausibly there is such a thing as a true physics, an ideal physics that we are striving towards, a physics that includes both particular statements as well as laws. That true physics is true, and hence consistent. It is also the sort of theory we can produce, so it has countably many statements (maybe finitely, but perhaps we could continually add to it). Finally, it is very likely to be a first-order theory, since it looks like all of science involves first-order theories.
Suppose there is a spacetime. Then the true physics posits it. Imagine we now have the true physics. By downward Löwenheim-Skolem, the true physics is consistent with spacetime being countable. So, by Ockham's Razor, wouldn't we have good reason to think that spacetime is countable, since that's more parsimonious than its being uncountable? And, now returning to the early 21st century of the actual world, doesn't the fact that if we had the true physics we would have good reason to think spacetime is countable, give us good reason to accept the counterintuitive conclusion that spacetime is actually countable?
I am not sure. For even if a countable spacetime is ontologically simpler, its description in our mathematical language is more complex than that of an uncountable spacetime manifold. Does that matter? Yes, but only if our mathematical language actually cuts mathematical reality at the joints or if we are created to get science right. (I suspect a naturalistic physicist could have a hard time resisting the argument for a countable spacetime. But this is all very, very speculative, and my mind fogs up when I think about the relativity of uncountability, intended models and the like.)
For every initial ordinal k, there is a possible world with exactly k photons. But there is no set of all initial ordinals (proof: suppose there is such a set; the union of the members of any set of ordinals is an ordinal; so the union of the initial ordinals is an ordinal; it must have the same cardinality as some initial ordinal in the set; but for any ordinal in the set, there is a larger one in the set). So there is no set of all possible worlds.
This argument doesn't use the Axiom of Choice and hence it improves on the argument I gave here.
Presentism has some ethics problems stemming from its claim that persons who don't exist now don't exist.
When I visualize a car in my imagination, the experience is obviously different from seeing a car. It's not even close. Similarly, if I imagine a sound, the experience is obviously different from hearing it. In part this is due to shortcomings of my imagination. But I suspect it's not just that. Rather, imagined experiences are qualitatively different from actual experiences. This isn't the difference disjunctivists get at between hallucinations and veridical experiences. I am willing to concede that a hallucination and a veridical experience could be phenomenally the same, but then both would be different from imagined experiences. There are, of course, structural analogies. Imagining a red triangle is related to imagining a blue square much as seeing a red triangle is related to imagining a blue square. And there may be some resemblance between imagining a red triangle and seeing a red triangle.
Here's a hypothesis about dreams: The "visual" experiences in dreams are phenomenally more like the ones in visual imagination than like seeing, but one's ability to tell the difference is suppressed.
I want to explore an argument against the moral permissibility of lying. Start with this thought:
Next, I want to bring in this thesis which generalizes Aquinas' idea that legislation that commands immoral activity is null and void, an empty gesture, and not a law:
Finally, let's add an uncontroversial observation:
Now, let's see what follows from (1)-(3). For a reductio, suppose lying is sometimes permissible. Then it's sometimes required by (3). Suppose then you're in a situation where lying is morally required. But when you lie, you assert contrary to your beliefs. So by (1), when you lie you violate a genuine norm. Hence a genuine norm requires you to do something immoral, namely to refrain from lying in this case. But that contradicts (2). So, it can't be the case that lying is sometimes permissible.
I worry that the argument proves too much. Suppose that you're playing cards with a tyrant. If you win, innocents go free; if you lose, they are killed. Surely you should cheat. But cheating violates the norms of card-playing, so a parallel argument shows it's wrong to cheat.
I say that the rules of the game lack normative force in this case, and indeed that, as we would say, this is not a game anymore. I don't know exactly how to characterize games, but it seems essential to a game that, roughly, they just be a bit of fun. Russian roulette is not a game, and its rules have no normative force. Just as property rights cease in cases of grave need according to Aquinas, so too when so much is at stake it's not a game, and if it's not a game, the person who pulls cards out of her sleeve to save lives isn't cheating in a game because she isn't playing a game.
