Life, teleology, and the Holy Spirit

I suppose I think all substances have teleology. For as Rob Koons and others have noted, a causal power always has the immediate effect of its exercise as its telos, and substances seem to always have causal powers.

But I think we can make a distinction between having the immediate effect of one’s causal power’s exercise as a telos and having a further telos for the causal power. In the latter case, the substance is exercising the causal power as a means to an end—whether intentionally or not. This seems to happen for all living things. It is not merely the telos of a bacterium to seek food, but to seek food in order to ingest it. Thus the seeking behavior is ordered in the bacterium’s teleology to the ingesting, and the ingesting is presumably ordered to further goods of bacterial functioning. On the other hand, when an electron repels another electron, the repulsion is the only telos the electron is pursuing. Of course, someone else (God or an electrical engineer, say) may have a further purpose for that repulsion, but that doesn’t seem to be the electron’s telos.

It seems that we have a difference between living and non-living substances, then: non-living substances have only immediate teleology, while living substances have both immediate and mediate teleology.

What about God? Well, initially it seems easy to say that, of course, God engages in means-end reasoning in creation all the time (e.g., making fruit for primates like us to eat), and hence has mediate teleology. But if mediate teleology is essential to life, it is troubling to identify God’s mediate teleology with anything done within creation, since God does not need to create.

Does God in himself have mediate teleology? One might see a positive answer within a certain version of western trinitarian theology: The Father generates the Son in part in order that the Holy Spirit might proceed through the Son. Thus there is a mediate teleology within God’s trinitarian being.

If this is the right answer, then we have a way in which the filioque is needed for God to be alive, and in which the Holy Spirit is life-giver—as per the Nicene Creed—not just to creatures, but to the blessed Trinity.

Perhaps there are other trinitarian things one can invoke besides the filioque. The Father generates the Son in order that the Son might love him back. But in any case, it is difficult to see how there can be essential mediate teleology in God apart from something like the doctrine of the Trinity.

Do we thus have another argument for the multiplicity of persons in God?

1. God is simple.

2. God does not have to create.

3. Life essentially involves mediate teleology.

4. God is essentially alive.

5. If God is essentially alive and simple and does not have to create, the only way for him to have essential mediate teleology requires a multiplicity of hypostases.

All that said, I am not 100% convinced that we should think of mediate teleology as an essential feature of life.

Molinism and trials

A standard thing that theists have long said is that some difficult situations are “trials” where you have right and wrong options, and where you have an opportunity to grow closer to God through the right choice.

Suppose Molinism is true. Now suppose Curley the crooked politician has failed a trial by accepting a bribe. On Molinism, God knew that if Curley were to be offered a bribe in these circumstances, Curley would fail the trial. Now, presumably, God could also have tweaked the circumstances of the trial in different ways. For instance, he could have made sure that Curley had a headache at the time, or had noticed the beauty of God’s creation while walking to work through the city park, or had tripped and bruised his knee, etc. All these things would affect the psychological state that Curley was in while being bribed. Now, just as we would expect re-runs of Curley’s choice (with a memory wipe between re-runs) to result sometimes in the acceptance of the bribe and sometimes in its rejection in a way that looks random (as per van Inwagen’s rewind argument), likewise we would expect the results of Curley’s counterfactual choice to vary between the variant circumstances. In particular, we would expect some of the variant circumstances to be such that Curley would have passed the test.

Now, given that, we have a puzzle: Why didn’t God modify the circumstances in such a way? It seems like it would have been easy to do so without interfering in anyone’s freedom.

Of course, this is just a species of the problem of evil. But there is a difference between this and some other problems of evil. If we ask why God might have allowed someone to suffer, we can answer by saying that God might have planned to draw a greater good out of the suffering. But it is problematic to say that God planned to draw a greater good out of Curley’s sin. For to say that appears to imply that God intended Curley’s sin as a means to an end. But it is wrong to intend that someone sin, even as a means to much greater good.

What we need for theodicy here is a significant good achieved not by Curley’s sin, but by something independent of Curley’s sin. Let’s say that Curley would have rejected the bribe if he had a headache. Then God needs a significant reason not to have given Curley a headache, and a reason not dependent on the goods God would draw out of Curley’s sin. Since a headache is a minor bad, the good of avoiding a headache is not enough to do the job, it seems.

One solution is that God has good reason to minimize his interference in nature, even if the interference is really minor.

