Characterizing actions by the reasons against them

It is plausible that the reasons for which one chooses an action help determine the kind of action it is. Plausibly, an action is a murder if one performs it because it will kill an innocent.

But it is also interesting that the reasons against which one chooses an action also help determine the character of an action. This is true both in good and bad actions. Some actions are acts of courage in part because they are done contrary to reasons of one’s own safety. And some actions are acts of gross negligence in part because they are done contrary to reasons of the safety of another. If, on the other hand, the reasons of safety did not enter into deliberation at all, the act, in both cases, may well be a case of recklessness.

Intending the end without intending the known means

It is said that:

• he who intends the end intends the means.

But the person who doesn’t know how a computer keyboard works does intend to close circuits when writing an email, even though the closing of circuits is the means to writing emails.

Perhaps, though, when they learn how computer keyboards work, that might change their intention, so that now they intend to close circuits whenever they intentionally type a character? But that is psychologically implausible: the activity of the practical intellect involved in typing is normally unchanged by learning how a keyboard works. (There are, of course, special circumstances where it may change. For instance, if one knows that one is near some very delicate electrical equipment whose functioning could be affected by the closing of these circuits, then one’s deliberation might change.) The knowledge of what happens in typing remains merely non-occurrent knowledge, not affecting the activity of the practical intellect or the will.

One might think, though, that if one occurrently knows that the means to typing an email is the closing of circuits, one is intending to close circuits. But even this need not be true. For instance, a person who is writing a technical article on how keyboards work may well be occurently knowing that their movements are transformed into data in computer memory by means of closing electrical circuits, but this occurrent knowledge may very well still not affect either their practical intellect or their will. (Indeed, when I wrote the opening paragraph of this post, I no doubt occurrently knew how keyboards work, but I don’t think this affected my intentions.)

For one’s knowledge to affect one’s intentions it needs to enter into the deliberation. For that, it needs to be occurrently and practically taken by the agent as practically relevant. For most people under most circumstances, that computer keyboards work by closing circuits is not practically relevant. But if it is Sabbath and one is an Orthodox Jew who believes that closing circuits is forbidden on the Sabbath, then the knowledge is apt to be taken as practically relevant: if one still types, that is apt to become an act of rebellion or of akrasia, and if one refrains from typing, that act is apt to be done as a mitzvah. However, one could imagine the sad case of such an Orthodox Jew who types on the Sabbath anyway, and eventually becomes so calloused that the fact that circuits are being closed stops entering into deliberation, though the fact is still known by the theoretical intellect. Such a person’s intentions may eventually drift to those of the typical gentile.

So, what is one to say about the principle that he who intends the end intends the means? There is of course a trivial version:

• he who intends the end intends the intended means.

Maybe we can do a little better:

• in intending the end one intends the means insofar as they enter into deliberation.

I am not sure this is right, but it’s the best I can do right now.

Note an interesting thing. If this last version is right, then the means may enter into deliberation on the opposite side, against the action. For instance, if one thinks it’s forbidden to close electrical circuits on the Sabbath, but one chooses to do so, that the means involve the closing of electrical circuits is apt to enter into deliberation on the con side of typing, not on the pro side (unless one is positively rebellious).

Internal reference frame

Suppose a long snake is stretched out and its front half is annihilated instantaneously. This presumably instantly destroys the snake's form or soul. So the tip of the snake's tail instantly ceases to be informed by the snake form. But then there will be a reference frame according to which the front half is annihilated before the tail loses its form. In that frame, the tip of the tail still has a snake form at a time at which the snake's front half doesn't exist. That seems wrong. So it seems there should be a privilege to reference frames where the front half is destroyed simultaneously with the tail losing its form. But a global privileged frame is unattractive. Maybe, however, we should suppose that particular substances carry along privileged frames of their own, frames internal to them. Then there will be a privilege frame for each substance, but these frames need not cohere into a global privileged frame.

