Maybe we can create spacetime

Suppose a substantivalist view of spacetime on which points of spacetime really exist.

Suppose I had taken a different path to my office today. Then the curvature of spacetime would have been slightly different according to General Relativity.

Question: Would spacetime have had the same points, but with different metric relations, or would spacetime have had different points with different metric relations?

If we go for the same points option, then we have to say that the distance between two points is not an essential property of the two points. Moreover it then turns out that spacetime has degrees of freedom that are completely unaccounted for in General Relativity, degrees of freedom that specify ``where’’ (with respect to the metric) our world’s points of spacetime would be in counterfactual situations. This makes for a much more complicated theory.

If we go for the different points option, then we have the cool capability of creating points of spacetime by waving our arms. While this is a little counterintuitive, it seems to me to be the best answer. Perhaps the best story here is that points of spacetime are individuated by the limiting metric properties of the patches of spacetime near them and by their causal history.

Classical mereology and causal regresses

Assume classical mereology with arbitrary fusions.

Further assume two plausible theses:

1. If each of the ys is caused by at least one of the xs and there is no overlap between any of the xs and ys, then the fusion of the ys is caused by a part of the fusion of the xs.

2. It is impossible to have non-overlapping objects A and B such that A is caused by a part of B and B is caused by a part of A.

It follows that:

3. It is impossible to have an infinite causal regress of non-overlapping items.

For suppose that A₀ is caused by A₋₁ which is caused by A₋₂ and so on. Let E be a fusion of the even-numbered items and O a fusion of the odd-numbered ones. Then by (1), a part of E causes O and a part of O causes E, contrary to (2).

This is rather like explanatory circularity arguments I have used in the past against regresses, but it uses causation and mereology instead.

Per se and per accidens multiplication of causes

Can there be an infinite sequence of efficient causes? Famously, Aquinas says both “No” and “Yes”, and makes a distinction between a per se ordering (“No”) and an accidental ordering (“Yes”). But it is difficult to reconstruct how the distinction goes, and whether there is good reason to maintain given modern physics.

Here is the central passage from Summa Theologiae I.46.2 reply 7, in Freddoso’s translation:

It is impossible to proceed to infinity per se among efficient causes, i.e., it is impossible for causes that are required per se for a given effect to be multiplied to infinity—as, for instance, if a rock were being moved with a stick, and the stick were being moved by a hand, and so on ad infinitum.

By contrast, it is not impossible to proceed to infinity per accidens among agent causes, i.e., it is not impossible if all the causes that are multiplied to infinity belong to a single order (ordinem) of causes and if their multiplication is incidental (per accidens)—as, for instance, if a craftsman were to use many hammers incidentally, because one after another kept breaking. In such a case, it is incidental to any given hammer that it acts after the action of a given one of the other hammers. In the same way, it is incidental to this man, insofar as he generates, that he himself was generated by another. For he generates insofar as he is a man and not insofar as he is the son of some other man, since all the men who generate belong to the same order (gradum) of efficient causality, viz., the order of a particular generating cause. In this sense, it is not impossible for man to be generated by man ad infinitum.

However, it would indeed be impossible for the generation of this man to depend upon that man, and upon an elemental body [a corpore elementari], and upon the sun, and so on ad infinitum.

What’s going on here? Re-reading the text (and double-checking against the Latin) I notice that per se and per accidens are introduced not as modifying the causal relations, but the infinite multiplication of causes. No indication is given initially that the causation functions differently in the two cases. Further, it is striking that both of the examples of per accidens multiplication of causes involve causes of the same type: hammers and humans (Freddoso’s “man” translates homo throughout the text).

To a first approximation, it seems then that what is forbidden is a regress of infinitely many types of causes, whereas a regress of infinitely many tokens is permitted. But that is too simple. After all, if an infinite causal sequence of humans generating humans were possible, it would surely also be possible for each of these humans to be qualitatively different from the others—say, in exact shade of eye color—and hence for there to be infinitely many types among them. In other words, not just any type will do.

Let’s focus in on two other ingredients in the text, the observation that the humans all “belong to the same order of efficient causality”, and the sun–elementary body–human example. Both of these rang a bell to me, because I had recently been writing on the Principle of Proportionate Causality. At Summa Theologiae I.4.2, St Thomas makes a different distinction that distinguishes between the human–human and the sun–body–human cases:

whatever perfection exists in an effect must be found in the effective cause: either in the same formality, if it is a univocal agent—as when man reproduces man; or in a more eminent degree [eminentiori modo], if it is an equivocal agent—thus in the sun is the likeness of whatever is generated by the sun’s power.

Here is a suggestion. In distinguishing per se and per accidens infinite multiplication of causes, Aquinas is indeed distinguishing counting types and tokens. But the types he is counting are what one might call “causal types” or “perfections”. The idea is that we have the same causal type when we have univocal agency, “as when man reproduces man”, and different causal type when we have equivocal agency, as when the sun generates something, since on Aquinas’ astronomical theory the sun is sui generis and hence when the sun generates, the sun is quite different from what it generates. In other words, I am tentatively suggesting that we identify the gradus of efficient causality of I.46.2 with the modus of perfection of I.4.2.

The picture of efficient causation that arises from I.4.2 is that in a finite or infinite causal regress we have two types of moves between effect and cause: a lateral move to a cause with the same perfection as the effect and an ascending vertical move to a cause that has the perfection more eminently.

The lateral moves only accidentally multiply the explanations, because the lateral moves do not really explain the perfection. If I got my humanity from another human, there is a sense in which this is not really an explanation of where my humanity comes from. The human I got my humanity from was just passing that humanity on. I need to move upwards, attributing my humanity to a higher cause. On this reading, Aquinas is claiming that there can only be finitely many upwards moves in a causal regress. Why? Maybe because infinite passing-on of more to less eminent perfections is just as unexplanatory as finite passing on of the same perfection. We need an ultimate origin of the perfections, a highest cause.

