Monday, February 18, 2019

Musical beauty and virtual music

We have beautiful music at home on a hard drive. But wait: the arrangement of magnetic dipoles on a disc is not musically beautiful! So it seems inaccurate to say that there is music on the hard drive. Rather, the computer, hard drive, speakers and the orientations of magnetic dipoles jointly form a device that can produce the sound of beautiful music on demand.

One day, however, I expect many people will have direct brain-computer interfaces. When they “listen to music”, no sounds will be emitted (other than the quiet hum of computer cooling fans, say). Yet I do not think this will significantly change anything of aesthetic significance. Thus, the production of musical sounds seems accidental to the enjoyment of music. Indeed, we can imagine a world where neither composers nor performers nor audiences produce or consume any relevant sounds.

Perhaps, then, we should say that what is of aesthetic significance about my computer, with its arrangements of magnetic dipoles, is that it is a device that can produce musical experiences.

But where does the musical beauty lie? Is it that the computer (or the arrangement of magnetic dipoles on its drive) is musically beautiful? That seems wrong: it seems to be the wrong kind of thing to be musically beautiful. Is it the musical experiences that are musically beautiful? But that seems wrong, too. After all, a musical performance—of the ordinary, audible sort—can be musically beautiful, and yet it too gives rise to a musical experience, and surely we don’t want to say that there are two things that are musically beautiful there.

Perhaps a Platonic answer works well here: Maybe it is some Platonic entities that are trulymusically musically beautiful, and sometimes their beauty is experienced in and through an audible performance and sometimes directly in the brain?

Another possibility I am drawn to is that there is a property that isn’t exactly beauty, call it beauty*, which is had by the musical experiences in the mind. And it is this property that is the aesthetically valuable one.

And of course what goes for musical beauty goes for visual beauty, etc.

Friday, February 15, 2019

Natural law: Between objectivism and subjectivism

Aristotelian natural law approaches provide an attractive middle road between objectivist and subjectivist answers to various normative questions: the answers to the questions are relative to the kind of entity that they concern, but not to the particular particular entity.

For instance, a natural law approach to aesthetics would not make the claim that there is one objective beauty for humans, klingons, vulcans and angels. But it would make the absolutist claim that there is one beauty for Alice, Bob, Carl and Davita, as long as they are all humans. The natural lawyer aestheticist could take a subjectivist’s accounts of beauty in terms, of say, disinterested pleasure, but give it a species relative normative twist: the beautiful to members of kind K (say, humans or klingons) is what should give members of kind K disinterested pleasure. The human who fails to find that pleasure in a Monet painting suffers from a defect, but a klingon might suffer from a defect if she found pleasure in the Monet.

Supervenience and omniscience

Problem: It seems that if God necessarily exists, then the moral automatically supervenes on the non-moral. For, any two worlds that differ in moral facts also differ in what God believes about moral facts, and presumably belief facts are non-moral. This trivializes the mechanism of supervenience for theists.

Potential Solution: Divine simplicity makes God’s beliefs about God-external facts be externally constituted. Thus, a part of what makes it true that God believes that there are sheep are the sheep. If so, then perhaps a part of what makes it true that God believes a moral fact is that very moral fact. Thus, God’s beliefs about moral facts are partly constituted by the moral facts, and hence are not themselves non-moral.

Wednesday, February 13, 2019

Anti-reductionism and supervenience

In the philosophy of mind, those who take anti-reductionism really seriously will also reject the supervenience of the mental on the non-mental. After all, if a mental property does not reduce to the non-mental, we should be able to apply a rearrangement principle to fix the non-mental properties but change the mental one, much as one can fix the shape of an object but change its electrical charge, precisely because charge doesn’t reduce to shape or shape to charge. There might be some necessary connections, of course. Perhaps some shapes are incompatible with some charges, and perhaps similarly some mental states are incompatible with some physical arrangement. But it would be surprising, in the absence of a reduction, if fixing physical arrangement were to fix the mental state.

Yet it seems that in metaethics, even the staunchest anti-reductionists tend to want to preserve the supervenience of the normative on the non-normative. That is surprising, I think. After all, the same kind of rearrangement reasoning should apply if the normative properties do not reduce to the non-normative ones or vice versa: we should be able to fix the non-normative ones and change the normative ones at least to some degree.

Here’s something in the vicinity I’ve just been thinking about. Suppose that A-type properties supervene on B-type properties, and consider an A-type property Q. Then consider the property QB of being such that the nexus of all B-type properties is logically compatible with having Q. For any Q and B, having QB is necessary for having Q. But if Q supervenes on B-type properties, then having QB is also sufficient for having Q. Moreover, QB seems to be a B-type property in our paradigmatic cases: if B is the physical properties, then QB is a physical property, and if B is the non-normative properties, then QB is a non-normative property. (Interestingly, it is a physical or non-normative property defined in terms of mental or normative properties.)

