Proof

The folk seem to think that science can "prove" things. I used to think this just meant that they were confused about how science works. But there is a more charitable reading, which I got from a comment by Dan Johnson on prosblogion. Rather than taking the folk to be confused about how science works, we can take seriously the idea that meaning is a function of use, and take the folk to simply use the word "prove" differently from how philosophers do. The legal sense of "prove", as in "prove beyond reasonable doubt", seems to prove the point. :-) For if it is not otiose to specify that a proof is "beyond reasonable doubt", it must be possible to prove in a way that admits doubt! And hence a "proof", in the ordinary sense of the word, does not mean what philosophers and mathematicians mean by the word.

An argument against four-dimensional mereological sums

Say that x is a four-dimensional mereological sum provided that x is a mereological sum with the property that not all of its parts exist at all the same times, i.e., x has parts a and b such that a exists at some time at which b does not. Mereological sums of stages will, typically, be four-dimensional mereological sums. Plausibly, a four-dimensional mereological sum exists at t provided that it overlaps the spacetime region of time t (times are spacelike hypersurfaces, I suppose).

1. Without backwards causation, it is not possible to make it the case that an object did not exist yesterday.
2. If there are four-dimensional mereological sums, then it is possible to make it the case that an object did not exist yesterday.
3. Hence, there are no four-dimensional mereological sums.

The argument for (2) is simple. If four-dimensional mereological sums exist, then there could be a four-dimensional mereological sum that existed prior to t₀ but that contains a particle a that comes into existence after t₀. Then at t₀ it would be possible, without backwards causation to make the sum not have existed by preventing the coming-into-existence of a—for if one prevented that, then the four-dimensional mereological sum would never have existed.

Causal closure of the physical

If causal closure of the physical holds, then there are uncaused physical states of affairs. Thus, at least one of the following two theses is true:

1. Some physical states of affairs have a non-physical cause.
2. Some physical states of affairs have no cause.

Now, what I don't see is why (2) should be in any way preferable to (1). For instance, to the extent that some physical state of affairs lacks a physical cause, science has nothing to tell us about the explanation of this state of affairs. For all that science cares, that state might have a non-physical explanation or it might have no explanation. Allowing the first option need no more impede the progress of science than allowing the second. Granted, the first option may let one prematurely say when faced with difficulties that some state of affairs for which a physical cause has not been found has a non-physical cause. But the second option lets one say, equally prematurely, that it has no cause.

Imagine two worlds. In w₁, there are non-physical causes for all the physically uncaused physical states of affairs. In w₂, there are no causes for any of the physically uncaused physical states of affairs. Moreover, the physical parts of w₁ and w₂ are exactly alike, and match our observations. Is there very good reason to prefer w₂ to w₁ as a hypothesis accounting for our observations? Well, maybe sometimes: it depends on how weird the non-physical stuff in w₁ is. But in general, no. Roughly, what w₂ gains in parsimony it may lose in explanatory value.

So we do not have very good reason to believe (2) and deny (1). And (1) has a serious advantage over (2): unlike (2), (1) is compatible with our PSR-ish intuitions.

Haecceities, strong essentiality of origins and science

1. (Premise) If essentiality of origins doesn't hold, then every particle has a haecceity.
2. (Premise) A haecceity of x is an intrinsic property of x.
3. (Premise) A haecceity of x isn't a physical property of x or a function of any physical properties of x.
4. (Premise) There is a particle each of whose intrinsic properties is a physical property or a function of physical properties.
5. Therefore, there is a particle that lacks a haecceity. (2-4)
6. Therefore, essentiality of origins holds. (1, 5)

Why believe (1)? Because if there are no haecceities then the only plausible account of transworld identity is that x in w₁ is identical with y in w₂ if and only if x and y have the same origins. And this forces essentiality of origins.
I think the problematic premise is (4). But it is still somewhat plausible.

More on childbirth and the problem of evil

Say that a "God-disproving evil" is an evil that God, if he existed, would have no justification in permitting. Here is an argument:

1. (Premise) If there are God-disproving evils, then pain in childbirth is a God-disproving evil.
2. (Premise) If a pain is a God-disproving evil, then probably significant numbers of theists who suffer this pain thereby become atheists.
3. (Premise) Very few theists who give birth and suffer the pain of childbirth thereby become atheists.
4. Therefore, probably, the pain of childbirth is not a God-disproving evil. (2 and 3)
5. Therefore, probably, there are no God-disproving evils. (1 and 4)

I am not particularly impressed with this version of the argument, though I do think the argument is sound with the conditionals interpreted as material.

