An example of a value-driven epistemological approach to metaphysics

1. Everything that exists is intrinsically valuable.

2. Shadows and holes are not intrinsically values.

3. So, neither shadows nor holes exist.

Robert Garcia coming to Baylor

I’m very happy that Robert Garcia, an excellent metaphysician from Texas A&M, has accepted a tenured position in our department at Baylor, and will be joining us this fall.

Towards a postcorpuscular ontology

My intuition is that quantum physics presents a picture of reality on which fundamental particles rarely if ever exist simpliciter. Most of the time, the world is in a superposition of the particle existing and not-existing, though perhaps with a much heavier weight being given to the one state rather than the other. Perhaps just at the moment of quantum collapse a particle simply exists. But immediately afterwards, there will be some interaction at the tail end of the wavefunction that makes the particle’s “existence” be in a superposition. And superposed existence is not real existence, since superposed existence comes in degrees, while real existence does not (at least not in the relevant sense of “degrees”).

If my intuition is right, then over the past hour, I take it that on a quantum picture at most instants of time no particles of my body were really existing. Maybe occasionally some particles flashed into being due to some collapse, but at most times there weren’t any particles there.

This means that at most times over the past hour one of the following was true:

1. I didn’t exist

2. I existed immaterially

3. I existed materially without having any particles.

Option (1) leads to ethical and theological difficulties. On that view, I am constantly popping in and
out of existence. But if so, then I am constantly dying and being resurrected. And that robs death and resurrection of their deep moral significance.

Option (2) leads to the interesting question whether I always exist immaterially, or only when none of my particles exist. If always, we get a very strong dualism. If sometimes, then we get a very funny semi-dualism: most of the time I’m immaterial.

Option (3) seems to me to be the most plausible. But on option (3), we should not think of material existence as a function of being constituted by particles. The kind of picture of material existence we get from van Inwagen, where living things come into existence by having their constituent particles get caught up in a life is untenable. Perhaps, instead, material existence is a function of having a certain kind of relationship to the wavefunction of the universe (perhaps a relationship of partly constituting or being partly constituted by that wavefunction).

If my argument is right, then Aristotelian metaphysicians should stop worrying very much about the pesky problem of what happens to the identities of fundamental particles when they get incorporated into our bodies. If there are ever any particles at all, then on quantum grounds independent of Aristotelian metaphysics, they are evanescent beings that do not persist long enough—for their existence soon becomes superposed—to cause much of a problem on that score. I suppose it could still be a problem if they come back into existence later. But it is dubious whether the numerically same particles can come back into existence. Indeed, the whole business of the particles “in the body” is so dubious on quantum grounds, that there is little theoretical cost to such seemingly absurd solutions as saying that there are no electrons in the body—for it seems we should anyway think that most of the time there aren’t any electrons in the body.

In the above, I allowed that perhaps when we have the right eigenstate, for a very short time a particle exists. But even that, I think, is dubious. The change from the system being in an eigenstate of particle number and not being in an eigenstate of particle number seems to be a merely quantitative change in the wavefunction, and hence we have little reason to think it corresponds to substantial generation or corruption.

There is one way out of all of the above: to accept a Bohmian interpretation of quantum mechanics. If I am right, then much contemporary metaphysics is being done on the implicit assumption that something like Bohmianism is right. But why assume that?

Variety and ontology

A major part of the ontologist’s dream has always been to find a small number of fundamental categories—maybe one, maybe two or three or maybe ten—into which everything falls.

Aristotle says somewhere that the philosopher knows all things—in general terms. That’s the kind of knowledge the ontologist’s dream accomplishes. But I worry: isn’t there a deep hubris in thinking we can categorize fundamental reality? And aren’t we destroying the deep richness of reality by pushing into into a handful of categories?

Well, maybe not. After all, all books could be seen as finite sequences of a small number of symbols. (Recall the lovely argument in Plato’s Euthydemus that one can’t learn from books, because if you don’t know the alphabet, you can’t read, and if you know the alphabet, you already know all that is in the books, namely letters.) And yet among these arrangements—all of which are ontologically the same sort of thing—there are the Summa Theologiae, The Deluge, Hamlet, the Psalms, the best of the scientific literature… and the latest tweets from world leaders, too. One doesn’t destroy the richness of literature by noting that ontologically it’s all of a piece. Being all of a piece ontologically is compatible with great variation.

