More on directed activity without ends

In my previous post I focused on how the phenomenon of games with score undercuts the idea that activity is for an end, for some state of affairs that one aims to achieve. For no matter how good one’s score, one was aiming beyond that.

I want to consider an objection to this. Perhaps when one plays Tetris, one has an infinite number of ends:

• Get at least one point.

• Get at least two points.

• Get at least three points.

• ….

And similarly if one is running a mile, one has an infinite number of ends, namely for each positive duration t, one aims to run the miles in at most t.

My initial worry about this suggestion was that it has the implausible consequence that no matter how well one does, one has failed to achieve infinitely many ends. Thus success is always muted by failure. In the Tetris case, in fact, there will always be infinitely many failures and finitely many successes. This seemed wrong to me. But then I realized it fits with phenomenology to some degree. In these kinds of cases, when one comes to the end of the game, there may always be a slight feeling of failure amidst success—even when one breaks a world record, there is the regret that one didn’t go further, faster, better, etc. Granted, the slightness of that feeling doesn’t match the fact that in the Tetris case one has always failed at infinitely many ends and succeeded only at finitely many. But ends can be prioritized, and it could be that the infinitely many ends have diminishing value attached to them (compare the phenomenon of the “stretch goal”), so that even though one has failed at infinitely many, the finitely many one has succeeded at might outweigh them (perhaps the weights decrease exponentially).

So the game cases can, after all, be analyzed in the language of ends. But there are other cases that I think can’t. Consider the drive to learn about something. First, of course, note that our end is not omniscience—for if that were our end, then we would give up as soon as we realized it was unachievable. Now, some of the drive for learning involves known unknowns: there are propositions p where I know what p is and I aim to find out if p is true. This can be analyzed by analogy with the the infinitely-many-ends account of games with score: for each such p, I have an end to find out whether p. But often there are unknown unknowns: before I learn about the subject, I don’t even know what the concepts and questions are, so I don’t know what propositions I want to learn about. I just want to learn about the subject.

We can try to solve this by positing a score. Maybe we let my score be the number of propositions I know about the subject. And then I aim to have a score of at least one, and a score of at least two, and a score of at least three, etc. That’s trivial pursuit, not real learning, though. Perhaps, then, we have a score where we weight the propositions by their collective importance, and again I have an infinite number of ends. But in the case of the really unknown unknowns, I don’t even know how to quantify their importance, and I have no concept of the scale the score would be measured on. Unlike in the case of games, I just may not even know what the possible scores are.

So in the case of learning about a subject area, we cannot even say that we are positing an infinite number of ends. Rather, we can say that our activity has a directedness—to learn more, weighted by importance—but not an end.

Of Tetris, ends, and the beatific vision

Suppose I am playing Tetris seriously. What am I aiming at?

It’s not victory: one cannot win Tetris.

A good score, yes. But I wouldn’t stop playing after reaching a good score. So a merely good score isn’t all I am aiming at. An excellent score? But, again, even if I achieved an excellent score, I wouldn’t stop, so it’s not all I am aiming for. A world-record score? But I wouldn’t stop as soon as my score exceeded the record. An infinite score? But then I am aiming at an impossibility.

A phrase we might use is: “I am trying to get the best score I can.” But while that is how we speak, it doesn’t actually describe my aim. For consider what “the best score I can get” means. Does the “can” take into account my current skill level or not? If it does take into account my skill level, then I could count as having achieved my end despite getting a really miserable score, as long as that maxed out my skills. And that doesn’t seem right. But if it does not take into account my current skill level, but rather is the most that it could ever be possible for me, then it seems I am aiming at something unrealistic—for my current skill level falls short of what I “can” do.

What is true of Tetris is true of many other games where one’s aims align with a score. In some of these games there is such a thing as victory in addition to score. Thus, while one can time one’s runs and thus have just a score, typical running races include victory and a time, and sometimes both enter into the runner’s aims. This is not true of all games: some, like chess, only have victory (positions can be scored, but the scores are only indicative of their instrumentality for victory).