But if one wants more than soundness, I am not happy with (1). Maybe a better version would be: The sort of reasoning that makes one think that there are God-disproving evils makes one think that pain in childbirth is one. And then (2) and (3) serve to make one more suspicious of that sort of reasoning.

If one does like (1)-(5), we can add two fun steps:

6. (Premise) Probably, if there is no God, there are God-disproving evils.
7. Therefore, probably there is a God. (5 and 6)

Why accept (6)? Well, because if there is no God, and if a world somewhat like ours is actual (this is part of the background of the "Probably" in (6)), we would expect there to be nasty and pointless natural evils.

A modification to the Deductive-Nomological account of explanation

there is a deficiency in the standard formulation of the deductive-nomological (D-N) model of explanation. On the standard model, one explains by citing laws and initial conditions that jointly explain the explanandum. But in fact the explanans not only should state the laws but also that they are laws or at least consequences of laws. For suppose I wish to explain why Mappy liked one of my buttons. I cite three facts: Mappy is a magpie, all my buttons are shiny and all magpies like shiny things, and on the D-N model I am done. But knowing these three facts and justifiably believing that they explain why Mappy liked one of my buttons is not sufficient for my knowing why Mappy liked one of my buttons. For to know why Mappy liked one of my buttons, I need to know that it is a law or a consequence of a law that magpies like shiny things. Unless I know this, I do not know why Mappy liked one of my buttons. Imagine, after all, someone who knows all the three facts cited but who incorrectly justifiably believes that (a) it is a mere accidental generalization that magpies like shiny things and (b) it is a law of nature that all my buttons are shiny. Such a person knows each of the three facts, but does not know why Mappy liked one of my buttons. Therefore, we should take it as part of the explanans that it is a law that magpies like shiny things.

What I am up to

In case anybody is curious what I'm spending my time on this summer, my main project is finishing up my book on modality.  It's due at the end of September.  I have resolved to finish my proofreading by August 20.  I need to proofread or delete 28 pages per weekday for that to happen (if I add text, I have to proofread more, obviously).  Then I need to fill in some cross-references and bibliographic stuff.  Then I will hand it to a grad student I will pay to proofread it, and then off to the press it goes, in fulfillment of my contract.

Library of Historical Apologetics

This looks like an amazing resource, coordinated by Tim McGrew. Here is what they say about themselves:

At the Library of Historical Apologetics, our mission is to be the world’s leading resource for lay apologists, pastors, students, and scholars seeking historical apologetics materials for self-study, church classes, sermon preparation, and research. Our digital collection currently contains references to about 3,000 items with a focus on works in English from the 17th through the early 20th centuries.

Beyond simply providing access to these materials, our long-term vision is to create a digital learning environment that incorporates personal and collaborative reading, note taking, and study tools. We want to support a community in which more experienced scholars help newcomers find the material they need and construct secondary resources such as curricula, study guides, and course syllabi that can be shared by all users.

This project is directed by Dr. Timothy McGrew, who is Professor of Philosophy at Western Michigan University, where he has taught since 1995, serving as department chairman from 2005-2009. The Institute for Digital Christian Heritage is providing technical and administrative assistance in the form of project planning, implementation and evaluation.

Justice and taxation

No system of taxation currently in use distributes the financial burden in a completely fair way. I think this is something that just about everyone will agree on, though where exactly the unfairness is located is a controversial question. I do not mean that the unfairness is intentional or even foreseen by the legislators, but more like this: there will either be a pair of individuals A and B such that it would be fairer if A were taxed more and B less (it's also possible, but less likely, that (a) everybody is taxed more than justice allows or that (b) everybody is taxed less than justice requires; I'll neglect (b), and leave the extension of the arguments to (a) as an exercise).

This is not something we can complain about much. No legal system can cover all cases adequately. But here is an interesting consequence: An across-the-board increase in taxes is very likely to exacerbate some instances of injustice. For if fairness requires that A be taxed more and B less, then when we raise A's and B's taxes, we will likely be overtaxing B by a greater amount than before, and hence the injustice to B will very likely be the greater. (This can be controversial. One might think that what matters are the ratios, not the absolute amounts. I am inclined to disagree.) This means that we have a prima facie consideration of justice against across-the-board tax increases.

