Thursday, May 25, 2017

Can destruction be good for something?

It is good for a mouse to occupy a limited region of space: if a mouse were cat-sized, it would be incapable of excellent engagement in many of its characteristic behaviors (scurrying around in narrow passages). If time is relevantly like space, we would expect that there be things for which it is good that they occupy a limited interval of time--i.e., it is good for them to die, or at least good for them to die in a particular way. (It is good for a mouse to be spatially bounded--but only certain kinds of spatial bounds, those delimited by healthy skin and fur, are good for the mouse.)

One category of things whose destruction is a part of their flourishing is things whose purpose is to give rise to something else. For instance, sperm and egg are destroyed in giving rise to a zygote, and that it is their flourishing to be destroyed in this manner. But that's not the only category. It may be a part of the flourishing of a skin cell that it perish in order to make way for a newer skin cell. Both of these categories are subsumed in the category of things directed at the good of something other than themselves.

But I think human beings are not like that.

Tuesday, May 23, 2017

Natural Law decision theory

One of the things I’ve learned from the St Petersburg Paradox and Pascal’s Wager is that we are rationally required to have attitudes to risk that significantly discount tiny chances of benefits, rather than to maximize expected utility. This requirement is rational because failure to have such attitudes to risk makes one subject to two-person diachronic Dutch Books. But it is also clearly irrational to significantly discount large chances of benefits.

But where are the lines to be drawn? Maybe it’s not worth enduring an hour of sitting on an uncomfortable chair for a 1/101000 chance of any finite length of bliss, but enduring an hour of sitting in such a chair for a 45% chance of 1000 years of bliss is worthwhile. As long as we thought the decisions were to be made on the basis of expected utility, we could have said that the lines are to be non-arbitrarily drawn by multiplying probabilities and utilities. But that fails.

It is possible, I suppose, that there is a metaphysically necessary principle of rationality that says where the line of the negligibility of chances is to be drawn. Perhaps an hour in the uncomfortable chair for a 1/101000 chance of a finite benefit cannot possibly be worthwhile, but for a 1/106 chance of a large enough finite benefit it is worth it, and there is a cut-off precisely at π ⋅ 10−9. But the existence of any such a metaphysically necessary cut-off is just as implausible as it is to think that the constants in the laws of nature are metaphysically necessary.

(Vagueness is of no help. For even if the cut-off is vague, the shape—vague or exact—of the vagueness profile of the cut-off will still look metaphysically contingent.)

One could leave it to the individual. Perhaps rationality requires each individual to have a cut-off but where the cut-off lies is up to the individual. But rationality also places constraints on that cut-off: the person who is unwilling to sit in an uncomfortable chair for an hour for a 45% chance of 1000 years of bliss is irrational. (I deliberately made it 45%. The cut-off isn’t at 1/2, which would be satisfyingly non-arbitrary.) And where the constraints on the cut-off lie is itself something to be explained, and again it is implausible that it is metaphysically necessary.

In morals, we also have similar cut-off phenomena. It is morally wrong to put someone in prison for life for stealing an ordinary book, while a week of community service is morally permissible. Whence the cut-off? The problem in both cases comes from two features of the situation:

  1. We have a parameter that seems to have a normative force independent of our minds.

  2. That parameter appears to be contingent.

Utilitarianism provides an elegant answer, but no analog of that answer seems to apply in the rationality/risk case. Kantianism is out of luck. Divine command theory provides an answer, but one whose analogue in the case of rationality is quite implausible: it is irrational to be unwilling to sit in the uncomfortable chair for the 45% chance of the great benefit, rather than forbidden by God.

Natural Law, on the other hand, provides a framework for both the moral and the rational cases by saying that the parameter necessarily comes from our nature. Our nature is independent of our minds, and hence we do justice to (1). But while it is presumably not a contingent fact that we have the nature we do, it is a contingent fact that the persons that inhabit the world have the natures they do. Humans couldn’t have these normative risk or moral parameters other than they do, but there could easily have existed non-humans somewhat similar to us who did. The explanation is parallel to the Kripkean explanation of the seeming arbitrariness of water having two hydrogen atoms. Water couldn’t have had a different number of hydrogen atoms, but something similar to water could have had.

More and more, I think something like Natural Law is a powerful framework in normative areas outside of what is normally construe to be moral theory: in decision theory and epistemology. (I hedge with the “normally construe”, because I happen to think that both decision theory and epistemology are branches of moral theory.)

Wednesday, May 17, 2017

Could God be divinity?

Here's a plausible thesis:

  1. If it is of x's essence to be F, then Fness is prior to x.
This thesis yields a fairly standard argument against the version of divine simplicity which identifies God with the property of divinity. For if God is divinity, then divinity is prior to divinity by (1), which is absurd.

But (1) is false. For, surely:

  1. It is of a property's essence to be a property.
But propertyhood is a property, so it is of propertyhood's essence to be a property, and so propertyhood is prior to propertyhood if (1) is true, which is absurd. So, given (2), we need to reject (1), and this argument against the God=divinity version of divine simplicity fails.

What else might properties do?

Suppose that we think of properties as the things that fulfill some functional roles: they are had in common by things that are alike, they correspond to fundamental predicates, etc. Then there is no reason to think that these functional roles are the only things properties do. It is prima facie compatible with fulfilling such functional roles that a property do many other things: it might occupy space, sparkle, eat or think.

Can we produce arguments that the things that fulfill the functional roles that properties are defined by cannot occupy space, sparkle, eat or think? It is difficult to do so. What is it about properties that rules out such activity?

Here's one candidate: necessity. The functional roles properties satisfy require properties to exist necessarily. But all things that occupy space are contingent. And all things that sparkle or eat also occupy space. So no property occupies space, sparkles or eats. (Yes, this has nothing to say about thinking.) Yeah, but first of all it's controversial that all properties are necessary. Many trope theorists think that typical tropes are both contingent and properties. Moreover, it may be that my thisness is a property and yet as contingent as I am. Second, it is unclear that everything that occupies space has to be contingent. One might argue as follows: surely, for any possible entity x, it could be that all space is vacant of x. But it does not follow that everything that occupies space has to be contingent. For we still have the epistemic possibility of a necessary being contingently occupying a region space. Christians, for instance, believe that the Second Person of the Trinity contingently occupied some space in the Holy Land in the first century--admittedly, did not occupy it qua God, but qua human, yet nonetheless did occupy it--and yet the standard view is that God is a necessary being. (Also, God is said to be omnipresent; but we can say that omnipresence isn't "occupation" of space, or that all-space isn't a region of space.)

So the modal argument isn't satisfactory. We still haven't ruled out a property's occupying space, sparkling or eating, much less thinking. In general, I think it's going to be really hard to find an argument to rule that out.

Here's another candidate: abstractness. Properties are abstract, and abstracta can't occupy space, sparkle, eat or think. But the difficulty is giving an account of abstracta that lets us be confident both that properties are abstract and that abstract things can't engage in such activities. That's hard. We could, for instance, define abstract things as those that do not stand in spatiotemporal relations. That would rule out occupying space, sparkling or eating--but the question whether all properties are abstracta would now be as difficult as the question whether a property can occupy space. Likewise, we could define abstract things as those that do not stand in causal relations, which would rule out sparkling, eating and thinking, but of course anybody who is open to the possibility that properties can do these activities will be open to properties standing in causal relations. Or we could define abstractness by ostension: abstract things are things like properties, propositions, numbers, etc. Now it's clear that properties are abstracta, but we are no further ahead on the occupying space, sparkling, eating or thinking front--unless perhaps we can make some kind of an inductive argument that the other kinds of abstracta can't do these things, so neither can properties. But whether propositions or numbers can do these things is, I think, just as problematic a question as whether properties can.

All in all, here's what I think: If we think of the Xs (properties, propositions, numbers, etc.) as things that fulfill some functional roles, it's going to be super-hard to rule out the possibility that some or all Xs do things other than fulfilling these functional roles.

For more related discussion, see this old contest.