Foresight and intention

The Principle of Double Effect controversially teaches that when an effect is bad, it is typically worse to intend it than to merely foresee it. I think it's interesting and somewhat refreshing to reflect on reverse cases, where we distinguish between intending and foreseeing a good effect. Obviously it's better if a legislator intends rather than merely foresees that the legislation furthers the public good. Here, it's clear that here a foresight-intention distinction captures something important.

The argument from apparently gratuitous evil

I think the following two claims are plausible:

1. If God exists and there is a lot of evil, then we would expect that some of the evil is such that we cannot see its point.

2. If God doesn’t exist and there is a lot of evil, then we would expect that some of the evil is such that we cannot see its point.

Premise 2 is pretty plausible: without God, and given a lot of evil, we’d expect evils to be pretty much random, some of them connected to goods that give them a point and others not. Now, if God exists and allows for a lot of evil, then there will be a point to all the evil allowed. And it would be intrinsically good for us to see the point of any particular evil, since knowledge is intrinsically good. But given the assumption that God has allowed a lot of evil, it would be surprising if all of this evil was such that its point (a) could be understood by us and (b) it would be on balance good for us to understand its point. In regard to (a), we can cite our cognitive limitations. In regard to (b), we can cite the fact that it is likely that some of the justifications for permissions of evil would involve soul-building, whereas it is very plausible that some soul-building would require techniques that are hidden from its beneficiaries.

Thus, once one has already taken into account the fact that there is a lot of evil, observing that there are evils that we cannot see the point of does not yield much evidence for or against the existence of God. It may, of course, yield some evidence if the degrees of expectation in (1) and (2) are different, but not much.

If this is right, then Rowe-style “evidential” arguments from evil don’t accomplish much beyond the “naive” argument that God wouldn’t allow so much evil.

Of course, one might try to argue that it’s not just the existence of pointless evil that is relevant, but how common it is. But then one would need to get into a messy discussion of just how common it is, and how common one would expect it to be on theism and on atheism.

Perdurance

Here’s an interesting thing. Suppose perdurance is true. Then God cannot be in time. For if perdurantism is true and God is in time, then God is composed of infinitely many temporal parts. But:

1. This violates divine simplicity.

2. These parts are concrete and presumably not created by God, so there are concrete things other than God that God didn’t create.

3. God acts in virtue of the temporal parts acting, but then God’s actions are not the fundamental explainers.

4. The temporal parts are all-knowing, so God is not the only all-knowing entity.

This is utterly unacceptable. So, one cannot both accept perdurantism and that God is in time.

Change, time and contradiction

According to Aristote:

1. Time is the measure of change.

2. The law of non-contradiction says that a thing cannot have and lack the same property in the same respect at the same time.

The law of non-contradiction seems to be the fundamental basis of logic. Yet it presupposes the concept of time, which in turn presupposes that of change. Thus, it seems, for Aristotle, the concept of change is more fundamental than logic itself. That doesn’t seem very plausible to me.

But perhaps there is a different way to understand the “at the same time” qualifier in (2). Sometimes, we give a rule with something we call an exception, but it’s not really an exception. For instance, we could say: “It is an offense to lie to an officer of the law, except unintentionally.” Of course, there is no such thing as an unintentional lie, but it is useful to emphasize that unintentional falsehoods are not forbidden by the rule.

Now, Aristotle is, as far as I know, a presentist. On presentism, the only properties a thing has are its present properties, and it lacks precisely those properties it doesn’t presently have. So it’s not really possible for an object to have and lack the same property, since the having and lacking would have to be both present, and hence at the same time. But it is useful to emphasize that having the same property at one time and lacking it another is not forbidden by the law of non-contradiction, and hence the logically unnecessary qualifier “at the same time”. Strictly speaking, I think “in the same respect” isn’t needed, either.

