Discrete time and Aristotle's argument for an infinite past

Aristotle had a famous argument that time had no beginning or end. In the case of beginnings, this argument caused immense philosophical suffering in the middle ages, since combined with the idea that time requires change it implies that the universe was eternal, contrary to the Jewish, Muslim and Christian that God created the universe a finite amount of time ago.

The argument is a reductio ad absurdum and can be put for instance like this:

1. Suppose t₀ is the beginning of time.

2. Before t₀ there is no time.

3. It is a contradiction to talk of what happened before the the beginning of time.

4. But if (1) is true, then (2) talks of what is before the beginning of time.

5. Contradiction!

It’s pretty easy to see what’s wrong with the argument. Claim (2) should be charitably read as:

• Not (before t₀ there is time).

Seen that way, (2) doesn’t talk about what happened before t₀, but is just a denial that there was any such thing as time-before-t₀.

It just struck me that a similar argument could be used to establish something that Aristotle himself rejects. Aristotle famously believed that time was discrete. But now argue:

6. Suppose t₀ and t₁ are two successive instants of time.

7. After t₀ and before t₁ there is no time.

8. It is a contradiction of what happened when there is no time.

9. But if (7) is true, then (7) talks of what is when there is no time.

10. Contradiction!

Again, the problem is the same. We should take (7) to deny that there is any such thing as time-after-t₀-and-before-t₁.

So Aristotle needed to choose between his preference for the discreteness of time and his argument for an infinite past.

What if there is no tomorrow?

There are two parts of Aristotle’s theory that are hard to fit together.

First, we have Aristotle’s view of future contingents, on which

1. It is neither true nor false that tomorrow there will be a sea battle

but, of course:

2. It is true that tomorrow there will be a sea battle or no sea battle.

Of course, nothing rides on “tomorrow” in (1) and (2): any future metric interval of times will do. Thus:

3. It is true that in 86,400,000 milliseconds there will be a sea battle or not.

(Here I adopt the convention that “in x units” denotes the interval of time corresponding to the displayed number of significant digits in x. Thus, “in 86,400,000 ms” means “at a time between 86,399,999.5 (inclusive) and 86,400,000.5 (exclusive) ms from now.”)

Second, we have Aristotle’s view of time, on which time is infinitely divisible but not infinitely divided. Times correspond to what one might call happenings, the beginnings and ends of processes of change. Now which happenings there will be, and when they will fall with respect to metric time (say, 3.74 seconds after some other happening), is presumably something that is, or can be, contingent.

In particular, in a world full of contingency and with slow-moving processes of change, it is contingent whether there will be a time in 86,400,000 ms. But (3) entails that there will be such a time, since if there is no such time, then it is not true that anything will be the case in 86,400,000 ms, since there will be no such time.

Thus, Aristotle cannot uphold (3) in a world full of contingency and slow processes. Hence, (3) cannot be a matter of temporal logic, and thus neither can (2) be, since logic doesn’t care about the difference between days and milliseconds.

If we want to make the point in our world, we would need units smaller than milliseconds. Maybe Planck times will work.

Objection: Suppose that no moment of time will occur in exactly x₁ seconds, because x₁ falls between all the endpoints of processes of change. But perhaps we can still say what is happening in x₁ seconds. Thus, if there are x₀ < x₁ < x₂ such that x₀ seconds from now and x₂ seconds from now (imagine all this paragraph being said in one moment!) are both real moments of time, we can say things about what will happen in x₁ seconds. If I will be sitting in both x₀ and x₂ seconds, maybe I can say that I will be sitting in x₁ seconds. Similarly, if Themistocles is leading a sea battle in 86,399,999 ms and is leading a sea battle in 86,400,001 ms, then we can say that he is leading a sea battle in 86,400,000 ms, even though there is no moment of time then. And if he won’t lead a sea battle in either 86,399,999 ms or in 86,400,000 ms, neither will he lead one in 86,400,000 ms.

Response: Yes, but (3) is supposed to be true as a matter of logic. And it’s logically possible that Themistocles leads a sea battle in 86,399,999 ms but not in 86,400,001 ms, in which case if there will be no moment in 86,400,000 ms, we cannot meaningfully say if he will be leading a sea battle then or not. So we cannot save (3) as a matter of logic.