That said, I still have the worry. While there is great richness in literature, culture be impoverished if there weren’t painting, sculpture, dance, etc. Similarly, even if there can be enormous richness among monads, their apperceptions and their appetitions, wouldn’t reality be impoverished if monads, perceptions and appetitions were all there is?

Humean metaphysics implies Cartesian epistemology

Let’s assume two theses:

1. Humean view of causation.

2. Mental causalism: mental activity requires some mental states to stand in causal relations.

If I accept these two theses, then I can a priori and with certainty infer a modest uniformity of nature thesis. Here’s why. On mental causalism, mental activity requires causation. On Humeanism, causation depends on the actual arrangement of matter. If the regularities found in my immediate vicinity do not extend to the universe as a whole, then they are no causal laws or causal relations. Thus, given causalism and Humeanism, I can infer a priori and with certainty from the obvious fact that I have mental states that there are regularities in the stuff that my mind is made of that extend universally. In other words, we get a Cartesian-type epistemological conclusion: I think, so there must be regularity.

In other words, Humean metaphysics of nature plus a causalist theory of mind implies a radically non-Humean epistemology of nature. The most plausible naturalist theories of mind all accept causalism. So, it seems, that a Humean metaphysics of nature plus naturalism—which is typically a part of contemporary Humean metaphysics—implies a radically non-Humean epistemology of nature.

So Humean metaphysics and epistemology don’t go together. So what? Why not just accept the metaphysics and reject the epistemology? The reason this is not acceptable is that the Cartesian thesis that the regularity of nature follows with certainty from what I know about myself is only plausible (if even then!) given Descartes’ theism.

A method for blocking deflation of ontological debates

Consider Hirsch-type deflationary views on which many differences in ontology are simply verbal differences. A standard case is nihilism and universalism about composition: the nihilist says that multiple things can never compose a whole and the universalist says that every plurality must compose a whole. The deflationist sees the two views as notational variants. The universalist’s sentences describe the same facts as the nihilist’s. We can maybe even translate with little if any loss between the two idioms, replacing the nihilist’s quantifiers with quantifiers restricted to simples on the universalist’s side, and replacing the universalist’s quantifiers with plural quantification, or quantification over sets, or some other device acceptable to the nihilist.

Note, first, that in this particular case there is a bit of a problem. The universalist might allow for composed objects that have no simple parts—“gunk”. The claim that possibly there is gunk is one that cannot be translated into any statement in the nihilist’s language that has a hope of being true. The nihilist’s usual way of translating a universalist’s statement is to use plural quantification. So the statement that possibly there is gunk is going to get translated into something like the statement that possibly there is a plurality of things none of which is a simple. But that’s obviously false given nihilism, since the nihilist’s quantifiers can only quantify over simples, and so the statement basically says that there are simples none of which is a simple. Thus, we have a genuine, non-verbal disagreement.

So the only way we can take a nihilist-universalist disagreement to be merely verbal is if both theorists deny the possibility of gunk. I think they should deny the possibility of gunk.

Here is a second case, where disagreement on composition cannot be deflated. Consider a brutal composition view like Markosian’s. On this view, there will be possible worlds with the same simple objects standing in the same non-mereological relations but differing as to composition facts. For instance, in one world there might be three rocks that make up a whole and in the other world the very same three rocks do not make up a whole, even though they are arranged in exactly the same way. Any nihilist or universalist description of the two worlds will be unable to distinguish such worlds, but on a brutal composition view, there can be such pairs. Here we have a real disagreement, one that cannot be taken to be merely verbal. The brutal composition theorist has more possibilities than the nihilist and universalist. And the brutal composition theorist’s statement that the two worlds differ in composition facts but not in non-mereological facts either has no translation into either nihilist or universalist language or translates into something that is clearly false on the given theory.

The brutal compositionalist has an additional “degree of freedom”, as the scientist would say, on her theory than the nihilist or universalist does. The case here is similar to those dualists who believe in the possibility of zombies. While the disagreement between a dualist who thinks the mental supervenes on the physical and the pure physicalist could seem to be merely verbal to some (though I think it’s a mistake to see it that way), the disagreement between a dualist who thinks that the mental does not supervene on the physical and the pure physicalist is certainly not merely verbal.

