More on promulgation of laws

Laws need to be promulgated to be valid. Why? A Thomistic story is that valid laws create genuine reasons to act, and reasons are the sort of thing that’s available to a reasonable person. So, the laws need to be practically available to reasonable governed persons. In particular, if everyone has forgot about a law, and the books it was written in have burned down, the law is gone—promulgation is an ongoing affair. And the “practically” rules out such things as: “If you go to room 19235 in the Library of Congress, and enter a certain seven digit combination in the lock that only Congress knows, the doors will open and you will have books of all the laws in front of you.”

All this does not mean that the laws have to be made known to the reasonable persons. For it is encumbent on reasonable persons to educate themselves on laws that are relevant to them. However, since in a modern state the body of laws is too large for a typical reasonable person to study them all, availability also requires more than, say, that the laws be in public libraries, on the Internet, and to hired lawyers.

For it is not reasonable to expect that every reasonable person before they perform some ordinary action will go and search the laws. Rather, as participants in a society we rightly get a sense of what actions are ordinary, intrinsically moral, and done by people without any consciousness that some law might constrain them. And in the case of such actions, it’s not reasonable to be expect someone to look further. If there is a law prohibiting such an action, then I am inclined to think it is invalid—it is failing the promulgation condition, at least in this context.

An interesting thing about this view is that it gives some of the same results as the idea that unenforced laws are not valid. When a law has not been generally enforced, eventually ordinary people will forget (if they ever knew) that the law was there, and will go about their ordinary actions without any consciousness that they might be constrained by a law here. And then it’s not reasonable to expect people to know about the law, and the promulgation condition fails. However, not all cases of unenforced laws are like that. In some cases, people generally do know that there is a law, but they also know it is unenforced and generally ignored, and in such cases there is no promulgation failure.

Here is a somewhat hypothetical example. Ordinary people buy coffee filter cones without any worry that there might be some law requiring them to report the number of cones they purchased to the state and to keep track of destroyed cones in a log. If there is such a law, certainly no one enforces it. Thus, the ordinary reasonable person has no duty to look up whether there is such a law the first time they buy a coffee filter cone in any given state, and if it turns out that there is such a putative law, it has failed to be promulgated to them, and it’s not valid (i.e., it’s not a law) at least in the case of ordinary consumers. (I said this is somewhat hypothetical. Texas has a law governing “precursor chemical laboratory apparatus”. One of the controlled items on their report form is filter funnels, which is precisely what a coffee filter cone is. One assumes that that’s not what they mean, but I am not a lawyer. Transformers are also listed so maybe phone chargers would need to be reported to the state?)

On the other hand, there are non-ordinary actions where a reasonable participant in society knows that it’s not unlikely there are relevant laws, and it is reasonably expected that one find out what the laws are—hiring a lawyer if necessary. If I were to set up shop selling explosives, for instance, I would know that there are likely to be local, state and federal regulations I need to educate myself on.

I should note that my intuitions are driven by my conviction that valid laws are morally binding. So genuine laws aren’t like mere rules in a game or something like that. One could have a hybrid view on which we distinguish between laws and laws^*, where a law is morally binding on the governed while a law^* is something the state merely has moral permission to enforce in principle. If this distinction were to work, one could have a stronger promulgation condition for laws and a weaker one for laws^*.

The command version of divine command theory

Suppose that morality is grounded in God’s commands. What are God’s commands?

The most obvious idea would be that God’s commands are speech acts of command or legislation like: “Thou shalt not steal.”

But this is implausible. For such speech acts to be binding, they must be promulgated. But where? If we take seriously that these are genuinely speech acts, we have three main options:

1. A text from God

2. One or more human individuals speaking for God

3. A voice in people’s heads, from God or a representative of God.

I don’t think any of these are plausible once we take into account that morality applies to all, but no text has been accessible to all, no human individuals seemingly speaking for God have been audible to all, and lots of people have never heard such a voice in their heads.

So, I think, the divine command theorist needs to understand “command” in some less literal sense. I think the most plausible story would connect with Biblical descriptions of God’s law written in people’s minds or hearts. There will then be a substantive question of what kind of a feature of the mind or heart the commands are, with the two main options being:

4. Emotions (sentimentalist divine command)

5. Intuitions (cognitivist divine command).

(Combinations are also possible.)