I like this approach, but it fits better with the sun–elemenatary body–human example than the hand–stick–rock example. It seems, after all, that in the hand–stick–rock example we have the same relevant perfection in all three items—locomotion, which is passed from hand to stick and then from stick to rock. This would thus seem like a per accidens multiplication rather than a per se one. If so, then it is tempting to say that Aquinas’ hand–stick–rock example is inapt. But perhaps we can say this. Hand-motion is probably meant to be a voluntary human activity. Plausibly, this is different in causal type from stick-motion: going from stick to hand is indeed an explanatory ascent. But it’s harder to see the progression from rock to stick as an explanatory ascent. After all, a rock can move a stick just as much as a stick can move a rock. But perhaps we can still think we have an ascent from rock-moving to stick-moved-by-hand, since a stick-moved-by-hand maybe has more of the perfection of the voluntary hand motion to it? That sounds iffy, but it’s the best I can do.

I wish Aquinas discussed a case of stick–stick–stick, where each stick moves the next? Would he make this be a per se multiplication of causes like the hand–stick–rock case? If so, that’s a count against my reading. Or would he say that it’s an accidental multiplication? If so, then my tentative reading might be right.

It’s also possible that Aquinas’ examples of hand–stick–rock and sun–elementary body–human are in fact more unlike than he noticed, and that it is the latter that is a better example of per se multiplication of causes.

Towards a solution to the "God as author of evil" problem for the Thomistic model of meticulous providence

On the Thomistic primary/secondary causation model of meticulous divine providence, when we act wrongly, God fully determines the positive aspects of the action with primary causation, and we in parallel cause the action with secondary causation.

Like many people, I worry that this makes God the author of sin in an objectionable way.

Alice and Bob are studying together for a calculus exam that will be graded on a curve. In order that she may do terribly on the exam, and thus that he might do better, and hence be more likely to get into his dream PhD program in ethics, Bob lies to Alice, who has missed three weeks of class, that the derivative of the logarithm is the exponential.

What does God cause in Bob’s action on the Thomistic model? It seems that all of the following are positive aspects:

1. The physical movements in Bob’s mouth, throat, and lungs.

2. The sounds in the air.

So far we don’t have a serious theological problem. For (1) and (2) are not intrinsically bad, since Bob could virtuously utter the same sounds while playacting on stage. But let’s add some more aspects:

3. Bob’s intention that the speech constitute an assertion of the proposition that the derivative of the logarithm is the exponential.

4. Bob’s intention that the asserted proposition be a falsehood that Alice comes to believe and that leads to her doing terribly on the exam.

Perhaps one can argue that falsity a negative thing—a lack of conformity with reality. However, intending falsity seems to be a positive thing, a positive (but wicked) act of the will. Thus it seems that (3) and (4) are positive things. But once we put together all of (1)–(4), or even just (3) and (4), then it’s hard to deny that what we have is something wicked, and so if God is intending all of (1)–(4), it’s hard to avoid the idea that this makes God responsible for the sin in a highly problematic way.

There may be a way out, however. In both written and spoken language, meaning is normally not constituted just by the positive aspects of reality but also by negative ones. In spoken language, we can think of the positive aspects as the peaks of the soundwaves (considered as pressure waves in the air). But if you remove the troughs from the soundwaves, you lose the communication. In print, on the other hand, the meaning depends not just on the ink that’s there, but on the ink that’s not there. A page wholly covered with ink means nothing. We only have meaningful letters because the inked regions are surrounded by non-inked regions.

It could well turn out that the language of the mind in discursively thinking beings like us is like that as well, so that a thought or intention is constituted not only by ontologically positive but also by ontologically negative aspects. Now you could be responsible for the ink within the print inscription

5. The derivative of the logarithm is the exponential

without being responsible for the inscription. For instance, you and a friend might have had a plan to draw a black rectangle and you divided up the labor as follows: you inked the region of rectangle covered by the letters of “The derivative of the logarithm is the exponential” and then your friend would ink the rest of the containing rectangle—i.e., everything outside the letters. But your friend didn’t do the job. Similarly, then, if intentions are constituted by both positive and negative features, God could intend the positive features of an intention without being responsible for the intention as such.

This does place constraints on the language of the mind, i.e., on the actual mental accidents that constitutes our thoughts, and specifically our intentions. Note, though, that we don’t need that all intentions have a negative constituent. Only intentions to produce negative things, like falsehood, need to have a negative constituent for us to avert the problem of God willing intentional sin. We could imagine a written language where positive phrases are written in two colors of ink, one for the letters and the other for the surrounding rectangle, and their negations are written by omitting the ink for the letters. In such a language, statements involving positive phrases are purely positive, while those involving negative phrases are partly negative.

I am not very happy with this solution. I still worry that being responsible for the ink in (5) makes one responsible for (5) when one chooses not to have the rest of the rectangle filled in.

Three fixity principles

In debates about free will and foreknowledge as well as about compatibility and incompatibilism, fixity-of-history theses come up. Here is such a thesis:

1. If a decision is causally or logically necessitated by the history behind the decision, then one could not have decided otherwise.

But now we have a crucial question as to what is meant by “the history behind the decision”. There are at least two takes on this. On the temporal version, the history behind the decision is the sum total of what happened temporally prior to the decision. On the causal version, the history is the sum total of what happend causally prior to the decision.

This is not just a nitpicking question. Linda Zagzebski for instance nicely shows that if we go for the causal-history version of (1), then the main argument for the incompatibility of free will and foreknowledge does not get off the ground assuming God’s forebelief is not causally prior to the action. On the other hand, if we go the temporal-history version, then we have a prima facie argument for such incompatibility (though I think it’s blockable).