In general, thus, the modal ramifications of theories can block deflationary moves. One theory may allow for a possibility that simply rules out the other theory (e.g., gunk ruling out nihilism), or one theory may posit contingent facts that do not supervene on reality as describable in the other theory (the brutal composition or zombie cases).

This leaves the possibility that there will be some ontological debates that are merely verbal. Perhaps the debate between the nihilist and the anti-gunk universalist is merely verbal. But that some pairs of ontological theories disagree merely verbally is not a very interesting deflationary thesis.

Moreover, I think that once we see that there are nearby debates that are clearly not merely verbal, the plausibility of the deflationary move in the cases that looks more verbal goes down. Once we realize that among the views under discussion there is a brutal composition view on which there is a possible world just like ours but where nihilism contingently holds and a possible world just like ours but where universalism contingently holds, it becomes pretty clear that holding nihilism to hold necessarily will also differ from holding universalism to hold necessarily. (That said, there may be particular variants on universalism that just are notational variants on nihilism. Say, ones where the quantifiers are stipulated in terms of plural quantification over simples.)

Philosophy as metaphysics: A very biased view

Realism and anti-reductionism

The ordinary sentence "There are four chairs in my office" is true (in its ordinary context). Furthermore, its being true tells us very little about fundamental ontology. Fundamental physical reality could be made out of a single field, a handful of fields, particles in three-dimensional space, particles in ten-dimensional space, a single vector in a Hilbert space, etc., and yet the sentence could be true.

An interesting consequence: Even if in fact physical reality is made out of particles in three-dimensional space, we should not analyze the sentence to mean that there are four disjoint pluralities of particles each arranged chairwise in my office. For if that were what the sentence meant, it would tell us about which of the fundamental physical ontologies is correct. Rather, the sentence is true because of a certain arrangement of particles (or fields or whatever).

If there is such a broad range of fundamental ontologies that "There are four chairs in my office" is compatible with, it seems that the sentence should also be compatible with various sceptical scenarios, such as that I am a brain in a vat being fed data from a computer simulation. In that case, the chair sentence would be true due to facts about the computer simulation, in much the way that "There are four chairs in this Minecraft house" is true. It would be very difficult to be open to a wide variety of fundamental physics stories about the chair sentence without being open to the sentence being true in virtue of facts about a computer simulation.

But now suppose that the same kind of thing is true for other sentences about physical things like tables, dogs, trees, human bodies, etc.: each of these sentences can be made true by a wide array of physical ontologies. Then it seems that nothing we say about physical things rules out sceptical scenarios: yes, I know I have two hands, but my having two hands could be grounded by facts about a computer simulation. At this point the meaningfulness of the sceptical question whether I know I am not a brain in a vat is breaking down. And with it, realism is breaking down.

In order for the sceptical question to make sense, we need the possibility of saying things that cannot simply be made true by a very wide variety of physical theories, since such things will also be made true by computer simulations. This gives us an interesting anti-reductionist argument. If the statement "I have two hands" is to be understood reductively (and I include non-Aristotelian functionalist views as reductive), then it could still be literally true in the brain-in-a-vat scenario. But if anti-reductionism about hands is true, then the statement wouldn't be true in the brain-in-a-vat scenario. And so I can deny that I am in that scenario simply by saying "I have two hands."

But maybe I am moving too fast here. Maybe "I have two hands" could be literally true in a brain-in-a-vat scenario. Suppose that the anti-reductionism consists of there being Aristotelian forms of hands (presumably accidental forms). But if, for all we know, the form of a hand can inform a bunch of particles, a fact about a vector or the region of a field, then the form of a hand can also inform an aspect of a computer simulation. And so, for all we know, I can literally and non-reductively have hands even if I am a brain in a vat. I am not sure, however, that I need to worry about this. What is important is form, not the precise material substrate. If physical reality is the memory of a giant computer but it isn't a mere simulation but is in fact informed by a multiplicity of substantial and accidental forms corresponding to people, trees, hands, hearts, etc., and these forms are real entities, then the scenario does not seem to me to be a sceptical scenario.