A possible solution: Perhaps Aristotle should just replace (2) with:

4. It is true that will be: no tomorrow or tomorrow a sea battle or tomorrow no sea battle.

I am a bit worried about the "will" attached to a “no tomorrow”. Maybe more on that later.

An attempt to define possible futures for open futurism

On all-false open future (AFOF), future contingent claims are all false. The standard way to define “Will p” is to say that p is true in all possible futures. But defining a possible future is difficult. Patrick Todd does it in terms of possible worlds apparantly of the classical sort—ones that have well-defined facts about how things are at all times. But such worlds are not in general possible given open future views—it is not possible to simultaneously have a fact about how contingent events go on all future days (assuming the future is infinite).

Here is an approach that maybe has some hope of working better for open future views. Take as primitive not classical possible worlds, but possible moments, ways that things could be purely at a time. Possible moments do not include facts about the past and future.

Now put a temporal ordering on the possible moments, where we say that m₁ is earlier than m₂ provided that it is possible to have had m₁ obtaining before m₂.

For a possible moment m, define:

• open m-world: a maximal set of possible moments including m such that (a) all moments in the set other than m are earlier or later than m and (b) the subset of moments earlier than m is totally ordered

• possible history: a maximal totally ordered set of possible moments

• possible future: a possible history that contains m.

Exactly one possible moment is currently actual. Then:

• possible future: a possible future of the currently actual moment.

Now consider the problem of entailment on AFOF. The problem is this. Intutiively, that I will freely mow my lawn entails that I will mow my lawn, but does not entail that I will eat my lawn. However, since on AFOF “I will freely mow my lawn” is necessarily false—it is false at every possible moment, since “will” claims concerning future contingent claims are always false—both entailments have necessarily false antecedents and hence are trivially true.

Given a set S of moments and a moment m ∈ S, any sentence of Prior’s (or Brand’s) temporal logic can be evaluated for truth at (S,m). We can now define two modalities:

• p is OW-necessary: p is true at (W,m) for every open m-world W

• p is PH-necessary: p is true at (H,m) for every possible history H that contains m.

And now we have two entailments: p OW/PH-entails q if and only if the material conditional p → q is OW/PH-necessary.

Then that I will freely mow my lawn is OW-impossible, but PH-possible, and that I will freely mow my lawn OW-entails that I will eat my lawn, but does not PH-entail it. The open futurist can now say that our intuitive concept of entailment, in temporal contexts, corresponds to PH-entailment rather than OW-entailment.

I think this is helpful to the open futurist, but still has a serious problem. Consider the sentence “I will mow or I will not-mow.” On AFOF, this is false. But it is true at every possible history. Hence, it is PH-necessary. Thus, PH-necessity does not satisfy the T-axiom. Thus PH-entailment is such that a truth can PH-entail a falsehood. For instance, since “I will mow or I will not-mow” is PH-necessary, it is PH-entailed by every tautology.

On trivalent logics, if "I will mow or I will not-mow" is neither true nor false, we have a similar problem: a truth PH-entails a non-truth.

There are is a more technical problem on some metaphysical views. Suppose that it is contingent whether time continues past a certain moment. For instance, suppose there is no God and empty time is impossible, and there is a particle which can indeterministically cease to exist, and the world contains just that particle, so at any time it is possible that time is the last—the particle can pop out of existence. Oddly, because of the maximality condition on possible histories, there is no possible future where the particle pops out of existence.

I wonder if there is a better way to define entailment and possible futures that works with open future views.

Aristotelianism and transformative technology

The Aristotelian picture of us is that like other organisms, we flourish in fulfilling our nature. Our nature specifies the proper way of interacting with the world. We do not expect an organism’s nature to specify proper ways of interacting with scenarios far from its niche: how bats should fly in weightless conditions; how cats should feed in an environment with unlimited food supply; how tardigrades should live on the moon.

But with technology, we have shifted far from the environment we evolved for. While adaptability is a part of our nature, some technological innovations seem to go beyond the adaptability we expect, in that they appear to impact central aspects of the life of the social beings we are: innovations like the city, writing, and fast and widely accessible global communication. We should not expect for our nature specify how we should behave with respect to these new social technologies. We should have a skepticism that our nature contains sensible answers to questions about how we should behave in these cases.