It’s worth noting that a score can be either absolute, such as time in running, and relative, such as one’s place among the finishers. In the case of place among finishers, one may be aiming for victory—first place—but one need not be. One might, for instance, make a strategic decision that one has no realistic hope for first place, and that aiming at first place will result in a poorer placement than simply aiming to “place as well as one can” (bearing in mind that this phrase is misleading, as already mentioned).

Insofar as aims align with a score, we can say that we have directed activity, but there seems to be no end, so the activity is not end-directed. We might want to say that the score is the “end”, but that would be misleading, since an end is a state you are aiming at. But typically you are not just aiming at the state of having a score—in Tetris, you get a score no matter what you do, though it might be zero. In timed fixed-distance sports, you need to finish the distance to have a time, and for some endurance races that in itself is a serious challenge, though for “reasonable” distances finishing is not much of an accomplishment.

I think what we should say is that in these activities, we have a direction, specified by increasing score, but not an end. The concept of a direction is more general than that of an end. Wherever there is an end, there is a direction defined by considering a score which is 1 if one achieves the end and 0 if one fails to do so.

So far all my examples were games. But I think the distinction between direction and end applies in much more important cases, and helps make sense of many phenomena. Consider our pursuits of goods such as health and knowledge. Past a certain age, perfect health is unachievable, and hence is not what one is aiming at. But more health is always desirable. And at any age, omniscience is out of our grasp, but more knowledge is worth having. Thus the pursuits of health and knowledge are examples of directed but not always end-directed activities. (Though, often, there are specific ends as well: the amelioration of a specific infirmity or learning the answer to a specific question.)

(Interesting question for future investigation: What happens to the maxim that the one who wills the end wills the means in the case of directed but not end-directed activity? I think it’s more complicated, because one can aim in a direction but not aim there at all costs.)

I think the above puts is in a position to make progress on a very thorny problem in Thomistic theology. The beatific vision of God is supremely good for us. But at the same time, it is a supernatural good, one that exceeds our nature. Our nature does not aim at this end, since for it to aim at this end, it would need to have the end written into itself, but its very possibility is a revealed mystery. Our desire for the beatific vision is itself a gift of God’s grace. But if our nature does not aim at the beatific vision, then it seems that the beatific vision does not fulfill us. For our nature’s aims specify what is good for us.

However, we can say this. Our nature directs us in the direction of greater knowledge and greater love of the knowable and the lovable. It does not limit that directedness to natural knowledge and love, but at the same time it does not direct us to supernatural knowledge and love as such. As far as we naturally know, it might be that natural knowledge and love is all that’s possible, and if so, we need go no further. But in fact God’s grace makes the beatific vision possible. The beatific vision is in the direction of greater knowledge and love from all our natural knowledge and love, and so it fulfills us—even though our nature has no concept of it.

Imagine that unbeknownst to me, a certain sequence of Tetris moves, which one would only be able to perform with the help of Alexey Pajitnov, yields an infinite score. Then if I played Tetris with Pajitnov’s help and I got that infinite score, I would be fulfilled in my score-directed Tetris-playing. However, it would also be correct that if I didn’t know about the possibility of the infinite score, it wasn’t an end I was pursuing. Nonetheless, it is fulfilling because it is objectively true that this score lies in the direction that I was pursuing.

Similarly, our nature, as it were, knows nothing of the beatific vision, but it directs us in a direction where in fact the beatific vision lies, should God’s grace make it possible for us.

This also gives a nice explanation of the following related puzzle about the beatific vision. When one reads what the theologians say about the beatific vision, it appears attractive to us. That attractiveness could be the result of God’s grace, but it is psychologically plausible that it would appear attractive even without grace. The idea of a loving union of understanding with an infinite good just is very attractive to humans. But how can it be naturally attractive to us when it exceeds our nature? The answer seems to me to be that we can naturally know that if the beatific vision is possible, it lies in the direction we are aimed at. But, absent divine revelation, we don’t know if it is possible. And, trivially, it’s only a potential fulfillment of our nature—i.e., a good for us to seek—if it is possible.