Another solution, and I both like it and yet feel it’s a bit of a cheat, is for the Molinist to embrace what I called the “Undefined” answer to the question of correlations between conditional of free will. On that answer, we cannot say that it is likely that in one of the variant circumstances Curley would have chosen differently.

Of course, the best answer is to abandon Molinism for mere foreknowledge.

An argument against the conjunction of perdurantism and physicalism

1. I think a thought.

2. For each thought I think derivatively, there is a unique entity that thinks it non-derivatively.

3. On standard perdurantism, all my thoughts are derivative, and derivative precisely from temporal parts thinking these thoughts.

4. Given physicalism, there is no unique temporal part thinking any of my thoughts non-derivatively.

5. So, at least one of standard perdurantism and physicalism is false.

There are two controversial premises: 2 and 4.

Regarding 2, there are two alternatives. Either there is an infinite regress of entities engaged in derivative thought behind my thought, or else my thought is derived from two or more entities non-derivatively thinking my thoughts. The infinite regress story is very implausible. And the two primary non-derivative thinkers story seems highly counterintuitive.

There are two arguments for 4. First, none of my thoughts are thought by an instantaneous temporal part: all my thoughts take time. But at least given physicalism, it seems obvious that the temporal boundaries of my thoughts are going to be sufficiently fuzzy that there won’t be a privileged temporal part for any of my thoughts—a temporal part that’s a picosecond longer or shorter would be just as good a non-derivative candidate for where I derive my thought from.

Second, temporal parts depend on reference frames, and I don’t have a privileged reference frame, so I don’t have a privileged temporal part non-derivatively thinking my thought.

A difference among relations

I want to get at a certain difference between relations like love and hate, on the one hand, and relations like causation and parthood, on the other.

One way to see the difference is that there are significant formal constraints on the distribution of causation and parthood, but no formal contraints on the distribution of love and hate. For instance, there cannot be cycles of causation and parthood must be transitive. But there are no such constraints on love and hatred: any combination of loves and hatreds is possible for ordinary human beings.

Another way to see what seems to be the same difference is this. Bracketing considerations of God’s goodness, God can just directly freely insert and remove instances of love and hatred within a bunch of people without changing anything else. But it seems that God can’t just directly freely insert and remove instances of causation and parthood within a bunch of entities. It seems he can’t, for instance, reverse the direction of causation between my father and myself, or will me to be a part of my heart.

I find it a very mysterious feature of causation and parthood that it has such formal constraints.

The lack of free recombinability for a relation is sometimes explained by the relation being non-fundamental. For instance, “darker than” must be transitive, but the reason is that its obtaining depends on more fundamental facts, such as how dark the two relata are, and this dependence induces the logical features of the relation. It could turn out that causation and parthood do depend on more fundamental things, though this does not seem very plausible. But at the same time, it seems pretty plausible that whatever more fundamental things causation and parthood depend on, these will include relations, and relations of a sort that have the non-recombinability features of causation and parthood.

Anyway, it seems to me that there is some fundamental difference between fundamental relations that have no formal constraints and fundamental relations that do have formal constraints, and I don’t know what accounts for it. I feel that this difference is a mere indicator of some deeper difference in kind. Causation and parthood “look” very different from love and hatred.

Causal well-foundedness

I have defended causal finitism at length, mainly (but not only) as a way of getting out of paradoxes.

I want to think about a weaker thesis than causal finitism today. Causal finitism says that there is no item that has infinitely many things causally prior to it.

A weaker thesis is that causal priority (which I will assume to be transitive) is causal well-foundedness, namely that any set S of items contains a minimal item—an item that has nothing in S causally prior to it. Assuming the Axiom of Choice (and its applicability to sets of “items”), this is equivalent to saying there are no backwards infinite regresses ... < A₋₃ < A₋₂ < A₋₁ < A₀, where < indicates causal priority.

The arrangement of the Grim Reapers appears not to be well-founded: each one’s actions respond to the actions of the one before. So causal well-foundedness seems to rule out that paradox just as well as causal finitism.

At the same time, just as causal finitism implies the existence of a first cause (and hence yields a kalaam argument), so does causal well-foundedness: just take the set of all items that are causally prior to something, and a minimal item will be a first cause.

So far, no differences.