I am pretty confident that we should go for the causal-history version, and this has to do with the fact that the temporal-history version is not strong enough to capture our fixity intuitions. Suppose that we live in a world with simultaneous causation—say, a Newtonian world with rigid objects such that if you push object A and A pushes B, then B begins to move at exactly the same time as you start pushing (rather than with a delay caused by then need for a compression wave traveling through nonrigid materials at less than the speed of light). Then we could imagine cases where someone’s decision is causally necessitated by something outside the agent that is simultaneous with the decision. Such causal necessitation would just much make it true that one could not have decided otherwise as would causal necessitation by something in the past.

Furthermore, if backwards causation is possible, then a neurosurgeon in the future who used a backwards-causing machine to determine your decision would clearly prevent you from deciding otherwise, even though the neurosurgeon’s action was not in the temporal history. We may not believe backwards causation is possible, but it is clear that if it were possible, then deterministic backwards causation would be just as threatening for free decisions as deterministic forwards causation. This shows that causal determination is indeed a threat.

Of course, my above argument only shows that if we need to choose between the causal and temporal history versions of (1), we should definitely go for the causal one. But perhaps we don’t need to choose. We could accept both versions. But if we think we accept both versions, I think what we really should accept is an even stronger principle, where “history” is causal-cum-temporal (cct). On that stronger principle, event A counts as in the cct history of event E provided that it is either temporally or causally prior to E. The resulting fixity principle is pretty strong principle, but also a bit gerrymandered. And I think accepting this principle not that plausible, because the much simpler causal version captures our intuitions about all the ordinary cases (not involving God, or backwards or simultaneous causation), since in all ordinary cases causal and temporal history coincide, and we should not go for a more complex principle without pretty good reason.

Causal histories and freedom

Linda Zagzebski proposes the plausible principle that one is able to ϕ only if ϕing is compatible with one’s causal history relevant to ϕing.

Suppose Alice is considering whether to rob a bank. While she is doing so, God loudly announces to her nearby friend Bob that Alice will not rob the bank. God’s announcement is in Swahili, which Bob knows and Alice used to know in childhood but completely forgot. But the sound of the language her loving parents spoke to her as a child leads to Alice putting more emphasis on virtue in her deliberation, and she freely decides not to rob the bank.

Since God cannot lie, and since God’s announcement is a part of Alice’s causal history in her deliberation, Alice’s robbing the bank is incompatible with causal history and by Zagzebski’s principle, Alice cannot rob the bank. Yet it is unclear how God’s announcement removes her freedom to rob. After all, had God announced in Swahili that Alice will have breakfast, that would have influenced her deliberation in the same way, and yet obviously she would still have been free to rob the bank. But since Alice doesn’t know Swahili, the content seems causally irrelevant.

I think there are two ways out of this. First, we might cut events very finely. There is (a) God’s saying something or other in Swahili and there is (b) God’s saying in Swahili that Alice will not rob the bank. To determine the causal history, we pare away from the events all that’s causally irrelevant, and so we include (a) but not (b) in the causal history.

Alternately, we might say this. Whether or not Alice knows Swahili, her decision is affected by the detailed facts about the sounds in God’s announcement. Indeed, by essentiality of origins, her deliberation is a numerically different process because of the difference of sounds. And now we can say that God cannot make the announcement, because doing so would result in a circularity in the explanatory order: God would be making the announcement because Alice is not going to rob and Alice is not going to rob because God is making the announcement because she is not going to rob. So it is not so much that the announcement takes away God’s freedom, but that God cannot produce explanatory circularities.

It’s worth noting that Molinism does not seem to help. Sure, the subjunctive conditional of free will

1. Were God to announce in Swahili that Alice won’t rob, Alice wouldn’t rob

is true. But it is necessarily true independently of Molinism!

Permanence and meaning

Consider this strong meaning-permanence thesis:

1. There being a permanent end to all humanly relevant events would render all of our present activities meaningless.

And this weak one:

2. There being a permanent end to all humanly relevant events would render some of our present activities meaningless.

Here is a quick and easy argument that both are false. Let’s imagine that we believe in a narrative N where there are humanly relevant events that are go on forever and that render some of our present activities meaningful. After all, if there is no such narrative, then it is odd to say that a permanent end to humanly relevant events renders some or all of our present activities meaningless, since these activities would necessarily be meaningless even if there were no such end.

Now, let’s imagine that we came to think that the events and experiences in N exponentially speed up with respect to objective time, in such a way that the first “year”, by human reckoning (revolutions of the earth about the sun, say), described by N takes an objective year, but the second “year” takes half a year, the third “year” takes a quarter of a year, and so on. Thus, we come to think that all the events and experineces in N take place objectively in two years. This is then followed by a clean wipe of reality, and a new creation that has no meaningful connection to any humanly relevant events. Call this story N^*. I think it makes little human difference whether reality is described by N or by N^*. In terms of subjective time, the humanly relevant events of N^* take infinitely long. The only difference is that after the humanly relevant events there are other events that are not humanly relevant. Enriching reality with these events surely does not take away meaning.

So, none of our present activities lose meaning on N^*. But on N^* there is a permanent end of humanly relevant events. Thus, (1) and (2) are both false.

Perhaps this was too quick, though. What if your life project is to fill as much of time with humanity as you can? Then on N, if there are humans always, your project is successful, But on N^*, your project is not successful, because there is infinite humanless time after the end of humanity in two objective years, and so humans occupy only an infinitesimal fraction of time.

But I think it’s mistaken to think that it should be our project to fill up time or space with humans or human events. In other words, the filling-up project is meaningless regardless of success. Take the spatial analogue. Suppose somehow we didn’t know about other galaxies (maybe there are dust clouds shielding them from our view) and we have filled up our galaxy with humans. Would we lose any real meaning in our activities if we found out that reality is richer than we thought, and contains other galaxies beyond our reach? I don’t think so.