Thus we appear to have an Aristotelian argument for avoiding the more transformative types of technology, since we are more likely to have meaningful answers to questions about how to lead our lives if our lives are less affected by social transformations. To be on the safe side, we should live in the country, and have most of our social interaction with a relatively small number of neighbors in person.

The theistic Aristotelian, however, has an answer to this. While evolution cannot foresee the Internet, God can, and he can give us a normative nature that specifies how we should adapt to vast changes in the shape of our lives. We do not need to avoid transformative technology in general, though of course we must be careful lest the transformation be for ill.

Optimalism and logical possibility

Optimalism holds that, of metaphysical necessity, the best world is actualized.

There are two ways to understand “the best world”: (1) the best of all metaphysically possible worlds and (2) the best of all (narrowly) logically possible worlds.

If we understand it in sense (1), then the best world is the best out of a class of one, and hence it’s also the worst world in the same class. So on reading (1), optimalism=pessimalism.

So sense (2) seems to be a better choice. But here is an argument against (2). It seems to be an a posteriori truth that I am living life L_AP (the life in our world associated with the name “Alexander Pruss”) and that Napoleon is living life L_NB (the life in our world associated with the name “Napoleon Bonaparte”). There seems to be a narrowly logically possible world just like this one where I live L_NB and Napoleon lives L_AP. That world with me and Napoleon swapped is neither better nor worse than this one. Hence our world is not the best one. It is tied or incommensurable with a whole bunch of worlds where the identities of individuals are permuted.

Maybe my identity is logically tied to certain aspects of my life, though? Leibniz certainly thought so—he thought it was tied to all the aspects of my life. But this is a controversial view.

All-false open futurism

On All-False Open Futurism (AFOF), any future tensed statement about a future contingent must be false. It is false that there will be a sea battle tomorrow, for instance.

Suppose now I realize that due to a bug, tomorrow I will be able to transfer ten million dollars from a client’s account to mine, and then retire to a country that won’t extradite me. A little angel says to me:

1. Your freely taking your client’s money without permission tomorrow entails your being a thief tomorrow.

I don’t want to be a thief, tomorrow or ever, so I am about to decide not to do it. But now a little devil convinces me of AFOF and says that while (1) is true, so is:

2. Your freely taking your client’s money without permission tomorrow entails your being a saint tomorrow.

Perhaps I am not very good at modal logic and the devil needs to explain. Given AFOF, it is necessarily false that I will freely take my client’s money without permission tomorrow, and a necessary falsehood entails everything. So, the devil adds, I might as well buy my plane tickets now.

The angel, however, grants AFOF for the sake of argument, but says that notwithstanding (2), the following holds:

3. Tomorrow it will be the case your taking your client’s money without permission entails your being a thief.

For the entailment holds always.

At this point, we have an interesting question. Given AFOF, should I guide my actions by the entailment between future-tensed claims in (2) or by the future-tensed entailment claim in (3)? The angel urges that the devil’s reasoning undercuts all rationality, while the angel’s reasoning does not, and hence is superior.

But the devil has one more trick up his sleeve. He notes that it is a contingent question whether there will be a tomorrow at all. For God might freely decide to end time before tomorrow. Thus, that there will be a tomorrow is false on AFOF. But (3) implies that there will be a tomorrow, and so (3) is false as well. I try to argue on the basis of Scripture that God has made promises that entail a future eternity, but the devil is a lot better at citing the Bible than I, and convinces me that God might transfer us to a timeless state or maybe eternal life is a supertask lasting from 8 to 9 pm tonight. And in any case, surely it should not depend on revelation whether the angel has a good argument not to take the client’s money. This is a problem for AFOF.

Maybe this is the way out. The angel could say this:

4. Necessarily, if there will be a tomorrow, then it will be true tomorrow that taking your client’s money without permission entails your being a thief.

But while this conditional is true on AFOF, if the devil has made his case that God hasn’t promised there will be a tomorrow, he can respond with:

5. Necessarily, if God hasn’t promised there will be a tomorrow and there will be a tomorrow, then it will be true tomorrow that taking your client’s money without permission entails your being a saint.

For the antecedent of the conditional here is necessarily false on AFOF, it being contingent that there will be a tomorrow absent a divine promise. And it seems that (5) is even more relevant to guiding action than (4), then.

Maybe the defender of AFOF can insist that the future must be infinite. But this does not seem plausible.