Does this mean that we should reject the language of “end” with respect to the beatific vision? Yes and no. It is not an end in the sense of something that our nature aims at as such. But it is an end in the sense that it is a supreme achievement in the direction at which our nature aims us. Thus it seems we can still talk about it as a supernatural end.

Divine desire ethical theories are false

On divine desire variants of divine command ethics, necessarily an action is right just in case it accords with God’s what God wants.

But it seems:

1. Necessarily, if God commands an action, the action is right.

2. Possibly, God commands an action but does not want one to do it.

Given (1) and (2), divine desire ethics is false.

I think everyone (and not just divine command theorists) should agree about (1): it is a part of the concept of God that he is authorative in such a way that whatever he commands is right.

What about (2)? Well, consider a felix culpa case where a great good would come from obedience to God and an even greater one would come from disobedience, and in the absence of a command one would have only a tiny good. Given such a situation, God could command the action. However, it seems that a perfectly good being’s desires are perfectly proportioned to the goods involved. Thus, in such a situation, God would desire that one disobey.

This is related to the important conceptual point about commands, requests and consentings that these actions can go against the characteristic desires that go with them. In the case of a human being, when there is a conflict between what a human wants and what the human commands, requests or consents to, typically it is right to go with what is said, but sometimes there is room for paternalistically going with the underlying desire (and sometimes we rightly go against both word and desire). But paternalism to God is never right.

Another argument for animals in heaven

1. All embodied humans are animals.

2. Some embodied humans will be in heaven.

3. So, there are animals in heaven.

But of course given the subject heading, you were likely interested whether there are non-human animals in heaven. That, too, can be argued for on the basis of the fact that we are animals.

4. The complete fulfillment of an animal requires it to be in an appropriate ecosystem.

5. Humans are animals.

6. An ecosystem appropriate to humans includes plants and non-human animals.

7. After the resurrection, the human beings in heaven will be completely fulfilled.

8. Thus, the human beings in heaven will be among plants and non-human animals.

Are there animals in heaven?

This argument is not a complete answer to the question, but is a start:

1. It is unlikely that all non-human earth animals will go extinct before the Second Coming.

2. It is unfitting that the Second Coming be a time where all non-human earth animals go extinct.

3. What is unfitting is unlikely.

4. So, it is likely that some non-human earth animals will survive the Second Coming.

Thomism and presentism

According to Thomism:

1. That I exist is explanatorily prior to all the other facts about me.

Obviously:

2. That yesterday I safely crossed a street is explanatorily prior to the fact that I presently exist.

3. If presentism is true, the fact that I presently exist is the same fact as that I exist.

4. There are no circles of explanatorily priority.

5. That yesterday I safely crossed a street is a fact about me.

It logically follows from these that:

6. Presentism is not true.

(For from 2 and 3, if presentism is true, that I safely crossed a street is prior to the fact that I exist. But by 1 and 5 that I exist is prior to the fact that I exist. If presentism is true, we thus have a priority circle, so by 4, we don’t have presentism.)

More steps in the open future and probability dialectics

I’ve often defended a probabilistic objection to open future views on which either future-tensed contingents are all false or are neither true nor false. If T(q) is the proposition that q is true, then:

1. P(T(q)) = P(q).

But on the open future views, the left-hand-side is zero, since it’s certain that q is not true. So the right-hand-side is zero. But then both q and its negation have zero probability, and we can’t make any predictions about the future.

An open futurist might push the following response. First, deny (1). Then insist that P(q) for a future contingent q is the objective tendency or chance towards q turning true. Thus, P(coin will be heads) is 1/2 for a fair indeterministic coin, since the there is an objective tendence of magnitude 1/2 for the coin to end up heads.