The above argument is compatible with a modified version of (1):

3. There being a permanent end to all humanly relevant events after a finite number of events would render all of our present activities meaningless.

For we might think that the reason ordinary stories about a permanent end have a tendency to make us think our activities are meaningless does not have to do with time, but with the idea that the narrative structure for humans requires infinity.

Divine speech acts

Suppose random quantum processes result in deep marks on a stone that spell out:

• Thou shalt not eat goat. – God

What would need to be true for it to be the case that God said (or wrote) that, thereby forbidding us to eat goat?

I assume that God always cooperates with creaturely causation, so divine causation is involved in the above production. However, such divine cooperation with the production of something that looks like an inscription or sounds like an utterance does not suffice to make it be the case that God said the thing. Imagine that a cult leader makes the above inscription. God is still cooperating with the cult leader’s causality, but we don’t want to attribute the inscription to God’s authorship.

One obvious answer is by analogy to our language. A part of what makes a performance a speech act of a particular sort is a certain kind of intention, e.g., that the performance be taken to be that sort of speech act. So maybe it just depends on God’s intentions. If God merely intends cooperation with quantum processes, there is no inscription, just random marks on stone that happen to look like an inscription. But if God intends the marks to be taken to be an inscription, they are an inscription.

This solution, however, is unhelpful given divine simplicity. The intention is a contingent feature of God, and on divine simplicity the contingency of contingent divine features is always grounded in some contingent arrangement of creatures. There cannot be two worlds that are exactly alike in their created aspects but where God has different intentions in the two worlds. So given divine simplicity, there has to be a characterization of what makes the marks a divine command in terms of what creation is like. (My view of divine intentions is, roughly, that God intends F in doing A iff intending F would be a good reason for God to do A. This presupposes divine omnirationality.)

Here is one possibility.

1. Something that looks or sounds like a speech act is a divine speech act if and only if it was directly produced by God without secondary causes.

But this seems mistaken. Imagine that in the sight of a tribe, God created a stone and a stylus ex nihilo, and then miraculously moved the stylus in such a way as to inscribe the prohibition on eating goat. Then, surely, the members of the tribe upon seeing the stylus moving through the air and gouging clear text in the stone would be right to attribute the message to God. But the inscription was not directly produced by God: it was produced by means of a stylus.

Perhaps:

2. Something that looks or sounds like a speech act is a divine speech act if and only if it was a deterministic result of something done by God without secondary causes.

This still seems a bit too restrictive. Imagine that while God used the stylus to inscribe the stone in our previous story, he nonetheless allowed for ordinary quantum randomness in the interaction between the hard stylus and the softer stone, which randomness ensured that there was a tiny probability that no inscription would result—that, say, stylus atoms would quantum tunnel through the stone atoms.

One might replace “deterministic” with “extremely probable”. But just how probable would it have to be?

Here is a different suggestion that seems to me more promising.

3. Something that looks or sounds like a speech act is a divine speech act to humans if and only if a normal human who knew all the metaphysical and physical facts about the production of this act, as well as the human social context of the production, would reasonably take it to be a divine speech act.

This suggestion allows for the possibility that a normal human would be mistaken about whether something is a divine speech act—but the mistake would then be traced back to a mistake about the relevant metaphysical, physical and social facts.

The applicability of (3) is still difficult. Take the initial example where the apparent divine prohibition on eating goat appears from quantum randomness. Would a reasonable and normal human who knew it to have appeared from quantum randomness with ordinary divine cooperation of the sort found in all creaturely causation think it to be a divine speech act? I don’t know. I don’t know that I am a reasonable and normal human, and I don’t actually know what to think about this.

Causation and the grounding problem for presentism

The past-grounding problem for presentism is of explaining what grounds facts about the past. The tensed-property solution is that presently existing objects have past-tensed properties like “Existing a hundred million years after a dinosaur” which ground the facts about the past.

Here is a problem. The presently existing objects exist at least partly because of how the world was a hundred million years ago. If how the world was a hundred million years ago is grounded in the properties of presently existing things, then we have a circularity in the order of explanation: the present objects’ existence is partly-explained by how the world was, and how the world was is grounding-explained by the objects’ possession of the properties, while the objects’ possession of the properties is partly ontologically explained by the objects’ existence.

Objection 1: This won’t bother one if one thinks one can have explanatory circularity as long as the explanations are of different sorts. But I think explanations of different sorts are still explanations, and circularity is still bad.

Objection 2: It seems that B’s being caused by A is explanatorily prior to B’s existing, so sometimes an instance of property possession is prior to existence. But I think this is mistaken. What’s prior to B is A’s exercise of causality, not B’s being caused by A.

Objection 3: If we solve the past-grounding problem by making use of past-tensed properties of God, then the problem disappears. For God doesn’t exist now because of how the world was a hundred million years ago. God exists now because God is a necessary being. I think this is a good response if one doesn’t believe in divine simplicity, but I am convinced of divine simplicity, which prohibits God from having contingent properties.

Nomically possible branches and open future views

Some open future views rely on the concept of a nomically possible branch—a complete sequence of how things might go given the laws of nature.

The problem with the concept is this. A nomically possible branch seems to be something like an exhaustive collection of propositions about all times, specifying precisely what happens at all times, with the collection as a whole compatible with the laws of nature. But now consider a world where indeterminism never gives out on any branch: no matter how things go, at every time there will still be more branching. (Our world may well be like that.) Then on an open future view, the propositions making up a branch cannot be all true together—for at no time t can the exhaustive propositions about t’s future be true, as that would violate open futurism given that branching never gives out.

For a while I thought that a decent solution to this is to say that a branch only needs to satisfy the weaker condition that for every time t, all the propositions in the branch about times up to t can be true together with the laws of nature.

