From chickens and eggs to a cosmological argument

Suppose we have an infinite regress of chickens and eggs, with no first item, and suppose that if there is any last item, it’s not a chicken.

Plausibly, then:

1. The plurality of the chickens explains the eggs.

But also plausibly:

2. If x has an explanation, then x has a fundamental explanation.

However:

3. No plurality of chickens and eggs fundamentally explains the eggs.

4. So, something that is other than a plurality of chickens and eggs fundamentally explains the eggs.

Why is (3) true? Well, there are two kinds of chicken and egg pluralities.

1. Pluralities with an earliest item.
2. Pluralities with no earliest item.

A Type I plurality does not explain the chickens and eggs, because it does not explain any chickens and eggs earlier than the earliest item in the plurality.

A Type II plurality at best non-fundamentally explains the eggs. For given a Type II plurality, choose any item x in the plurality. Item x is a chicken or egg, and there is an earlier chicken or egg y in the plurality. Since y explains x, by a plausible case of transitivity, the subplurality where we drop x also explains the eggs. So the initial Type II plurality did not fundamentally explain the eggs.

Since every plurality of chickens and eggs is of Type I or Type II, we have (3).

The argument above applies beyond chickens and eggs. Suppose:

5. Every physical item in the world is caused.

Then:

6. Either there is a physical item with a non-physical cause or every physical item has a physical cause.

Add:

7. There are no loops of physical causes.

8. Physical causation is transitive.

As I show in my 1999 paper using Zorn’s Lemma, if every physical item has a physical cause, it is then possible to partition the physical items into an “even” and an “odd” subset, where every item in the even subset causes an item in the odd subset, and every item in the odd subset causes an item in the even subset. Call the odd items “eggs”. Call the non-final even items “chickens” (a non-final item is one that causes a further physical item). Then, plausibly, the chickens explain the eggs. By the argument above, something non-physical thus explains the eggs. Anything non-physical that explains the eggs explains all of physical reality (because for any physical item, it is either an egg or there is an egg prior to it). So:

9. There is a non-physical item that explains all of physical reality.

I think the thing that needs the most defense is premise (2). It’s somewhat close to causal finitism.

Motivating panpsychism

There is something attractive about an ontology where all the properties are powers, but it seems objectionable.

First, a power is partly defined by the properties it can produce. But if these in turn are powers, then we have a vicious regress or circularity.

At the same time, mental properties do not seem to be purely powers: they seem to have a categorical qualitative character that is not captured by the power to produce something else.

What is attractive about a pure powers ontology is the conceptual simplicity, and the fact that categorical properties seem really mysterious.

There is, however, a modification we can make to a pure powers ontology that gets us out of the problem. There are two kinds of properties: powers and qualia. The mysteriousness objection does not apply to qualia, because we experience them. On this ontology, powers bottom out in the ability to produce qualia.

For this to avoid implausible anthropocentrism, we need panpsychism—only then will there be enough qualia outside of living things for the powers of fundamental physics to bottom out in. So we have an interesting motivation for panpsychism: it yields an attractive ontology for reasons that have nothing to do with the usual concerns in the philosophy of mind.

It’s worth noting that this ontology is similar to Leibniz’s. Leibniz had two kinds of properties: appetitions and perceptions. The appetitions are (deterministic) powers. Perceptions are similar to qualia, but not quite the same, because (a) perceptions need not be conscious, and (b) perceptions are always representational. Unfortunately, the representational aspect leads to a regress or circularity problem, much as the power powers ontology did, since representationality will define a perception in terms of other appetitions and perceptions.

Existence

In his famous critique of the ontological argument, Kant said that existence is not a property. Frege and Russell gave a very influential response to Kant (though not framed as such): the existence of an object is not a property of the existent object, but it is a second-order property of an abstract object. Thus, the existence of Biden is the second-order property of being instantiated possessed not by Biden himself but by the abstract object Bidenness.

But now consider this very plausible principle:

1. The existence of an object is explanatorily prior to all the (other) properties of that object.

The parenthetical “other” is included to make (1) acceptable both to Frege-Russell and to “pre-Kantians” who think existence is a property of the existent object.

But combining (1) with the Frege-Russell account leads to an explanatory priority regress:

• Biden’s maleness is posterior to Biden’s existence.

• Biden’s existence is Bidenness’s being instantiated.

• Bidenness’s being instantiated is posterior to Bidenness’s existence.

• Bidenness’s existence is Bidennessness’s being instantiated.