In this post I want to discuss my next step in the dialectics. I think there may be a problem with combining the objective tendency response with epistemic probabilities. Suppose that yesterday a fair coin was flipped. If the coin was heads, then tomorrow two fair indeterministic coins will be flipped, and if the coin is tails, then tomorrow one fair indeterministic coin will be flipped. Let H be the proposition that tomorrow at least one coin will be heads. If yesterday we had heads, then the objective tendency of H is 3/4. If yesterday we had tails, then the objective tendency of H is 1/2. But we need to be able to say:

2. P(H) = (1/2)(3/4) + (1/2)(1/2) = 5/8.

Now note that we are quite certain that 5/8 is not the objective tendency of H. The objective tendency of H is either 1/2 or 3/4.

So the open futurist needs a more sophisticated story. Here seems the right one. We say that P(q) is the average of the objective tendencies towards q weighted by the subjective probabilities of these tendencies. This is basically causal probability. The story requires that there be a present fact about all the objective tendencies.

On the technical side, this works. But here is a philosophical worry. If P(H) = 5/8 neither represents the objective tendency of H (which is either 1/2 or 3/4) nor one’s credence that H is true (which is zero on open-futurism), why is it that we should be making our decisions about the future in the light of P(H)?

Having multiple sufficient causes

It would be useful for discussions of causal exclusion arguments for physicalism to have a full taxonomy of the kinds of cases in which one effect E can have two sufficient causes C₁ and C₂.

Here is my tentative list of the cases:

1. Overdetermination: C₁ and C₂ overdetermine E

2. Chaining: C_i sufficiently causes C_j which sufficiently causes E (where i = 1 and j = 2 or i = 2 and j = 1)

3. Constitution: C_i sufficiently causes E by being partly constituted by C_j which sufficiently causes E (where i = 1 and j = 2 or i = 2 and j = 1)

4. Parthood: C_i sufficiently causes E by having the part C_j which sufficiently causes E (where i = 1 and j = 2 or i = 2 and j = 1).

If parthood is a special case of constitution, then (4) is a special case of (3). Moreover (2)–(4) are all species cases of:

5. Instrumentality: C_i sufficiently causes E by means of C_j sufficiently causing E (where i = 1 and j = 2 or i = 2 and j = 1).

Note that the above cases are not mutually exclusive. We can, for instance, imagine a case where we have both chaining and overdetermination. Let’s say I aim a powerful heat gun at a snowball. Just in front of the snowball is a stick of dynamite. The heat melts the snowball. But it also triggers an explosion which blows the snowball apart. Thus, we have overdetermination of the destruction of the snowball by two causes: heat and explosion. However, we also have chaining because the heat causes the explosion.

I wonder if we can come up with an argument that (1)–(4), or maybe (1) and (5), are the only options. That seems right to me.

Force-realism and simultaneous causation

If a charged particle is an electromagnetic field, the field exerts a Lorentz force F = qE + qv × B, where q and v are the charge and velocity of the particle, E is the electric field and B is the magnetic field. All of these quantities are taken at one location in spacetime. Thus, if realism about forces is correct, we have simultaneous causation: the electromagnetic field simultaneously causes the force.

Not everyone is a realist about forces, though. One might think that the electromagnetic field directly causes the subsequent change in velocity instead of causing a force which in turn causes the change in velocity.

Theism and the absolute present

Some people believe in an absolute present. An absolute present would define a privileged absolute reference frame. Suppose that there is an absolute present. Would we have any reason to think that the privileged absolute reference frame is anywhere close to our reference frame? If not, then for all we know, the things around us have an absolute geometry quite different from the one we think they have: that clock on the wall isn’t absolutely a circle, but an oval, say.

If the reason for accepting an absolute present is doing justice to common sense, then we not only need an absolute presnet, but an absolute present that defines a frame close to our frame. And that would be almost literally a version of anthropocentrism.

Of course, if we are in the image and likeness of God, the anthropocentrism may be defensible. And maybe only then.

If this is right, then the A-theory of time (which seems to require an absolute present) makes a lot more sense on theism. (Anecdotally, there is a correlation between being a theist and accepting the A-theory of time.) But on the other hand, the A-theory of time requires God’s beliefs to be changing.