Tuesday, May 16, 2017

Pascal's Wager and the bird-in-the-hand principle

My thinking about the St Petersburg Paradox has forced me to reject this Archimedean axiom (not the one in the famous representation theorem):

  1. For any finite utility U and non-zero probability ϵ > 0, there is a finite utility V such that a gamble that offers a probability ϵ of getting V is always better than a certainty of U.
Roughly speaking, one must reject (1) on pain of being subject to a two-player Dutch Book. But rejecting (1) is equivalent to affirming:
  1. There is a finite utility U and a non-zero probability ϵ > 0, such that no gamble that offers a probability ϵ of getting some finite benefit is better than certainty of U.
With some plausible additional assumptions (namely, transitivity, and that the same non-zero probability of a greater good is better than a non-zero probability of a lesser one), we get this bird-in-the-hand principle:
  1. There is a finite utility U and a non-zero probability ϵ > 0, such that for all finite utilities V, the certainty of U is better than a probability ϵ of V.
Now, Pascal's Wager, as it is frequently presented, says that:
  1. Any finite price is worth paying for any non-zero probability of any infinite payoff.
By itself, this doesn't directly violate the bird-in-the-hand principle, since in (3), I said that V was finite. But (4) is implausible given (3). Consider, for instance, this argument. By (3), there is a finite utility U and a non-zero probability ϵ > 0 such that U is better than an ϵ chance at N days of bliss for every finite N. A plausible limiting case argument suggests that then U is at least as good as an ϵ chance at an infinite number of days of bliss, contrary to (4)--moreover, then U+1 will be better than an ϵ chance at an infinite number of days of bliss. Furthermore, in light of the fact that standard representation theorem approaches to maximizing expected utility don't apply to infinite payoffs, the natural way to argue for (4) is to work with large finite payoffs and apply domination (Pascal hints at that: he gives the example of a gamble where you can gain "three lifetimes" and says that eternal life is better)--but along the way one will violate the bird-in-the-hand principle.

This doesn't, however, destroy Pascal's Wager. But it does render the situation more messy. If the probability ϵ of the truth of Christianity is too small relative to the utility U lost by becoming a Christian, then the bird-in-the-hand principle will prohibit the Pascalian gamble. But maybe one can argue that little if anything is lost by becoming a Christian even if Christianity is false--the Christian life has great internal rewards--and the evidence for Christianity makes the probability of the truth of Christianity not be so small that the bird-in-the-hand principle would apply. However, people's judgments as to what ϵ and U satisfy (2) will differ.

Pleasantly, too, the bird-in-the-hand principle gives an out from Pascal's Mugger.

Friday, May 12, 2017

More on St Petersburg

I’ve been thinking about what assumptions generate the St Petersburg paradox. As stated, the paradox depends on the assumption that we should maximize expected utility, an assumption that will be rejected by those who think risk aversion is rational.

But one can run the St Petersburg paradox without expected utility maximization, and in a context compatible with risk aversion. Suppose finite utilities can be represented by finite real numbers. Assume also:

  1. Domination: If a betting portfolio B is guaranteed to produce at least as good an outcome as A no matter what, then B is at least as good as A.

  2. Archimedeanism: For any finite utility U and non-zero probability ϵ > 0, there is a finite utility V such that a gamble that offers a probability ϵ of getting V is always better than a certainty of U.

  3. Transitivity: If C is better than B and B is at least as good as A, then C is better than A.

(Note: For theistic reasons, one might worry about Construction when the Vi are very negative, but we can restrict Construction to positive finite utilities if we add the assumption in Archimedeanism that V can always be taken to be positive.)

For, given these assumptions, one can generate a gambling scenario that has only finite utilities but that is better than the certainty of any finite utility. Proceed as follows. For each positive integer n, let Vn be any finite utility such that probability 1/2n of Vn is better than certainty of n units of utility (this uses Archimedeanism; the apparent use of the Axiom of Choice can be eliminated by using the other axioms, I think) and Vn ≥ Vn − 1 if n > 1. Toss a fair coin until you get heads. Let your payoff be Vn if it took n tosses to get to heads.

Fix any finite utility U. Let n be a positive integer such that U < n. Then the gambling scenario offers a probability of 1/2n of getting at least Vn, so by Domination, Transitivity and the choice of Vn, it is better than U.

And the paradoxes in this post apply in this case, too.

If we have expected utility maximization, we can take Vn = 2n and get the classic St Petersburg paradox.

Given the plausibility of Domination and Transitivity, and the paradoxes here, it looks like the thing to reject is Archimedeanism. And that rejection requires holding that there is a probability ϵ so small and finite utility U so large that no finite benefit with that probability can outweigh U.

Wednesday, May 10, 2017

Teleology and the direction of time

It would be depressing to think that one will never swim as fast as one is swimming today. But it would uplifting to think that that one has never swum as fast as one is swimming today.

I used to think the direction of time was defined by the predominant direction of causation. That may be the case, but if one takes humanistic cases like the above as central, one might think that perhaps the predominant direction of teleology is a better way to define the direction of time. Of course, telê are there to be achieved, and so the direction of teleology needs to fit well with the direction of causation, at least in the case of things that concern us. Moreover, there is some reason to think that teleology is behind all causation—causation aims at an effect.

Certamen machine

My kids are involved in a Classics oriented quiz game called Certamen at school. These involve teams and buttons and a machine that determines the order in which buttons were pressed. Surprisingly, these machines seem to cost a ridiculous $500 and up, despite seeming to be quite a simple thing: 12 buttons, display which order the buttons are pressed in, lock out fellow team members once one member of a team has pressed it.

So I offered my kids' school to design and build one for them as a fun summer project for me and an opportunity for my kids to learn to solder. I ordered about $60 of parts, mostly from Aliexpress, centered on an Arduino Mega (I haven't done any Arduino-based programming, but I've used the Arduino toolchain with an ESP8266 before). The parts have started to come in, including the Mega, so I've started writing some code and prototyping. According to my oscilloscope, the quick and dirty polling code I have gets a worst-case detection speed of 0.1 milliseconds, which should be good enough for a quiz game. (I continue to be grateful to the Austin guy who gave had an oscilloscope for sale for $50 on Craigslist, but when I wanted to buy it, gave it to me for free because he liked the sorts of things I was going to use it for.)

I am a bit nervous about signal problems over the three five-meter CAT6 cables (the most expensive single parts of the project) from the control box to the buttons, but I ordered some capacitors for noise suppression, and once my RJ45 jacks come in, I can do some testing.

Monday, May 8, 2017

Good-bye, (Aristotelian) matter

Of course, there are material things like oaks and people, and it’s distinct from immaterial things like angels. But for a long time I’ve been wondering why my fellow Aristotelians think that there is matter, a component of material things. In the process of reflection, I have given up on matter as a fundamental ontological category. Of course, for theological and common-sense purposes, I need to have the concept of a material substance, but here I hope there is some reduction, such as that a material substance is a substance that has at least one geometric property. My Aristotelianism now inclines to be more like Leibniz’s than like the historical Aristotle’s or Aquinas’s. Material substances, on my view, are much like Leibniz’s monads; they are like Aristotle’s gods or Aquinas’s angels, plus whatever properties or causal powers are needed for them to count as material. I am my own form, and in this form there inhere accidents.

What philosophical work does matter play, particularly in Aristotelian theories?

  1. Many Aristotelians say that something remains through substantial change, namely matter.

The persistence of matter through substantial change is said to do justice to the intuition that the corpse is the remains of the living creature: that there is something in the corpse that was in the living creature. But it is notoriously difficult to remain faithful to the Aristotelian emphasis that identity always comes from form and allow that anything in the corpse is identical to anything in the prior living body. Absent a solution to this, the Aristotelian has to say that there is one bunch of matter prior to death, a bunch of matter informed by the form of the living body, and a different bunch of matter after death, informed by the forms of the substances making up the corpse. But that does not do justice to the common-sense intuition.

In the vicinity, too, there is the question of why it is that the corpse is physically like the living body. But this is not to be accounted for by matter, but by accidents such as shape, mass and color. Accidents are possessed by substances. Either accidents can or cannot survive the destruction of their underlying substance. If they can, then we have an explanation of why the corpse is physically like the living body. If they cannot, then adding that there is matter in both—and even that it is the same matter—does not help: we simply have to bite the bullet and say that the accidents of the living body have the power to cause similar accidents in the corpse.

  1. Matter may play a role in diachronic identity.

But since immaterial substances like angels can persist over time, matter isn’t needed to solve the problem of diachronic identity. Moreover, the problem of diachronic identity seems to me, as a four-dimensionalist, to be a pseudoproblem (see also this]). It is no more a problem how the same thing can exist in 2017 and in 2018 than it is a problem how someone can exist in the room and in the hall—just put a leg in each, and you’ll see how. Matter does nothing to help with the latter problem, since presumably it isn’t the same chunk of matter that’s in the room as in the hall. So, why should matter help with the former?

  1. Matter may play a role in problems of material composition.

Matter may also play a role in some specific solutions to the problem of material composition. One might, for instance, identify the lump with the matter and the statue with the substance composed of it, or the lump with one thing made of the matter and the statue with another thing made of the same matter, and then explain away the commonality of many properties, like mass, by the identity of matter. But either the statue and the lump have numerically the same accident of mass or they do not. If they do, then since accidents inhere in substances, not in matter, the commonality of matter doesn’t do any work. If they do not, then the commonality of matter doesn’t seem to have done much—we still have to explain why the two have an exactly similar accident of mass, given that they have numerically distinct ones.

What matter does do, I think, is help differentiate the classic statue–lump case from the horse–ghost case where Bucephalus’s ghost happens to walk right through the living Seabiscuit, in such a way that the ghost horse and the living horse happen to occupy exactly the same space. For we can say that the ghost case is a case of merely spatial colocation, while the statue–lump case is a case of having the same matter. And intuitively there is a difference between the two cases. Interestingly, though, this isn’t the material composition problem that matter usually gets invoked to solve. And since I don’t believe in statues, or in any other entities that could plausibly be thought to make there be two entities of one chunk of matter, this does little for me.