Molinism and sceptical theism

When we think of God’s reasons for permitting evils, we tend to think of fairly “natural” connections between evils and goods. But given Molinism, there could be some really weird connections. For instance, it could be that if Alice hadn’t been cut off by Bob in traffic today, Carl who witnessed this would have joined a terrorist organization. Not because there is any intrinsic connection between seeing someone get cut off in traffic and joining a terrorist organization, but just because that’s how the conditionals of free will worked out.

Indeed, a Molinist should expect there to be cases where the Molinist conditionals work out the opposite way to the “natural” connections. Thus, we can have cases where becoming more cowardly results in one’s behaving more courageously, just as a Molinist God might know that if the coin loaded in favor of heads would show tails in the next ten tosses while the coin loaded in favor of tails would show heads in the text ten tosses.

So there seems to me to be a very nice affinity between Molinism and sceptical theism.

It’s really too bad that Molinism is false.

Exercise and posession of virtue

The exercise of generosity is good to have. So is its possession. How do the two compare?

One might think the possession of generosity only has value as an instrument towards generous activity. But that seems wrong. It is bad for one to be deficient in generosity even if one will never again have the opportunity to practice generosity (say, because there is no afterlife and one has been marooned on a desert island).

But at the same time, it seems to me that the possession of generosity is of fairly low value as compared to the exercise of it. Suppose I am going to be a coma for the rest of my life and there is no life after death, and I have a choice between two actions, one of which will be generous and the other will increase my generosity (e.g., I have a choice whether I should give some money to a hungry person or to spend it on neurosurgery to eliminate something that blocks me from having much of a virtue of generosity). It seems plausible that I should do the generous deed: living (even in a coma) with generosity is better than living without it, but not by much. Similarly, if I am going to be in a coma for the rest of my life, and I have the opportunity to have one last look at a beautiful landscape, that seems worth doing, even if the price of that look is that I will lose my eyes. It is better to have eyes than not, but if the eyes aren’t going to ever get used, the value of merely having them seems small.

Perhaps, though, in a full Christian picture of life that includes the afterlife, there aren’t going to be cases where one is choosing between the exercise and the possession of generosity. If before the coma I don’t do the generous deed, then maybe I am like the guy who buried his talent, and the generosity will be taken away from me in the next life. Or at least it won’t be increased a hundredfold. I am inclined to say that given the full Christian picture, the exercise of generosity (and other virtues) should generally be chosen over the immediate possession of generosity, but will tend to result in greater possession of generosity.

Conscience and the deontic logic of attempts

When people talk of the value of obedience to conscience, it often makes it sound like there is some sort of a relationship to a mysterious faculty with a mysterious authority.

And that may all be true. But there is also a rather simple and deflationary but still, I think, useful way to think of obedience to conscience.

When I obey my conscience I am just trying to do what I ought thing. There is nothing particularly mysterious about what is right about that. If I ought to do A, I ought to try to do A. I ought to honor my parents. So, I also ought to try to honor them. Similarly, I ought to do what I ought, so I ought to try to do what I ought.

And with respect to the duty to try to do what I ought, it doesn’t matter that due to a mistake on my part I will be unable to do what I ought. That I have wrongly written down my mother’s phone number does not excuse me from trying to call her on her birthday. I ought to dial that number, because not dialing that number would be constitute a failure to try to call her, given my belief that it’s her number. Similarly, even if I am mistaken in thinking that I ought to do B, I still ought to do B, because a failure to do B would be constitutive of a failure to try to do what I ought, given my belief that B is what I ought to do.

(This is all a little less trivial when we realize that the duty to do one’s duty is actually a bit controversial. One might think that one only has first order duties, and lacks the second order duty to see to it that one fulfills the first order duties. But that would, I think, be mistaken. If I know that partaking of alcohol would cause me to neglect my first order duties, I thereby have a second order duty to avoid such partaking.)