• Bidennessness’s being instantiated is posterior to Bidennessness’s existence.

• Bidennessness’s existence is Bidennessnessness’s being instantiated.

• …

How can we arrest this regress? A natural move is to restrict the Frege-Russell view of existence to contingent entities. Thus, Biden’s existence is the instantiation of Bidenness, but Bidenness is a necessary entity, and its existence is not the instantiation of some further entity. Indeed, perhaps, the pre-Kantian view holds of Bidenness: Bidenness’s existence could just be a property of Bidenness.

Note that if the pre-Kantian view holds of necessary beings, then Kant’s critique of the ontological argument falls apart, since God is a necessary being.

But let’s think through the pre-Kantian view a little bit. Suppose that x is an object and e is its existence, and suppose e is a property of x. But how can x possess e without already existing prior to having e? (I.e., surely, (1) is true with the parenthetical “other” removed.) There seems to be one possible move here: perhaps x = e. That would be a view on which some objects are identical with their own existence—a view very much like St. Thomas’s, who held that God, and God alone, was identical with his own existence.

So, interestingly, thinking the Frege-Russell view through leads fairly naturally to a view like Thomas’s.

I am attracted to this variant of the Thomistic view:

2. Uncaused objects are identical with their existence.

3. The existence of a caused object is its being caused.

The worry that an object cannot possess a property without “already” existing does not appear pressing when the property in question is being caused.

Moreover, we might even more speculatively add:

4. An object’s being caused is its cause’s causing of it.

On this view, a contingent thing’s existence, like on the Frege-Russell view, is a property of something other than the thing: it is a property of the cause (perhaps an extrinsic property of the cause, when the cause is God, so as not to violate divine simplicity).

Two kinds of Platonism

There are two kinds of Platonism. Both hold that there are properties. But they differ as to the grounding relation that holds between predication and property possession (I will also assume that what goes for properties goes for relations, but sometimes formulate things just in terms of properties for simplicity). Both agree that if there is a property of Fness (there might not be if F is gerrymandered or negative, on sparse Platonisms), then x is F if and only if x instantiates Fness. Deep Platonism further affirms:

1. If there is a property of Fness, then the fact that x is F is grounded in the fact that x instantiates Fness.

Shallow Platonism denies (1). It is likely to instead affirm:

2. If there is a property of Fness, then the fact that x is F partly grounds or explains the fact that x instantiates Fness.

Deep Platonism faces two problems. The first is the Regress Problem. For if Deep Platonism is true, then "instantiates" seems non-gerrymandered and positive, and so it should correspond to a Platonic entity, the relation of instantiation. Then, the fact that x instantiates Fness will be grounded in the fact that x and Fness instantiate instantiation. But this leads to a vicious regress where each instantiation relation is grounded in the next.

The second is the Creation Problem. Everything that exists and is distinct from God is created by God. If the properties are all distinct from each other, then at most one is identical with God, and hence all but at most one property are created by God. But explanatorily prior to creating anything, will have multiple properties such as that he is able to do something and that he knows something. But how can he have those properties when there is at most one property at this point in the explanatory story?

Both problems have Deep Platonist solutions. For instance, one might say that "instantiates" is the unique non-gerrymandered and positive predicate that has no Platonic correspondent, or one might say that (1) has an exception in the case of instantiation. And one might say that God has at most one property, say divinity, and he is identical to that property. (But this, too, seems to lead to exceptions for (1), or perhaps an implausible view of what predicates correspond to properties. For there sure seem to be many other non-gerrymandered and positive predicates, like "is wise" and "is powerful", that apply to God.)

But Shallow Platonism has a particularly neat solution to both problems. There either is no regress, or if there is a regress, it is an unproblematic forward regress: because x is F, x and Fness instantiate instantiation, and because of that x, Fness and instantiation instantiate instantiation, and so on. Forward regresses are not at all problematic. And while it may be explanatorily prior to the creation of properties (or of all but one property) that God is wise, it is not explanatorily prior to the creation of properties that God instantiates wisdom.

Cannonball and regress

From my first year of graduate school, I've been pushing a cannonball argument against Hume's idea that a regress of causes provides a complete explanation. The argument isn't very complex, but it has some complexity (it talks of complete states and all that), and it has occurred to me that it can be simplified.