  1. Isn’t hylo-morphism the distinctively Aristotelian solution to the mind-body problem?

Sure. But, even more than the classic Aristotelian solution, my view is a dissolution to the mind-body problem rather than a solution. The form of course affects the accidents that constitute and shape our embodiment. All of this is due to the nexus—ontological, teleological and causal—that exists between the substance and its accidents (both substance–accident and accident–accident). It’s not a case of one thing moving another: it is just the common story of the form affecting the accidents and the accidents affecting one another.

And, yes, of course I agree with the Council of Vienne that the soul is the form of the body. On my view, talk of the soul is talk of the substance qua form and apart from the accidents constituting its materiality, and the substance qua form is a base for all the accidents which constitute us as having bodies. So, the soul is the form of the body.

  1. Physics talks of matter.

Sure, but physics probably doesn’t have a fundamental distinction between matter and energy, I think.

Anyway, I don’t deny that there is matter in the sense of substances that are so configured as to count as material. Quite possibly, where you have a heap of sand, you have a heap of material substances, and hence matter. (But perhaps not: perhaps fundamental physical reality is just a handful of fields.)

All in all, I just see little if any benefit to matter. And there is much mystery about it. Ockham’s razor cuts it away.

Unless, of course, we come to some philosophical problem that can’t be solved without matter, or can’t be solved as well without it…

A way to argue against Strong AI

  1. Strong AIs are finite persons who are implemented by software. (Definition.)

  2. The correct theory of personal identity for Strong AIs would be a version of the psychological theory.

  3. Necessarily, the same theory of personal identity applies to all possible finite persons.

  4. We are finite persons.

  5. So, if Strong AIs are possible, a version of the psychological theory of personal identity applies to us.

  6. But the psychological theory of personal identity is false.

  7. So, Strong AIs are impossible.

Of course, the hard part is to argue for (6), since (6) is so widely accepted.

Friday, May 5, 2017

How not to defend penal substitution

Consider the standard problem for penal substitution views:
  • How is it that an innocent person's suffering harsh treatment removes the guilt of this guilty?
This is just a quick remark. Here is how not to solve the problem: Don't invoke God's sovereignty or power to claim that God can transfer guilt and punishment at will. For if God can transfer guilt and punishment at will, then God could transfer the guilt and punishment to a tree. But wouldn't it be better that a tree should be harshly punished for eternity (say, constantly have its bark ripped off as it grows back) than that Christ suffer?

Thursday, May 4, 2017


Somehow, I find writing parsers and interpreters one of the most satisfying computer programming activities I've done. I've done this a couple of times in my life, sometimes from scratch and sometimes using a tool like bison. Maybe it's because the resulting linguistic adeptness that the computer shows--even in the case of a very simple language--is somehow impressive. It's fun, for instance, to write a parser that translates a formula like "x^3*y-y^3*x" into a LISP-like representation ["-",["*",["^","x",3],"y"],["*",["^","y",3],"x"]], and that can then interpret the representation given values for x and y. Most recently, I had the fun of doing this in the OpenSCAD 3D design language, to enable passing formulas to functions/modules. This was kind of challenging for me as I'm not very comfortable with functional languages.

What Galileo should have said

The big theological problem that Galileo's opponents had for Galileo wasn't the (not very convincing) biblical arguments that the sun moves and the earth stands still, but a theological objection to Galileo's inference from (a) the greater simplicity of the Copernican hypothesis over its competitors and (b) the fact that the hypothesis fits the data to (c) the truth of the Copernican hypothesis. The theological objection, as I understand it, was that Galileo was endangering the doctrine of divine omnipotence, since if there is an omnipotent God, he can just as easily have made true one of the less simple hypotheses that fit the data. (And, indeed, an earth-centered system can be made to fit the data just as well as a sun-centered one if one has enough epicycles.)

What Galileo should have said is that his argument does not, of course, establish the Copernican hypothesis with certainty, but only as highly probable, and that his argument had the form of the well-established theological argument ex convenientia, or from fittingness: "It was fitting for God to do it, God was able to do it, so (likely) God did it." Such arguments were widely given in the Middle Ages for theological views such as the immaculate conception of Mary. The application is that it is fitting for God to do things in the more elegant Copernican fashion, an omnipotent God was able to do things in such wise, and so (likely) God did it. Not only would the argument form have been one that Galileo's interlocutors would have been familiar with and friendly towards, but Galileo would have the dialectical advantage that he could not be reasonably said to be challenging divine omnipotence if his own argument depended on it. (Maybe Galileo did say something like this. I've seen the use of the argumentum ex convenientia in astronomy attributed to Kepler. Maybe Kepler got it from Galileo.)

And, to be honest, I think that all science is essentially founded on arguments ex convenientia. Which are good arguments.

Tuesday, May 2, 2017

Grounding accidents in substances

Consider this plausible principle:

  1. x partially grounds y if and only if there are cs that fully ground y and x is one of the cs.

But now consider this plausible-sounding Aristotelian claim:

  1. The substance (or its form or its essence—the details won’t matter) partially grounds each of its accidents.

Note that the grounding here is not full. For if my substance fully grounded my accident of sleepiness, then my substance would be metaphysically sufficient for my sleepiness, and I would be always sleepy, which is fortunately not the case.

So, by 2, my sleepiness is partly grounded by my substance (i.e., me?), and merely partly. By 1, then, it follows there are other things, beside my substance, such that my sleepiness is fully grounded by my substance and those other things. What are those other things? Is it other accidents of me? If so, then the problem repeats for them. Or is it something beyond my substance or accidents? But what would that be?

I am inclined to think that the solution to this problem is to reject 1. Somehow, 1 is reminiscent to me of the false view that:

  1. x indeterministically causes y only if there are cs that deterministically cause y and x is one of the cs.

Compositional and non-compositional trope theories

There are two kinds of trope theories: Those on which the tropes are parts of the particular object—call these “compositional” trope theories—and those on which the relation between the object and its tropes is not a whole-to-part relation. Compositional trope theories have an initial advantage over non-compositional ones: they have no need to introduce a new relation to join objects to their tropes.

But this is only an apparent advantage. Consider this old argument. Assume compositional trope theory. Suppose my toe is blue. Then its blueness trope is a part of the toe, which is in turn a part of me, and so the blueness trope is a part of me. Hence I am blue.

Of course, the compositionalist has an answer to this argument: there are two different kinds of parthood here. The toe is, as the medievals would say, an integral part of me. And the blueness trope is a non-integral part of the toe. Transitivity holds for integral parts. It may or may not hold for non-integral parts, but it certainly doesn’t hold across types of parthood: if y is an integral part of x and z is a non-integral part of y, it does not follow that y is any kind of part of x.

But notice now that the compositionalist has lost the main advantage over the non-compositionalist. The compositionalist’s initial advantage was not having to introduce a new kind of relation over and beyond the familiar composition relation. But the familiar composition relation was the one between wholes and integral parts, and our compositionalist now has to introduce a new relation over and beyond that. Granted, it is a new relation of the same type as the familiar one. But this actually makes the compositionalist’s theory more complicated. For now the compositionalist has two relations, integral composition and non-integral composition, plus a new relation type, composition. But the non-compositionalist need only have two relations, integral composition and the object-to-trope relation. These two relations don’t need to have a new relation type to fall under. In other words, the non-compositionalist has only one mystery in her theory—what is the object-to-trope relation—while the compositionalist has two mysteries—what is the object-to-trope relation and what is the type composition.

The same point applies more generally to compositional ontologies versus relational ontologies.

Rapid cell replacement: A failed argument against materialism

I thought I had a nice argument against materialism, but it didn’t work out. Still, it’s fun to think about the argument and why it doesn’t work.

Start with this plausible thesis, which seems at least naturally necessary:

  1. If any cell in a human body blinks out of existence and a new cell, exactly like the one before, blinks into existence sufficiently quickly in the same orientation, then the result would not interrupt the human’s life or any train of consciousness.

Now imagine that very, very quickly one-by-one every cell in my body blinks out of existence and is replaced by a new cell formed by a coincidental quantum fluctuation. Moreover, suppose each replacement happens sufficiently quickly in the sense of (1), and indeed so quickly that all of the replacements are done in less than the blink of an eye. Applying claim (1) billions of times, I conclude that neither my existence nor my train of consciousness would be interrupted by this process.

But if materialism is true, the resulting entity would have insufficient causal connection to me to be me. Thus, if materialism is true, I would have to cease to exist as a result of these rapid replacements. But it seems this would violate (1) at some point. (Moreover, the resulting being would not be the product of natural selection, so on evolutionary functionalist theories, the being would not have mental states. Furthermore, in any case, its brain states would not have the kinds of connections with the external world that give rise to content according to the best materialist theories, so its thoughts would be largely contentless.)