Alternate timelines

The following sound right:

1. It is always the case that s if and only if s at all times.

2. It is always the case that s if and only if it is, always was and always will be the case that s.

But suppose, as may very well be the case, that we inhabit a multiverse whose universes all have temporally unrelated time sequences. Then (1) and (2) are apt to disagree. For (2) tells us that it is always the case that s just in case s at all past, present and future times. But in our multiverse scenario, there are times that are not past, present or future (from our point of view—which is surely the point of view we are speaking from). Thus, there is apt to be a difference between what happens at all times and what was, is and will be. For what happens at all times includes stuff that happens in other universes, since there are times that are found in other universes than ours. But what happens in the past, present or future only includes only what happens in our universe.

So, should we take (1) or (2) as the correct reading of “always”? I don’t know. (Note: I am assuming that the quantification over times in (1) is unrestricted, and hence not limited to times in our universe.) It’s a bit puzzling.

Moreover, one would have to say that right now, only a time in our time sequence is present. For if two times are present, they are simultaneous, but there are no simultaneity relations between our times and times in other time sequences. In fact, the times in the other time sequences never were and never will be present, since if they were or will be present, then they would not be temporally unrelated to times in our sequence. It sure sounds odd to talk of times that were not present, are not present and will never be present. But the ontology, nonetheless, seems to make perfect sense.

Or at least it makes perfect sense to me, a B-theorist. Could it make sense to a presentist? I am not sure. The presentist needs to make a distinction between “real” events like World War II and the 2020 Olympics, on the one hand, and merely possible events like the arrival of the Vulcans on Earth in 2053. None of these events are present, but obviously World War II and the 2020 Olympics are in some way real, while the arrival of the Vulcans is a mere fiction. The standard way for presentists to distinguish the arrival of the Vulcans from World War II and the 2020 Olympics is to say that World War II occurred and the 2020 Olympics will occur, while the arrival of the Vulcans neither occurred, nor is occurring nor will occur.

But if there are other time sequences, then the events on these time sequences are more like World War II and the 2020 Olympics than they are like first contact with the Vulcans. I do not see, however, how a presentist can possibly express the kind of reality the other time sequences in our (hypothetical) multiverse have.

(Here is a practical good from being able to make the distinction: It is right and proper to pray for all the beings in all the universes. But we shouldn’t pray for Vulcans and other fictional entities.)

In fact, I think the problem comes up even earlier, before considering any events. I don’t think the presentist can make any sense of the hypothesis of universes temporally unrelated to ours.

Thus we have an argument against presentism:

3. It is possible to have each of two temporally unrelated time sequences.

4. If presentism is true, it is not possible to have each of two temporally unrelated time sequences.

5. So, presentism is not true.

Omniscience

The following account of the doctrine of propositional omniscience is incomplete:

1. x is omniscient iff x knows every truth and believes no falsehood.

For suppose that x believes no falsehood and knows every truth but is suffering from retrieval problems for the truths that x believes, in such a way that it takes x a minute to recall what is the capital of China. That’s not omniscience—it’s not sufficiently perfect as knowledge. This suggests to me that omniscience requires occurrent knowledge of every truth: a total contemplation of all of reality.

Moreover, suppose x knows every truth but some of these truths x is not sure of. Again, that’s not omniscience. Nor would it be omniscience if x were sure of every truth and believed no falsehood, but there was some falsehood to which x assigned a small degree of belief—say, a credence of 0.2. (For one, such a being would have probabilistically inconsistent credences, as it would assign credence 1 to the negation of that falsehood.)

So, propositional omniscience should at least be:

2. x is omniscient iff x occurrently knows every truth for sure and has no degree of belief in any falsehood.

And, of course, propositional omniscience is unlikely to be all of omniscience.