But now isn’t it just as weird for a staunch anti-reductionist to think that there is a non-normative property that is necessary and sufficient for, say, being obligated to dance as it is for a staunch anti-reductionist to think there is a physical property that is necessary and sufficient for feeling pain?

Tuesday, February 12, 2019

Supervenience and natural law

The B-properties supervene on the A-properties provided that any two possible worlds with the same A-properties have the same B-properties.

It is a widely accepted constraint in metaethics that normative properties supervene on non-normative ones. Does natural law meet the contraint?

As I read natural law, the right action is one that goes along with the teleological properties of the will. Teleological properties, in turn, are normative in nature and (sometimes) fundamental. As far as I can see, it is possible to have zombie-like phenomena, where two substances look and behave in exactly the same way but different teleological properties. Thus, one could have animals that are physically indistinguishable from our world’s sheep, and in particularly have four legs, but, unlike the sheep, have the property of being normally six-legged. In other words, they would be all defective, in lacking two of their six legs.

This suggests that natural law theories depend on a metaphysics that rejects the supervenience of the normative. But I think that is too quick. For in an Aristotelian metaphysics, the teleological properties are not purely teleological. A sheep’s being naturally four-legged simultaneously explains the normative fact that a sheep should have four legs and the non-normative statistical fact that most sheep in fact have four legs. For the teleological structures are not just normative but also efficiently causal: they efficiently guide the embryonic development of the sheep, say.

In fact, on the Koons-Pruss reading of teleology, the teleological properties just are causal powers. The causal power to ϕ in circumtances C is teleological and dispositional: it is both a teleological directedness towards ϕing in C and a disposition to ϕ in C. And there is no metaphysical way of separating these aspects, as they are both features of the very same property.

Our naturally-six-but-actually-four-legged quasi-sheep, then, would differ from the actual world’s sheep in not having the same dispositions to develop quadrapedality. This seems to save supervenience, by exhibiting a difference in non-normative properties between the sheep and the quasi-sheep.

But I think it doesn’t actually save it. For the disposition to develop four (or six) legs is the same property as the teleological directedness to quadrapedality in sheep. And this property is a normative property, though not just normative. We might say this: The sheep and the quasi-sheep differ in a non-normative respect but they do not differ in a non-normative property. For the disposition is a normative property.

Perhaps this suggests that the natural lawyer should weaken the supervenience claim and talk of differences in features or respects rather than properties. That would allow one to save a version of supervenience. But notice that if we do that, we preserve supervenience but not the intuition behind it. For the intuition behind the supervenience of the normative on the non-normative is that the normative is explained by the non-normative. But on our Aristotelian metaphysics, it is the teleological properties that explain that actual non-normative behavior of things.

Thursday, February 7, 2019

Properties, relations and functions

Many philosophical discussions presuppose a picture of reality on which, fundamentally, there are objects which have properties and stand in relations. But if we look to how science describes the world, it might be more natural to bring (partial) functions in at the ground level.

Objects have attributes like mass, momentum, charge, DNA sequence, size and shape. These attributes associate values, like 3.4kg, 15~kg m/s north-east, 5C, TTCGAAAAG, 5m and sphericity, to the objects. The usual philosophical way of modeling such attributes is through the mechanism of determinables and determinates. Thus, an object may have the determinable property of having mass and its determinate having mass 3.4kg. We then have a metaphysical law that prohibits objects from having multiple same-level determinates of the same determinable.

A special challenge arises from the numerical or vector structure of many of the values of the attributes. I suppose what we would say is that the set of lowest-level determinates of a determinable “naturally” has the mathematical structure of a subset of a complete ordered field (i.e., of something isomorphic to the set of real numbers) or of a vector space over such a field, so that momenta can be added, masses can be multiplied, etc. There is a lot of duplication here, however: there is one addition operator on the space of lowest-level momentum determinates and another addition operator on the space of lowest-level position determinates in the Newtonian picture. Moreover, for science to work, we need to be able to combine the values of various attributes: we need to be able to divide products of masses by squares of distances to make sense of Newton’s laws of gravitation. But it doesn’t seem to make sense to divide mass properties, or their products, by distance properties, or their squares. The operations themselves would have to be modeled as higher level relations, so that momentum addition would be modeled as a ternary relation between momenta, and there would be parallel algebraic laws for momentum addition and position addition. All this can be done, one operation at a time, but it’s not very elegant.