But my recent example of random transtemporal causation is problematic for this solution. Suppose that today an indeterministic event E causes a green flash of light to happen on a random future day, and that the laws guarantee that no green flashes happen for any other reason. Then a branch that contains E but no green flashes of light satisfies the weaker possibility condition: for at every time t, all the propositions in the branch about times up to t can be true together with the laws of nature, since E does not causally guarantee that a green flash will happen at or before t, but only that a green flash will happen at some time or other.

Probably the best move for the open futurist is to deny causation across temporal gaps or any other mechanism that nomically guarantees that some event will happen without guaranteeing a time by which it will happen.

Random causation across temporal gaps

Suppose that causation across temporal gaps is possible: that an object x can have a direct effect in a future time, with no intermediate causes. Given that a cause clearly can have a random effect—say, you press a button and you get a green light or a red light at random—then it should also be possible for a cause to have an effect at a random future time.

Now imagine a button that, when pressed, causes a flash of light at a random time in the future, from tomorrow onward, with the probability that the flash happens in n days being 1/2ⁿ.

This is not very different from a button that, when pressed, triggers a sequence of fair coin tosses, one per day, with a beep that goes off as soon as heads comes up. The probability that there will be a beep in n days is 1/2ⁿ.

But there is still an important difference between the flash and the beep, even though they are probabilistically isomorphic. The flash is guaranteed but the beep is not (it is possible to get tails everyday). On open-future views, it is true that the flash will happen but not true that the beep will.

One could imagine the flash method being used by God in connection with indefinite-time future promises like “One day I’m going to make a flash of light.” God can just create the button that causes the flash to happen on a random future day and then trigger the button.

A Thomistic argument for the Principle of Proportional Causality

The Principle of Proportionate Causality (PPC) defended by Aquinas and other scholastics says that a perfection P can only be caused by something that has P either formally or eminently. To have P formally is to have P. Roughly, to have P eminently is to have a perfection greater than P.

(Some add: “has P virtually” to the list of options. But to have P virtually is just to have the power to produce P, and as our student Colin Causey has noted, this trivializes PPC.)

There are obvious apparent counterexamples to PPC:

• Two parents who are bad at mathematics can have a mathematical genius as a child.

• Ugly monkeys typing at random can produce a beautiful poem.

• A robot putting together parts at random can make a stronger and smarter robot.

It’s tempting to throw PPC out. But there are also cases where one feels a pull towards PPC:

• How can things that represent come from non-representing stuff?

• How can the conscious come from the non-conscious?

• How can something with dignity come from something without any?

• How can the active come from the inactive?

• How can an “ought” come from a mere “is”, i.e., something with normativity from something without any?

Many contemporary philosophers think there is no impossibility even in these cases, but I think most will agree that there is something puzzling about these kinds of causation—that we have some sort of an intuition towards PPC in these cases, of a sort we do not have in the cases of the “obvious apparent counterexamples”. What is the difference between the cases?

Well, in the counterexamples, the differences between the cause and the effect are, arguably, a matter of degree. The two parents have a much lower degree of mathematical ability. The monkeys have a certain beauty to them—being productive of beauty is a kind of beauty—albeit perhaps a lesser one than their lucky output. The robot’s output is just a more sophisticated bunch of moving parts than the robot itself.

But in the examples where one feels pulled to PPC, the differences appear to be differences in kind. Indeed, I think we can all agree that the most plausible way to resist the implied claim in the “How can…?” questions that the thing is impossible is to show how to reduce the seemingly more perfect thing to something of the same sort as the alleged cause.

But “differences in kind” doesn’t seem quite sharp enough. After all, pretty much everyone (even, I assume, young earth creationists) will agree that dogs can come from wolves.

I’ve been puzzled by how one might understand and argue for PPC for a long time, without much progress. This morning I had an inspiration from Nicholas Rescher’s article on Aquinas’ “Principle of Epistemic Disparity”, that lesser minds cannot comprehend the ways of greater ones.

Suppose we order the types of good by a comprehensibility relation ≤ where G ≤ H means that it is possible to understand G by understanding H. Then ≤ is a partial preorder, i.e., a reflexive and transitive relation. It generates a strict partial preorder < where G < H provided that G ≤ H but not H ≤ G.

Next, say that good types G₁ and G₂ are cases of the same perfection provided that G₁ ≤ G₂ and G₂ ≤ G₁, i.e., that each can be understood by the other. Basically, we are taking perfections to be equivalence classes of types of good, under the relation ∼ such that G₁ ∼ G₂ if and only if G₁ ≤ G₂ and G₂ ≤ G₁. The relation ≤ extends in a natural way to the perfections: P ≤ Q if and only if whenever G is a case of P and H is a case of Q then G ≤ H. Note that ≤ is a partial order on the perfections. In particular, it is antisymmetric: if we have P ≤ Q and Q ≤ P, then we have P ≠ Q. Write P < Q provided that P ≤ Q and P ≠ Q.

Now on to a Thomistic argument for the PPC.

Being, truth and goodness are transcendentals. The cognitively more impressive perfection Q is thus also axiologically more impressive. Thus:

Axiological Thesis: If P < Q for perfections P and Q, then Q is a better kind of perfection than P.

The following is plausible on the kind of Aristotelian intrinsic notion of causation that Thomas works with:

Causal Thesis: By understanding the cause one understands the effect.

Thomistic ideas about transcendentals also yield:

Understandability Lemma: To understand a thing one only needs to understand the goods instantiated by the thing.

Finally, let’s add this technical assumption:

Conjunction Lemma: The conjunction of co-instantiable goods is a good.