Musings on mathematics, logical implication and metaphysical entailment

I intuitively find the following picture very plausible. On the one hand, there are mathematical claims, like the Banach-Tarski Theorem or Euclid's Theorem on the Infinitude of the Primes. These are mysterious (especially the former!), and tempt one to some sort of non-realism. On the other hand, there are purely logical claims, like the claim that the ZFC axioms logically entails the Banach-Tarski Claim or that the Peano Axioms logically entail the Infinitude of the Primes. Pushed further, this intuition leads to something like logicism, which we all know has been refuted by Goedel. But I want to note that the whole picture is misleading. What does it mean to say that p logically entails q? Well, there are two stories. One is that every model of p is a model of q. That's a story about models, which are mathematical entities (sets or classes). Claims about models are mathematical claims in their own right, claims in principle just as tied to set-theoretic axioms as the Banach-Tarski Theorem. The other reading is that there is a proof from p to q. But proofs are sequences of symbols, and sequences of symbols are mathematical objects, and facts about the existence or non-existence of proofs are once again mathematical facts, tied to axioms and subject to the foundational worries that other mathematical facts are. So the idea that there is some radical difference between first-order mathematical claims and claims about what logically entails what, such that the latter is innocent of deep philosophy of mathematics issues (like Platonism), is untenable.

Interestingly, however, what I said is no longer true if we replace logical entailment with metaphysical entailment. The claim that the ZFC axioms metaphysically entail the Banach-Tarski Claim is not a claim of mathematics per se. So one could make a distinction between the mysterious claims of mathematics and the unmysterious claims of metaphysical entailment--if the latter are unmysterious. (They are unmysterious if one accepts the causal theory of them.)

This line of thought suggests an interesting thing: the philosophy of mathematics may require metaphysical entailment.

The essential properties of our spacetime

Suppose that spacetime really exists. Name our world's spacetime "Spacey". Now, we have some very interesting question of which properties of Spacey are essential to it. Consider a possible but non-actual world whose spacetime is curved differently, say because some star (or just some cat) is in a different place. If that world were actual instead of ours, would Spacey still exist, but just be curved differently, or would a numerically different spacetime, say Smiley, exist in Spacey's place?

There are three different views one could have about some kind K of potential properties of a spacetime:

1. All the properties in K that Spacey has are essential to Spacey.
2. None of the properties in K are essential to Spacey.
3. Some but not all the properties in K that Spacey has are essential to Spacey.

Suppose K is the geometric properties. It's plausible that at least the dimensionality is essential to Spacey: if Spacey is four-dimensional, it is essentially four-dimensional. Any world with a different number of dimensions doesn't have our friend Spacey as its spacetime. If so, we need only to decide between (1) and (3).

Here is an argument for (3). Spacey's properties can be divided into earlier and later ones, since one of the four (or more) dimensions of Spacey is time. Further, according to General Relativity, some of Spacey's later geometric properties are causally explained at least in part by Spacey's own earlier causal influences. But if (1) were true, then Spacey would not have existed had the later geometric properties been different from how they are, and a part of the explanation of why it is Spacey that exists lies in the exercise of Spacey's own causal influences. But nothing can even partly causally explain its own existence. (Interesting consequence: If Newtonian physics were right, we might think that view (1) was true with respect to geometric properties. But this is implausible given General Relativity.)

Similar arguments go for the wavefunction of the universe, if it's a fundamental entity.

A Metaphysicality Index

A grad student was thinking that Platonism isn't dominant in philosophy, so I looked at the PhilPapers survey and indeed a plurality of the target faculty (39%) accepts or leans towards Platonism. Then I got to looking at how this works across various specializations: General Philosophy of Science, Philosophy of Mind, Normative Ethics, Metaethics, Philosophy of Religion, Epistemology, Metaphysics, Logic / Philosophy of Logic and Philosophy of Mathematics. And I looked at some other views: libertarianism (about free will), theism, non-physicalism about mind, and the A-theory of time.

Loosely, the five views I looked at are "metaphysical" in nature and their denials tend to be deflationary of metaphysics. I will say that someone is "metaphysical" to the extent that she answers all five questions in the positive (either outright or leaning). We can then compute a Metaphysicality Index for an individual, as the percentage of "metaphysical" answers, and then an average Metaphysicality Index per discipline.

Here's what I found. (The spreadsheet is here.) I sorted my selected M&E specialities from least to most metaphysical in the graph.

On each of the five questions, the Philosophers of Science were the least metaphysical. This is quite a remarkably un-metaphysical approach.

With the exception of Platonism, the Philosophers of Religion were the most metaphysical. (A lot of Philosophers of Religion are theists and may worry about the fit between theism and Platonism, and may think that God's ideas can do the work that Platonism is meant to do.)