At noon the cannonball is at rest and precisely then a cannon is fired. At every time after noon, the cannonball is moving. (Maybe the whole thing takes place in space.) We now have this dialogue:

• You: Why is the cannonball ball moving at one minute after noon?
• Me: Because it's moving at half a minute after noon and there is inertia.
• You: But why is the cannonball ball moving at half a minute after noon?
• Me: Because it's moving at a quarter of a minute after noon and there is inertia.
• You: But why is the cannonball ball moving at a quarter of a minute after noon?
• Me: Because it's moving at an eighth of a minute after noon and there is inertia. Don't you see the pattern?
• You: I do see the pattern, but why is it moving at any of these times: a minute after noon, half a minute after noon, a quarter of a minute after noon, an eighth of a minute after noon and so on? Why is the cannonball moving at all at any time after noon?
• Me: Don't you see, I've explained each item in the chain, and so I've explained the chain!

You should object that as long as I haven't mentioned the cannon being fired, I haven't explained why it is that the cannonball is moving at all. If my chainwise explanation was a good explanation, then a complete explanation of all the motion of the of the cannonball could be given without mentioning the cannon. And that's absurd. So an infinite chain does not give an explanation of itself.

Now suppose that there was no such time as noon and no cannon. Would the infinite chain then explain itself? No! For the chain is no more explanatory if there is
no such time as noon and no cannon. Taking away the real explanation does not turn the chain into an explanation.

A recipe for counterexamples to the Hume-Edwards-Campbell Principle

The Hume-Edwards-Campbell (HEC) principle says that if you have a bunch of items, and each one is explained, then the whole bunch might be explained. In particular, any infinite regress might be a complete explanation. The Hume-Edwards principle replaces the "might" with "is". I've published counterexamples to the HEC before, but here is a cool recipe for generating counterexamples.

Let p₁,p₂,... be an explanatory regress of propositions, so p₂ explains p₁, p₃ explains p₂, and so on. Suppose (as might easily be the case) that there is some proposition q such that (a) q couldn't be self-explanatory, and (b) the p_i are all clearly completely explanatorily irrelevant to q. Now, let q_i=p_i&q. Then q₁,q₂,... are an infinite explanatory regress. But if q couldn't be self-explanatory, this regress can't be completely explanatory as it does nothing to advance the explanation of q.

I might have got the basic idea here from Dan Johnson. I can't remember. The counterexamples depend on the idea that if A explains B and Q is irrelevant, then A&Q explains B&Q. I am a bit less sure of that than when I started writing this post (which was quite a while ago).

Collimating a collimator

Collimating a Newtonian telescope basically means aligning the optical axis of the primary mirror with the optical axis of the eyepiece.  An easy way to do this is to use a collimator, e.g., a laser collimator.  The collimator is basically a tube that contains a laser that you put in place of the eyepiece.  You adjust the angle of the secondary mirror in the telescope so the beam hits the center of the primary mirror, and then you adjust the angle of the primary mirror so that the beam comes back on itself.  But it is crucial for this procedure with a laser collimator that the collimator be itself collimated, i.e., that the laser's axis be aligned with the tubing that the laser is in.

Now, if we were writing a philosophy paper, at this point it would be very tempting to say: "And a vicious infinite regress ensues."  But that would too quick.  For a laser-collimator collimator is very simple: a block of wood with two pairs of nails, where each pair makes an approximate vee shape.  You then lay the laser collimator on the two vees, aim it at a fairly distant wall, and spin it.  Then you adjust the adjustments screws on the laser collimator until the beam doesn't move as you spin the collimator on its axis, at which point the laser is collimated to its housing.  Moreover, because of how the geometry works, the vees don't need to be very exactly parallel--all the work is done by spinning.  So, it seems, the regress is arrested: the laser-collimator collimator does not itself need collimation.

Potential lesson: Perhaps sometimes we philosophers are too quick after one or two steps in a regress to say that the regress is vicious and infinite.  For sometimes after two steps, the regress may be stopped with a bit of cleverness.

Well, actually, that's not quite right.  For the double-vee collimator depends on the laser collimator's housing being a cylinder.  And one might argue that manufacturing an exact cylinder requires a procedure like collimation.  For suppose that we manufacture the cylinder by taking a block of aluminum, spinning it in a lathe and applying a lathe tool.  But to get an exact cylinder, the lathe tool needs to remain, at the end, at an equal distance to the lathe's rotational axis.  So that's another alignment procedure that's needed.  I don't know how that's done, being foggy on the subject of lathes, but I bet it involves aligning some sort of a guide parallel to the lathe's rotational axis or by moving the workpiece parallel to the rotational axis.  So another collimation step will then be needed when manufacturing the lathe.

