Five-dimensional universalism (hereby stipulated) holds that if f is a partially defined mapping f from worlds to regions such that (a) if f(w) is defined, then f(w) is a nonempty region of w's spacetime and (b) f(w) is nonempty for some w, there is an object Of that exists in every world w for which f(w) is defined and occupies precisely f(w) at w. We will call a function f with the above properties a "modal profile", indeed the modal profile of Of.
I think that to do justice to the vast flexibility of our language about artifacts, if we want to be realists about artifacts, we will need to be five-dimensional universalists. Mere four-dimensionalism mereological universalism is insufficient, because there can be always coincident artifacts with different modal properties.
But:
The argument for (2) is that there are way too many possible worlds with spacetimes to make up a set[note 1], and for each such world w there is a different modal profile[note 2], so there is no set of all modal profiles.
Here is an argument against eternalism:
So how to break this impasse? One way would be to opt for a theory other than eternalism and presentism, say growing block. Another way is to keep on adding disanalogies between times and places or between times and worlds until one of the disanalogies ends up being much stronger. Yet another way, and I think the most promising, is to embrace both (2) and (5), but explain the disanalogy in a way that is compatible with presentism or eternalism (whichever is one's preference).
One should also note that arguments from analogy tend not to be the strongest.
Consider this argument:
The right way out of the argument is, of course, to reject (2). But in this post I want to undercut the argument in a very different way. Basically, I will argue against (3) by offering a just-so story that is compatible with both our best science and a literalistic reading of Genesis 1-3, without scientific revisionism, scientific irrealism, or invocations of divine or demonic deception.
I am not claiming the story is true. In fact, I think it's false. It is in tension with the Thomistic view of the soul which I hold (but I think it may be logically compatible with it—but that's a longish story). As I said, the right way out is to deny (2).
The story is simple. First, everything happens exactly as it is described in Genesis 1-3 interpreted literalistically. Everything, including a light-studded dome ("firmament"), with waters above and below, creation in six days, vegetation without any sun or moon. Eve is literally taken from Adam's side, and so on. Then Adam and Eve sin, exactly as described in Genesis 3. All this happens in a universe ("Paradise") where all of this is possible by the laws of nature.
God then kicks them out of this universe. In the process, he destroys their bodies and puts their souls in stasis. But in Paradise, there was a law of nature that when the forbidden fruit is eaten, a Big Bang will occur (or this could be a miracle), initiating a 14 billion year process leading to some pretty clever apes in a universe better suited to sinners like Adam and Eve. God then takes the matter of two of these clever apes (if animals have souls, he de-souls them first, or perhaps he simply miraculously ensures that these two don't get souls) and instills Adam and Eve's souls in this matter.
And so all the science as to what has happened in the material universe since the Big Bang is right. Of course, science doesn't talk about souls.
A materialist Christian could also run a variant of this story of Adam and Eve being asleep for fourteen billion years, but it would involve some miracles in the physical world and maybe disagreement with science at one point. (Maybe Adam and Eve's brains are put in the bodies of some apes. Or maybe God is capable of so guiding indeterministic processes that there develop two apes that are just like Adam and Eve, and God can replace them with Adam and Eve.)
Of course, I don't believe these stories. But they do show that premise (3) of the anti-Christianity argument is false.
I think (4) is plausible, as well. For while some cases of severe suffering of children are things agents are responsible for even if naturalism is true—say, suffering directly imposed by agents—there will be many cases which are not like that. Say, a couple lovingly procreates in order to share their good life with a child, and the child has a congenital disease that causes severe suffering. There is no naturalistically-acceptable agential explanation.
What sort of non-naturalistic agential explanation could be given of these injustices? Here are the three most obvious options:
Which is the right story? Well, it's not an evil deity and it's not reincarnation.
Kripke argued that it is not possible for there to be unicorns. For "unicorn" is a natural kind term. But there are many possible natural kinds of single-horned equines that match our unicorn stories, and there is no possible natural kind that has significantly more right to count as the kind unicorn. So none of them count, and no possible world contains unicorns.
But there is another approach, through vagueness and supervaluationism. Let's say that the term "unicorn" is vague. It can be precisified as a full description of any one of the possible natural kinds of single-horned equines that match our unicorn stories.