Unsurprisingly, the Metaphysicians came out pretty metaphysical, though not as metaphysical as the Philosophers of Religion. (And this isn't just because the Philosophers of Religion believe in God by a large majority: even if one drops theism from the Metaphysicality Index, the Philosophers of Religion are at the top.

Interestingly, the Philosophers of Mathematics were almost as metaphysical as the Metaphysicians (average Metaphysicality Index 29.2 vs. 29.8). They were far more Platonic than anybody else. I wonder if Platonism is to Philosophy of Mathematics like Theism is to Philosophy of Religion. The Philosophers of Mathematics were also more theistic and more non-physicalistic than any group other than the Philosophers of Religion.

It's looking to me like the two fields where Platonism is most prevalent are Logic (and Philosophy of Logic) and Philosophy of Mathematics. This is interesting and significant. It suggests that on the whole people do not think one can do mathematics and logic in a nominalist setting.

For the record, here's where I stand: Platonism: no; Libertarianism: yes; God: yes; Non-physicalism: yes; A-theory: no. So my Metaphysicality Index is 60%.

Grounding grounding

Suppose Bill is a bachelor and Marcus is married. I claim that <Bill is a bachelor> stands in the same relation to <Bill is a never-married marriageable man> as <Marcus is a bachelor> stands to <Marcus is a never-married marriageable man>. But the propositions about Bill are true while those about Marcus are false. Since grounding is a relation that holds only between truths, the relevant relation that the two pairs of propositions have in common is not the grounding relation. It is something else. Call it ontological explanation, following Dan Johnson's dissertation. (Since, I think, explanation is factive, so that only truths can be explained, and they can only be explained by truths, ontological explanation isn't explanation strictly speaking.)

Abbreviate "<x is a bachelor>" as b_x and "<x is a never-married marriageable man>" as n_x. Then, necessarily, for every human being (at least) x, n_x ontologically explains b_x. Let B be Bill and M be Marcus. Then, n_B ontologically explains and grounds b_B, while n_M ontologically explains but does not ground b_M.

Moreover, we are in a position to offer a grounding for the proposition <n_B grounds b_B>. This grounding is given by the contingent truth n_B and the necessary truth <n_B ontologically explains b_B>. So at least in this case, the grounding truth is itself grounded in a truth about Bill together with a necessary truth of ontological explanation.

So at least sometimes we can find a grounding for grounding truths partly in terms of ontological explanation truths. This gives some evidence that ontological explanation facts are more primitive than grounding facts.

Is this pattern in general true? Is it the case that if p grounds q, then p together with <p ontologically explains q> grounds <p grounds q>? Not if ontological explanation is like Johnson thinks it is. For Johnson thinks that that if a ontologically explains b, then a is metaphysically necessary and sufficient for b. But p can ground q without being necessary for q: that I am sitting grounds that I am sitting or standing.

Perhaps we can modify Johnson's account by holding on to the sufficiency while dropping the necessity. Then we will have something like ontological explanation where a ontologically explains b only if a is metaphysically sufficient for b. In that case, the general pattern might hold. What grounds that <<I am sitting> grounds <I am sitting or standing>>? It is <I am sitting> and <<I am sitting> ontologically explains <I am sitting or standing>>. Of course, the falsehood <I am standing> also ontologically explains that I am sitting or standing.

If this is right, then we can get below the hood on grounding: the more primitive notion is ontological explanation (modified from Johnson's account as above). If Johnson is right to require necessity, we still can get below the hood on grounding in some cases.

Here is one reason all this might matter. Consider propositional desires other than beliefs. Let's say Marcus wishes he were a bachelor. It is important, both to Marcus and to the analysis of the situation, that <Marcus is a bachelor> is ontologically explained by <Marcus is a never-married marriageable man>. There is something about being never-married, or being marriageable, or being a man, or a combination of these that implicitly appeals to Marcus. (Likewise, ontological explanation seems potentially relevant to Double Effect.)

One could try to handle the stuff about ontological explanation by using counterfactual grounding. The relation between n_x and b_x is that n_x would ground (or would necessarily ground) b_x were n_x true. But it is implausible that such a counterfactual fact is prior to the grounding fact if x is Bill.

"Using as"

I can use a fork as a backscratcher or my thumb and forefinger as the prongs of a slingshot.