Causing via a part

Assume this plausible principle:

1. If a part x of z causes w, then z causes w.

Add this controversial thesis:

2. For any x and y, there is a z that x and y are parts of.

Thesis (2) is a consequence of mereological universalism, for instance.

Finally, add this pretty plausible principle:

3. All the parts of a physical entity are physical.

Here is an interesting consequence of (1)–(3):

4. If there is any non-physical entity, any entity that has a cause has a cause that is not a physical entity.

For if w is an entity that has a cause x, and y is any non-physical entity, by (2) there is a z that x and y are both parts of. By (3), z is not physical. And by (1), z causes w.

In particular, given (1)–(3) and the obvious fact that some physical thing has a cause, we have an argument from causal closure (the thesis that no physical entity has a non-physical cause) to full-strength physicalism (the thesis that all entities are physical). Whatever we think of causal closure and physicalism, however, it does not seem that causal closure should entail full-strength physicalism.

Here is another curious line of thought. Strengthen (2) to another consequence of mereological universalism:

5. The cosmos exists, i.e., there is an entity c such that every entity is a part of c.

Then (1) and (5) yield the following holistic thesis:

6. Every item that has a cause is caused by the cosmos.

That sounds quite implausible.

We could take the above lines of thought to refute (1). But (1) sounds pretty plausible. A different move is to take the above lines of thought to refute (2) and (5), and thereby mereological universalism.

All in all, I suspect that (1) fits best with a view on which composition is quite limited.

Semantic determinacy and indeterminacy

There are arguments that our language is paradoxically indeterminate. For instance, Wittgenstein-Kripke arguments for underdetermination of rules by cases, Quine’s indeterminacy of translation arguments, or Putnam’s model-theoretic arguments.

There are also arguments that our language is paradoxically determinate. First order logic shows that there is a smallest number of grains of sand that’s still a heap.

In other words, there are cases where we want determinacy, and we find indeterminacy threatening, and cases where we want indeterminacy, and we find determinacy puzzling. I wonder if there is any relevant difference between these cases other than the fact that we have different intuitions about them.

If we are to go with our intuitions, we need to bite the bullet on, or refute, both sets of arguments, in their respective cases. But if we embrace determinacy everywhere or embrace indeterminacy everywhere, then it’s neater: we only need to bite the bullet on, or refute, one family of arguments.

I find embracing determinacy everywhere rather attractive.

Species relativity of priors

1. It would be irrational for us to assign a very high prior probability to the thesis that spiky teal fruit is a healthy food.

2. If a species evolved to naturally assign a very high prior probability to the thesis that spiky teal fruit is a healthy food, it would not be irrational for them to do this.

3. So, what prior probabilities are rational is species relative.

Reducing exact similarity

It is a commonplace that while Platonists need to posit a primitive instantiation relation for a tomato to stand in to the universal redness, trope theorists need an exact similarity relation for the tomato’s redness to stand in to another object’s redness, and hence there is no parsimony advantage to Platonism.

This may be mistaken. For the Platonist needs a degreed or comparative similarity relation, too. It seems to be a given that maroon is more similar to burgundy than blue is to pink, and blue is more similar to pink than green is to bored. But given a degreed or comparative similarity relation, there is hope for defining exact similarity in terms of it. For we can say that x and y are exactly similar provided that it is impossible for two distinct objects to be more similar than x and y are.

That said, comparative similarity is perhaps too weird and mysterious. There are clear cases, as above, but then there are cases which are hard to make sense of. Is maroon more or less similar to burgundy than middle C is to middle B? Is green more or less similar to bored than loud is to quiet?

Do particles have a self-concept?

Of course not.

But consider this. A negatively charged substance has the power to attract other substances to itslf. Its causal power thus seems to have a centeredness, a de se character. The substance’s power somehow distinguishes between the substance itself and other things.

Put this way, Leibniz's (proto?)panpsychism doesn’t seem that far a departure from a more sedate commitment to causal powers.