Yet another counterexample to act utilitarianism

It is wrong to torture a stranger for 99 minutes in order to avoid 100 minutes of equal torture to oneself.

Entailment and Open Future views

This is probably an old thing that has been discussed to death, but I only now noticed it. Suppose an open future view on which future contingents cannot have truth value. What happens to entailments? We want to say:

1. That Jones will freely mow the lawn tomorrow entails that he will mow the lawn tomorrow

and to deny:

2. That Jones will freely mow the lawn tomorrow entails that he will not mow the lawn tomorrow.

Now, a plausible view of entailment is that:

3. p entails q if and only if it is impossible for p to be true while q is false.

But if future contingents cannot have truth value, then that Jones will freely mow the lawn tomorrow cannot be true, and hence by (3) it entails everything. In particular, both (1) and (2) will be true.

Presumably, the open futurist who believes future contingents cannot have truth value will give a different account of entailment, such as:

4. p entails q if and only if there is no history in which p is true and q is false.

But what is a history? Here is a possible story. For a time t, let a t-possibility be a maximal set of propositions that could all be true together at t. Given the open future view we are exploring, a t-possibility will not include any propositions reporting contingent events after t. If t₁ < t₂, and A₁ is a t₁-possibility while A₂ is a t₂-possibility, we can say that A₁ is included in A₂ provided that for any proposition p in A₁, the proposition that p was true at t₁ is a member of A₂. We can then say that a history h is a function that assigns a t-possibility h(t) to every time t such that h(t₁) is included in h(t₂) whenever t₁ < t₂.

(Technical note: Open theism implies a theory of tensed propositions, I assume. Thus if A is a t₁-possibility, then it is not a t₂-possibility if t₂ ≠ t₁, since any t-possibility will include the proposition that t is present.)

But what does it mean to say that a proposition p is true in a history h. Here is a plausible approach. Suppose t₀ is the present time. Given a proposition p that says that s, let p_t0 be the backdated proposition that at t₀ it was such that s (with whatever shifts of tense are needed in s to make this grammatical). Then p is true in h provided that there is a time t₁ > t₀ such that p_t0 is a member of h(t₁). In other words, a proposition p is true in h provided that eventually h settles its truth value.

This works nicely for letting us affirm (1) and deny (2). In every history in which it becomes true that Jones will freely mow the lawn it becomes true that Jones will mow the lawn, while this is not so if we replace the consequent with “Jones will not mow the lawn.” But what about statements that quantify over times? Consider:

5. Jones will mow the lawn, and for every time t at which Jones will mow the lawn, there will be a time t′ that is more than a year after t such that Jones will freely mow the lawn at t′.

This entails:

6. Jones will mow the lawn, and for every time t at which Jones will mow the lawn, there will be a time t′ that is more than a year after t such that Jones will mow the lawn at t′.

but does not entail:

7. Jones will not mow the lawn.

But there is no history h at which (5) is true by the above account of truth-at-a-history given our open future view. For let t₀ be the present and let p be the proposition expressed by (5). Then at any future time t and any history h, the proposition p_t0 is not a member of h(t). For if it were a member of h(t), it would be affirming the existence of an infinite number of future free mowings, and such a proposition cannot be true on our open future view. Since there is no history h at which (5) is true, by (4) we have it that (5) entails both (6) and (7), which is the wrong result.

What if instead of saying that future contingents lack truth value, we say that they are all false? This requires a slight modification to the account of p being true at a history. Instead of saying that p is true at h provided that there is some future time t such that p_t0 is in h(t), we need to say that there is some future time t such that p_t0 is in h(t′) for all t′ ≥ t. This gives the right truth values for (1) and (2), but it also makes (7) true.

I think the above open futurist accounts of entailment work nicely for statements with a single unbounded quantifier over times, but once we get alternating quantifiers like in (5), where the second conjunct is of the form ∀t∃t′ϕ, things break down.

Perhaps the open futurist just needs to be willing to bite the bullet and say that (5) entails (7)?

Open Theism and divine promises

Open Theist Christians tend to think that there are some things God knows about the future, and these include the content of God’s promises to us. God’s promises are always fulfilled.