But the argument I just gave doesn’t work. First, (1) is false in the case of a human zygote, since the destruction of one’s only cell would kill one. What made (1) plausible was the thought that we had many cells, and the replacement of any one of them with a randomly produced cell would make no difference. So, (1) needs to be modified to remain plausible:

  1. If any cell in a human body consisting of many cells blinks out of existence and a new cell, exactly like the one before, blinks into existence sufficiently quickly in the same orientation, then the result would not interrupt the human’s life or any train of consciousness.

But now it no longer follows that a quick cell-by-cell replacement would have to keep me alive. For here is a possible hypothesis: For a replacement cell to come to be a part of the body, it has to come to be sufficiently causally intertwined with the rest of the body. This takes some time. It could well be that if the cells are replaced one by one in less than the blink of an eye, the new cells don’t have time to become intertwined with the rest of the body. Thus, the body comes to have fewer and fewer cells as the gradual replacement process continues. If the replacement process were to stop, pretty quickly the replacement cells would come to be causally intertwined with the veteran cells, and would come to be a part of the body. But it doesn’t stop. As a result, eventually the process leads to a state where I don’t have “many” cells in my body, and hence (2) becomes inapplicable.

What if, on the other hand, the replacement is done more slowly, so that there is time for cells to causally intertwine and become a part of the body? Then there need be no problem for materialism, because now the resulting entity does have a sufficient causal connection to me to be me.

There is, of course, a vagueness problem for the materialist: When do I cease to exist in the process? But that's another argument. I think typical materialists who think that they exist cannot escape vague existence.

Monday, May 1, 2017

Desire-belief theory and soft determinism

Consider this naive argument:

  1. If the desire-belief theory of motivation is true, whenever I act, I do what I want.
  2. Sometimes in acting I do what I do not want.
  3. So the desire-belief theory is false.

Some naive arguments are nonetheless sound. (“I know I have two hands, …”) But that’s not where I want to take this line of thought, though I could try to.

I think there are two kinds of answers to this naive argument. One could simply deny (2), espousing an error theory about what happens when people say “I did A even though I didn’t want to.” But suppose we want to do justice to common sense. Then we have to accept (2). And (1) seems to be just a consequence of the desire-belief theory. So what to can one say?

Well, one can say that “what I want” is used in a different sense in (1) and (2). The most promising distinction here seems to me to be between what one wants overall and what one has a desire for. The desire-belief theorist has to affirm that if I do something, I have a desire for it. But she doesn’t have to say that I desire the thing overall. To make use of this distinction, (2) has to say that I act while doing what I do not overall want.

If this is the only helpful distinction here, then someone who does not want to embrace an error theory about (2) has to admit that sometimes we act not in accord with what we overall want. Moreover, it seems almost as much a truism as (2) that:

  1. Sometimes in acting freely I do what I do not want.

On the present distinction, this means that sometimes in acting freely, I do something that isn’t my overall desire.

But this in turn makes soft determinism problematic: for if my action is determined and isn’t what I overall desire, and desire-belief theory is correct, then it is very hard to see how the action could possibly be free.

There is a lot of argument from ignorance (the only relevant distinction seems to be…, etc.) in the above. But if it can be all cashed out, then we have a nice argument that one shouldn’t be both a desire-belief theorist or a soft-determinist. (I think one shouldn’t be either!)

Friday, April 28, 2017

Saying with possible worlds what can't be said with box and diamond

The literature contains a number of examples of a modal claim that can be made with possible worlds language but not in box-diamond language. Here is one that occurred to me that is simpler than any of the examples I’ve seen:

  • Reality could have been different.

Very simple in possible worlds language: There is a non-actual world. (Note: This doesn’t work on the version of Lewis’s modal realism that allows for duplicate worlds. All the worse for that version.) But no box-diamond statement expresses (*). One can, of course, say that there aren’t any unicorns but could be, which implies (*), but that’s not the same as saying (*).

Fun with St Petersburg

Consider any game, like St Petersburg where the expected payoff is infinite but the prizes are guaranteed to be finite. For instance, a number x is picked uniformly at random in the interval from 0 to 1 not inclusive, and your prize is 1/x.

Suppose you and I independently play this game, and we find our winnings. Now I go up to you and say: “Hey, I’ve got a deal for you: you give me your winnings plus a million dollars, and then you’ll toss a hundred coins, and if they’re all heads, you’ll get one percent of what I won.” That’s a deal you can’t rationally refuse (assuming I’m dead-set against your negotiating a better one). For the payoff for refusing is the finite winnings you have. The payoff for accepting is −1000000 + 2−100⋅0.01⋅(+∞) = +∞.


Now let’s play doubles! There are two teams: (i) I and Garibaldi, and (ii) you and Delenn. The members of each team don’t get to talk to each other during the game, but after the game each team evenly splits its winnings. This is what happens. The house calculates two payoffs using independent runs of our St Petersburg style game, w1 and w2. I am in a room with you; Garibaldi is in a room with Delenn. I and Delenn are each given w1; you and Garibaldi are each given w2. Now, by pre-arrangement with Garibaldi, I offer you the deal above: You give me a million, and then toss a hundred coins, and then you get one percent of my winnings if they’re all heads. You certainly accept. And Garibaldi offers exactly the same deal to Delenn, and she accepts. What’s the result? Well, the vast majority of the time, the Pruss and Garibaldi team ends up with all the winnings (w1 + w2 + w1 + w2 = 2w1 + 2w2), plus two million, and the you and Delenn team end up out two million. But about once in 2100 runs, the Pruss and Garibaldi team ends up with 1.99w1 + 1.99w2, plus two million, while you and Delenn end up with 0.01w1 + 0.01w2 − 2000000.

And, alas, I don’t see a way to use Causal Finitism to solve this paradox.

Thursday, April 27, 2017

Materiality and spatiality

I’ve been fond of the theory that materiality is just the occupation of space. But here is a problem for that view.

I have argued previously that we should distinguish between the internal space (or geometry) of an object and external space. Here is quartet of considerations:

  • Imagine a snake one light-year in length out in empty space arranged in a square. Then imagine that God creates a star in the middle of the square. The star instantly disturbs the geometry of space and makes the distances between parts on opposite sides of the square be different from what they previously where. But this does not make any intrinsic change to the snake until physical influence can reach the snake from the star, which will take about 1/8 of a year (the sides of the square will be 1/4 light-years, so the closest any part of the snake is to the center is 1/8 light years). The internal geometry of the snake differs from the external one.

  • We have no difficulty imagining a magical house whose inside is larger than its outside.

  • Christ in the Eucharist has very different (larger!) internal size and geometry from the external size and geometry of where he is Eucharistically located.

  • Thought experiments about time travel and the twin paradox suggest that we should distinguish internal time from external time. But space is like time.

Now, if internal and external space can come apart so much, then it is plausible that an object could have internal space or geometry in the absence of any connection to external space. Furthermore, if a material object ceased to have an occupation relation to external space but retained its internal geometry, it would surely still be material. Only a material object can be a cube. But a cubical object could remain a cube in internal geometry even after losing all relation to external space. But if so, then materiality is not the occupation of external space.

In fact, even independently of the above considerations about internal and external space, it just doesn’t seem that objects are material in virtue of a relation to something beyond them—like external space.

So, it seems, objects aren’t material in virtue of the occupation of external space. Could they be material in virtue of the occupation of internal space? Not substances! A substance does not occupy its internal space. It has that internal space, and is qualified by it, but it seems wrong to say that it is in it in the sense of occupation. (Perhaps the proper parts of material substances do occupy the substance’s internal space.) But some substances, say pigs or electrons, are material. So materiality isn’t a function of the occupation of internal space, either. And unless we find some third sort of space, we can’t say that materiality is a function of the occupation of space.

Perhaps, though, we can say this. Materiality is the possession or occupation of space. Then material substances are material by possessing internal space, and the proper parts of material substances are material by occupying the substance’s internal space. On this view, the materiality of me and my heart are analogically related—a fine Aristotelian idea.

But I have a worry. Point particles may not exist, but they seem conceivable. And they would be material. But a point particle doesn’t seem to have an internal space or geometry. I am not sure what to say. Perhaps, a point particle can be said to be material by occupying external space (in my proposed account of materiality, I didn’t specify that the space was internal). If so, then a point particle, unlike a square snake, would cease to be material if it came to be unrelated to external space. Or maybe a point particle does have an internal zero-dimensional space. It is hard to see what the spatiality of this “space” would consist in, but then we don’t have a good account of the spatiality of space anyway. (Maybe the spatiality of an internal space consists in a potentiality to be aligned with external space?) And, finally, maybe point particles that are points both externally and internally (particles that have non-trivial internal geometry but that are externally point-like aren’t a problem for the view) either aren’t material or aren’t possible.