But both cases face the following problem: How do we distinguish the attitudes, emotional or cognitive, that constitute divine commands from attitudes of the same sort that do not. Some people have moral attitudes that are screwed up—this might reduce or remove culpability, but nonetheless the screwed up attitudes are not divine commands.

I see three main options for making the distinction:

1. The properly functioning moral attitudes define morality.

2. Morality is defined by the moral attitudes that God has directly instilled either in each individual or in the ancestors of all individuals from whom they are passed on genetically and/or culturally.

3. God’s mental attitudes of approval or disapproval for moral attitudes distinguishes whether the attitudes define morality.

Option (a) pushes divine command theory very close to theistic natural law. Some people will like that (C. Stephen Evans likes to say that natural law is compatible with divine command theory).

Option (b) is interesting and promising.

Option (c) pushes the command version of divine command, which is what I have been exploring, closer to the divine will version. And it has problems with divine simplicity on which God doesn’t have intrinsic contingent features, and the approval/disapproval sounds to me like it would likely need to be an intrinsic contingent feature of God.

Lying and epistemic utility

Epistemic utility is the value of one’s beliefs or credences matching the truth.

Suppose your and my credences differ. Then I am going to think that my credences better match the truth. This is automatic if I am measuring epistemic utilities using a proper scoring rule. But that means that benevolence with respect to epistemic utilities gives me a reason to shift your credences to be closer to mine.

At this point, there are honest and dishonest ways to proceed. The honest way is to share all my relevant evidence with you. Suppose I have done that. And you’ve reciprocated. And we still differ in credences. If we’re rational Bayesian agents, that’s presumably due to a difference in prior probabilities. What can I do, then, if the honest ways are exhausted?

I can lie! Suppose your credence that there was once life on Mars is 0.4 and mine is 0.5. So I tell you that I read that a recent experiment provided a little bit of evidence in favor of there once having been life on Mars, even though I read no such thing. That boosts your credence that there was once life on Mars. (Granted, it also boosts your credence in the falsehood that there was such a recent experiment. But, plausibly, getting right whether there was once life on Mars gets much more weight in a reasonable person’s epistemic utilities than getting right what recent experiments have found.)

We often think of lying as an offense against truth. But in these kinds of cases, the lies are aimed precisely at moving the other towards truth. And they’re still wrong.

Thus, it seems that striving to maximize others’ epistemic utility is the wrong way to think of our shared epistemic life.

Maximizing others’ epistemic utility seems to lead to a really bad picture of our shared epistemic life. Should we, then, think of striving to maximize our own epistemic utility as the right approach to one’s individual epistemic life? Perhaps. For maybe what is apt to go wrong in maximizing others’ epistemic utility is paternalism, and paternalism is rarely a problem in one’s own case.

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.

Requests and obligations

By requesting something from someone, we create a reason for them to fulfill the request. On an individualistic view of human beings, this is a rather awesome power—somehow I reach into your space of reasons and create a new one.

It is tempting to downplay the force of reasons created by a request. After all, it seems that a mere request can always be legitimately turned down.

But that’s not right. There are times when a request creates an obligation. For it may be that apart form the request one’s reasons for an action were nearly conclusive, and with the request they become conclusive.

And besides that, a successfully transmitted request always creates a moral obligation to consider the request. Sometimes, the request may be quickly rejectable on the basis of a background policy. But a quick rejection still requires a consideration.

Questions, of course, are a type of request: they are a request for an answer. Thus, they too always create a moral obligation.

Wolterstorff on worship and intention

In Acting Liturgically, Wolterstorff offers a necessary and sufficient condition for when someone “is performing acts of worship or just saying the words and making the gestures”:

if a participant performs some prescribed verbal or gestural action with the intention of not thereby performing whatever be the act of worship prescribed to be performed thereby, then he has not performed that act of worship; otherwise he has

In other words:

1. One worships with the action as the community does if and only if one does not intend to dissent from the community’s understanding of the action.

But both directions of the biconditional are false.

Case 1: Alice visits a foreign country where she does not know the language and enters an ornate religious building. She believes the building to be a pagan temple and, seeing people kneeling, she thinks them to be thereby worshiping some pagan deity. She feels an urge to pray to God, and she kneels with the dual intention of thereby worshiping God and of not doing what the local community is doing. Her worship is heartfelt and sincere. But unbeknownst to her, the building is a church and the people are worshiping God by kneeling.

