Tuesday, March 14, 2023

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.


Austin McCoy said...


When you say that our natures are not directed to the supernatural good "as such," do you mean something like, "not under that description"? Because this seems compatible to me with our natures being directed to the supernatural good de re. Why would our nature need to "know" it is aimed at the supernatural good for it to be so directed? I guess I have Augustine's "restless soul" notion in the back of my mind. Sure, we cannot achieve the end without God's help, but I have a hard time seeing how our hearts would remain restless lest they rest in God unless resting in God was written into our natures. This seems compatible with needing God's help.

Thorny theological challenges, I realize.

ccmnxc said...

If we have a direction without an end, would this count as an essentially ordered series without a first member?

Alexander R Pruss said...


The _de re_ suggestion is another possibility, but it would require, I think, that my nature have some _de dicto_ end that can in fact only be fulfilled by the beatific vision. What could that be? Well, maybe something like: "A totally satisfying state." But no natural tendency is in vain. So if my nature has as its natural end a totally satisfying state _de dicto_, then a totally satisfying state is available for me. But I think it is easy to convince ourselves that no purely natural state is totally satisfying. So we now have an argument from our nature that there is a supernatural state available to us. And that, I think, violates the complete gratuity of that state.

So here is my picture. If God chose not to make the beatific vision available to humans, we would just have an endless directedness towards greater and greater knowledge and greater and greater friendship. That would be a kind of restlessness. I don't think this restlessness would be a _bad_ thing. Our proper activity would be an increase of knowledge and love. We just wouldn't have _satisfaction_. But even without satisfaction, we could enjoy ourselves. Lack of satisfaction is not the same as dissatisfaction. Imagine that you are really into Tetris. You are on a roll. You've beaten the highest score anybody ever got. And you are going on, and on. There can be a delight in the "being on a roll" experience. In practice, at some point, of course, we get bored, because humans aren't made for Tetris. But imagine that we were. Then we could just go on and on, much as a dog could play catch for eternity without getting bored.

Now, in fact, things aren't so positive. Our restlessness has a negativity and dissatisfaction as Augustine notes. What are we to make of this?

I think there are two stories possible. I suspect both are true and complementary.

Story 1: When we aim for score in a game, we sometimes also have an end--a score that we aim at. For instance, yesterday I was out doing a two mile kayak paddle, and I really wanted to do it under half an hour. But I wasn't just aiming for under half an hour--I would have been pleased if the time was shorter than that, and the shorter the better. But half an hour would satisfy the end (in the end, I did 29:34). So if it's not looking like I am going to get half an hour, I have the dissatisfying restlessness. And if it's looking like I'm on track for half an hour, I have a non-dissatisfying restlessness (I am still paddling hard).

So, on my first story, our nature sets both a direction and a natural goal. If we don't get the natural goal, then we are dissatisfied. If we get the natural goal, we are not dissatisfied, but we are not satisfied, since we can keep on going, as the direction points beyond the goal. The natural goal is a certain level of knowledge and friendship with God which can, in principle, be achieved by our natural resources. However, we are fallen and sinful, and so in practice, apart from God's grace, we are not on track to achieve even that natural goal. Thus so often we are restless *and* dissatisfied. If we were to achieve the natural goal, we would keep on pushing forward, but we need not be dissatisfied.

Story 2: God is generous with his grace, and God's grace gives us a dissatisfaction with anything less than the beatific vision as a sign that there is more available for us. The fact that we all find ourselves with this dissatisfaction is empirical evidence for how widespread God's grace is.


Though I worry a bit that too much of the above reflection is based on vain pursuits of score in video games and athletic activities.

Alexander R Pruss said...


I don't think so. Let's say that I am playing Eggsplode. Maybe when my score is 290,000, I tell myself: "I hope I get to 300,000." And when I get to 300,000, maybe I tell myself: I hope I get to 350,000. This is looking like a vicious regress. But I don't think it is. Getting 300,000 isn't just a *means* to getting 350,000. (If it were, we would be on our way a vicious regress.) Indeed, 300,000 is a very respectable score. My aim is has a direction, towards increasing score, and it should not be thought of as just a series of means-end relations. That's indeed the main point of my post: we should stop thinking of action in terms of means-ends relations, because the means-end approach is just one among many ways that action can be directed, and we generate needless philosophical problems by shoehorning everything into the means-end approach.

Wesley C. said...
This comment has been removed by the author.
Wesley C. said...

@Alex Can't even the direction itself be viewed as an end though, even if very abstracted in comparison to more concrete ones? Because while each individual score is truly an end in itself, the general direction of wanting higher scores over time is itself an end in a meta way, that is above the smaller specific ends of specific scores but without turning those into just means.

And maybe one can easily phrase the overall direction in more generalised language such as "The main end of Tetris for me is getting high and higher scores overall as there is no specific limit to the score number" which would seem to account for the fact there is no specific score to reach yet it can still be viewed as also being an end in itself, even if it's not tied to a very specific concrete end result?

Alexander R Pruss said...

Hmm. Given eternal life playing Tetris, I guess the end could be ever-increasing score. But supposing one only has a finite amount of time, that can't be one's end, since an end has to be achievable.

Also, I think this approach only works because of the accidental fact that Tetris gives you an ever increasing score along the way. But take something like running where you only get a score (time, lower being better) once the game is over. Then I don't think this approach works.

Guarded Acumen said...

Bernard Suits defines what it means to ‘play a game’ as follows: “To play a game is to attempt to achieve a specific state of affairs [prelusory goal], using only means permitted by rules [lusory means], where the rules prohibit use of more efficient in favor of less efficient means [constitutive rules], and where the rules are accepted just because they make possible such activity [lusory attitude].”

Now, while this is a definition of ‘gameplay’ rather than of ‘game’, a definition of ‘game’ is contained within it. A game, for Suits, is an activity directed at achieving a prelusory goal, using only lusory means, in accordance with constitutive rules, which are accepted by adopting a lusory attitude. To play a game is simply to engage in the activity of the game: “we can play a game, but this means simply to participate in it.”

Beginning with the prelusory goal, in playing a game, one always aims at a goal which can be described independently of the game. In golf, this is that a ball enter a hole in the ground; in mountain-climbing, that one stand on top of a mountain; in Olympic 200-meter sprinting, that one cross a line on the track before one’s competitors. Suits calls this goal ‘prelusory,’ from the Latin ludus for ‘game’, because it can be understood and achieved apart from the game, and he argues that every game has such a goal.

Of course, the goal of every game is to win, but the prelusory goal of a game is “analytically distinct” from the goal of winning. Crossing the finish line ahead of one’s competitors is the prelusory goal of the 100m dash, but it is distinct from winning, since one can cross the finish line first by cheating, and therefore fail to win. The prelusory goal is a precondition of winning; it makes possible the distinct goal of winning. To win is to follow a set of rules in the pursuit of the prelusory goal. Cheaters know, however, that one can appear to win by achieving the prelusory goal without following the rules—by crossing the finish line by cutting across the track, for example.

So, in playing a game, while one also aims at a goal internal to it, such as winning the race, climbing the mountain, or breaking par this ‘lusory’ goal is derivative, since achieving it involves achieving the prior prelusory goal in a specified way.

Guarded Acumen said...

I forgot to add that Tetris would be an example of what Suits calls an open game, as opposed to a closed game. An open game is a game which has no inherent goal whose achievement ends the game, e.g. crossing a finish line. The prelusory goal isn't an end-state that brings the game to an end. Games which do have such goals we may call closed games.