And now on to the PPC. Suppose x causes y to have a good G and y has a type of good G that is a case of a perfection P. By the Causal Thesis, we understand G by understanding x. By the Conjunction Lemma, let H be the conjunction of all the good of x. By the Understandability Lemma, we understand x by understanding H. Thus, G ≤ H. Let Q be the perfection that H is a case of. Then P ≤ Q and x has Q. Then either P = Q or P < Q. In the former case, the cause has P formally. In the latter case, by the Axiological Thesis, the cause has P eminently.

Of course, the Axiological and Causal Theses, together with the Understandability Lemma, all depend on large and controversial parts of Aquinas’ system. But I think we are making some progress.

I am also toying with an interesting concept. Say that a perfection Q is irreducible provided that it cannot be understood by understanding any conjunction of perfections P such that P < Q. It’s not obvious that there are irreducible perfections, but I think it is plausible that there are. If so, one might have a weaker PPC restricted to irreducible perfections. I have yet to think through the pluses and minuses here.

Proportionate causality

Let’s assume for the sake of argument:

Aquinas’ Principle of Proportionate Causality: Anything that causes something to have a perfection F must either have F or some more perfect perfection G.

And let’s think about what follows.

The Compatibility Thesis: If F is a perfection, then F is compatible with every perfection.

Argument: If F is incompatible with a perfection G, then having F rules out having perfection G. And that’s limitive rather than perfect. Perhaps the case where G = F needs to be argued separately. But we can do that. If F is incompatible with F, then F rules out all other perfections as well, and as long as there is more than one perfection (as is plausible) that violates the first part of the argument.

The Entailment Thesis: If F and G are perfections, and G is more perfect than F, then G entails F.

Argument: If F and G are perfections, and it is both possible to have F without having G and to have F while having G, it is better to have both F and G than to have just G. But if it is better to have both F and G than to have just G, then F contributes something good that G does not, and hence we cannot say that G is more perfect than F—rather, in one respect F is more perfect and in another G is more perfect.

From the Entailment Thesis and Aquinas’ Principle of Proportionate Causality, we get:

The Strong Principle of Proportionate Causality: Anything that causes something to have a perfection F must have F.

Interesting.

Punishment, causation and time

I want to argue for this thesis:

1. For a punishment P for a fault F to be right, P must stand in a causal-like relation to P.

What is a causal-like relation? Well, causation is a causal-like relation. But there is probably one other causal-like relation, namely when because of the occurrence of a contingent event E, God knows that E occurred, and this knowledge in turn explains why God did something. This is not exactly causation, because God is not causally affected by anything, but it is very much like causation. If you don’t agree, then just remove the ``like’’ from (1).

Thesis (1) helps explain what is wrong with punishing people on purely statistical grounds, such as sending a traffic ticket to Smith on the grounds that Smith has driven 30,000 miles in the last five years and anyone who drove that amount must have committed a traffic offense.

Are there other arguments against (1)? I think so. Consider forward-looking punishment where by knowing someone’s present character you know that they will commit some crime in ten days, so you punish them now (I assume that they will commit the crime even if you do not punish them). Or, even more oddly, consider circular forward-looking punishment. Suppose Alice has such a character that it is known that if we jail her, she will escape from jail. But assume that our in society an escape from jail is itself a crime punishable by jail, and that Alice is not currently guilty of anything. We then jail her, on the grounds that she will escape from jail, for which the punishment is us now jailing her.

One may try to rule out the forward-looking cases on the grounds that instead of (1) we should hold:

2. For a punishment P for a fault F to be right, P must come after F.

But that’s not right. Simultaneous causation seems possible, and it does not seem unjust to set up a system where a shoplifter feels punitive pain at the very moment of the shoplifting, as long as the pain is caused by the shoplifting.

Or consider this kind of a case. You know that Bob will commit a crime in ten days, so you set up an automated system that will punish him at a preset future date. It does not seem to be of much significance whether the system is set to go off in nine or eleven days.

Or consider cases where Special Relativity is involved, and the punishment occurs at a location distant from the criminal. For instance, Carl, born on Earth, could be sentenced to public infamy on earth for a crime he commits around Alpha Centauri. Supposing that we have prior knowledge that he will commit the crime on such and such a date. If (2) is the right principle, when should we make him infamous on earth? Presumably after the crime. But in what reference frame? That seems a silly question. It is silly, because (2) isn’t the right principle—(1) is better.

Objection: One cannot predict what someone will freely do.

Response: One perhaps cannot predict with 100% certainty what someone will freely do, but punishment does not require 100% certainty.

Causation and counterfactuals

Suppose that an extremely reliable cannon is loaded with a rock, and pointed at a window, and the extremely reliable timer on the cannon is set for two minutes. Two minutes later, the cannon shoots out the rock causing the window to break.

The Lewisian counterfactual account of causation accounts for the causation by the counterfactual:

1. Were the cannon not to have fired the rock, the window wouldn’t have broken.

But imagine that a risk-taking undersupervised kid was walking by towards the end of the the two minutes, and on a whim considered swapping the rock in the cannon for their steel water bottle. The decision whether to do the swap was an extremely conflicted one, and a single neuron’s made the difference, and resulted in the swap not happening.

We can set up the story in such a way that on Lewis’s way of measuring the closeness of worlds, a world where the kid swapped the rock for the water bottle is closer than any worlds where the timer wasn’t set or where the cannon misfired or where the cannon wasn’t loaded or anything like that. In that case on a Lewisian analysis of counterfactuals:

2. Were the cannon not to have fired the rock, the window would still have broken.

But surely whether the kid walks by or not, the cannon’s firing the rock caused the window to break.

We have systematic overdetermination in our movements

The causal exclusion argument requires us to deny that there is systematic overdetermination between mental and physical causes.