Alice is worshiping God by kneeling. An intention to worship God by kneeling while acting in a heartfelt and sincere way is sufficient for the kneeling to constitute worship of God. But by Wolterstorff principle, because she also intends—perhaps in Wolterstorff’s own words (she might be a reader of his)—to “not thereby perform[…] whatever be the act of worship prescribed to be performed” by the kneeling, she is not performing “that act of worship”. But that act of worship—the one the community has prescribed the kneeling to constitute—is worship of God. So if Wolterstorff’s no-intended-dissent condition is necessary for worship, Alice doesn’t worship God. But she does. So the no-intended-dissent condition is not necessary.

Objection: Alice is not worshiping communally but individually. The community is worshiping communally. So, Alice does not perform what the community understands the action to be, namely communal worship.

Response: Add to the story that this particular church has a special meaning for “kneeling”: it’s not just worship, but individual worship.

Case 2: Bob visits a foreign country where he does not know the language and enters an ornate religious building. He believes the building to be a Christian church and, seeing people kneeling, he thinks them to be worshiping God. He intends to worship God, kneels and prays in a heartfelt and sincere way. The thought that there might be some pagans in this country does not even occur to him, since the country is known for being very Christian. He kneels with the intention of worshiping God. But unbeknownst to him, the building is a pagan temple and the people are worshiping a pagan deity by kneeling.

Since it doesn’t occur to Bob that the community’s kneeling might be worship of a pagan deity, he does not form any intention to dissent from the community’s understanding. Granted, his own explicit intention to worship God disagrees with the community’s understanding of what they are doing. But to have an intention that in fact disagrees with the community’s understanding of what they are doing is not the same as intending to do otherwise than the community understands. Compare: If an expert uses complicated verbage to deny the existence of life on Mars, and I misunderstand him to be saying there is life on Mars, and I say “Indeed, there is life on Mars”, I am not intending to say otherwise than the expert did—even though what I am intending to say is, as a matter of fact, otherwise than what the expert said.

It is tempting to say that explicit intentions about the meaning of the action trump implicit ones, and so both Alice and Bob are worshiping God, and neither is worshiping a pagan deity. But that’s not quite right. A religious person may intend for the community’s understanding of an action to trump at least certain aspects of their own understanding. For instance, when a Christian prays the Nicene Creed, they may have their own understanding of “consubstantial with the Father”, but they would do well to defer to the Church for what it really means. Thus, their explicit intention to worship the Son as X (where X is their understanding of consubstantiality with the Father) is overridden by their faithful intention to worship the Son under whatever description the Church means by these words.

So, probably, what we want to say is that the individual worshiper can have a complex of set of intentions with priorities between them. For instance, the faithful Christian who prays the Nicene Creed may have intentions where their understanding of “consubstantial” is subordinated to the community’s understanding, but only within some limits. If it were to turn out that what the community means by “consubstantial with the Father” is that the Father and the Son are finite deities with beards of equal bushiness, then the faithful Christian’s intention to worship an immaterial and infinite God trumps their intention to go with the community’s understanding. I suspect there is no good way to encapsulate the complex ways that the prioritization between intentions can go in a simple definition like Wolterstorff’s.

Could there be a grain of truth in Wolterstorff’s condition? I think one could say that one defaults to worshiping as the community does in the absence of overriding intentions. I am not sure I would agree with that, but it might be true.

I am grateful to Tyler Sharp and Juliana Kazemi for pointing me to Wolterstorff’s very interesting ideas on this, and for conversations on this. In a recent conference presentation, they gave an example that has a lot of similarity with Case 2.

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.

Appearances of atemporality

Here’s a way to think about presentism. We have a three-dimensional reality and temporal modal operators, such as Prior’s P, F, H and G (pastly, futurely, always-pastly and always-futurely), with appropriate logical rules.

But now imagine this scenario: Reality consists of an eternally frozen time slice from a complex two-way-deterministic Newtonian world resembling our world—“frozen Newtonian world” for short. There are particles at various positions with various momenta (I assume that q = mdx/dt is a law of nature rather than a definition of momentum, and momentum is fundamental), but they are ever still, unchanging in their Newtonian properties. Now if Q is one of the operators P, F, H and G, define the operator Q′ as follows:

• Q′p if and only if either (a) reality consists of an eternally frozen Newtonian world and in an unfrozen Newtonian world that agrees with reality on its present slice we would have Qp or (b) we have Qp and reality does not consist of an eternally frozen Newtonian world and we have Qp.