I claim that when I do so, there isn't a backscratcher or a set of prongs that comes into existence when I do so.

For consider the three possibilities on which it is correct to say that prongs come into existence:

1. The thumb and forefinger cease to exist and prongs come into existence, made out of the former digits.
2. A set of prongs comes into existence in exactly the space occupied by the thumb and forefinger, and are made out of the same matter as the prongs.
3. The thumb and forefinger are both a thumb and forefinger and a pair of prongs after the transformation.

The first option is obviously false.  I didn't temporarily come to have only eight fingers when I did it for the purposes of the photo.

The second option doesn't match the how we talk.  I would say: "I used my fingers as the prongs of a slingshot."  But according to (2), I had the prongs of a slingshot right there in the very same region of space occupied by my fingers--why didn't I use them as the prongs of a slingshot, since they are surely at least as usable for that purpose.  Or did I use both my digits and the prongs as prongs?  But I need only two things for slingshot prongs, not four.

Moreover, as I am typing with both hands, surely the prongs no longer exist.  When did they cease to exist?  Right after the shot?  But when I took the picture, I didn't actually take a shot--I only used my fingers as prongs for show.  (I did take a shot on other occasions, shooting a little fuzzy ball from the kids' craft drawer.)  When I relaxed the fingers?  But why not, instead, think of the relaxed fingers as folded prongs?  A slingshot could, after all, fold.  It's not like I destroyed the prongs when I relaxed my fingers--they're ready for convenient use at any other time.  Yet if they do continue to exist, do I have forty-four other pairs of prongs on my hands (granted, 25 of the pairs--the ones with one finger from one hand and the other from the other--can only be used by having a friend pull back the pocket or by pulling the pocket back with the teeth) if I form the odd ambition to use a different pair every day for the next forty-four days?  And if the prongs ceased to exist, will the very same pair of prongs be resurrected the next time I use my thumb and forefinger as prongs?  These questions seem silly, and their silliness suggests that they are predicated on a mistake.

The third option fits better with our "use as" talk.  I used my fingers as prongs, and I used the prongs as prongs, but there aren't four things there, because the fingers were prongs.  But we get the wrong modal properties.  For suppose that I decided to reinforce the prongs by supergluing steel rods to them.  The steel rods would come to be a part of the prongs, but they wouldn't come to be a part of the fingers.  Hence the fingers are not identical with the prongs, by Leibniz's Law.  

All this fits with common sense.  I used fingers as slingshot prongs or a fork as a backscratcher, and there were no slingshot prongs or a backscratcher there.

But can this line be maintained?  Suppose I cease to use the fork as a fork, and start to use it exclusively as a backscratcher.  Suppose in our culture, everybody owns a backscratcher, as our greeting ritual is a light scratching of each other's backs.  And backscratchers look just like American forks.  Surely what I would have would be a backscratcher.  Yet, surely, whether a backscratcher comes into existence shouldn't depend on how permanently it is used as such.  Still, that seems to be how we talk.  If all we are doing is descriptive metaphysics, we may stop here.

But if we want to do more gutsy metaphysics, we might at this point question the initial intuition that I had a fork there.  Perhaps the fundamental concepts are not of backscratchers or slingshots (or prongs thereof) or even forks, but of using some thing or things (particles, say) as backscratcher, slingshot (or prongs thereof) or fork. To use as a backscratcher is like to dance a waltz--if we want to do serious metaphysics, we shouldn't ask where the token backscratcher is in the using or where the token waltz is in the dancing.

Rob Koons has defended the idea that artifacts are token social practices. What I am saying is quite similar, except that I do not want to identify the artifacts with social practices. But all the reality there is in artifacts is the reality of things used as, or meant to or designed to be used as something or other.

Artifacts

Suppose I am a plumber, and I take a section of pipe, insert a blowgun dart, and blow.  I just shot a dart out of a blowgun.  When did the pipe turn into a blowgun, though?

Did it happen when I formed the intention to use the pipe as a blowgun?  No: I do not have the power to make new material objects come into existence just by thinking about it.

When I picked up the pipe?  There are at least there is contact.  But surely it's not the right kind of contact.  It would be magic if I could make a new material object come into existence by just picking up a material object with a certain thought in mind.