Wednesday, April 26, 2017

Surviving furlessness and inner earlessness

If we are animals, can we survive in a disembodied state, having lost all of our bodies, retaining only soul or form?

Here is a standard thought:

  1. Metabolic processes, homeostasis, etc. are defining features of being animals.

  2. In a disembodied state, one cannot have such processes.

  3. Something that is an animal is essentially an animal.

  4. So something that is an animal cannot survive in a disembodied state.

But here’s a parody argument:

  1. Fur and mammalian inner ear bones (say) are defining features of being mammals.

  2. In a furless and internally earless state, one cannot have such structures.

  3. Something that is a mammal is essentially a mammal.

  4. So something that is a mammal cannot survive in a furless and internally earless state.

I think 5-7 are no less plausible than 1-3. But 8 is clearly false: clearly, it is metaphysically possible to become a defective mammal that is furless and internally earless.

The obvious problem with 5, or with the inferences drawn from 5, is that what is definitory of being a mammal is being such that one should to have fur and such-and-such an inner ear. The same problem afflicts 2: why not say that being such that one should have these processes and features is definitory of being a mammal.

Person is not a natural kind

  1. God is not a member of any natural kind.

  2. If person is a natural kind, then every person is a member of a natural kind.

  3. God is a person.

  4. So, person is not a natural kind.

Monday, April 24, 2017

Do God's beliefs cause their objects?

Consider this Thomistic-style doctrine:

  1. God’s believing that a contingent entity x exists is the cause of x’s existing.

Let B be God’s believing that I exist. Then, either

  1. B exists in all possible worlds


  1. B exists in all and only the worlds where I exist.

(Formally, there are other options, but they have no plausibility. For instance, it would be crazy to think B exists in some but not all the worlds where I exist, or in some but not all the worlds where I don’t exist.)

Let’s consider (3) first. This, after all, seems the more obvious option. God’s beliefs are necessarily correct, so in worlds where I don’t exist, God doesn’t believe that I exist, and hence B doesn’t exist. Then, B is a contingent being that causes my existing. Now apply the Thomistic principle to this contingent being B. It exists, so God believing that B exists is the cause of B’s existing. Let B2 be God’s believing that B exists. Since B2 causes B, B2 must be distinct from B, as causation cannot be circular. Furthermore, if (3) is the right option in respect of B and me, then an analogue for B2 and B should hold: B2 will exist in all and only the worlds where B exists. The argument repeats to generate an infinite regress of divine believings: Bn is God’s believing that Bn − 1 exists and Bn causes Bn − 1. This regress appears vicious.

So, initial appearances aside, (3) is not the way to go.

Let’s consider (2) next. Then B exists in some possible world w1 where I don’t exist. Now, at w1, God doesn’t believe that I exist, since necessarily God’s beliefs are correct. This seems to be in contradiction to the claim that B exists at w1. But it is only in contradiction if it is true at w1 that B is God’s believing that I exist. But perhaps it’s not! Perhaps (a) the believing B exists at the actual world and at w1 but with different content, or (b) B exists at w1 but isn’t a believing at w1.

Let’s think some more about (2). Let w2 be a world where only God exists (I am assuming divine simplicity; without divine simplicity, it might be that in any world where God exists, something else exists—viz., a proper part of God). Then by (2), B exists at w2. But only God exists at w2. So, God is identical to B at w2. But identity is necessary. Thus, God is actually identical to B. Moreover, what goes for B surely goes for all of God’s believings. Thus, all of God’s believings are identical with God.

It is no longer very mysterious that God’s believing that I exist is the cause of my existence. For God’s believing that I exist is identical with God, and of course God is the cause of my existence.

The difficulty, however, is with the radical content variation. The numerically same mental act B is actually a believing that I exist, while at w2 it is a believing that I don’t exist. Furthermore, if truthmaking involves entailment, we can no longer say that B truthmakes that God believes that I exist. For B can exist without God’s believing that I exist.

All this pushes back against (1). But now recall that I only called (1) a “Thomistic-style” doctrine, not a doctrine of St. Thomas. The main apparent source for the doctrine is Summa Theologica I.14.8. But notice some differences between what Aquinas says and (1).

The first is insignificant with respect to my arguments: Thomas talks of knowledge rather than belief. But (1) with knowing in place of believing is just as problematic. Obviously, it can’t be a necessary truth that God knows that I exist, since it’s not a necessary truth that I exist.

The second difference is this. In the Summa, Aquinas doesn’t seem to actually say that God’s knowledge that x exists is the cause of x’s existence. He just says that God’s knowledge is the cause of x’s existence. Perhaps, then, it is God’s knowledge in general, especially including knowledge such necessary truths as that x would have such-and-such nature, that is the cause of x’s existence. If so, then God’s knowledge would be a non-determining cause of things—for it could cause x but does not have it (and, indeed, in those worlds where x does not exist, it does not cause x). This fits well with what Aquinas says in Article 13, Reply 1: “So likewise things known by God are contingent on account of their proximate causes, while the knowledge of God, which is the first cause, is necessary.”

Maybe. I don’t know.

Thoughts on theistic Platonism

Platonists hold that properties exist independently of their instances. Heavy-weight Platonists add the further thesis that the characterization of objects is grounded in or explained by the instantiation of a property, at least in fundamental cases. Thus, a blade of grass is green because the blade of grass instantiates greenness (at least assuming greenness is one of the fundamental properties).

Heavy-weight Platonism has a significant attraction. After all, according to Platonism (and assuming greenness is a property),

  1. Necessarily (i) an object is green if and only if (ii) it instantiates greenness.

The necessary connection between (i) and (ii) shouldn’t just be a coincidence. Heavy-weight Platonism explains this connection by making (ii) explain or ground (i). Light-weight Platonism, which makes no claims about an explanatory connection between (i) and (ii), makes it seem like the connection is a coincidence.

Still, I think it’s worth thinking about some other ways one could explain the coincidence (1). There are three obvious formal options:

  1. (ii) explains (i)
  2. (i) explains (ii)
  3. Something else explains both (i) and (ii).

Option (2) is heavy-weight Platonism. But what about (2) and (3)? It’s worth noting that there are available theories of both sorts.

Here’s a base theory that can lead to any one of (2)–(4). Properties are conceptions in the mind of God. Furthermore, instantiation is divine classification: x’s instantiating a property P just is God classifying x under conception P. It is natural, given this base theory, to affirm (3): x’s instantiating greenness just is God’s classifying x under greenness, and God classifies x under greenness because x is green. Thus, x instantiates greenness because x is green.

But, interestingly, this base theory can give other explanatory directions. For instance, Thomists think that God’s knowledge is the cause of creation. This suggests a view like this: God’s classifying x under greenness (which on the base theory just is x’s instantiating greenness) causes x to be green. On this view, x is green because x instantiates greenness. If the “because” here involves grounding, and not just causation, this is heavy-weight Platonism, with a Thomistic underpinning. Either way, we get (2).

And here is a third option. God wills x to be green. God’s willing x to be green explains both x’s being green and God’s classifying x as green. The latter comes from God’s willing as an instance of what Anscombe calls intentional knowledge. This yields (4).

So, interestingly, a theistic conceptual Platonism can yield any one of the three options (2)–(4). I think the version that yields (3)—interestingly, not the Thomistic one—is the one that best fits with divine simplicity.

Thursday, April 20, 2017

Are we in a computer simulation?

Do we live in a computer simulation?

Here’s a quick and naive thought. We would expect most computer simulations to be of pretty poor quality and limited in scope. If we are in a simulation, the simulation we are in is of extremely high quality and of great scope. That’s not what we would expect on the simulation hypothesis. So, probably, we don’t live in a computer simulation.

But the following argument is pretty convincing: 1. If materialism is true, then probably a computer simulation of a brain can think (since the best materialist theory of mind is functionalism). 2. If a computer simulation of a brain can think, then most thinkers live inside computer simulations.

So, the argument that we don’t live in a computer simulation gives us evidence against materialism.


Suppose that somewhere in the galaxy there is a planet where there are large six-legged animals with an inner supportive structure, that evolved completely independently of any forms of life on earth and whose genetic structure is not based on DNA but another molecule. What I said seems perfectly possible. But it is impossible if animals are simply the members of the kingdom Animalia, since the six-legged animals on that planet are neither DNA-based nor genetically connected to the animalia on earth.

On the other hand, the supposition that somewhere (maybe in another universe) there is water that does not have H2O in it is an impossible one. So is the supposition that there are horses without DNA.

So the kind animal is disanalogous to the kinds water and horse. The kind water is properly identified with a chemical kind, H2O, and the kind horse is properly identified with a biological species, Equus ferus. But the kind animal does not seem to be properly identified with any biological kind.

One can have DNA-based animals and non-DNA-based animals. If the Venus fly-trap evolved the ability to move from place to place following its prey, it would be an animal, but still a member of Plantae. Animals are characterized largely functionally, albeit not purely functionally, but also in reference to the function of their embodiment—there cannot be any animals that are unembodied.