Moreover, I think the above considerations generate a prima facie consideration of justice against government spending. For if overall spending were even slightly lowered, a slight across-the-board decrease in taxes would be made possible, and that would slightly decrease the severity of the unfairness to B.

Of course, the reasons above are only prima facie and defeasible. Double Effect can permit the increase of spending and across-the-board increase in taxations when the injustices are not intended and a sufficiently serious good—perhaps itself a good of justice—is being pursued. So while the above considerations sound like they would generate fiscally conservative conclusions, in practice the effect of the considerations could be quite small or nonexistent. Or it could be large. I don't know. But it is still interesting to me that the defeasible reasons against spending and across-the-board tax increases are reasons of justice—I didn't think of them that way before I noticed the above arguments. And I suppose it would be healthy for legislators to think of them as reasons of justice, if they are indeed such.

A weakness, however, in the above arguments is that it is not clear whether it makes sense to talk of unintentional injustice. If I am convicted of a crime I did not commit, but on excellent evidence and with solid legal procedures, have I really suffered an injustice? If the answer is negative, then we may not be able to say, strictly speaking, that B has suffered an injustice by being taxed too much. Maybe, though, the thing to say is this. My conviction of a crime I did not commit is not an injustice; but justice requires that such convictions be minimized. Likewise, the allocation of too high a tax burden to B is not an injustice; but justice requires that such misallocations be minimized.

The incorrect conviction analogy also suggests that we have a prima facie reason of justice not to increases criminal sentences across the board. For each across the board increase of sentences is likely to result in some innocent serving an even greater sentence than otherwise. (However, there is a difference with the taxation case. For while justice does not intrinsically call for taxation (though taxation may be a necessary means to ends that justice requires the pursuit of), justice does intrinsically call for the punishment of the guilty.)

Novels, art and collaboration

I am reading R. Austin Freeman's Eye of Osiris which so far is a pretty decent mystery. The quality of the writing is not bad, though not so great. It is unduly prolix at some times (I suppose one could say that that makes for some character development of the narrator, though, but that could still be done otherwise), and occasionally at the beginning there is a lack of clarity. This brought home to me the obvious fact that the skill of story-making is very different from the skill of story-telling. While there may be some correlation between the two skills, I do not know that the correlation is very strong. In any case, one would expect that there are a number of people who would be excellent at story-making but whose story-telling is subpar, and a number of people who would be great at story-telling but only if someone else made up the plot. But now the puzzling fact is that there are very few co-authored novels, and off-hand I can't think of any famous ones written by two authors working together (a number of works do draw on older texts or traditional elements, and maybe that should count co-authorship, but I don't want to count that as "working together").

There are artistic genres where collaboration is routine. Film, theater and music perforances are obvious cases. I do not know if Greek statues were carved by one person and painted by another, but it certainly would make sense to have that sort of division of labor. On the other hand, my sense is that painters, writers and contemporary sculptors tend to work alone.

Here is a hypothesis: The artistic vision tends to be hard or impossible to communicate except by means of the genre of art in which it is to be embodied. But collaboration would require communication of the artistic vision. And that artistic vision cannot be communicated except by the work being produced, which presents a vicious circularity in the case of collaborative works.

This argument can't apply always, because there are collaborative works. But maybe we can say something about these exceptional cases. I don't know if the painting and the sculpting were separate in Greece. But if they were, we might say that the sculpting was to some degree an independent work of art, which communicated its vision by itself. After all, most of the Greek statues we see in museums have lost their paint, and yet the sculptures appear to us to be complete works of art—so much so, that in times past people didn't seem to know they were originally polychrome.

The case of directors and conductors is a bit different. But there we can take the director or conductor as in some important sense the author of the performance as a whole. There is a communication between the director and conductor and collaborators, but in an important sense this communication is itself essentially a part of the genre (cases of films written, directed and starred in by one person are defective cases of the cinematographic art), in a way in which communication between authors is accidental to the novel. Moreover, note that the director and conductor only communicates to each individual collaborator a part of the artistic vision.

So this might explain why a superlative novel is unlikely to be produced by two or more authors. But still, a decent novel could be, and sometimes is.