But alas once we start looking at other paradoxes, differences arise. Thomson’s lamp is unaffected by causal well-foundedness: the story is well-founded. Similarly, it seems one can shuffle an infinite deck of cards using a well-founded supertask. Likewise, there are paradoxes arising from from infinitely many things affecting a single result without any chain, like the paradox where infinitely many people roll independent and fair dice without seeing the results, and an angel announces that all but finitely many got sixes.

So you get what you pay for. Causal well-foundedness is a weaker assumption than causal finitism, but it also rules out fewer paradoxes.

Beginnings and causation

Some people think that it’s way more obvious that a contingent thing that has a beginning has to have a cause than that a contingent that has no beginning has to have a case.

Here’s one reason to be suspicious of this intuition. Whether something contingent needs to have a cause should not depend on its orientation. But whether something has a beginning is a function of its orientation in spacetime. Take an object that has extends backward in time to infinity but forwards only finitely, and hence has no beginning. Consider this as a four-dimensional object. You can then rotate it so it extends forwards in time to infinity but only a finite distance backward. You’ve merely changed its orientation, but now the object has a beginning.

This is very much a four-dimensionalist argument, of course.

Schaffer and well-foundedness of priority

Jonathan Schaffer in his famous “Monism: The Priority of the Whole” paper assumes that priority relations are well-founded. The standard definition of well-foundedness in this context would say that every non-empty set has an element that has nothing prior to it in that set.

Imagine a world w with a continuously subdivided entity E made of pointlike simples (like a real line is made of points in standard mathematical constructions) that lies between the 0 and 1 coordinates on the x-axis, and suppose that for any real number a strictly between 0 and 1 there is the part E_a of E that is composed of all the simples with x-coordinate less than a. Assume further that either proper parts are always prior to wholes or wholes are always prior to proper parts.

In either case, we don’t have well-foundedness. For let C be the chain consisting of all the objects E_a for 0 < a < 1. Since E_a is a proper part of E_b if and only if a < b, C does not have a minimal element on either of the two priority relations (the part-before-whole and the whole-before-part one).

Schaffer’s justification for assuming well-foundedness is that without it, we could have a world with no basic entities. But notice that although w violates well-foundedness, it could still have basic entities. For it could be an atomic world—E itself is made of pointlike simples—in the case of the part-to-whole priority relation and it could be a priority monist world.

Perhaps Schaffer is misusing the term “well-founded”. He glosses it as “all priority chains terminate”. This is ambiguous between two readings. On a stronger reading, any priority chain terminates inside itself: there is an item in the chain that is prior to all the other items in the chain. Assuming the Axiom of Choice, Zorn’s Lemma shows that this stronger reading is equivalent to the standard definition of well-foundedness. But on the weaker reading, the idea would be that for any priority chain C, there is an entity that is prior to all the entities in C other than perhaps itself, but without the entity being required to be itself in the chain. This is equivalent to the priority ordering being the reverse of an inductive order.

On the weaker reading, assuming the Axiom of Choice, each non-basic item has something basic prior to it. This seems to me to be what Schaffer needs for his arguments.

That said, I think there is something to be said for the standard sense of “well-founded”, even if it is incompatible with the above world with the continuously subdivided entity E and whole-to-part or part-to-whole priority. Indeed, I am now thinking that well-foundedness is a really nice condition, but assuming there are continuously subdivided entities it does rule out both kinds of priority relations. But that should be fine. And in fact Schaffer could embrace the denial of whole-to-part and part-to-whole priority. In that paper, he only commits himself to integrated wholes being prior to their parts.

Still, here's one reason this matters. Plausibly, you could have infinite upward nesting: one integrated whole as part of another as part of another ad infinitum. Schaffer thinks that wholes are prior to parts, such such infinite upward nesting would violate would-foundedness in the standard mathematical sense. But it wouldn't violate the weaker condition, as long as the infinite cosmos as a whole was prior to all of the parts.

Ontology matters

Among things that metaphysicians wonder about is the question of what things referred to in ordinary language exist: Are there tables, chairs, people, shadows, holes, rocks, particles, etc.?

When metaphysicians discuss this question, others are apt to wonder about a different question: Why does anyone care? After all, the metaphysics will admit that whether there are chairs or not, there are particles (or there is a wavefunction) that’s chairwise arranged, and that’s what we really care about, no?

Here are two reasons to care, assuming theism. All the things that exist are either God or lovingly created by God. Thus, in finding out that a certain kind of non-divine thing exists, we have found out that God has lovingly created the thing. And to find out that God has lovingly created a thing surely matters. Furthermore, anything that exists is either God or its being is a participation in God. And to find out that there is a case of participation in God surely matters.