And so the regress does continue.  But still only finitely.  At some point, parallelism can be achieved, within desired tolerance, by comparing distances, e.g., with calipers.  There is still a collimation issue for the calipers, but while previous collimations involved the spatial dimensions, the collimation of calipers uses spatial and temporal dimensions: in other words, the calipers must keep their geometrical properties over time.  For instance, if one sets the calipers to one distance, and then compares another, the caliper spacing had better not change over the amount of time it takes the calipers to move from one place to another.  So calipers allow one to transfer uniformity over time into uniformity over space.

But how do we ensure uniformity over time?  By using a rigid material, like hardened steel.  And how do we ensure the rigidity of a material?  This line of questioning pretty quickly leads to something that we don't ensure: laws of nature, uniform over space and time, that make the existence of fairly rigid materials possible.  And if we then ask about the source of these laws and their uniformity, the only plausible answer is God.  So, we may add to God's list of attributes: ultimate collimator.

There are, of course, other ways of manufacturing cylinders than by using a lathe.  One might cast a cylinder in a cylindrical mould--but that just adds an extra step in the regress, since the mould has to be manufactured.  Or one might extrude a cylinder by pushing or pulling the material for it through a circular die.  In the latter case, one still has to make a circular die, perhaps with a spinning cutter at right angles to a flat piece, and one has to ensure that the material is moved at right angles to the die.  So one has changed the problem of parallelism into the very similar problem of aligning at right angles.  And I suspect we eventually get back to something like rigid materials anyway.

So the lesson that sometimes regresses stop after one or two steps is not aptly illustrated with the case of the collimator.  That regress is still, perhaps, finite--but it goes further back, and eventually to God.

A regress for bundle theory

According to bundle theory, each individual is a bundle of properties. But what is an individual? Presumably, individuals are existing entities that we can individuate, quantify over and predicate things of. Take that as a sufficient condition for being an individual. But then a property is also an individual. (If one balks at this, I expect that it is simply because one has stipulated this fact away, say by defining individuals as existing entities that we can individuate, quantify over and predicate things of which are not properties. If so, then the class of "individuals" is gerrymandered. But we needn't worry about words. Call something that we can individuate, quantify over and predicate things of an "individual*", and construe what I say below as about individuals*.)

But now the regress is obvious. Socrates, let us say, is a bundle of humanity, maleness, snubnosedness, smartness, hellenicity, etc. Fine. But humanity is also an individual. So, humanity is itself a bundle of properties. What properties? I don't know. Maybe properties like propertyhood, unchangingness, animal-kind-hood, rational-being-kind-hood, etc. Already it gets weird—we have no idea what to say. And then the problem returns for the properties that humanity is a bundle of. What, say, is propertyhood a bundle of? What is animal-kind-hood a bundle of? Obviously, a regress ensues. Is it vicious? I suspect so. We have bundles of bundles of bundles of .... If the bundling is done set-wise, then the sets will violate regularity.

And in any case if the individuation of bundles is by their members, that never bottoms out. On an abundant theory of properties, our non-property individuals all look like {{{...},{...},{...},...},{...},{...}},{...},...}, with exactly the same structure of braces. (That's for the set-theoretic construction. Otherwise, replace the braces by whatever bundling method we have.) On a sparse theory of properties, if it turns out that non-property individuals have finitely many properties, and that properties all have finitely many properties, maybe then we can differentiate these things by the structure of the rooted property-tree (individual x has 7 properties at the first level, the first of which branches has 19 properties, etc.) But that's as crazy as Pythagoreanism.

So maybe the bundle theorist will limit her theory of predication to individuals that are not themselves properties. But if she does that, she still needs a story about how we manage to predicate things of properties. For we do. Humanity is a universal. It is unchanging. It is non-spatio-temporal. It is different from hellenicity. And so on. And whatever non-bundle theory of predication that we give for the properties of properties, the opponent of bundle theory will say: Why not just simplify and give that for the individuals that are not properties?

Or one might take first-order properties to be bundles of individuals. But that's terrible. First, they'd have to be bundles of possible individuals. Second, we now have circularity in place of regress, which is worse.

This arguments seems to force the bundle theorist to say that eventually we get to properties that have no properties (what about their abstractness? their propertyhood? maybe we say that these are not genuine properties--maybe abstractness is just the denial of concreteness). Todd Buras then points out to me that these properties with no properties are just like the bare particulars avoiding which was one of the main motives for bundle theory!

Note: The argument works equally well if we have bundles of tropes instead of bundles of universals.