The Incarnation and timelessness

Consider the standard argument against the Incarnation:

1. Everything that is God is F (omnipotent, omniscient, impassible, etc.).

2. Everything that is human is non-F.

3. Christ is God and human.

4. So, Christ is F and non-F.

5. Contradiction!

But it is only a contradiction to be F and non-F at the same time: we’ve known this since Aristotle.
Thus the kenotic theologian gets out of the argument by holding that Christ was F prior to the Incarnation and wasn’t F after the Incarnation. (A difficult question for the kenoticist: is he now F?) But that’s contrary to the teaching of the Councils.

However, the “at the same time” observation does not need to lead to kenoticism. In fact, the Christian who is a classical theist should deny that Christ is F and non-F at the same time. For it is strictly false to say that Christ is F at t for any divine attribute F and any time time t, since God has the divine attributes timelessly rather than at a time.

This is not kenoticism. Rather, the view is that Christ is F timelessly eternally and non-F at t (for any t after the beginning of the Incarnation). Kenoticism on this view is metaphysically absurd, because God cannot cease to be F: one can only cease to be something that one used to be, and there is no “used to be” where there is no temporality.

But we sometimes say things like:

• While he was suffering on the cross, Christ was upholding the existence of the universe.

I think there are two ways of make sense of such statements. First, maybe, things that happen timelessly count honorifically as holding at all times. (Compare David Lewis’s idea that abstract objects count as existing in all his worlds.) Second, the statement can be understood as follows:

• While he was suffering on the cross, the following proposition was true: Christ is upholding the existence of the universe.

So, orthodox Christians do not actually need to talk of natures to get out of (1)-(5). Of course, if we want to allow—as I think we should—for the logical possibility of multiple simultaneous incarnations, then the temporal qualification way out won’t help. (Nor will the kenotic solution help in that case, either.)

Note, by the way, that once we realize that there can be timelessly eternal existence, we need to modify Aristotle’s temporal qualification to the law of non-contradiction:

• it is impossible to be F and non-F in the same respect at the same time or both eternally.

More complications for Dutch Book results

Think of a wager as a sequence of event-payoff pairs:

• W = ((e₁, u₁),...,(e_n, u_n)).

There are then two different ways to calculate the expected value of the wager. First, directly:

1. E^D(W)=u₁P(e₁)+...+u_nP(e_n).

Second, indirectly by letting U_W be the utility function defined by W, i.e., U_W = u₁ ⋅ 1_e1 + ... + u_n ⋅ 1_en (where 1_e is the function that is 1 if e happens and 0 otherwise) and then calculating the expected utility of the function U_W:

2. E^I(W)=E(U_W).

If the credence function P is additive, then the two ways are equivalent. But without additivity, they come apart. Moreover, there is more than one way of calculating E(U) if the credences are inconsistent, but for now I will assume the standard Lebesgue sum way where, assuming U has only finitely many values, E(U)=∑_yyP(U = y).

The most common de Finetti Dutch Book Theorem, which says that inconsistent probabilities give rise to a Dutch Book, makes use of the direct way of calculating the values of wagers. Specifically, it considers wagers where you pay an amount x for a chance to win amount y if event E eventuates, and it calculates the value of such a wager as yP(E)−x. However, if instead one uses the indirect method of calculation, the value of such a wager becomes (y − x)P(E)−xP(E^c), where E^c is the complement of E.

This actually makes a real difference to Dutch Book theorems. Consider this inconsistent credence for a coin toss:

• P(H)=1/4

• P(T)=1/4

• P(H&T)=0

• P(H ∨ T)=1.

Then for any credence function U, it turns out that E^I(U)>0 if and only if the expected value of U is positive given the standard consistent fair-toss measure. The reason is this. Either U has the same value at heads and tails or it does not. If it has the same value at heads and tails, then E^I(U) has the same value as the expectation using the fair measure, since P agrees with the fair measure regarding H ∨ T. On the other hand, if U has different values at heads and tails, then E^I(U)=(1/4)U(H)+(1/4)U(T) which is exactly half of the fair measure’s expectation for U, and hence, again, E^I(U)>0 if and only if the fair measure says the expectation is positive. It seems to follow that E^I recommends exactly the same wagers as the standard consistent fair-toss measure.