Then the primed operators behave logically just like the unprimed ones. But according to the primed operators, “there is change and motion”. For instance, for a typical particle z eternally frozen at location x, it will be the case that P′(z is not at x) and F′(z is not at x), since in an unfrozen Newtonian world whose present slice is just like our world’s, there will be past and future times at which z is not at x.

So what? Well, the presentist’s big intuition is that on a B-theory of time there is no change: there is just a four-dimensional block, where one dimension just happens to be called “time” and things are different at different locations along that dimension, but simply calling a dimension “time” doesn’t make it any different from the spatial ones.

But the B-theorist can respond in kind. On presentism there is no change: there is just a three-dimensional world related to other three-dimensional worlds via certain modal operators that are called “pastly”, etc., but simply calling a modal operator P “pastly” doesn’t make it any different from deviant operators like P′.

The presentist will, presumably, say that it’s not just a matter of calling the operator P “pastly”, but rather the operator is the primitive pastly operator, so that if something pastly is different from how it’s now, it has changed. But now the B-theorist can just respond in the same way. It’s not just a matter of calling one of the four dimensions “time”, but rather the dimension is the primitive time dimension, so that if something is different at a different time from how it is now, it has changed or will change.

(Granted, a B-theorist does not need to think that the distinction between space and time is primitive. I am inclined not to, and hence I cannot make the above response.)

Presumably, even after this dialogue, the B-theorist’s alleged reality will look static to the presentist. But I think the presentist’s alleged reality can look atemporal to the B-theorist—it’s just a three-dimensional world with no time dimension and some modal operators relating it to other three-dimensional worlds.

Always-false open-futurism and the end of time

On always-false open-futurism, reports of future contingents are always false.

Now, imagine that it is contingent whether the time continues past t₁. Perhaps God sustains the world in existence, and has promised to sustain it until t₁ inclusive, but is free to stop sustaining it right then.

Suppose it is now t₁. Thus, now is potentially the last moment of time, but potentially not. What does the previous sentence mean? It seems to mean the conjunction of these two claims:

1. How things are now is compatible with its not being the case that there will be time.

2. How things are now is compatible with its being the case that there will be time.

But on always-false open-futurism, when the very existence of future time is contingent in light of how things are now, all will-claims have to be false. Thus, how things are now necessitates that its not the case that there will be time. In other words, we don’t have (2).

If this is correct, then on always-false open-futurism there cannot be a moment which is both potentially the last moment of time and potentially not the last moment of time. Each moment of time either is necessarily not last or necessarily last. This is a bit of a burden for the theory.

On trivalent open-futurism on which will-claims about future contingents are neither true nor false, the problem disappears. That now is potentially the last moment of time but potentially not can be taken to be equivalent to:

3. It is neither true nor false that there will be time.

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.

Divine willing

A correspondent asked me how a simple God can choose. I've thought much about this, never quite happy with what I have to say. I am still not happy (nor is it surprising if "how God functions" is beyond us!) but the following helps me a little.

Suppose I am choosing between making a brownie or a smoothie, and end up making a smoothie. Then there are four stages with each stage causing the next:

1. Deliberation between brownie and smoothie (and any other options).

2. An internal intention for a smoothie.

3. Physical movements.

4. Output: smoothie!

At Stage 1, I am still open between brownie and smoothie. Starting with Stage 2, I am internally set on the smoothie, and at that point I become morally responsible for setting myself on the smoothie.

Now one great thing about God’s power is that God doesn’t need means: he can produce effects directly.

In particular, God will omit stage 3: he doesn’t need moving limbs (nor anything else beyond himself) to produce the smoothie in the way that I need them.

Now suppose we apply perfect being theology to God. It’s a perfection of power not to need means. But stage 3 is not the only means in the above story: stage 2 is also a means. If God really doesn’t need means, then stage 2 will also be omitted in God, and we will have the two (non-temporal) stage production:

1. Deliberation between brownie and smoothie (and infinitely many other options).

2. Output: smoothie!

In particular, nowhere in this account is there an internal intention. It’s not needed: God acts directly on the external world.