Could one, then, say the same thing about the person who says to the murderer at the door regarding the intended victim: "He's not at home"? The parallel claim would be that the norms of assertion don't apply, and hence the words aren't an assertion at all. The murderer is deceived into taking the words to be an assertion, but they aren't one at all. There is something attractive about this view, in that it would allow one to maintain the traditional Christian view that lying is always wrong while allowing one to solve the murderer-at-the-door problem. But I think this doesn't work. Unlike playing cards, asserting isn't a game, something that ceases when there is too much at stake. It isn't even like the institution of private property, which dissolves according to Aquinas in cases of grave need since it's ordered to the preservation of life. Assertion is ordered to a different good than the preservation of life: truth. Moreover, it just seems quite implausible to say that the person saying "He's not at home" to the murderer isn't making an assertion.
These claims are really plausible:
But actually there is no contradiction. To get the claim that my existence is explanatorily prior to my being caused out of (3), we need to add the premise that my being caused is a different fact about me from my existing. But why add a premise that makes for a contradiction? We should instead conclude that the fact of my existence is the same fact as my being caused by my parents.
But if it's the same fact, then we have an interesting ontological conclusion: My existing is my being caused by my parents (and presumably by all the other causes cooperating with them, including especially God). I've argued for something like this conclusion here, but this is a much neater argument.
There may be another corollary. It seems that my esse, my existence, is modally essential to me--I couldn't exist with a different esse. But if my esse is my being caused by my parents, then I couldn't have had other parents.
Objection 1: We should restrict (3) to facts about the present time. But my having been caused by my parents isn't like that.
Response: Run the argument in the first moment of my existence (assuming there is one; if not, run it for some creature which has a first moment of existence; presumably if the ontological thesis I am arguing for is true for some creature, it's true for them all).
Objection 2: If my existing is the same as my being caused by my parents, how can (1) be true: isn't (1), then, a claim that I exist because I exist?
Response: Even if the fact (or state of affairs or event--there are multiple ways to formulate the argument) of my existence is the same as the fact of my being caused by my parents, the proposition that I exist is not the same as the proposition that I am caused by my parents.
Some people distinguish the (non-instrumental) value of an individual's feature from the (non-instrumental) value for the individual of that feature. Ockham's razor, on the other hand, suggests we identify them. There is an interesting kind of argument from the nature of love for such an identification. Love has at least three aspects: benevolence, appreciation and pursuit of union. (For more on this, see One Body.) Love isn’t merely a conjunction of these aspects. The aspects are tightly intertwined, with each furthering the others. And the identification of (non-instrumental) value-of with value-for gives us a particularly elegant account of part of this intertwining. Appreciation is appreciation of what is valuable. When I appreciate the value of an individual, I seek to preserve and promote that value. Now when I act benevolently for an individual, I seek to preserve and promote what is of value for the individual. If the value-of and value-for are the same, then this appreciation motivates the benevolence and the benevolence is an expression of the appreciation. And a benevolence that is an expression of appreciation is a benevolence that escapes the danger of being patronizing and condescending.
On the other hand, if value-of and value-for were different, then not only would we lack this elegant intertwining, but there could be a real conflict between appreciation and benevolence. For appreciation would naturally lead me to promote the value of the beloved, which would take time away from the benevolent promotion of the value for the beloved, and conversely. The identity of value-of and value-for makes it possible for love to have an intrinsic unity between the appreciative and benevolent aspects. And union can then flows from these, since through benevolence one unites oneself to the beloved in will and through appreciation one unites in intellect.
Fido exists now because of various things Fido did a couple of minutes ago, such as breathe, pump blood with his heart, etc. So, it seems, Fido's existence is caused by Fido. But self-causation is absurd. So what's going on? Well, that depends on the theory of persistence.
Perdurantists and exdurantists have no problem at all. One temporal part causes another. There isn't even a whiff of absurd self-causation, either. Four-dimensionalist worm-theorists who don't believe in temporal parts can say that Fido doesn't cause his existence, but only aspects of his spatiotemporal dimensions. So on four-dimensional theories, we don't have absurdity.