Common descent

Is common descent a part of contemporary evolutionary theory? It sure seems to be. But here is an argument to the contrary that puzzles me. Start with this thought experiment:

1. Organisms not based on DNA are found by a deep-sea vent or in some other hard to access isolated location on earth. Subsequent study reveals that they do not have a common ancestor with any of the DNA-based organisms that we know of but derive from a different abiogenesis.

Here is a surmise:

2. Most biologists are very sure of evolution, but either not sure or not as sure that (1) won't happen.

It follows from (2) that:

3. Either evolution is compatible with (1) or most biologists have inconsistent probabilities in this area.

If we deny the second disjunct, we get that evolution is compatible with (1). But (1) does not seem to be compatible with common descent. Hence we have an argument that evolution does not entail common descent.

I could be wrong about (2). But it does seem plausible. Here is one reason to think (2). Biologists are very sure of evolution. But (maybe) it would be unreasonable to be very sure (1) won't happen. So either biologists aren't very sure (1) won't happen or they are unreasonable in matters relevant to biology. Supposing they are not unreasonable in matters relevant to biology, we conclude that (2) is true.

Here are two ways out of the argument:

4. Common descent is not the thesis that all earthly organisms have common ancestry. Rather, it is the thesis that all the presently known earthly organisms (Daphnia magna, Quercus alba, Homo sapiens, Cantharellus cibarius, ...) have common ancestry. Problem: Does that mean that whenever a new species is discovered, the content of evolution changes?
5. "Evolution" is ambiguous between "the central aspects of the general picture that evolutionary theory gives" and "the currently best models of evolution". The former is what biologists are quite sure of. The latter is what entails common descent. Problem: If we asked biologists what the central aspects of the general picture that evolutionary theory gives are, common descent would likely be listed.

I am not happy with any of the ways out of the argument. Maybe (4) is the way to go? Or maybe we just need to suppose biologists are not entirely reasonable in their discipline (who is, after all?)? Or maybe my surmise (2) is false.

Are naturalists Pelagians?

Yes, they are: For they think that the central goals of human life are of a sort that can be achieved by natural powers alone.

No, they aren't: For they think that intimate union with God cannot be achieved by natural powers alone.

OK, so what's the right answer? In a sense, both yes and no. If we define Pelagianism by the natural achievability of the central goals of human life, then yes. If we defined it by the natural achievability of intimate union with God, then no. On Christian doctrine, the two definitions will come to the same thing. But on naturalism, they don't.

This might, however, yield a question-begging (but perhaps still useful) argument against naturalism. According to naturalism, the central goals of human life can be achieved by natural powers alone. But union with God cannot be. And union of God is a central goal of human life.

Is Leibniz an idealist?

I continue to be surprised why Leibniz gets described as an idealist. If Leibniz is an idealist, Dretske is committed to idealism, too, and that seems mistaken. Leibniz thinks everything has soul, and every soul has perceptions, but not all the perceptions are conscious, and some souls have no conscious perceptions. As far as I can tell, the claim that x has a soul with perceptions comes down to two things: (a) x has a substantial form, and (b) x has representations. Claim (a) holding for all x does not imply idealism: Aristotle surely does not count as an idealist. Claim (b) holding for all objects x is something that Dretske is committed to, assuming that we, reasonably, take having information to entail having representations (information surely represents; and on a Dretskean view it seems pretty easy to argue that everything that can be affected by something else carries information). We could take this to be an argument that Dretske is an idealist, but it is better to take it to be an argument that Leibniz is not.

Deep Thoughts XXVII

Only the eternal is forever.

[Actually, this is only a necessary truth on some readings of "forever" and "eternal". We need to read "eternal" as compatible with merely futureward eternity, but not pastward eternity. We need to read "forever" as implying infinite futureward temporal extent, so that existing at every time not count as sufficient for existing forever (imagine a world where the timeline has only a finite extent from beginning to end—we don't want to count a being that exists from the beginning to the end of time as existing forever in that world). It's worth noting that the converse of the above Deep Thought might not be a necessary truth. For a timeless being can be eternal, but I am not sure a timeless being counts as existing "forever", except of course in an analogical sense.]

Crime and punishment

Justice demands a punishment proportionate to the gravity of the crimes. In particular, a greater punishment is called for for committing eleven instance of some type of crime than for committing ten of them. But we do not have much reason to think that the person who committed the eleven is a worse person than the one who committed the ten. Hence, pace Hume, punishment is not based solely on the character as evidenced by the crime.