We might ask: How does God know that he intends to create a smoothie? I think it’s by direct observation of the output, stage B in the divine case. (And God’s knowledge of contingencies is extrinsically grounded in the contingencies.)

If that sounds wrong, let’s ask how we know what we intend. Sometimes we know what we intend by introspection: by observing the internal intention of stage 2. But not always. Sometimes stage 2 is not conscious—we deliberate, we presumably form an internal intention but we are not directly aware of it, and then we act. When we deliberate whether to do something minor like whether to lift the left or the right hand, sometimes the first thing we are aware of is not an internal intention or specific act of will, but the movement of the hand itself. Thus, even in us, knowledge of our intentions is sometimes read off from stage 3.

Moreover, in some cases, for us, stage 3 is not distinct from stage 4. For we have bodies that we move, and sometimes—as in the hand-lift case—the output is the same as the physical movements. In some such cases, then direct knowledge of the merges stages 3 and 4 is how we know our own intention. There may even be rare cases where stage 3 and stage 4 are distinct, but in our consciousness, the knowledge of stage 4 comes first. Suppose I am deliberating whether to press the space-bar or the enter key in response to the computer saying “Press any key”. I choose to press the space-bar. It may well be that in the order of consciousness, I first feel the impact of my finger on the keyboard, then I discern the subtler kinesthetic sensation of my finger having moved through the air, and then only then do I realize what key I intended to press. I don’t know if this is how it happens—it’s too fast to be confident of phenomenology—but it seems like an intelligible possibility.

In any case, there is nothing absurd about knowing an intention by direct observation of the output.

While writing the above, it occurred to me that perhaps we shouldn’t be all that confident that we always have a stage 2. In the cases where our knowledge of what we intend comes from knowledge of stage 3 or 4, and we do not have direct conscious access to an internal act of intention, the internal act of intention is a mere theoretical posit. Perhaps that theoretical posit is correct, but perhaps it is not. If it is not, then one can intend a specific output without having an internal specified act of intention.

Why do we like being confident?

We like being more confident. We enjoy having credences closer to 0 or 1. Even if the proposition we are confident in is one that is such that it is a bad thing that it is true, the confidence itself, abstracted from the badness of the state of affairs reported by the proposition, is something we enjoy.

Here is a potential justification of this attitude in many cases. We can think of the epistemic utility of one’s credence r in a proposition p as measured by an accuracy scoring rule given by two functions T(r) and F(r), where T(r) gives the value of having credence r in p when p is actually true and F(r) gives the value when p is actually false. Most people thinking about scoring rules think they should satisfy the technical condition of being strictly proper. But strict propriety implies that the function V(r) = rT(r) + (1−r)F(r) is strictly convex. Now suppose the scoring rule is also symmetric, so that T(r) = F(1−r). Then V(r) is a strictly convex function that is symmetric about r = 1/2. Such a function has its minimum at r = 1/2, and is strictly decreasing on [0,1/2] and strictly increasing on [1/2,1]. But the function V(r) measures your expectation of your epistemic utility. How happy you are about your credence, perhaps, corresponds to your expectation of your epistemic utility. So you are most unhappy at credence 1/2, and you get happier that closer you are to 0 or 1.

OK, it’s surely not that?!

Observations and risk of confirmation/disconfirmation

It seems that a rational agent cannot guarantee their credence in a hypothesis H to go up by choosing what observation to perform. For if no matter what I observe, my credence in H goes up given my observation, then my credence should already have gone up prior to the observation—I should boost my credence from the armchair.

But this reasoning is false in general. For in performing the observation, I not only learn which of the possible observable results is in place, but I also learn that I have performed the observation. In cases where the truth of H has a correlation with whether I actually perform the observation, this can have a predictable direction of effect on my credence in H.

Suppose that the hypothesis H is the conjunction that I am going to look in the closet and there is life on Mars. By looking to check if there is a mouse in my closet, I ensure that the first conjunct of H is true, and hence I increase my credence in H—no matter what I find out about mice.

This is a very trivial fact. But it does mean that we need to qualify the statement that any observation that can confirm a hypothesis can also disconfirm it. We need to specify that the confirmation and disconfirmation happen after one has already updated on the fact that one has performed the observation.