The pace of reception of goods

Suppose I know that from now on for an infinite number of years, I will be offered an annual game. A die will be rolled, I will be asked to guess whether the die will show six, and if I guess right, I will get a slice of delicious chocolate cake (one of my favorite foods).

Intuitively, I rationally should guess “Not a six”, and thereby get a 5/6 chance of the prize instead of the 1/6 chance if I guess “Six”.

But suppose that instead of the prizes being slices of chocolate cake, there is an infinite supply of delightful and varied P. G. Wodehouse novels (he’s one of my favorite authors), numbered 1, 2, 3, …, and each prize is the opportunity to read the next one. Moreover, the pleasure of reading book n after book n − 1 is the same regardless of whether the interval in between is longer or shorter, there being advantages and disadvantages of each interval that cancel out (at shorter intervals, one can make more literary connections between novels and remember the recurring characters a little better; but at longer intervals, one’s hunger for Wodehouse will have grown).

Now, it is clear that there is no benefit to guessing “Not a six” rather than “Six”. For whatever I guess, I am going to read every book eventually, and the pace at which I read them doesn’t seem prudentially relevant.

At this point, I wonder if I should revise my statement that in the cake case I should guess “Not a six”. I really don’t know. I can make the cake case seem just like the book case: There is an infinite supply of slices of cake, frozen near-instantly in liquid helium and numbered 1, 2, 3, …, and each time I win, I get the next slice. So it seems that whatever I do, I will eat each slice over eternity. So what difference does it make that if I guess “Not a six”, I will eat the slices at a faster pace?

On the other hand, it feels that when the pleasures are not merely equal in magnitude but qualitatively the same as in the cake case, the higher pace does matter. Imagine a non-random version where I choose between getting the prize every year and getting it every second year. Then on the every-second-year plan, the prize days are a proper subset of the prize days on the every-year plan. In the cake case, that seems to be all that matters, and so the every-year plan is better. But in the Wodehouse case, this consideration is undercut by the fact that each pleasure is different in sort, because I said the novels are varied, and I get to collect one of each regardless of which installment plan I choose.

Here is another reason to think that in the cake case, the pace matters: It clearly matters in the case of non-varied pain. It is clearly better to have a tooth pulled every two years than every year. But what about varied torture from a highly creative KGB officer? Can’t I say that on either installment plan, I get all the tortures, so neither plan is worse than the other? That feels like the wrong thing to say: the every-second-year plan still seems better even if the tortures are varied.

I am fairly confident that in the novel case—and especially if the novels continue to be varied—the pace doesn’t matter, and so in the original game version, it doesn’t matter how I gamble. I am less confident of what to say about the cake version, but the torture case pushes me to say that in the cake version, the pace does matter.

Two beauties

In a number of cases of beauty, beauty is doubled up: there is the beauty in an abstract state of affairs and there is the beauty in that state of affairs being real, or at least real to an approximation. For instance, the mathematics of Relativity Theory is beautiful in itself. But that it is true (or even approximately true) is also beautiful.

This shows an interesting aspect of superiority that painting and sculpture have over the writing of novels. The novelist discovers a beautiful (in a very broad sense of the word, far broader than the “pretty”) abstract state of affairs, and then conveys it to us. But the painter and sculptor additionally doubles the beauty by making something real an instantiation of it, and it is by making that instantiation real that they convey it to us. The playwright is somewhere in between: the beautiful state of affairs is made approximately real by a play.

The above sounds really Platonic. But we can also read it in an Aristotelian way, if we understand the abstract states of affairs as potentialities. The painter, sculptor and novelist all discover a beautiful potentiality. The painter and sculptor brings that potentiality to actuality. The novelist merely points it out to us.

An argument for theism from certain values

Some things, such as human life, love, the arts and humor, are very valuable. An interesting question to ask is why they are so valuable?

A potential answer is that they have their value because we value (desire, prefer, etc.) them. While some things may be valuable because we value them, neither life, love, the arts nor humor seem to be such. People who fail to value these things is insensitive: they are failing to recognize the great value that is there. (In general, I suspect that nothing of high value has the value it does because we value it: our ability to make things valuable by valuing them is limited to things of low and moderate value.)

A different answer is that these things are necessarily valuable. However, while this may be true, it shifts the explanatory burden to asking why they are necessarily valuable. For simplicity, I’ll thus ignore the necessity answer.

It may be that there are things that are fundamentally valuable, whose value is self-explanatory. Perhaps life and love are like that: maybe there is no more a mystery as to why life or love is valuable than as to why 1=1. Maybe.

But the arts at least do not seem to be like this. It is puzzling why arranging a sequence of typically false sentences into a narrative can make for something with great value. It is puzzling why representing aspects of the world—either of the concrete or the abstract world—in paint on canvas can so often be valuable. The value of the arts is not self-explanatory.