Is animal a genuine natural kind? Or is it a non-natural kind, constructed in the light of our species’ subjective interests? I don’t know. I take seriously, though, the possibility that there is an "Aristotelian" philosophical categorization that goes across biological categories.

Wednesday, April 19, 2017

How likely are you to be in a random finite subset of an infinite set?

Suppose that out of a set of infinitely many people, including you, a finite subset is chosen at random. How likely are you to be in that subset? Intuitively, not very likely. And the larger the infinity, the less likely.

But how do you pick out a finite subset at random? Here’s a natural way. First, pick out a subset at random, by flipping a fair coin for each person in the original set, and including a person in the subset if the comes up heads. Almost surely, this will generate an infinite subset (a consequence of the law of large numbers). But suppose this experiment is repeated—perhaps uncountably infinitely often—until the set picked out is finite. (This construction requires that the set of potential repetitions be well-ordered.) Or maybe you just get lucky, and to everybody’s surprise the set picked out is finite.

So now we have a method for picking out a finite subset at random (though it may take some luck). How likely are you to be in that finite subset?

Well, think about it step-by-step. Before you learned that the set picked out by the heads was finite, your probability that you were in the set was the probability that your coin landed heads, i.e., 1/2. Then you learn that the set of people for whom heads was rolled is finite. But this fact tells you nothing about your coin toss. For the claim that the set of people with heads is finite is logically equivalent to the claim that the set of people other than you with heads is finite. And the latter claim tells you nothing about your coin toss.

So, your probability needs to stay at 1/2.

Thus, the probability that a random finite subset of the infinitely many people includes you is finite. This is a little counterintuitive when the infinity is countable. And it becomes far more counterintuitive the larger this infinity gets. It is a stupendously implausible claim when that infinity is large, say ℶω.

Causal finitism blocks the story by making it impossible for you to find out that the set of people who got heads is finite.

Tuesday, April 18, 2017

A modified consciousness-causes-collapse interpretation of quantum mechanics

Here are two technical problems with consciousness causes collapse (ccc) interpretations of quantum mechanics. In both, suppose a quantum experiment with two possible outcomes, A and B, of equal probability 1/2.

1. The sleeping experimenter: The experimenter is dreamlessly asleep in the lab and the experiment is rigged to wake her up on measuring A by ringing a bell. If conscious observation causes collapse, then when A is measured, the experimenter is woken up, and collapse occurs. Presumably, this happens half the time. But what happens the other half the time? No conscious observation occurs, so no collapse occurs, so the system remains in a superposition of A and B states. But that means that when the experimenter naturally wakes up several hours later, and then collapse will happen. However, when collapse happens then, it has both A and B outcome options at equal chances. But that means that overall, there is a 75% chance of an A outcome, which is wrong.

2. Order of explanation: The experimenter is awake. On outcome A, a bell rings. On B, a red light goes on. In fact, A is observed. What caused the collapse? It wasn’t the observer’s hearing the bell, because the bell’s occurrence is explanatorily posterior to the collapse. But we said that it is conscious observation that causes the collapse. Which conscious observation was that, if it wasn’t the hearing of the bell? Note that the observer need not have been conscious prior to hearing the bell or seeing the light—the experiment can be rigged so that either the bell or the light wakes up the observer. Perhaps the cause of the collapse was the state of being about to hear a bell or see a red light, or maybe it was the disjunctive state of hearing a bell or seeing a red light. But the former is a strange kind of cause, and the second would be a weird case where the disjunction is prior to its true disjunct.

The first problem strikes me as more serious than the second—the second is a matter of strangeness, while the first yields incorrect predictions.

I’ve been thinking about a curious ccc interpretation that escapes both problems. On this interpretation, the universe branches like in Everett-style multiverse explanations, but a conscious observation in any branch causes collapse. Collapse is the termination of a bunch of branches, including perhaps the termination of the branch in which the collapse-causing observation occurred. The latter isn’t some sort of weird retroactive thing—it’s just that the branch terminates right after the observation.

In case 2, the universe branches into an A-universe and a B-universe (or into pluralities of universes of both sorts). In the A-universe a bell is heard by the observer. In the B-universe a red light is seen by her. When this happens, collapse occurs, and there is no future to the observer after the observation of the red light, because in fact (or so case 2 was set up) it is the observation of A that won out. Or at least this is how it is when the two observations would be simultaneous. Suppose next that the bell observation would be made slightly earlier. Then as soon as the bell observation is made, the B-branch is terminated, and the red light observation is never made. On the other hand, if the light observation is timed to come first, then as soon as the light observation is made in the B-branch, this observation terminates the B-branch, and shortly afterwards the bell is heard in the remaining branch, the A-branch.

Case 1, then, works as follows. The universe branches into an A-universe, with a bell, and a silent B-universe. As soon as the bell is heard in the A-universe, the observation causes collapse, and one of the branches is terminated. If it’s the A-branch that’s terminated, then the observer heard the bell, but the future of that observation is annihilated. Instead, a couple of hours later the observer wakes up in the B-branch, and deduces that B must have been measured. If it’s the B-branch that’s terminated, on the otehr hand, then the observer’s observing of the bell has a future.

Prior to collapse, on this interpretation, we are located in multiple branches. And then our multilocation is wholly or partly resolved by collapse in favor of location in a proper subset of the branches where we were previously located. What happened to us in the other branches really did happen to us, but we never remember it, because it’s not recorded to memory.

On this interpretation, various things are observed by us which we never remember, because they have no future. This is a bit disquieting. Suppose that instead of the red light in case 2, the experimenter is poked with a red hot poker. Then if she hears the bell ring, she is relieved to have escaped the pain. But she didn’t: for if the poking is timed at or before the ringing, then the poking really did happen to her, albeit in another branch and not recorded to memory.

Fortunately for us, the futureless unremembered bad things were very brief: they only lasted for as short a period of time as was needed to establish them as phenomenologically different from the other possible outcome. So in the poked-with-a-poker branch, one only feels the pain for the briefest moment. And that’s not a big deal.

I worry a bit about quantum Zeno issues with this interpretation.

Thursday, April 13, 2017

Lying and killing

It initially seems to be a strange combination of views that (a) killing in defense of the innocent is sometimes permissible, but (b) lying is never permissible, not even in defense of the innocent. Yet that is the predominant view in the Christian tradition. Does this mean that truth is more valuable than life? That doesn't sound right, at least not in general.

I want to try a very speculative solution to this paradox, one I don't want to fully endorse as it raises some further problems. Thomas Aquinas has an interesting position on the lethal defense of the innocent: only officers of the state are permitted to kill intentionally, while private citizens may use defensive means that they foresee could be lethal only if they don't intend death.

Why the difference? Well, here is my crazy thought: perhaps all instances of permissible intentionally lethal defense of the innocent are effectively instances of the death penalty. In emergency situations, where there is an imminent threat to innocents, the state authorizes its officers to execute aggressors on the spot, without the usual legal safeguards. Every instance of permissible killing in a just war is an execution--we just don't call it that, because the emergency context makes very different procedures appropriate. Note, further, that as we learn from John Paul II's Evangelium Vitae, the death penalty is only permissible when there are no other means to the defense of society. Thus the intentionally lethal means to the defense of the innocent can only be deployed as a last resort. That is why, say, prisoners of war are not killed--there is no longer a need for an emergency execution once they are disarmed.

Suppose that this eccentric theory of lethal police and military action is correct. Then it is easy to see why there is a distinction between intentional killing and lying. Permissible intentional killing is an act of justice, an imposition of a just penalty on an aggressor. If we add Boethian idea that it is an intrinsic benefit to one to have justice done to one, then the aggressor is directly benefited by being punished. But even without that idea, the distinction between a defensive act of justice and a merely defensive act seems significant. There is a fine Kantian thought that just punishment constitutes a showing of respect to the person being punished; but a lie is innately disrespectful to the rationality of the person lied to.

Still, the puzzle remains. Why is it that the greater harm of death is appropriate punishment while the lesser harm of being lied to is not? But not every harm is appropriate as a punishment, and sometimes a lesser harm is inappropriate as punishment while a greater is appropriate. Sometimes, this is for reasons of dignity. Thus, it is a lesser harm to lose one's arms than to lose one's life, but judicial amputation is barbaric and contrary to the dignity of the criminal (it is hard to fully explain this intuitive judgment). Sometimes, the lesser harm just wouldn't fit the crime, or maybe ven any crime. Suppose a politician misused her office. Public infamy could be fitting punishment. But while the harm to reputation is greater in public infamy than in gossip, it just wouldn't be a fitting punishment to have officers of the court gossip about the politician behind her back. In fact, being gossiped about simply doesn't seem to be the right sort of harm to be a punishment--maybe it is the essential isolation of it from the consciousness of the person being gossiped about that makes it be inappropriate. I have the intuition that being lied to is pretty much like that--it is essentially isolated from the consciousness of the person being lied to (it's not a lie if they tell you they're lying to you!), and it just doesn't seem the right kind of harm to be a punishment.