Now consider the sentence that Kripke is unwilling to assert but which seems intuitively correct:
Sam invites me to a home-sewn costume party. While I'd love to come, I would much rather not spend the time to sew costume. Sam offers to do it for me. I know that it would take many hours for him to do it, and I would feel bad having him put this effort in when I could do it myself.
This generates a circular preference structure if we restrict to pairwise comparisons, assuming in each case that the third option is not available:
But if all three options are available, then I think I am stuck sewing a costume for me. For I just can't let Sam do the work for me simply because it's a lot of trouble for me, assuming I can do the work myself. Initially my choices were between sewing for myself and missing the party, and I preferred missing the party. But Sam's offering of a third option forced me to switch.
This kind of thing is a way for Sam to manipulate my behavior if I am a nice guy who doesn't want to put Sam to the trouble. In the case at hand, this means that Sam probably should not make me the offer to sew the costume, since by offering, he brings it about that I will go to the trouble myself. In cases where it is important that I go to the party, this manipulation may be perfectly fine—I've used it in an important case several years ago.
The length of a pencil is measured in a straight line from tip to end. This is equal to the length of the region of space occupied by the pencil. The length of a rope is measured along the rope, so that the length does not change much when the rope is coiled or uncoiled, and so unless the rope is straightened out, the length of the rope is not equal to any dimension of the region of space occupied by the rope. The length of a bow is (typically) the length of the string plus three inches. On the other hand, the length of a computer program is something quite different, not measured in length-dimensions, but in units like lines or lines-of-code or characters.
Similar points apply to almost all other predicates. These are a matter of decision rather than discovery. When we extend our language to start talking about pencils, ropes, bows and programs, we also need to decide how all the many predicates that could apply to them are to be extended. Quantifier pluralism requires predicate pluralism.
In Ephesians 4:25, Paul talks of us Christians being all members of one another. Karol Wojtyla thought of romantic love as directed at mutual possession (I am grateful to John Crosby for pointing this out). Plausibly, this possession is not like ownership, but more like the body parts are related to the person they belong to.
A sensible reading of these and other texts requires a non-authoritarian view of the relations between ourselves and our body parts, a view on which our authority over our body parts is limited. This has serious repercussions for things like sterilization, gender-reassignment surgery and more radical forms of elective cosmetic surgery.
A plausible account of necessity is that p is necessary provided that p can be proved in the correct logical system K and p is possible provided that its negation cannot be proved. Assuming K is axiomatizable and proves enough of the axioms of arithmetic, this account can be shown to be incorrect.
Fix any sentence s in K. It follows from Goedel's Second Incompleteness theorem that there is no K-proof of s's being K-unprovable (for if there were such a proof, then it would follow that there is a K-proof of K's consistency, since if K is inconsistent, then every sentence, including s, can be proved in K). But on the account of modality under consideration, this means that it is possible that s is K-provable, i.e., it is possible that s is necessary.
In other words, this account of modality implies that every sentence is possibly necessary. But it is absurd to think that 0=1 is possibly necessary!
I think much the same reasoning can be used to disprove Swinburne's account of necessity, since where we are not dealing with directly referential rigid designators, Swinburne's account agrees with the provability account.
I am skirting over distinctions between s and its Goedel number, but I think that's a mere technicality to work out in greater precision.
This makes for a nice way to see a relationship between the two incompleteness theorems. The first one tells us that not everything true is provable. From the second we learn that not even everything necessary is provable.
Because of various difficulties in accounts of lying and related phenomena, I've been drawn to the simple theory on which it's always morally wrong to assert falsehoods, though of course if one is justified in believing the falsehood, one isn't culpable (and it's not lying then). But Heath White's argument which I reference in this comment suggests a pretty decisive argument to the contrary. Suppose that my daughter justifiably asserted to her brother: "Daddy won't play Monopoly with us tonight." It is within my power to make this false by playing Monopoly with the kids. But if I were to make it false, then on the view in question it would be the case that my daughter did something morally wrong. And surely I have a significant moral reason to avoid bringing it about that my child did something wrong, even if it would only be inculpably wrong and my bringing it about would not be intentional.