But it seems that the content of many of God’s promises depends on free choices. For imagine that all the recipients of God’s promise freely choose to release God from the promise; then God would be free not to follow the promise, it appears, and so he could freely choose not to act in according to the promise. Thus there seems to be a sequence of creaturely and divine free choices on which the content of the promise does not come about.

This argument may not work for all of God’s promises. Some of God’s promises are covenants, and it may be that covenants are a type of agreement in which neither party can release the other. There may be other unreleasable promises: perhaps when x promises to punish y, that’s a promise y cannot release x from. But do we have reason to think that God makes no “simple promises”, promises other than covenants and promises of punishment?

I do not think this is a definitive argument against open theism. The open theist can bite the bullet and say that God doesn’t always know he will fulfill his promises. But it is interesting to see that on open theism, God’s knowledge of the future is even more limited than we might have initially thought.

Open theism and the Incarnation

Here is a very plausible pair of claims:

1. The Son could have become incarnate as a different human being.

2. God foreknew many centuries ahead of time which human being the Son would become incarnate as.

Regarding 1, of course, the Son could not have been a different person—the person the Son is and was and ever shall be is the second person of the Trinity. But Son could have been a different human being.

Here is a sketch of an argument for 1:

1. If the identity of a human being depends on the body, then if the Son became incarnate as a 3rd century BC woman in India, this would be a different human being from Jesus (albeit the same person).

2. If the identity of a human being depends on the soul, then God could have created a different soul for the Son’s incarnation.

3. The identity of a human being depends on either the body or the soul.

I don’t have as good an argument for 2 as I do for 1, but I think 2 is quite plausible given what Scripture says about God’s having planned out the mission of Jesus from of old.

Now add:

3. If the Son could have become incarnate as a different human being, which human being he became incarnate as depends on a number of free human choices in the century preceding the incarnation.

Now, 1, 2 and 3 leads to an immediate problem for an open theist Christian (my thinking on this is inspired by a paper of David Alexander, though his argument is different) who thinks God doesn’t foreknow human free choices.

Why is 3 true? Well, if the identity of a human being even partly depends on the body (as is plausible), given that (plausibly) Mary was truly a biological mother of Jesus, then if Mary’s parents had not had any children, the body that Jesus actually had would not have existed, and an incarnation would have happened with a different body and hence a different human being.

Objection: God could have created Mary—or the body for the incarnation—directly ex nihilo in such a case, or God could have overridden human free will if some human were about to make a decision that would lead to Mary not existing.

Response: If essentiality of origins is true, then it is logically impossible for the same body to be created ex nihilo as actually had a partial non-divine cause. But I don’t want the argument to depend on essentiality of origins. Instead, I want to argue as follows. Both of the solutions in the objection require God to foreknow that he would in fact engage in such intervention if human free choices didn’t cooperate with his plan. God’s own interventions would be free choices, and so on open theism God wouldn’t know that he would thus intervene. One might respond that God could resolve to ensure that a certain body would become available, and a morally perfect being always keeps his resolutions. But while perhaps a morally perfect being always keeps his promises, I think it is false that a morally perfect being always keeps his resolutions. Unless one is resolving to do something that one is already obligated to do, it is not wrong to change one’s mind in a revolution. I suppose God could have promised someone that he would ensure the existence of a certain specific body, but we have no evidence of such a specific promise in Scripture, and it seems an odd maneouver for God to have to make in order to know ahead of time who the human that would save the world is.

What if the identity of a human depends solely on the soul? But then the identity of the human being that the Son would become incarnate as would depend on God’s free decision which soul to create for that human being, and the same remarks as I made about resolutions in the previous paragraph would apply.

The Reverse Special Composition Question

Van Inwagen famously raised the Special Composition Question (SCQ): What is an informative criterion for when a proper plurality of objects composes a whole.

There is, however, the Reverse Special Composition Question (RSCQ): What is an informative criterion for when an object is composed of a proper plurality?

The SCQ seems a more fruitful question when we think of parts as prior to the whole. The RSCQ seems a more fruitful question when we think of wholes as prior to the parts.