Theism can provide an explanation of this puzzling value: Artistic activity reflects God’s creative activity, and God is the ultimate good. Given theism it is not surprising that the arts are of great value. There is something divine about them.

Humor is, I think, even more puzzling. Humor deflates our pretensions. Why is this so valuable? Here, I think, the theist has a nice answer: We are infinitely less than God, so deflating our pretensions puts us human beings in the right place in reality.

There is much more to be said about arts and humor. The above is meant to be very sketchy. My interest here is not to defend the specific arguments from the value of the arts and humor, but to illustrate arguments from value that appear to be a newish kind of theistic argument.

These arguments are like design arguments in that their focus is on explaining good features of the world. But while design arguments, such as the argument from beauty or the fine-tuning argument, seek an explanation of why various very good features occur, these kinds of value arguments seek an explanation of why certain features are in fact as good as they are.

The moral argument for theism is closely akin. While in the above arguments, one seeks to explain why some things have the degree of value they do, the moral argument can be put as asking for an explanation of why some things (more precisely, some actions) have the kind of value they do, namely deontic value.

Closing remarks

1. Just as in the moral case, there is a natural law story that shifts the argument’s focus without destroying the argument for theism. In the moral case, the natural law story explains why some actions are obligatory by saying that they violate the prescriptions for action in our nature. But one can still ask why there are beings with a nature with these prescriptions and not others. Why is it that, as far as we can tell, there are rational beings whose nature prescribes love for neighbor and none whose nature prescribes hatred for neighbor? Similarly, we can say that humor is highly valuable for us because our nature specifies humor as one of the things that significantly fulfills us. (Variant: Humor is highly valuable for us because it is our nature to highly value it.) But we can still ask why there are rational beings whose nature is fulfilled by the arts and humor, and, as far as we can tell, none whose nature is harmed by the arts or humor. And in both the deontic and non-deontic cases, there is a theistic answer. For instance, God creates rational beings with a nature that calls on them to laugh because any beings that he would create will be infinitely less than God and hence their sensor humor will help put them in the right place, thereby counteracting the self-aggrandizement that reflection on one’s own rationality would otherwise lead to.

2. Just as in the moral case there is a compelling argument from knowledge—theism provides a particularly attractive explanation of how we know moral truths—so too in the value cases there is a similar compelling argument.

Authorless books

I've been imagining a strange scenario. I come across a text that I know for sure was generated by an entirely random process--say, the proverbial monkeys at the typewriter. I look at it. Mirabile dictu, it's coherent and reads just like a literary masterpiece--let's say it's just like something Tolstoy would have written had he written one more novel at the peak of his creative powers.

I think reading this random text could be a disquieting experience. I could read it shallowly, the way one reads some novels for mere entertainment. And in that context, it would work just as well as shallowly reading a real novel. But of course with a masterpiece, one wants to read it more deeply. In doing so, one draws connections between different parts of the texts ("Oh! So that's what that foreshadowed!" or "Ah, so that's why she did that!"), between the content and the mode of expression ("Look at all these short words describing the rapidity of the march"), between what is overtly the text and other texts, ideas, historical events and persons, etc. Drawing such connections, whether explicitly or just as a barely conscious sensation of something there--is a part of the enjoyment of reading a literary masterpiece, when done in moderation. But in our random text, all connections are merely coincidental. Nothing is there on purpose, not even unconsciously. When we read a literary giant like a Plato or a Tolstoy, when we see a compelling connection, we have good reason to think the author meant it to be there, and that sensing the connection is a part of a good reading of the text. But in the random text, there will be no such thing as a good reading or a misreading. And that would have to be disquieting. There is a sense in which we would be inventing all the connections. Reading would be more like creating than like discovering. I suppose death-of-author people think that's already the case with normal novels. But I don't think so. Real connections differ from chance ones.

At the same time, I think that in practice if I were reading this text which is just like a literary masterpiece, I'd end up suspending my disbelief about the author, and just delight in the connections and subtleties, even if they are merely apparent.

But maybe in a world with God there is no true randomness. So maybe the hypothesis of a book where nothing is intended is impossible?

Novels and worlds

As the length increases, the possibilities for good novels initially increase. It may not be possible to write a superb novel significantly shorter than One Day in the Life of Ivan Denisovich. But eventually the possibilities for good novels start to decrease, because the length itself becomes an aesthetic liability. While one could easily have a series of novels that total ten million words, a single novel of ten million words just wouldn't be such a good novel. Indeed, it seems plausible that there is no possible novel of ten million words (in a language like human languages) that's better than War and Peace or One Day or The Lord of the Rings.