If time is necessary, it's discrete

Say that a total order is locally finite provided that between any two elements there are at most finitely many elements. A locally finite total order is discrete: each non-extreme element has an immediate predecessor and successor.

Here’s a valid argument:

1. If time is necessary, the order structure of time cannot be problematically arbitrary.

2. The only possible order structures for time that are not problematically arbitrary are locally finite.

3. Thus, if time is necessary, it has to be locally finite, and in particular discrete.

Premise (1) is motivated by my and Josh Rasmussen’s research project on which fundamental and necessary things cannot be problematically arbitrary. But if time is necessary, it is very likely to be fundamental.

Why accept (2)? I am thinking like this. Suppose there are two times between which there are infinitely many times. The size of that infinity of times is arbitrary—is it countable, is it the continuum, is it something in between (if there is anything in between), is it something even bigger?

So, if time is necessary, the order of time is locally finite.

Up to isomorphism, the following are the only possible locally finite total orders:

1. ...,  − 3,  − 2,  − 1, 0, 1, 2, 3, ...: no beginning or end

2. ...,  − 3,  − 2,  − 1, 0: end but no beginning

3. 0, 1, 2, 3...: beginning but no end

4. 0, 1, 2, 3, ..., n (for some finite n): beginning and end.

Now a complex thesis:

4. If time is necessary, then either (i) necessarily time has structure A or B, or (ii) necessarily time has structure C or D.

Here’s why. If there were possible worlds where time has structure A or B and other possible worlds where time has structure C or D, it would be problematically arbitrary whether time starts off with an infinite past or a finite past.

Can we go further? Maybe, but I get less confident. Still, it seems like it would be weird that time could end at some point, but had to have started. Thus:

5. If time does not have to go on endlessly, there need not have been time at all.

It follows that:

6. If time is necessary, then it necessarily has structure A or it necessarily has structure C.

In other words, if time is necessary, it must be like the integers (option A) or like the natural numbers (option C).

Can we narrow it down further? Well, causal finitism suggests but does not prove that options with no beginning are problematic. That would get one down to option C. But this is a weak argument. Option A also has the disadvantage that it leaves unexplained why events in time didn’t all happen a day earlier than they did.

In any case, there is another move we can make at this point. It follows from 6 that:

7. If time is necessary, all the specifics of the order structure of time are necessary.

I am personally inclined to add:

8. The specifics of the order structure of time are not necessary.

9. So, time is not necessary.

But my intuitions for 8 aren’t that strong, so I don’t think this is a very strong argument for the contingency of time.

Evanescence

Compare two worlds:

• Evanescent World (EW): There is a rich three-dimensional reality that exists for only one moment of time.

• Timeless World (TW): There is a rich timeless three-dimensional reality.

Intuitively, EW is, well, evanescent, while TW is “permanent”.

On a B-theory of time, it is difficult to make sense of any such difference in evanescence between EW and TW. But a staunch B-theorist will say that this is a feature, not a bug.

However, an A-theorist will, I think, want to distinguish EW from TW. But it is difficult to do so.

Start with a moving spotlight theory. The difference between TW and EW seems to be that in EW we have time’s spotlight, and in Timeless we don’t. But time’s spotlight in EW is always (i.e., at all times, of which there is only one) lighting all of the three-dimensional reality. The spotlight is no more evanescent than the rest of the reality, and so adding the spotlight does not seem to make the Evanescent world be really evanescent.

Now, consider any of the three major A-theories: moving spotlight, presentism and growing block. At the one and only moment of time in EW, one could say (if one could speak in one moment):

1. It is not the case that there will be anything

2. It is not the case that there was anything.

But one could say the very same thing in TW (if one could speak timelessly, which is no harder than speaking in one moment). And in neither EW nor in TW can one say things like:

3. Reality will vanish.

For “will” cannot reach beyond time.

What can the A-theorist do? I think they can do only thing: They can say that EW is evanescent precisely because:

4. In EW there is exactly one moment of time.

But this is something that the B-theorist can say as well. In other words, the alleged dynamism of time on the A-theory does not seem to do anything to help explain why EW is evanescent.