Consider this valid argument:
Premise 3 will be taken to be false by many if "refute" and "establish" are understood in the knowledge sense or even in the sense of knowledge-type justification, since knowledge and knowledge-type justification is not closed under entailment. Some will say that although it is established that I have two hands, and that I am a brain in a vat is incompatible with that, that I am a brain in a vat cannot be refuted. I think this response is mistaken—I know I am not a brain in a vat—but I won't insist on it.
On the other hand, if "refute" and "establish" are taken in the sense of assigning low and high rational probability, respectively, then 3 is surely true: if p and q are incompatible, and one has high probability, the other has low probability. Thus, it seems, that those who claim that evolution is established should either hold that Intelligent Design is compatible with evolution or stop arguing that it is irrefutable.
But perhaps what I just said isn't right. Maybe to refute q is both to get to assigning a low probability to q and to obtain significant incremental disconfirmation. Then 3 is false. For suppose that q has very low rational priors. Then we can establish p without getting any incremental disconfirmation for q—we get incremental confirmation for q, and q ends up with high probability, but p's probability is basically unchanged from the priors. Maybe it is empirically established that I have two hands, but the brain in a vat scenario continues to be ruled out by low priors.
If this response is right, then the evolutionary theorist who wants to claim that evolution is established while yet accepting 1 and 2 needs to hold that the rational priors of intelligent design are low. But are they?
The best kind of love involves benevolence. But how then can a love for God be of the best kind? Aquinas answers this problem basically by saying that we can do good to God by doing good to those God loves--namely, our neighbor. This is a good answer, but I also got another Thomistic answer from my friend Richard Sisca on Saturday: we can rejoice that God enjoys perfect beatitude. For Aquinas there are two ways of having the other's good in one's will: (a) by willing that good things should happen to the beloved; and (b) by mourning the evils and rejoicing in the goods that the beloved suffers or enjoys.
Mellor's argument against circular causation in Real Time II seems to me to basically come down to the following observation. If we have probabilistic causation of B by A and of A by B, then the four conditional chances involved in the causation, namely P(B|A), P(B|~A), P(A|B) and P(A|~B), fully determine all the unconditional probabilities of A, B and their negations. Namely, only one assignment to P(A) and P(B) does not generate a violation of the laws of probability. (For instance, if P(B|A)=P(A|B)=1/2 and P(B|~A)=P(A|~B)=1/4, then we have to set P(A)=P(B)=1/3, or we will violate the laws of probability.) But Mellor seems to think that in a causal system, we should be able to keep fixed the conditional chances and yet set some unconditional probability howsoever we wish.
Certainly, in ordinary non-looping causation, we can do that. If we have a events A1,A2,... occurring or not occurring in a sequence with no memory (i.e., we have a Markov chain with a binary state space), then no matter what the transition probabilities P(An|An−1) and P(An|~An−1) are, we can arrive at a coherent probability assignment to the system as a whole no matter what we let P(A1) be.
It is a quite interesting feature of circular causation that the conditional chances fix all the probabilities. But where is the absurdity?
Well, to be fair to him, Mellor does bring in frequencies. Suppose we have a large number of independent causal loops governed by the same chances happening side-by-side. Suppose the chances are all strictly between 0 and 1. Then any distribution of features between the loops should be metaphysically possible. Thus, we could have five million As and ten million non-As, or equal numbers, or ten million As and five million non-As. But now suppose that frequency of As and non-As in the system does not match the frequency which is determined by the unconditional probability P(A) that can be derived from the conditional chances. Then we can calculate the expected number of As and non-As that there should be after going around the A-B-A loop, and we will find that that expected number doesn't match the number we have. (Mellor does this explicitly.) And so what? Well, one problem here is that it is very unlikely that the expected number not match the observed number. Correct! But it should not surprise us that we have an unlikely scenario when we have started with an unlikely assumption. For the expected distribution of As and non-As is the one given by the unconditional probabilities P(A) and P(~A), and ex hypothesi our distribution departed from that. In unlikely circumstances, an unlikely result. What's strange about that? This is basically the same point that Nicholas Smith made here in the case of a somewhat different argument.