The difficulty with this account is that modeling intentionally lethal police and military action as a form of the death penalty suffers from serious problems. The main one is that we have good reason to think that many enemy soldiers, even if their side is opposed to justice, are likely to be non-culpable, because they are likely to be ignorant of the fact that their side is opposed to justice. Perhaps, though, in an emergency situation--and a war is always an emergency--the evidential standards can be much lower, and so we don't need to examine culpability. Another problem is that this account will not allow the police to engage in intentionally lethal action against a clearly insane attacker. But perhaps that's the right conclusion.

Wednesday, April 12, 2017

Types of normativity

It is widely thought that our actions are governed by at least multiple types of normativity, including the moral, the prudential and the epistemic, and that each type of normativity comes along with a store of reasons and an ought. Moreover, some actions—mental ones—can simultaneously fall under all three types of normativity.

Let’s explore this hypothesis. If we make this distinction between types of normativity, we will presumably say that morality is the realm of other-concerned reasons and prudence is the realm of self-concerned reasons. Suppose that at the cost of an hour of torture, you can save me from a minor inconvenience. Then (a) you have a moral reason to save me from the inconvenience and (b) you have a prudential reason not to save me.

It seems clear that you ought to not save me from the inconvenience. But what is this ought? It isn’t moral, since you have no moral reasons not to save me. Moreover, what explains the existence of this ought seem to be prudential reasons. So it seems to be a prudential ought.

But actually it’s not so clear that this is a prudential ought. For a further part of the explanation of why you ought not save me is that the moral reasons in favor of saving me from a minor inconvenience are so very weak. So this is an ought that is explained by the presence of prudential reasons and the weakness of the opposed moral reasons. That doesn’t sound like an ought belonging to prudential normativity. It seems to be a fourth kind of ought—an overall ought.

But perhaps moving to a fourth kind of ought was too quick. Consider that it would be wrongheaded in this case to say that you morally ought to save me, even though all the relevant moral reasons favor saving me and if these were all the reasons you had, i.e., if there were no cost to saving me from inconvenience, it would be the case that you morally ought to save me. (Or so I think. Add background assumptions about our relationship as needed to make it true if you’re not sure.) So whether you morally ought to save me depends on what non-moral reasons you have. So maybe we can say that in the original case, the ought really is a prudential ought, even though its existence depends on the weakness of the opposed moral reasons.

This, however, is probably not the way to go. For it leads to a great multiplication of types of ought. Consider a situation where you have moral and prudential reasons in favor of some action A, but epistemic reasons to the contrary. We can suppose that the situation is such that the moral reasons by themselves are insufficient to make it be the case that you ought to perform A, and the prudential reasons by themselves are insufficient, but when combined they become sufficiently strong in contrast with the epistemic reasons to generate an ought. The ought which they generate, then, is neither moral nor prudential. Unless we’ve admitted the overall ought as a fourth kind, it seems we have to say that the moral and prudential reasons generate a moral-and-prudential ought. And then we immediately get two other kinds of ought in other cases: a moral-and-epistemic ought and a prudential-and-epistemic ought. So now we have six types of ought.

And the types multiply. Suppose you learn, by consulting an expert, that an action has no cost and there are either moral or prudential considerations in favor of the action, but not both. You ought to do the action. But what kind of ought is that? It’s some kind of seventh ought, a disjunctive moral-exclusive-or-prudential kind. Furthermore, there will be graded versions. There will be a mostly-moral-but-slightly-epistemic ought, and a slighty-moral-but-mostly-epistemic ought, and so on. And what if this happens? An expert tells you, correctly or not, that she has discovered there is a fourth kind of reason, beyond the moral, prudential and epistemic, and that some action A has no cost but is overwhelmingly favored by the fourth kind of reason. If you trust the expert, you ought to perform the action. But what is the ought here? Is it "unknown type ought"?

It is not plausible to think that oughts divide in any fundamental way into all these many kinds, corresponding to different kinds of normativity.

Rather, it seems, we should just say that there is a single type of ought, an overall ought. If we still want to maintain there are different kinds of reasons, we should say that there is variation in what kinds of reasons and in what proportion explain that overall ought.

But the kinds of reasons are subject to the same line of thought. You learn that some action benefits you or a stranger, but you don’t know which. Is this a moral or a prudential reason to do the action? I suppose one could say: You have a moral reason to do the action in light of the fact that the action has a chance of benefiting you, and you have a prudential reason to do the action in light of the fact that the action has a chance of benefiting a stranger. But the reason-giving force of the fact that action benefits you or a stranger is different from the reason-giving force of the facts that it has a chance of benefiting you and a chance of benefiting the stranger.

Here’s a technical example of this. Suppose you have no evidence at all whether the action benefits you or the stranger, but it must be one or the other, to the point that no meaningful probability can be assigned to either hypothesis. (Maybe a dart is thrown at a target, and you are benefited if it hits a saturated non-measurable subset and a stranger is benefited otherwise.) That you have no meaningful probability that the action benefits you is a reason whose prudential reason-giving force is quite unclear. That you have no meaningful probability that the action benefits a stranger is a reason whose moral reason-giving force is quite unclear. But the disjunctive fact, that the action benefits you or the stranger, is a quite clear reason.

All this makes me think that reasons do not divide into discrete boxes like the moral, the prudential and the epistemic.

Tuesday, April 11, 2017

My old Right Reason posts

In case anybody is interested, I added a side-bar link to my old posts on the now-defunct Right Reason blog, from about a decade ago. I think some of the arguments I had posted there are still interesting.

GPS signals, normativity and the morality of lying

I will argue that lying is never permissible. The argument is a curious argument, maybe Kantian in flavor, which attempts to establish the conclusion without actually adverting to any explanation of what is bad about lying.

GPS satellites constantly broadcast messages that precisely specify the time at which the message is sent together with precise data as to the satellite orbit. Comparing receipt times of message from multiple GPS satellites with the positions of the satellites, a GPS receiver can calculate its position.

A part of the current design specifications of US GPS satellites is apparently that they can regionally degrade the signal in wartime in order to prevent enemies from making use of the signal (US military receivers can presumably circumvent the degradation).

Now, let’s oversimplify the situation and make up some details (the actual GPS signal specifications are here and the points I am making don’t match the actual specifications), since my point is philosophy of language, not GPS engineering. So I’m really talking about GPS satellites in another possible world.

Suppose that normally the satellite is broadcasting the time n in picoseconds up to a precision of plus or minus ten picoseconds, and suppose that currently we receive a message of n in the time field from a satellite. What does that message mean?

First of all, the message does not mean that the current time is n picoseconds. For the design specifications, I have stipulated, are that there is a precision of plus or minus ten picoseconds. Thus, what it means is something more like:

  1. The current time is n ± 10 ps, i.e., is within 10 ps of n ps.

But now suppose that it is a part of the design and operation specifications that in wartime the locally relevant satellites add a pseudorandom error of plus or minus up to a million picoseconds (remember that I’m making this up). Then what the message field means is something like:

  1. Either (a) this is a satellite that is relevant to a war region, the current time is n ± 106 ps and [extra information available to the military], or (b) the current time is n ± 10 ps.

In particular, when wartime signal degradation happens, the time field of the GPS message is (assuming the satellite is working properly) still conveying correct information—the satellite isn’t lying. For the semantic content of the time field supervenes on the norms in the design and operation specifications, and if these norms specify that wartime degradation occurs, then that possibility becomes a part of the content of the message.

Suppose lying is sometimes morally obligatory. Thus, there will be a sentence “s” and circumstances Cs in which it is both true that s and morally required to say that not s. Suppose Alice is uttering “Not s” in an assertoric way. Morality is part of Alice’s (and any other human being’s) “design and operation specifications”. Thus on the model of my analysis (2) of the semantic content of the (fictionalized) time field of the GPS message, what is being stated or asserted by Alice is not simply:

  1. Not s

but rather:

  1. Either (a) Cs obtains, or (b) not s.

But if that’s the content of Alice’s statement, then Alice is not actually lying when she says “Not s” in Cs. And the same point goes through even if Alice isn’t obligated but is merely permitted to say “Not s” in Cs. The norms in her design and operation specifications make (4) be the content of her statement rather than (3).

In other words:

  1. If lying that s is obligatory or permissible in Cs, then lying is actually impossible in Cs.

But the consequent of (5) is clearly false. Thus, the antecedent is false. And hence:

  1. Lying is never obligatory or permissible.

Note that a crucial ingredient in my GPS story is that the norms governing the degradation of GPS messages are in some way public. If these norms were secret, then the military would be making the GPS satellites do something akin to lying when they degraded their messages. But moral norms are essentially public.