So what? Well, if the A-theory explains anything better than the B-theory does, it better explains more ordinary evanescence, such as the evanescence of our lives—things flow out of existence with time, or something like that. But now take the limit case of ordinary evanescence: an entity that exists for only one moment, in a world like ours which begins long before the entity and ends long after it. And notice that the entity that exists for one moment of time in a world like ours is no more evanescent than every entity in EW. Thus there is something wrong with an A-theoretic explanation for evanescence that applies to the entity in a world like ours but not to all the entities of EW—it fails to really get at what evanescence is.

But if the A-theory really doesn’t explain evanescence better than the B-theory does, then I suspect it fails to be the better alternative.

Consensus gentium and double counting

Here’s a way that an atheist could undercut the consensus gentium argument (the argument for theism based on how much belief in God or gods there is in the world), building on my previous post.

Suppose that views about God or “big gods” came into the world as follows: Brilliant very early thinkers came up with plausible arguments for the existence of God. These arguments may have, for instance, included some selection taken from among cosmological, teleological, moral and religious experience arguments. These arguments were rationally taken up by their followers, but eventually supernaturalistic and maybe even theistic belief was simply passed on by testimony, with the selective advantages of supernaturalism (say, social cohesion effects) helping to keep communities where these beliefs were widespread going.

If this is right, then treating the consensus gentium argument as evidence for theism involves double counting. For the theist presumably also counts the evidential force of arguments like cosmological, teleological, moral and religious experience ones, and since on the above story theism (a) started with one or more of these, and (b) its further spread and persistence can be explained naturalistically quite well by selection effects.

Now, the above argument-focused story may not be plausible to all. But the atheist can make a further move. Dilemma. Either the above story is true or not. If it’s true, then the consensus gentium argument involves double counting. If it’s not true, then likely theism started in some way that is not rational, and then spread and persisted by naturalistic selection effects, and that’s not evidence for theism, either. So, either way, we can dismiss consensus gentium?

What do I say to this? As a theist who is convinced that the other arguments for theism do provide significant evidence, I don’t find it particularly hard to just concede the point.

But there is another move: a merely partial concession. The story about how belief in God is helpful to communities is a plausible story. But it is even more plausible on theism! For on theism, there is an additional probability that God would “go out of his way” and have rational animals exist in conditions where belief in God is helpful, precisely as a means to making belief in God persist and spread naturally. Thus, widespread of theistic belief may be probable on naturalism, but on theism is even more so. This may not be strong evidence for theism (the Bayes ratio can’t exceed 2, which is “substantial” but not “strong” on Jeffreys’ scale), but is still some evidence.

Debunking and testimony

An evolutionary debunking argument against theism can be employed defensively or offensively by an atheist. Applied defensively, it is a response to the theist’s offering an argument from the prevalence of belief in God. Applied offensively, it is suppose to show that whether or not God exists, because theistic beliefs come from a suspect source, they are not knowledge.

The focus of debunking argument tends to be on mimetic selection. The idea is that theistic (or maybe more generally supernaturalistic) beliefs confer some kind of a selective advantage on the communities or individuals exhibiting them, and hence we can explain naturalistically the prevalence of these beliefs. This explanation works whether or not God exists, and hence whether or not God exists, typical theists’ beliefs are not knowledge.

But there is a serious gap in this argument. Mimetic selection only operates on a belief once the belief is in place. But we still have to ask: Where did the belief come from in the first place? And I think that if we are to be honest, we have to say that not only is this something we don’t empirically know, but given how it concerns fine-grained details of events before written history, we have no empirical access to the answer. For any particular lineage of theistic beliefs, there was a first believer in the lineage. How did they come to believe? Well, we can make up a bunch of ideas:

1. They were philosophically inclined and came up with a good argument for theism (say, a good design argument).

2. They were philosophically inclined and came up with a bad argument for theism (say, a bad ontological argument).

3. They got an apparent perception of God from eating bad mushrooms.

4. They got an apparent perception of God from God.

5. They were bullied into believing in God by a tribal leader who claimed divine right of ruling.

6. They heard a fairy tale told by their parents and misunderstand it as history rather than fiction.

And a lot more. The point is that empirically we have no idea. This was very long ago, and we have no records of how it went. And it may be that for different mimetic lineages of theism the initial explanation is different.

Now notice that the options include ones that are friendly to theistic knowledge (1 and 4) as well as ones that are unfriendly (the others). Furthermore, if the lineage begins with one of the options friendly to theistic knowledge, then we might say that this knowledge was then testimonially transmitted. Of course, the selective facts helped with the transmission. But as long as the chain of testimony goes back to a case of genuine knowledge, the fact that the transmission was made possible by selective effects that are not as such truth conducive may not undercut the possibility that the chain actually does transmit knowledge.