Wouldn’t it be more elegant if instead we thought of the attributes as partial functions? Thus, mass would be a partial function from objects to the positive real numbers (using a natural unit system) and both Newtonian position and momentum will be partial functions from objects to Euclidean three-dimensional space. One doesn’t need separate operations for the addition of positions and of momenta any more. Moreover, one doesn’t need to model addition as a ternary relation but as a function of two arguments.

There is a second reason to admit functions as first-class citizens into our metaphysics, and this reason comes from intuition. Properties make intuitive sense. But I think there is something intuitively metaphysically puzzling about relations that are not merely to be analyzed into a property of a plurality (such as being arranged in a ball, or having a total mass of 5kg), but where the order of the relata matters. I think we can make sense of binary non-symmetric relations in terms of the analogy of agents and patients: x does something to y (e.g. causes it). But ternary relations that don’t reduce to a property of a plurality, but where order matters, seem puzzling. There are two main technical ways to solve this. One is to reduce such relations to properties of tuples, where tuples are special abstract objects formed from concrete objects. The other is Josh Rasmussen’s introduction of structured mereological wholes. Both are clever, but they do complicate the ontology.

But unary partial functions—i.e., unary attributes—are all we need to reduce both properties and relations of arbitrary finate arity. And unary attributes like mass and velocity make perfect intuitive sense.

First, properties can simply be reduced to partial functions to some set with only one object (say, the number “1” or the truth-value “true” or the empty partial function): the property is had by an object provided that the object is in the domain of the partial function.

Second, n-ary relations can be reduced to n-ary partial functions in exactly the same way: x1, ..., xn stand in the relation if and only if the n-tuple (x1, ..., xn) lies in the domain of the partial function.

Third, n-ary partial functions for finite n > 1 can be reduced to unary partial functions by currying. For instance, a binary partial function f can be modeled as a unary function g that assigns to each object x (or, better, each object x such that f(x, y) is defined for some y) a unary function g(x) such that (g(x))(y)=f(x, y) precisely whenever the latter is defined. Generalizing this lets one reduce n-ary partial functions to (n − 1)-ary ones, and so on down to unary ones.

There is, however, an important possible hitch. It could turn out that a property/relation ontology is more easily amenable to nominalist reduction than a function ontology. If so, then for those of us like me who are suspicious of Platonism, this could be a decisive consideration in favor of the more traditional approach.

Moreover, some people might be suspicious of the idea that purely mathematical objects, like numbers, are so intimately involved in the real world. After all, such involvement does bring up the Benacerraf problem. But maybe we should say: It solves it! What are the genuine real numbers? It's the values that charge and mass can take. And the genuine natural numbers are then the naturals amongst the genuine reals.

Friday, February 1, 2019

God, probabilities and causal propensities

Suppose a poor and good person is forced to flip a fair and indeterministic coin in circumstances where heads means utter ruin and tails means financial redemption. If either Molinism or Thomism is true, we would expect that, even without taking into account miracles:

  1. P(H)<P(T).

After all, God is good, and so he is more likely to try to get the good outcome for the person. (Of course, there are other considerations involved, so the boost in probability in favor of tails may be small.)

The Molinist can give this story. God knows how the coin would come out in various circumstances. He is more likely to ensure the occurrence of circumstances in which the subjunctive conditionals say that tails would comes up. The Thomist, on the other hand, will say that God’s primary causation determines what effect the secondary creaturely causation has, while at the same time ensuring that the secondary causation is genuinely doing its causal job.

But given (1), how can we say that the coin is fair? Here is a possibility. The probabilities in (1) take God’s dispositions into account. But we can also look simply at the causal propensities of the coin. The causal propensities of the coin are equibalanced between heads and tails. In addition to the probabilities in (1), which take everything including God into account, we can talk of coin-grounded causal chances, which are basically determined by the ratios of strength in the causal propensities. And the coin-grounded causal chances are 1/2 for heads and 1/2 for tails. But given Molinism or Thomism, these chances are not wholly determinative of the probabilities and the frequencies in repeat experiments, since the latter need to take into account the skewing due to God’s preference for the good.

So we get two sets of probabilities: The all-things-considered probabilities P that take God into account and that yield (1) and the creatures-only-considered probabilities Pc on which:

  1. Pc(H)=Pc(T)=1/2.

Here, however, is something that I think is a little troubling about both the Molinist and Thomist lines. The creatures-only-considered probabilities are obviously close to the observed frequencies. Why? I think the Molinist and Thomist have to say this: They are close because God chooses to act in such ways that the actual frequencies are approximately proportional to the strengths of causal propensities that Pc is based on. But then the frequencies of coin toss outcomes are not directly due to the causal propensities of the coin, but only because God chooses to make the frequencies match. This doesn’t seem right and is a reason why I want to adopt neither Molinism nor Thomism but a version of mere foreknowledge.