But it is interesting to note that in the real world there is systematic overdetermination of physical movements. Suppose I raise my arm. My muscle contraction is caused by a bunch of electrons moving in the nerves between the brain and the muscle. Suppose there are N electrons involved in the electrical flow, for some large number N. But now note that except in extremely rare marginal cases, any N − 1 of the electrons are sufficient to produce the same muscle contraction. Thus, my muscle contraction is overdetermined by at least N groups of electrons. Each of these groups differs from the original N electron group by omitting one of the electrons. And each group is sufficient to produce the effect.

One might try to defend the no-systematic-overdetermination view by saying that what doesn’t happen is systematic overdetermination by non-overlapping causes. There are two problems with this approach. First, it is not empirically clear that there isn’t systematic overdetermination by non-overlapping causes. It could turn out that typically twice as many electrons are involved in nerve impulses as are needed, in which case there are two non-overlapping groups each of which is sufficient. Second, the anti-physicalist can just say that there is overlap between the mental cause and the physical cause—the mental cause is not entirely physical, but is partially so.

Alternately, one might say that there may be systematic overdetermination of physical events by physical events, but not of physical events by physical and mental events. This would need an argument.

More on God causing infinite regresses

In my previous two posts I focused on the difficulty of God creating an infinite causal regress of indeterministic causes as part of an argument from theism to causal finitism. In this post, I want to drop the indeterministic assumption.

Suppose God creates a backwards infinite causal regress of (say) chickens, where each chicken is caused by parent chickens, the parent chickens by grandparent chickens, and so on. Now, I take it that the classical theist tradition is right that no creaturely causation can function without divine cooperation. Thus, every case where a chicken is caused by parent chickens is a case of divine cooperation.

Could God’s creative role here be limited to divine cooperation? This is absurd. For then God would be creating chickens by cooperating with chickens!

So what else is there? One doubtless correct thing to say is this: God also sustains each chicken between its first moment of life and its time of death. But this sustenance doesn’t seem to solve the problem, because the sustenance is not productive of the chickens—it is what keeps each chicken in existence after it has come on the scene. So while there is sustenance, it isn’t enough. God cannot create chickens by cooperating with chickens and by sustaining them.

Thus God needs to have some special creative role in the production of at least some of the chickens, fulfilling a task over and beyond cooperation and sustenance. Furthermore, this special task must be done by God in the case of an infinite number of the chickens, since otherwise there would be a time before which that task was not fulfilled—and yet God created infinitely the chickens before that time, too, since we’re assuming an infinite regress of chickens.

What happens in these cases? One might say is that in these special cases, God doesn’t cooperate with the parent chickens. But since no creaturely causation happens without divine cooperation, in these cases the parent chickens don’t produce their offspring, which contradicts our assumption of the chickens forming a causal regress. So that won’t do.

So in these cases, we seem to have two things happening: divine cooperation with chicken reproduction and divine creation of the chicken. Since divine cooperation with chicken reproduction is sufficient to produce the offspring, and divine creation of the chicken is also sufficient, it follows that in these cases we have causal overdetermination.

Now, we have some problems. First, does this overdetermination happen in all cases of chicken reproduction or only in some? It doesn’t need to happen in all of them, since it is overdetermination after all. But if it happens only in some, then it is puzzling to ask how God chooses which cases he overdetermines and which he does not.

Second, when there is overdetermination, the overdetermination is not needed for the effect. So it seems that if God’s additional role is that of overdetermining the outcome, that role is an unnecessary role, and the chickens could be produced by mere divine cooperation, which we saw is absurd. This isn’t perhaps the strongest of arguments. One might say that while in each particular case the overdetermining divine creative action is not needed, it is needed that it occur in some (indeed, infinitely many) cases.

Third, just as it is obviously absurd if God creates chickens merely by cooperating with chickens, it seems problematic, and perhaps absurd, that God creates chickens merely by cooperating with chickens and overdetermining that cooperation.

Famously, Aquinas thinks that God could have created an infinite regress of fathers and sons, and hence presumably of chickens as well. At this point, I can think of only one plausible way of getting Aquinas out of the above arguments, and it’s not a very attractive way. Instead of saying that God cooperates with the production of offspring, we can say that occasionalism holds in every case of substantial causation, that all causation of one substance’s existence by another is a case of direct divine non-cooperative causation, with the creaturely causation perhaps only limited to the transmission of accidents. Like all occasionalism, an occasionalism about substance causation is unappealing philosophically and theologically.

God and chancy infinite causal regresses

Suppose that a dod is a critter that chancily, with probability 1/2, causes one offspring during its life. The lifespan of a dod is one year. Further, imagine that like Sith, there are only ever one or two dods at a time, because each dod dies not long after reproducing, and if there were two or more mature dods at once, they’d fight to the death.

Now, imagine we have an infinite regress of dods, because each dod comes from an earlier dod. This would be hard to believe! After all, at any time at which we have a dod, we should be extremely (infinitely?) surprised that the dods haven’t died out yet. After all the probability that, given a dod at some time that there would be a dod in n years exponentially decreases with n.

Assuming causal finitism is false, it seems God could intentionally create an infinite regress of dods. But what would that look like? Here’s one story. God overrides the chances and directly and intentionally creates a backwards-infinite (and maybe even forwards-infinite, if he so chooses) sequence of dods. In that case, within that sequence the 1/2 chance of dod reproduction plays no explanatory role whatsoever. It seems we have occasionalism or a miracle or both. In any case, it does not appear that we actually have an infinite causal regress of dods in this case—the causation between dods, with its 1/2 chance, seems not to have any explanatory role. So the “overriding” story doesn’t work.