Except that this isn’t quite true, either. For in addition to two ways of calculating expected values, there are two ways of making decisions on their basis in the case where a sequence of wagers is offered:

3. Accept a wager whose individual expected utility is positive.

4. Accept a wager when the expected utility of the already-accepted wagers combined with the currently offered wager exceeds the expected value of the combination of the already-accepted wagers.

Here, the combination of two wagers is concatenation. For instance ((e₁, u₁),(e₂, u₂)) combiness with ((e₃, u₃)) to form the wager ((e₁, u₁),(e₂, u₂),(e₃, u₃)). Given consistent credences, we have, E(W₁ + W₂)=E(W₁)+E(W₂), and (3) and (4) are equivalent. But, again, for inconsistent credences this additivity property can fail, and so a choice needs to be made between (3) and (4).

Note that (4) is itself an oversimplification. For theoretically, what wagers one accepts earlier on may depend on one’s best estimate as to what wagers will be offered later.

All in all, I know of five utility maximization decision procedures for sequences of wagers, generated by the answers to these questions:

• Direct or indirect utility calculation for a wager? (D or I)

• If indirect, Lebesgue sum or level set integral for calculating expectations? (LSum or LSet)

• If indirect, is the presently offered wager combined with previously accepted wagers in calculating expectations? (Indiv or Combo)

For consistent probabilities, these are all equivalent.

Moreover, there are two kinds of Dutch Books. There are Simple Dutch Books, where from the original position the agent accepts a Dutch Book, and Incremental Dutch Books, where after accepting some wagers, the agent goes on to accept a Dutch Book.

What happens with Dutch Books varies between the different procedures, and I am still working out the details. Say that a credence P is monotonic provided that P(∅)=0, P(Ω)=1 and P(A)≤P(B) whenever A ⊆ B. Here is what I have:

• D: Simple Dutch Books whenever probabilities are inconsistent.

• I+LSum+Indiv: I conjecture Incremental Dutch Books for some but not all inconsistent monotonic credences.

• I+LSum+Combo: I conjecture Incremental Dutch Books for all non-additive credences.

• I+LSet+Indiv: I don’t know.

• I+LSet+Combo: No Dutch Books of either sort for any monotonic credences.

The intellect is not higher than the will

1. The perversion of the higher faculty is worse, other things being equal.
2. Moral wrongdoing is worse than error, other things being equal.
3. Moral wrongdoing is the perversion of the will.
4. Error is the perversion of the intellect.
5. So, the intellect is not higher than the will.

Expected utility and inconsistent credences

Suppose that we have a utility function U and an inconsistent credence function P, and for simplicity let’s suppose that our utility function takes on only finitely many values. The standard way of calculating the expected utility of U with respect to P is to look at all the values U can take, multiply each by the credence that it takes that value, and add:

1. E(U)=∑_yyP(U = y).

Call this the Block Way or Lebesgue Sums.

Famously, doing this leads to Dutch Books if the credence function fails additivity. But there is another way to calculate the expected utility:

2. E(U)=∫₀^∞P(U > y)dy − ∫_−∞⁰P(U < y)dy.

Call this the Level Set Way, because sets of points in a space where some function like U is bigger or smaller than some value are known as level sets.

Here is a picture of the two ways:

On the Block Way, we broke up the sample space into chunks where the utility function is constant and calculated the contribution of each chunk using the inconsistent credence function, and then added. On the Level Set Way, we broke it up into narrow strips, and calculated the contribution of each strip, and then added.

It turns out that if the credence function P is at least monotone, so that P(A)≤P(B) if A ⊆ B, a condition strictly weaker than additivity, then an agent who maximizes utilities calculated the Level Set Way will not be Dutch Booked.