If this is right, then there are possible English-language novels with the property that they could not be improved on. For there are only finitely many possible English-language novels of length below ten million, and any novel above that length will be outranked qua novel by some novel of modest length, say War and Peace or One Day.[note 1]

So, there are possible unimprovable English-language novels. Are there possible unimprovable worlds? Or is it the case that we can always improve any possible world, say by adding one more happy angelic mathematician? In the case of novels, we were stipulating a particular kind of artistic production: a novel. Within that artistic production, past a certain point length becomes a defect. But is an analogue true with worlds?

One aspect of the question is this: Is it the case that past a certain point the number of entities, say, becomes a defect? Maybe. Let's think a bit why super-long novels aren't likely to be that great. They either contain lots of different kinds of material or they are repetitive. In the latter case, they're not that great artistically. But if they contain lots of different kinds of material, then they lose the artistic unity that's important to a novel.

Could the same thing be true of worlds? Just adding more and more happy angels past a certain point will make a world repetitive, and hence not better. (Maybe not worse either.) But adding whole new kinds of beings might damage the artistic unity of the world.

Metaphysically Aristotelian quantification

There is a sense in Aristotelian metaphysics that "there are only substances". They are all there is a focal sense. Yet if we can talk about and quantify over accidents or modes, surely there are accidents or modes.

Here, then, is a simple quantified logic that preserves the Aristotelian intuition. This logic is developed only in the case of modes (or tropes) that are non-relational—that subsist in a single substance. The logic has the standard resources of first order sentential logic, together with the standard universal quantifier symbols ∀x and ∃x which quantify over substances x. But additionally there are two new quantifier symbols: ∀_ax and ∃_ax which quantify over a's modes x. Thus, "Some table has an accident" becomes:

1. ∃x(Table(x) and ∃_xy(Accident(y,x))).

Then we can say that only the substances exist simpliciter—only they are quantified over by the standard quantifiers Ax and Ex. Modes "exist" only relative to the substance of which they are modes—they are grounded in that substance, as is indicated in the language by the subscripted quantifiers.

We can say that the mode-quantifier ∃_ax yields existential quantification in an analogical sense. And we can spell out the analogy at least to some degree by giving rules of inference that are structurally analogous to those for the focal-sense quantifier ∃x.

Here's another application of the notion of relative existence. We might, for instance, hesitate to say that characters in novels really exist, but we might think (I am hesitant about that, too) that novels really exist. We might then think that for any novel N, there is a pair of quantifiers ∃_Nx and ∃_Nx over the entities-in-N. If S is some Star Trek novel, then when we say that ∃_Sx(Klingon(x)), we are not really saying that there really are Klingons. We are saying that virtually, in-the-novel, relative-to-the-novel there are Klingons. This is not a fact about Klingons but about the novel, and our primary ontological commitment is to the novel. Of course then our logic then needs to be suitably designed so that we cannot infer from ∃_Sx(Klingon(x)) that ∃x(Klingon(x)). This can all be done, and what I shall do below for modes can be done for characters in novels. Again, quantification over characters is quantification in an analogical sense.

The rest of this post is almost entirely technical and can be skipped.

We leave the truth-functional rules unchanged. We modify the quantificational rules as follows:

Universal elimination: From ∀xF(x) and Substance(a), you get to infer F(a). From ∀_axF(x) and Mode(d,a) you get to infer F(d).

Universal introduction: If you have a subproof assuming Substance(c) and concluding with F(c), and the subproof cites nothing involving c from outside of itself, then you get to infer ∀xF(x). If you have a subproof assuming Mode(c,a) and concluding with F(c), and the subproof cites nothing involving c from outside of itself, then you get to infer ∀_axF(x).

Existential elimination: If you have ∃xF(x) and a subproof from (F(c) and Substance(c)) to S, where the subproof cites nothing involving c from outside of itself and c does not appear in S, then you get to infer S. If you have ∃_axF(x) and a subproof from (F(c) and Mode(c,a)) to S, where the subproof cites nothing involving c from outside of itself and c does not appear in S, then you get to infer S.

Existential introduction: From Substance(a) and F(a), you get to infer ∃xF(x), and from Mode(c,a) and F(c), you get to infer ∃_axF(x).

And we add an additional equality introduction rule: If you have Mode(c,a) and Mode(c,b), then you get to infer a=b.

Models contain a substantial domain S and a function m that assigns to each member of S a set of objects, with the property m(x) and m(y) have no elements in common if x and y are distinct. We can define interpretations and satisfaction in a straightforward way, restricting the interpretations of the Substance and Mode predicates in such a way that I(Substance) is always equal to S and I(Mode) is the set of all pairs (x,y) such that x is in S and y is a member of m(x). (We don't put this rule in in the case of existence-in-a-novel.)

I haven't checked it, but I expect that we have soundness and completeness.

If, like Spinoza and unlike Aristotle, we want to allow for nested modes, this can be done, too.