The other option is the Thomistic story. God doesn’t override chances. Instead, through primary causation, God concurs in creaturely causation and makes the finite cause produce its effect in such a way that the finite cause is fully acting as an indeterministic cause (this goes along with a view on which God can make us freely and indeterministically choose things). But this is very strange. For what explanatory role does the 1/2 in the chancy causation play? Assuming God wanted there to be an infinite sequence of dods, he could do exactly the same thing if the chance were 1/10 or 9/10 or even 1. It seems that the dod reproduces if and only if God intends the dod to reproduce, and whether God intends the dod to reproduce seems to have nothing to do with the “1/2” in the dod’s reproductive probabilities—it’s not plausible that God has probability 1/2 of intending each given dod to reproduce. And if God had probability 1/2 of intending each given dod to reproduce, how could he intentionally ensure that there ever are any dods, since the probability that God has infinitely many of these individual-dod-reproduction intentions is zero.

So we have problems. This gives further evidence that theism implies causal finitism.

Information Processing Finitism, Part II

In my previous post, I explored information processing finitism (IPF), the idea that nothing can essentially causally depend on an infinite amount of information about contingent things.

Since a real-valued parameter, such as mass or coordinate position, contains an infinite amount of information, a dynamics that fits with IPF needs some non-trivial work. One idea is to encode a real-valued parameter r as a countable sequence of more fundamental discrete parameters r₁, r₂, ... where r_i takes its value in some finite set R_i, and then hope that we can make the dynamics be such that each discrete parameter depends only on a finite number of discrete parameters at earlier times.

In the previous post, I noted that if we encode real numbers as Cauchy sequences of rationals with a certain prescribed convergence rate, then we can do something like this, at least for a toy dynamics involving continuous functions on between 0 and 1 inclusive. However, an unhappy feature of the Cauchy encoding is that it’s not unique: a given real number can have multiple Cauchy encodings. This means that on such an account of physical reality, physical reality has more information in it than is expressed in the real numbers that are observable—for the encodings are themselves a part of reality, and not just the real numbers they encode.

So I’ve been wondering if there is some clever encoding method where each real number, at least between 0 and 1, can be uniquely encoded as a countable sequence of discrete parameters such that for every continuous function f from [0,1] to [0,1], the value of each parameter discrete parameter corresponding to of f(x) depends only on a finite number of discrete parameters corresponding to x.

Sadly, the answer is negative. Here’s why.

Lemma. For any nonempty proper subset A of [0,1], there are uncountably many sets of the form f⁻¹[A] where f is a continuous function from [0,1] to [0,1].

Given the lemma, without loss of generality suppose all the parameters are binary. For the ith parameter, let B_i be the subset of [0,1] where the parameter equals 1. Let F be the algebra of subsets of [0,1] generated by the B_i. This is countable. Any information that can be encoded by a finite number of parameters corresponds to a member of F. Suppose that whether f(x) ∈ A for some A ∈ F depends on a finite number of parameters. Then there is a C ∈ F such that x ∈ C iff f(x) ∈ A. Thus, C = f⁻¹[A]. Thus, F is uncountable by the lemma, a contradiction.

Quick sketch of proof of lemma: The easier case is where either A or its complement is non-dense in [0,1]—then piecewise linear f will do the job. If A and its complement are dense, let (a_n) and (b_n) be a sequence decreasing to 0 such that both a_n and b_n are within 1/2^n + 2 of 1/2ⁿ, but a_n ∈ A and b_n ∉ A. Then for any set U of positive integers, there will be a strictly increasing continuous function f_U such that f_U(a_n) = a_n if n ∈ U and f_U(b_n) = a_n if n ∉ U. Note that f_U⁻¹[A] contains a_n if and only if n ∈ A and contains b_n if and only if n ∉ A. So for different sets U, f_U⁻¹[A] is different, so there are continuum-many sets of the form f_U⁻¹[A].

Theistic Humeanism?

Here’s an option that is underexplored: theistic Humeanism. There are two paths to it.

The path from orthodoxy: Start with a standard theistic concurrentism: whenever we have a creaturely cause C with effect E, E only eventuates because God concurs, i.e., God cooperates with the creaturely causal relation. Now add to this a story about what creaturely causation is. This will be a Humean story—the best I know is the David Lewis one that reduces causation to laws and laws to arrangements of stuff. Keep all the deep theistic metaphysics of divine causation.

The path from heterodoxy: Start with the metaphysics of occasionalism. Don’t change any of the metaphysics. But now add a Humean analysis of creaturely causation in terms of regularities. Since the metaphysics of occasionalism affirms regularities in the world, we haven’t changed the metaphysics of occasionalism, but have redescribed it as actually involving creaturely causation.

The two paths meet in a single view, a theistic Humeanism with the metaphysics of occasionalism and the language of concurrentism, and with creaturely causation described in a Humean way.

This theistic Humeanism is more complex than standard non-theistic Humeanism, but overcomes the central problem with non-theistic Humeanism: the difficulty of finding explanation in nature. If the fact that heat causes boiling is just a statement of regularity, it does not seem that heat explains boiling. But on theistic Humeanism, we have a genuine explanatory link: God makes the water boil because God is aware of the heat.

There is one special objection to theistic Humeanism. It has two causal relations, a divine one and a creaturely one. But the two are very different—they don’t both seem to be kinds of causation. However, on some orthodox concurrentisms, such as Aquinas’s, there isn’t a single kind of thing that divine and creaturely causation are species of. Instead, the two stand in an analogical relationship. Couldn’t the theistic Humean say the same thing? Maybe, though one might also object that Humean creaturely causation is too different from divine causation for the two to count as analogous.

I suppose the main objection to theistic Humeanism is that it feels like a cheat. The creaturely causation seems fake. The metaphysics is that of occasionalism, and there is no creaturely causation there. But if theistic Humeanism is a cheat, then standard non-theistic Humeanism is as well, since they share the same metaphysics of creaturely causation. If non-theistic Humeanism really does have causation, then our theistic Humeanism really does have creaturely causation. If one has fake causation, so does the other. I think both have fake causation. :-)