Here is another fact about the Level Set Way. Suppose two credence functions U₁ and U₂ are certain to be close to each other: |U₁ − U₂|≤ϵ everywhere. Then on the Block Way, their expected utilities may be quite far apart, even assuming monotonicity. On the other hand, on the Level Set Way, their expected utilities are guaranteed to be within ϵ, too. The difference between the two Ways can be quite radical. Suppose a coin is tossed, and the monotone inconsistent credences are:

• heads: 0.01

• tails: 0.01

• heads-or-tails: 1

• neither: 0

Suppose that U₁ says that you are paid a constant $100 no matter what happens. Both the Block Way and the Level Set Way agree that the expected utility is $100.
But now suppose that U₂ says you get paid $99 on heads and $101 on tails. Then the Block Way yields:

• E(U₂)=0.01 ⋅ 99 + 0.01 ⋅ 101 = 1

while the Level Set Way yields:

• E(U₂)=1 ⋅ 99 + 0.01 ⋅ 2 = 99.02

Thus, the Block Way makes the expected value of U₂ ridiculously small, and far from that of U₁, while the Level Set Way is still wrong—after all, the credences are stupid—but is much closer.

So, it makes sense to think of the Level Set Way as harm reduction for those agents whose credences are inconsistent but still monotone.

That said, many irrational agents will fail monotonicity.

Presentism and the Cross

1. It is important for Christian life that one unite one’s daily sacrifices with Christ’s sufferings on the cross.

2. Uniting one’s sufferings with something non-existent is not important for Christian life.

3. So, Christ’s sufferings on the cross are a part of reality.

4. So, presentism is false.

Velocity and teleportation

Suppose a rock is flying through the air northward, and God miraculously and instantaneously teleports the rock, without changing any of its intrinsic properties other than perhaps position, one meter to the west. Will the rock continue flying northward due to inertia?

If velocity is defined as the rate of change of position, then no. For the rate of change of position is now westward and the magnitude is one meter divided by zero seconds, i.e., infinite. So we cannot expect inertia to propel the rock northward any more. In fact, at this point physics would break down, since the motion of an object with infinite velocity cannot be predicted.

But if velocity (or perhaps momentum) is an intrinsic feature that is logically independent of position, and it is merely a law of physics that the rate of change of position equals the velocity, then even after the miraculous teleportation, the rock will have a northward velocity, and hence by inertia will continue moving northward.

I find the second option to be the more intuitive one. Here is an argument for it. In the ordinary course of physics, the causal impact of physical events at times prior to t₁ on physical events after t₁ is fully mediated by the physical state of things at t₁. Hence whether an object moves after time t₁ must depend on its state at t₁, and only indirectly on its state prior to t₁. But if velocity is the rate of change of position, then whether an object moves via inertia after t₁ would depend on the position of the object prior to t₁ as well as at t₁. So velocity is not the rate of change of position, but rather a quality that it makes sense to attribute to an object just in virtue of how it is at one time.

This would have the very interesting consequence that it is logically possible for an object to have non-zero velocity while not moving: God could just constantly prevent it from moving without changing its velocity.

Guessing and omniscience

Suppose that yesterday you guessed that today I’d freely mow the lawn, and today I did freely mow the lawn. Then, the correctness of your guess is a doxastic good you possessed.

(Note: If the future is open, so that there was no truth yesterday that today I’d mow the lawn, it’s a little tricky to say when you possessed it. For when you guessed, it wasn’t true that you possessed the doxastic good of guessing correctly. Rather, now that it has become the case that this doxastic good is attributable to you.)

Now no one can have a doxastic good that God lacks. Thus, God had to have at least guessed the same thing yesterday. And God has no doxastic bads. So, God never gets anything wrong. But the only plausible way it can be true that

1. God always gets right the things we guess right, and

2. God never gets things wrong

is if God has comprehensive knowledge of the future.