But what about three-dimensionalist theories? Suppose Fido wholly exists at this time. Then it seems that all of Fido (now) is caused by Fido (five minutes ago), and that would be absurd. But that's not quite right. The eternalist or growing block three-dimensionalist can distinguish. Fido doesn't cause Fido's existing simpliciter. Fido only causes Fido's existing now. If we want more precision, we can say that Fido in virtue of existing five minutes ago causes himself to exist now. No problem, again.
That leaves the other three-dimensionalist option: presentism. And now we have a problem. According to presentism, to exist is to exist presently. Fido's present existence is (was? -- the tenses are hard to get right) caused by Fido. But that just means that Fido's existence is caused by Fido. And that's self-causation.
But perhaps we should take account of the sorts of things presentists say about the problem of transtemporal causation. Maybe it's not quite correct to say that Fido's existence is caused by Fido, but rather that Fido's existing is caused by Fido's having existed five minutes ago. Plus, talking like this makes causation a relation between states of affairs, and some will prefer that. But we still have a problem. For Fido's having existed five minutes ago is a state of affairs involving Fido. But it's absurd for Fido's existing to be caused by any state of affairs involving him, since Fido's existing is explanatorily prior to any state of affairs involving Fido.
Perhaps, though, the presentist can bring in Fido's haecceity H. Fido's existing is caused by H's having been instantiated five minutes ago. That is, I suspect, the presentist's best bet here. But there is a problem for that. For it sure seems like the state of affairs that caused Fido's present existence isn't a state of affairs of his haecceity having had something happen to it (say, being co-instantiated with respiration), but but it is the state of affairs of Fido having done certain things five minutes ago, like breathing. If it is states of affairs about haecceities that are causally relevant, then it looks like the things that are fundamentally involved in causation aren't particulars like Fido but are are abstracta like haecceities. And that's not right.
There is a direct argument here against presentism, too.
Some biological taxa are clades: a clade is a taxon that contains a descendant of every included organism. For instance Mammalia is a clade, while Reptilia is not, since birds aren't reptiles but are descendants of reptiles. There are biologists that wish that we used a phylogenetic classification scheme, one where all taxa are clades. But that's not what is traditionally done. Let's consider the hypothesis that the traditional approach is right in the sense that it cuts nature at joints. Then a taxon can change from being a clade to being a non-clade. I assume that Reptilia changed in this way when birds evolved. And whether such a change has occurred is a substantive question.
In principle, then, it is possible for the kingdom Animalia, which I understand is normally taken to be a clade, to change into a non-clade. And it is a substantive question, then, whether such a change occurred when humans evolved. It could be the case that sapience marks such a departure that we are a new kingdom, and Animalia is no longer a clade. I think a close relative of this thought--albeit without evolutionary connections--is behind the ordinary person's (as opposed to a philosopher's) resistance to the idea that we are animals: personhood is such a transformative feature that it marks a completely new kind of organism.
But while the question is substantive, it's not tenable to say we aren't animals. If we are not animals, it seems we aren't mammals. (Maybe more can be said, though?) But if we aren't mammals, then various natural kind-based explanations fail: we can't say, for instance, that we have complex bones in the inner ear because we have mammals.
Note, too, that the question raised in this post is orthogonal to the question that animalists are concerned with. For all that we animalists need for our positive theory is that we are organisms--whether the particular kind of organism we are is an animal, a plant, a fungus or something else is not very important for the theory.
I just had a really naive thought. Let's imagine what a definition of animals would be like. It would say something like this: Animals are things that maintain homeostasis, take in nutrients and grow, reproduce, initiate and control a large variety of types of motion in response to changing environmental features, etc. It's not very easy to come up with details of the definition, but it seems like it would go something like this. Well, it's pretty clear that we do these things, as well as doing any plausible items we'd want to add to the definition. So we're animals. Case closed.
What could an anti-animalist say? I guess her best hope would be: The definition is close to the truth, but not quite. Rather, animals are things that non-derivatively maintain homeostasis, take in nutrients and grow, etc., etc. But it seems to me that there is a natural dilemma. Derivative homeostasis (say) either is or is not a case of homeostasis. If it is, that seems all we need for animalhood (along with analogous other qualities). If it is not, then the anti-animalist can't say that we have homeostasis, and that's absurd.