When I inserted the dart?  Presumably, not any insertion will do, but one with a plan to blow.  For I could just be doing plumbing, using the outer diameter of the dart to measure the inner diameter of the pipe, and that shouldn't turn the pipe into a dart.  Again, we have some magic here--thinking about the pipe in one way while inserting the dart creates a blowgun while thinking about it another way leaves it a boring pipe.  Moreover, putting the dart into the pipe seems to be an instance of loading a blowgun rather than making a blowgun.

When I fired the dart?  Surely, that's too late.  As I lift up the pipe and point it at the target, I am surely pointing a blowgun!

Further complication: I now put the blowgun down among the pipes on the back of my truck, and next day install it in Mr. Smith's sprinkler system.  Does Mr. Smith now come to be a blowgun owner, with the rights, liabilities and responsibilities attendant on having such a weapon (blowguns are illegal in California or Canada, after all)?  Moreover, did I violate my contract with Mr. Smith, for I agreed to install pipes, whereas I installed a blowgun instead?  The last question is perhaps not so pressing--for perhaps the tubularly arranged matter I installed in his garden constitutes both a pipe and a blowgun.

One might think some of the difficulties could be removed by saying that throughout I was dealing with one object, a pipe, which acquired an extrinsic property, being a blowgun.  There need be no magic when a material object acquires an extrinsic property as a result of my thinking.  When I think about your car, your car acquires the property of being thought about by me.  But this is mistaken.  Suppose I add sights to the blowgun.  The sights come to be a part of the blowgun, but they do not come to be a part of the pipe--they are, rather, attached to the pipe.  So the blowgun seems to be a material object distinct from the pipe.

The solution to all this is to deny that there are pipes and blowguns.  There is just matter (or fields) arranged pipewise and blowgunwise.  And for convenience we adopt ways of speaking that make it sound like such objects are among the furniture of the universe.

A collection of research questions on infinity

Trent Dougherty, Rob Koons and I, with the help of one or two friends, made what we think is an interesting collection of research questions on infinity, relevant to philosophy as well as to mathematics, physics and theology.

Conceptual

• How can one classify and define infinities? (E.g., actual, potential, extensive, intensive, ordinal, absolute, unbounded.)
• What does it mean to say that a being is infinite?
• Can something like Cantor’s notion of the absolute infinite be made sense of?  Did Cantor’s theory have theological grounds?
• Are there better general ways of comparing the sizes of infinite sets than subset relations, cardinality, measure, dimension (Hausdorff, etc.) and Baire category?

Divine infinity

• In what way could God contain all mathematical infinities?
• Can an ontological argument based on the idea of an unlimited being be sustained?
• Could the notion of an infinite proof be used to explain the necessity of divine existence?
• Can one being know all orders and kinds of infinity?

Logic, epistemology and rationality

• What does the Löwenheim-Skolem Theorem say about our ability to meaningfully talk about infinities?
• Can one extend probabilistic reasoning to handle about a sample chosen from an infinite number (of moderate or high cardinality) of samples “on par” with one another?
• Do renormalization techniques have probabilistic and epistemological implications?
• Can one define a measure for the components of a multiverse, such as one resulting from string theory, in a way that yields epistemologically responsible predictions?
• How should one rationally reason when there are infinite utilities in view? Infinitesimal probabilities?
• How can one classify the paradoxes of infinity, what can one learn from them, and how can one resolve them? 
• Does one need a logic that handles infinite sentences or propositions and what are the prospects for one?
• Can one engage in plural quantification over proper-class-many objects?  Over greater infinities?
• Is infinity simpler than finite non-zero numbers for the purposes of measuring the complexity of a theory?  What sort of infinity?
• What infinite regresses are vicious?
• Are non-recursive infinite theories, such as “list theories” of mind, scientifically and philosophically acceptable?
• Can Leibniz’s notion of an infinite proof, or the notion of an infinite argument, be made sense of and made useful?
• Is it possible for finite and purely natural beings to come to the concept of infinity?

What infinities there are in physics and metaphysics

• Is a simultaneous infinite number of objects possible? Actual?
• Is an infinite past possible? Actual?
• Can space be infinite? Is it? 
• What alternatives are there to Archimedean spacetimes based on the real numbers?
• Is there an upper cardinality bound on the number of objects, or of physical objects, that could exist?  Could there be proper class many objects or physical objects?
• Are space and time infinitely subdivided or at least infinitely subdivisible? Are they necessarily so? Are they continuous? Necessarily so? 
• Are ‘supertasks’ possible? Non-well-founded processes and non-well-capped ones?
• Can causation proceed through an infinite number of causal intermediaries?
• Could there be infinite intensities: infinite energy, force, density, pleasure, pain?
• Could matter be infinitely complex? Could ‘gunk’ exist? Could matter be infinitely heterogeneous?