If by parts we mean something like “integral parts”, we have a pretty quick starter option for answering the RSCQ:

1. An object is composed of a proper plurality of parts just in case it takes up more than a point of space.

I am not inclined to accept (1) because I like the possibility of extended simples, but it is a pretty neat and simple answer. Suppose that (1) is correct. Then we have a kind of simplicity argument for the thesis that the whole is prior to its parts. If the parts are prior to the whole, SCQ is a reasonable question, but doesn’t have an elegant and plausible answer (let us suppose). If the whole is prior to the parts, SCQ is not a reasonable question but RSCQ instead is, and RSCQ has an elegant and plausible answer (let us suppose). So we have some reason to accept that the whole is prior to the parts.

Natural kinds across categories

Most philosophical discussions of natural kinds concern entities in the category of substance: particles, chemical substances, organisms, etc. But I think we shouldn’t forget that there is good reason to posit natural kinds of entities in other categories.

For instance, you and I are each engaging in a token activity that falls under the natural kind (say) mammalian breathing. The natural kind specifies some essential properties of the kind, namely that it is a kind of filling and/or emptying of the lungs, as well as some teleological features, such as that the filling and emptying should be rhythmic. Instances of the kind may be better or worse: given that I am congested after a long drawn-out cold, likely your breathing is better than mine.

There are, plausibly, such things as natural activities, which fall under activity natural kinds. These may kinds may include gravitational attraction, mating, fish respiration, etc.

Dispositions, too, may fall under natural kinds, indeed a nested sequence of them. We might say that some dispositions are habits, and some habits are virtues. Thus, perhaps, you and I each have a certain disposition to rationally withstand danger, a disposition that is a token of courage, a kind of virtue. Your and my courages are different: for instance, perhaps, I am more willing to withstand social danger while you are more willing to withstand physical danger. Whether indeed virtues are natural kinds seems to me to be a central question for the metaphysics of virtue ethics.

There may be natural kinds of relations, too. Thus, I think marriage is a natural kind. On the other hand, I think presidency is not.

Reasons and direct support

A standard view of reasons is that reasons are propositions or facts that support an action. Thus, that I promised to visit is a reason to visit, that pain is bad is a reason to take an aspirin, and that I am hungry is a reason to eat.

But notice that any such facts can also be a reason for the opposite action. That I promised to visit is a reason not to visit, if you begged me not to keep any of my promises to you. That pain is bad is a reason not to take an aspirin and that I am hungry is a reason not to eat when I am striving to learn to endure harship.

One might think that this kind of contingency in what the reasons—considered as propositions or facts—support disappears when the reasons are fully normatively loaded. That I owe you a visit is always a reason to visit, and that I ought to relieve my hunger is always a reason to eat.

This is actually mistaken, too. That I owe you a visit is indeed always a reason to visit. But it can also be a reason—and even a moral one—not to visit. For instance, if a trickster informs me that that if I engage in an owed visit to you, they will cause you some minor harm—say, give you a hangnail—then the fact that I owe you a visit gives me a reason not to visit you, though that reason will be outweighed (indeed, it has to be outweighed, or else it wouldn’t be true that I owe you the visit).

In fact, plausibly, that an action is the right one is typically also a moral reason not to perform the action. For whenever we do the right thing, that has a potential of feeding our pride, and we have reason not to feed our pride. Of course, that reason is always outweighed. But it’s still there. And we might even say that the fact that an action is wrong is a reason, albeit not a moral one, to perform that action in order to exhibit one’s will to power (this is a morally bad reason to act on, but one that is probably minimally rational—we understand someone who does this).

All this suggests to me that we need a distinction: some reasons directly support doing something. That I owe you a visit directly supports my visiting you, but only indirectly supports my not visiting you to avoid pride in fulfilling my duties.

But now it is an interesting question what determined what reasons directly support what action. One option is that the relation is due to entailment: a reason directly supports ϕing provided that that reason entails that ϕing is good or right. But this misses the hyperintentionality in reasons. It is necessarily true that it’s right for me to respect my neighbor; a necessary truth is entailed by every proposition; but that my neighbor is annoying is not directly a reason to respect my neighbor. One might try for some “relevant entailment”, but I am dubious. Perhaps the fact that an action is wrong relevantly entails that there is reason to do it to exhibit one’s will to power, but that ϕing is wrong is directly a reason not to ϕ, and only indirectly a reason to ϕ.

I suspect the right answer is that this direct support relation comes from our human nature: if it is our nature to be directly motivated to ϕ because of R, then R directly supports ϕing. Hmm. This may work for epistemic support, too.