Thus, once we think of the variety of ways that the lineage of theistic beliefs could begun, we see that an offensive debunking argument fails, as the offensive debunker would need to offer evidence that our lineage of theistic belief began in one of the knowledge-unfriendly ways. On the other hand, the same line of thought leaves unaffected the defensive debunker, who only needs a serious possibility that the lineage of theistic belief began in a way that gives no special credence to theism.

I think this line of thought is most plausible if you have an irreducible view of testimonial evidence.

Abstract objects and the Nicene Creed

There are Christians who believe in the existence of abstract objects, such as properties, that are neither grounded in God’s mind (as on Augustine’s view) nor created by God. One challenge on such a view is to make sense of the doctrine of creation which says that God creates everything other than himself.

A natural response is to restrict the quantifiers further. God is not the only exception to being created by God. Abstract objects are also an exception. When our Christian and Jewish forebears said that God created everything, they were only thinking of more ordinary objects than the abstract ones.

I doubt this. Take the beginning of the Creed of Nicaea:

I believe in one God, the Father almighty, maker of all things visible and invisible [poiêtên oratôn te pantôn kai aoratôn].

Now, the Fathers at Nicaea were more than aware of Platonic philosophy and of a broad variety of neo-Platonic views on which there were all sorts of uncreated entities, perhaps emanating from the One. Against that background, it seems very plausible that their talk of creation of the invisible is not only meant to tell us about angels, but is also meant to rule out such views. What invisible things reality might contain was mysterious and contentious at the time, and remains mysterious and contentious to our day, and the explicit inclusion of the invisible makes it quite implausible to think that the Creed is meant to apply to a restricted class of beings (apart from the obvious exclusion of God himself).

Furthermore, I think the use of the concrete word poiêtês (maker), as opposed to some more general philosophical term like aitia (cause) or archê (origin, principle) carries the message that God the Father almighty is engaging in intentional agency in producing the visible and the invisible. The agentiality and intentionality implied by the word seems to me to rule out—and quite possibly with the specific intention of doing so—emanationist views.

We are used to reciting the creed in the later version from the Council of Constantinople, where “of heaven and of earth” is added between “maker” and “of all things”. It may be tempting to see “of heaven and of earth” as restricting the visible and the invisible to the concrete occupiers of heaven and of earth. I think that would be a mistake. The Council of Nicaea was an ecumenical council in its own right, and its creed is still normative. If I am right in thinking that the Fathers really wanted to rule all the exotic uncreated entities of neo-Platonism, that remains binding. I would instead say that the Fathers at Constantinople added a clarification that it is not only the mundane things that God created, but also the heavenly. They weren’t narrowing the scope of creation.

Theoretical parsimony

As is usual, distinguish ontological parsimony, namely positing fewer beings, from ideological parsimony, namely positing fewer fundamental undefined concepts.

The principle that we should assign higher probabilities to more ontologically parsimonious theories is wacky. It violates the Principal Principle. If you are flipping a coin and planning to have children if and only if you get heads, then you should assign a slightly higher probability to tails. (Granted, this argument fails if eternalism is false. But you can tweak it by supposing that a hundred years ago Alice flipped a fair coin with that intention, and now you should again assign a slightly higher probability to tails.)

What about ideological parsimony? It initially sounds a lot better to assign higher probabilities to more ideologically parsimonious theories. Indeed, I think there has to be something right about such a principle of simplicity. But I don’t at present fully know how to formulate it in a way that escapes objection.

For suppose that we are non-reductionists about biological species, so we think that species are fundamental undefined concepts. You are working with a bacterium in the lab, and on a whim plan to flip a coin. On heads, you will irradiate the bacterium, and on tails you will do no such thing. Irradiated, the bacterium is more likely to produce a new species when it reproduces. So on ideological parsimony it seems we should assign a slightly higher probability to tails, as then it is more likely that the true theory of the world posits fewer species, and hence fewer fundamental undefined concepts.

Objection 1: Reductionism is the right theory about biological species.

Response: Maybe it is. But it’s not the case that it certainly is. And as long as there is a non-zero probability that non-reductionism about species is right, we should assign a slightly higher probability to tails—for conditionally on reductionism, the probabilities are equal, while conditionally on non-reductionism, we should assign a higher probability on tails.