Theological non-divine infinities

• Does complete human flourishing require eternal life?
• Does eternal life for humans have to be temporally everlasting?  Does it have to temporally everlasting with respect to external time?
• Could the years of an eternal life have an order type greater than ω?  Would that be better than an  ω-type infinity of eternal life?  
• Is it possible for there to be an infinite sin?  If so, would it deserve an infinite punishment?
• Does an everlasting punishment have to be an infinite punishment?

Leibniz on metaphysics

[I]n fact, metaphysics is natural theology, and the same God who is the source of all goods is also the principle of all knowledge. (Letter to Countess Elizabeth) 

God is not a proper part

Nothing is greater than God in any sense. But a whole is greater at least in some sense than a proper part. Therefore:

1. God is not a proper part of any whole.

This has at least three interesting consequences:

2. Unrestricted compositionality is false.
3. Some true propositions have no truthmaker.
4. At least some de re propositions do not contain the object that they are about as a part.

That (2) follows from (1) is obvious: if (1) is true, then there is no object that has both God and the CN Tower as parts.
That (3) follows is pretty easy, too. Consider the true proposition that God created elephants (or that God exists and elephants exist). If this has a truthmaker, that truthmaker contains God as a part. But that truthmaker cannot just be God, since if x is a truthmaker for p, then that x exists entails that p is true, while that God exists does not entail that God created elephants. So, the truthmaker would have to contain God as a proper part, which would violate (1). The argument leaves open the possibility that all true propositions are made true by one or more entities, so that the proposition that God created elephants might be made true by God and elephants (not considered as a composite object, but simply as a plurality). But it's still the case that the proposition lacks a truthmaker.
Finally, (4) follows from the observation that there are de re propositions about God, such as that God has created us.

Two metaphysical convictions

I have two basic metaphysical convictions that drive my metaphysics.  One is that there is no vagueness at the fundamental level.  So anything there is vagueness about is non-fundamental.

The other is that humans are among the fundamental substances.  We are not logical constructions out of other entities; we are not reducible to other entities; we are fundamental substances.

Together, these two convictions lead to various controversial things, especially since some people will think there is a tension between the two.

Why ontology matters

For all x, x should be loved if x exists (eternally or at some time or other) and x should not be loved if x does not exist. Thus fundamental ontology matters for life.

Divine simplicity and Aristotelian metaphysics

I've been told that Wolterstorff attributes the prominence of divine simplicity in the Christian tradition to the influence of Aristotelian metaphysics. Whatever the history of the issue may be, it seems that there is a perfectly good argument for divine simplicity that makes no reference to Aristotelian metaphysics, and whose only really controversial premise—the first one—is something that most theists should immediately accept (though Wolterstorff himself denies it). Let a "proper part" of X be a part of X that is not identical with X.

1. (Premise) Everything other than God himself is created by God.
2. (Premise) If God has proper parts, then at least one proper part of God is not created by God.
3. No proper part of God is identical with God. (By definition of "proper part".)
4. If God has proper parts, then there is something that is neither identical with God nor created by God. (By 2 and 3)
5. God has no proper parts. (By 1 and 4)

One might quibble about (3). One might think that all of God's current parts are created by God, because at some point created new parts for himself, and then destroyed the old, non-created ones. However, (1) is not only true now, but it was always true. So there couldn't have ever been any non-created divine proper parts. I guess one could have a super-weird view on which God from eternity has been replacing his parts, and never had any parts that were not created by him at an earlier time. But that constantly changing view of God is surely incompatible with any reasonable take on divine immutability. (Take it as a criterion of adequacy on a theory of immutability that it rejects this!)

The real controversy will be about (1). But here I just want to make one point. The deep plausibility of (1) to theists does not come from Aristotelian metaphysics: it comes, rather, from a commitment to God as creator that appears at the heart of Judaism and Christianity. In fact, it may be that the direction of justification between (1) and Aristotelian metaphysics goes the other way: it is (1) that pushes the theist to more immanent views of universals.