I know that these issues have been worked over, and regress-finding is a fun game for the philosophical family, so this regress is quite likely known. (If you have a reference, please let me know.)

Infinite causal regress

Could everything in existence be explained by an infinite causal regress? I've argued in print that the answer is negative. Here is another thought in favor of the negative answer.

Suppose we have a world where there is an infinite regress of past states and that there is some numerical time-varying property Q(t) in the universe (say, entropy or temperature or charge or volume) that keeps on changing in such a way that the property's having one the value it does in one year determines the value it has in another. Now, consider the claim that the limit of Q(t) as t goes to minus infinity is, say, q₀. (Of course, Q(t) might not in fact converge to anything, but since we're stipulating, we can stipulate that it does.) If the regress explains everything, it explains why it was that the limit is q₀. But even if a regress explains something, it surely doesn't explain the boundary values at the beginning of the regress, and q₀ is precisely such a boundary value. It would be almost as absurd to say that the limit of the temperature in a room tended to 11.0 degrees as t approached noon from above because it was 11.1 at 12:10, and 11.06 at 12:05, and 11.05 at 12:05, and 11.01 at 12:01, and so on, as it would be to say that the temperature of the room was 11.0 degrees at noon because it had such-and-such values after noon.

Suppose that we still insist that the boundary value q₀ is explained by the regress. Now suppose that we find another explanation, say in terms of an atemporal being creating the universe. What should we say? That we have two explanations of the same phenomenon, each on its own sufficient? That can happen, but surely that's not what is happening here. The right thing to say is that the regressive explanation of the boundary condition is no explanation at all.

Liar regress

This has turned into a week on the liar paradox. Here is an interesting variant on the liar paradox that includes no self-reference, either direct or indirect. There is a possible world which contains infinitely many sentence tokens s₁,s₂,.... (Perhaps they exist simultaneously, or perhaps they exist successively. If successively, they may exist successively in either direction—s₁ before s₂ before s₃ ... or s₁ after s₂ after s₃ ....) Now suppose that s_n says:

s_n+1 is false.

Now, in one sense there is no paradox here. We could just say that s₁,s₃,s₅,... are true and s₂,s₄,s₆,... are false. There is no contradiction. But that is ad hoc. There is no more reason for this truth-value assignment than for the opposite truth-value assignment. Truth is about reality. But the reality of the possible world containing these tokens is equally compatible with one truth-value assignment and with the other.

If I want to make the problem more pressing, I can suppose a doubly infinite sequence of sentence tokens: ...,s₋₃,s₋₂,s₋₁,s₀,s₁,s₂,s₃,.... Suppose that the tokens do not differ in any significant way (if the Principle of the Identity of Indiscernibles holds, they must differ in some way), because each one of them says:

The next token in the sequence is false.

Then there can be no reason for distinguishing, say, the even-numbered ones for being true and the odd-numbered ones for being false, rather than the other way around.

I can also do this as a version of the truth-teller paradox. Just let s_n say:

s_n+1 is true.

Then, if we're going to have a truth-value assignment, the same truth-value will be assigned to each sentence. But there is no more and no less reason to assign true to all of them than to assign false.

So not only must we be careful about self-reference, but also about regresses.

If affirming truth of a sentence is a way of taking up that sentence into one's own speech, as per one version of deflationism, then it is easy to see why we can't have self-reference, circular reference or infinite regress in respect of truth, since these processes fail to produce a finite well-formed sentence—they produce an infinite nonsensical sentence like "It is not the case that it is not the case that it is not the case that....". (Quantification would presumably be done in terms of possibly infinite conjunctions or disjunctions. But unfortunately, deflationism has trouble with quantification and modality. Thus, the claim that possibly George's favorite proposition is false, which claim is surely true, is troubling if we evaluate it by inserting George's favorite proposition in it—for that proposition might, as a matter of fact, be a necessary truth.) This book may be very much relevant, and may in fact already contain a full development of my inchoate ideas, and I've ordered it from interlibrary loan.

It's interesting, by the way, to note that some infinite sentences are nonsense, but others aren't. Thus,

1. 2 is even and 4 is even and 6 is even and ...

makes perfect sense. But

2. it is false that it is false that it is false that ...

is nonsense. It would be nice to have a criterion for when an infinite first-order sentence is nonsense. I think that the answer is that it is nonsense when one gets a vicious regress for explaining what makes it true.

Sorry, I'm rambling. This post is really just a bunch of notes for me to think about later.