Objection 2: There are so many species that the difference from positing one more is negligible.

Response: Maybe it is. But now parsimony cannot do the work it’s designed to do, and hence it is largely unmotivated. Here’s an example of the kind of work it’s designed for. You observe the world’s koalas and see no significant differences in behavior or appearance. You could suppose there are two species of koalas and you just haven’t been able to tell them apart. But that’s not parsimonious. So you suppose one species. But given how large the number of species on earth is, positing one more makes little difference—assuming the objection is correct.

Objection 3: A full story of the world will include the causal powers in the world. If the radiation has the causal power C_S to produce a new species S of bacteria, then a full description of the world will contain a description of C_S, and hence of S, even if S has no members. Thus it makes no difference to the ideological complexity of the world whether the radiation is applied or not.

Response: This seems the most powerful objection. But it might undercut the applications of parsimony. Plausibly, the world has a first cause behind everything else. Now either the first cause’s causal powers are such that their complete description includes all possible kinds or not (this may depend on questions involving the first cause’s simplicity). If it has such causal powers, then ideological parsimony does rather less work than we thought, since the total description of reality already includes the concepts of the two species of koalas as per my previous response. Suppose now the first cause’s causal powers are not such that their complete description includes all possible kinds. Imagine that you make the following plan. You will flip a fair coin. On heads you will pray that the first cause produce a new kind of thing. Now, the first cause might not fulfill your prayer—indeed, perhaps you are not even confident the first cause is a person. But it is at least slightly more likely that the first cause will make a new kind of thing if you pray than if you don’t. And that’s enough to change the epistemic probabilities for your coin flip, in an implausible way.

Six-dimensional universalism

Four-dimensional mereological universalism has been proposed as a way of letting ordinary objects into our ontology. If all pluralities have a fusion, one should expect a fusion of simples (or maybe time-slices of simples or something like that) that exactly correspond to the four-dimensional career of a chair, a horse, and an oak tree. But then some philosophers started taking seriously the observation that it’s not enough to have a fusion of the simples in an oak to have an oak. For the fusion of simples may not have the same modal properties as the oak. This led to what I call five-dimensional mereological univeralism. Say that a modal profile is a function that assigns to each world an empty or non-empty collections of simples (or time-slices of simples, etc.)

The five-dimensionalist mereologist then holds that for any modal profile that has at least one non-empty assignment there exists an object that matches that profile—an object that exists in all and only the worlds that the assignment assigns a non-empty set to, and in these worlds is a fusion of the simples in the assigned set.

I just realized another thing. The ordinary objects that the universalist wants to have in their ontology include artifacts like tables and ships. The vagueness of artifacts is deeply embedded into our thinking about them. While we could become convinced of the idea (indeed, I am convinced of it) that living things have souls, and the metaphysics of the relationship of these souls to bodies ensures that living things have non-vague spatial, temporal and modal boundaries, the analogous thesis for tables and ships seems much harder to swallow.

But now modal profiles are sharp. Thus, to model the vagueness of artifacts, we not only need every modal profile to be be filled, but we need every non-trivial vagueness profile to be filled. What’s a vagueness profile filled by a possible object x? To a first approximation, it’s a set of modal profiles, so that an object x has vagueness profile V if and only if it is definite that x fits some profile in V, and definite that x does not fit any profile outside V, and for any profile in V it’s vague or definite that x fits that profile. In other words, for mereological universalism to save all of our common sense about ordinary objects, it needs to be a six-dimensional universalism.

But six-dimensional universalism is crazy. Consider the vagueness profile R corresponding to Rover the dog in England and the vagueness profile F corresponding to Felix the cat in Canada. Then take their union: R ∪ F. If this vagueness profile is filled, it’s filled by an entity such that it is vague that it barks and vague that it meows, but definite that it clearly barks or clearly meows. En entity such that it is vague that it is in England and vague that it is wholly in Canada, but definite that it is in exactly one of England and Canada. And so on.

(Things are even worse if theism is true. Take God’s vagueness profile and mine. The union of these two profiles would be filled by an entity that is vaguely divine and vaguely a sinner.)

So, the argument goes like this. Mereological universalism only fully saves common sense if it is extended to six-dimensional universalism. The latter is absurd. So we’re not going to fully save common sense by going universalist.

I suppose one might be satisfied with stopping at five dimensions, at modal profiles, and ignoring our judgments of vagueness about artifacts. Maybe.