Habitual action

Alice has lived a long and reasonable life. She developed a lot of good habits. Every morning, she goes on a walk. On her walk, she looks at the lovely views, she smells the flowers in season, she gathers mushrooms, she listens to the birds chirping, she climbs a tree, and so on. Some of these things she does for their own sake and some she does instrumentally. For instance, she climbs a tree because she saw research that daily exercise promotes health, but she smells the flowers for the sake of the smelling itself.

She figured all this out when she was in her 30s, but now she is 60. One day, she realizes that for a while now she had forgotten the reasoning that led to her habits. In particular, she no longer knows which of her daily activities have innate value and which ones are merely instrumental.

So what can we say about her habitual activities?

One option is that they retain the teleology with which they were established. Although Alice no longer remembers that she climbs a tree solely for the sake of health, that is indeed what she climbs the tree for. On this picture, when we perform actions from habit, they retain the teleology they had when the habit was established. In particular, it follows that agential teleology need not be grounded in occurrent mental states of the agent. This is a difficult bullet to bite.

The other option is that they have lost their teleological characterization. This implies, interestingly, that there is no fact about whether the actions are being done for their own sake or instrumentally. In particular, it follows that the standard diviion of actions into those done for their own sake and those done instrumentally is not exhaustive. That is also a difficult bullet to bite.

I am not sure what to say. I suspect one lesson is that action is more complicated than we philosophers think, and our simple characterizations of it miss the complexity.

Acting without knowledge of rightness

Some philosophers think that for your right action to be morally worthy you have to know that the action is right.

On the contrary, there are cases where an action is even more morally worthy when you don’t know it’s right.

1. Alice is tasked with a dangerous mission to rescue hikers stranded on a mountain. She knows it’s right, and she fulfills the mission.

2. Bob is tasked with a dangerous mission to rescue hikers stranded on a mountain. He knows it’s right, but then just before he heads out, a clever philosopher gives him a powerful argument that there is no right or wrong. He is not fully convinced, but he has no time to figure out whether the argument works before the mission starts. Instead, he reasons quickly: “Well, there is a 50% chance that the argument is sound and there is no such thing as right and wrong, in which case at least I’m not doing anything wrong by rescuing. But there is a 50% chance that there is such a thing as right and wrong, and if anything is right, it’s rescuing these hikers.” And he fulfills the mission.

Bob’s action is, I think, even more worthy and praiseworthy than Alice’s. For while Alice risks her life for a certainty of doing the right thing, Bob is willing to risk his life in the face of uncertainty. Some people would take the uncertainty as an excuse, but Bob does not.

Acting because of and for reasons

It seems that:

1. If you pursue friendship because friendship is non-instrumentally valuable, then you pursue friendship non-instrumentally.

But not so. Imagine a rich eccentric offers you $10,000 to pursue something that is non-instrumentally valuable. You think about it, correctly decide friendship is non-instrumentally valuable, and pursue it to gain the $10,000. You are pursuing friendship because it is non-instrumentally valuable, but you are pursuing it merely instrumentally.

More generally, is there any conditional of the form:

2. If you pursue friendship because p, then you pursue friendship non-instrumentally

that is true in all cases, where p states some known reason for the pursuit of friendship? I don’t think so. For the rich eccentric can tell you that you will get $10,000 if it is both the case that p and you pursue friendship. In that case, if you know that it is the case that p, then your reason for pursuing friendship is p, since it is given p, and only given p, that you will get $10,000 for your pursuit of friendship.

Maybe the lesson from the above is that there is a difference between doing something because of a reason and doing it for the reason. That friendship is non-instrumentally valuable is a reason. In the first rich eccentric case, you are pursuing because of that reason, but you are not pursuing it for that reason. Thus maybe we can say:

3. If you pursue friendship for the reason that friendship is non-instrumentally valuable, then you pursue friendship non-instrumentally.

In the case where you are aiming only at the $10,000, you are pursuing friendship for the reason that pursuing friendship will get you $10,000, or more explicitly for the conjunctive reason that (a) if friendship is non-instrumentally valuable it will get you $10,000 to pursue it and (b) it is non-instrumentally valuable. But you are nonetheless pursuing friendship because it is non-instrumentally valuable.

There is thus a rather mysterious “acting for R” relation in regard to actions which does not reduce to “acting because R”.