Objection 1: The norms relevant to the determination of the content of a statement are not moral but linguistic norms. The moral norms require that Alice utter “Not s” in an assertoric way only when (4) obtains. But the linguistic norms require that Alice utter “Not s” in an assertoric way only when (3) obtains. And hence (3) is the content of “Not s”, not (4).

Response: This is a powerful objection. But compare the GPS case. We could try to distinguish narrowly technical norms of satellite operation from the larger norms on which GPS satellites are controlled by the US military in support of military aims. That would lead to the thought that the time field of the satellite (on my fictionalized version of the story) would mean (1). But I think it is pretty compelling that the time field of the satellite would mean (2). The meaning of the message needs to be determined according to the overall norms of design and operation, not some narrow technical subset of the specifications. Similarly, the meaning of a linguistic performance needs to be determined according to the overall norms of design and operation of the human being engaging in the performance. And it is precisely the moral norms that are such overall norms.

Second, linguistic norms are norms of voluntary behavior, since linguistic performance is a form of voluntary behavior. But a norm of voluntary behavior that conflicts with morality is null and void insofar as it conflicts, much as an illegal order is no order and an unconstitutional law is no law.

Third, on a view on which linguistic norms have the kind of independence from moral norms that the objection requires, it is difficult to specify what makes them linguistic. For we cannot simply say that they are the overall norms governing linguistic behavior. Moral norms do that, as well. A distinction like the one in the objection would make sense in the case of something where the rules are formalized. Thus, there are circumstances when the rules of chess require one to do something immoral. (For instance, suppose that a tyrant tells you she will kill an innocent unless you move a pawn forward by three squares. The rules of chess require you to refrain from doing that, but it is immoral for you to refrain from it.) But the rules of chess are simply a well-defined set of statements about what constitutes a game of chess, and it is relatively easy to tell if something is a rule of chess or not. But linguistic norms are just some among the many norms governing human behavior, and it is hard to specify which ones they are, if one can't do it by the subject matter of the norms. (I am also inclined to think that the rules of chess might not actually be norms; they are, rather, classificatory rules that specify what counts as a victory, loss, draw or forfeit; the norms governing play are moral.)

Objection 2: Content is not normatively determined.

Response: If that’s right, then my line of argument does fail. But I think a normative picture of content is the right one. In part it’s my Pittsburgh pedigree that makes me want to say that. :-)

Objection 3: Bite the bullet and say that when Alice utters “Not s”, she is in fact asserting (4) and not lying even if Cs obtains. While on this view, technically, lying is never permissible, in practice the view permits the same behaviors as a view on which lying is sometimes permissible.

Response: This just seems implausible. But I wish I had a better response.

Monday, April 10, 2017

Harmony between assertion and mind

Suppose that Gunther thinks that he believes that killing is always wrong, but in fact he believes killing is sometimes permissible. Now, Gunther asserts: “Killing is always wrong.” Is he lying?

On accounts on which to lie is to assert something that one does not believe—or maybe that one disbelieves—to be the case, Gunther has to be lying. But that seems mistaken. Lying is always a form of insincerity. But it seems that a sufficient condition for sincerity in speech is that one be trying one’s best to speak in accord with what one believes. And Gunther could well be doing that.

So maybe lying is asserting contrary to what one thinks one believes? But that seems mistaken. Someone who asserts what she knows is not lying. Suppose Agnieszka knows that caring for her friends is morally important. But her psychiatrist is incompetent and convinces her that she believes that caring for her friends is not morally important. The incompetent psychiatrist’s claims only affects Agnieszka’s second-order beliefs. So, now, Agnieszka asserts: “Caring for my friends is morally important. I wish I could get myself to believe that!” Agnieszka asserts what she knows. Hence, she isn’t lying.

Should we maybe say: To lie is to assert contrary to both what one thinks one believes and what one actually believes? But that seems really gerrymandered. And it also seems that if Agnieszka said: “Caring for my friends is not morally important”, she would be lying.

Maybe what we should do is just say that lying involves a lack of the right kind of harmony between assertion and one’s mind, and leave it as a separate task to figure out what the right kind of harmony should be? (The word “harmony” is one I’m getting from Tollefsen’s book on lying.)

Peter's denial and the ethics of lying

On views on which lying is sometimes permissible, lying to save one’s life from unjust persecution is a paradigm case of permissible lying. But Peter’s lies about his connection to Jesus—his famous three-fold denial of Jesus—fall precisely under that head. So if it is sometimes permissible to lie, it is hard to see how Peter acted wrongly.

Of course, even if lying is sometimes permissible, the purpose behind the lie can be wrong. Was that the case for Peter? I doubt it. Peter’s purpose was not to be suspected of being one of Jesus’s followers. Suppose that he chose a different means to that end, say by dressing in a non-Galilean way and affecting a non-Galilean accent. There would be nothing at all morally wrong with that—that’s presumably the sort of thing missionaries in repressive countries do all the time, without anybody (other than the repressive regime!) thinking it’s wrong.

Perhaps the difference in purpose is the one between (a) Peter not being thought to be one of Jesus’s followers and (b) Peter being thought to not be one of Jesus’s followers. Maybe if Peter affected non-Galilean dress, he would merely be intending (a), whereas his lies were done with the intention of (b). And maybe there is in general something wrong with intending to be thought not to be connected with Christ. Note first, however, that the defender of the permissibility of lying cannot say that the problem is with the intention to deceive. For paradigm cases of lies thought to be permissible are precisely ones where there is an intention to deceive (Nazi at the door cases, say). Second, apart from general worries about the permissibility of intentionally causing false belief, it does not seem plausible to think that it is always wrong to intend to be thought unconnected with Christ. Third, Peter need not have had intended (b): he might simply have intended (a) or he might have intended something in between—that the people he talked to would on balance have evidence that he is not connected to Christ. It does not seem that these subtle distinctions are in play in the Gospels, given that the texts do not tell us which thing Peter intended.

Maybe, though, one can argue that Matthew 10:33 (“If anyone denies me before human beings, I will deny him before my Father who is in heaven”) constitutes a special divine command, a sui generis prohibition on lying about one’s connection to Christ. That’s probably the best move for the defender of the permissibility of lying to make. I think there are some problems with this move.

First, we should limit the invocation of special divine commands that go over and beyond the natural law. We should do so both on the grounds of Ockham’s razor as well as on theological grounds. It seems that the crucial difference between the life of the Christian and Old Testament law is that the latter includes many divine commands that go over and beyond the natural law.

In fact, I like the hypothesis there are very few—and perhaps no—divine commands applicable to all Christians beyond the natural law. One might think that, say, the command to be baptized is such. But I am inclined to think not. There are consequences of baptism—grace and the forgiveness of sins. And there are consequences of refusal to be baptized—lack of the grace and the forgiveness of sins. The virtue of prudence requires of us to be baptized, but there need not be any separate divine command. There is, of course, the authority of the Church: we are to obey the elders. However, that is an instance of the authority a community has over its members for the common good of the community. (This community is a special supernatural one, of course.)

Second, the context of Matthew 10:33 is the persecution that the Church will endure. Thus if a new command is being promulgated, it seems likely to be directed at future times when the Church needs to be spreading the Gospel (hence the verse before, about acknowledging Christ before human beings). But Peter’s denial is not a part of that time. The Church has yet to be founded: the death and resurrection of Christ have not yet happened and the Holy Spirit has yet to be sent.

Of course, those of us who think all lying is wrong still have a puzzle. A lie in order to escape unjust persecution even if wrong seems to be a very minor wrong. But the Gospels do not present Peter’s denial as a minor wrong. So there is still the puzzle of where the gravity of Peter’s sin comes from. But here the task seems not to be so difficulty. It is reasonable to think of certain kinds of settings as greatly multiplying the gravity of an offense. To steal something worth less than a day’s wages is a venial sin according to reputable moral theologians. But to steal from a church a cheap mass-produced icon that is worth less than a day’s wages turns the theft into a sacrilege, a much more serious offense. The gravity is explained by the fact that it is a sacrilege, but the wrongness is explained by the fact that it is a theft—if the pastor gave one the icon, one could permissibly take it away and it would have been neither theft nor sacrilege. Similarly, pickpocketing in church is a more serious offense. Thus, I think we can say that Peter’s denial was wrong simply because it was a lie. But it was as wrong as it was because it was a lie about Peter’s affiliation with Jesus.

Friday, April 7, 2017

Aesthetic reasoning about necessary truths

We prefer more elegant theories to uglier ones. Why should we think this preference leads to truth?

This is a classic question in the philosophy of science. But I want to raise the question in connection with philosophical theories about fundamental metaphysics, fundamental ethics, philosophy of mathematics and other areas where our interest is necessary rather than contingent truth. Why should we think that the realm of necessity has the kind of aesthetic properties that would make more beautiful theories more likely to be true?

Here are two stories. The first story is that we are so constructed that we tend to find beauty in those philosophical theories that are true. It is difficult to explain why there would be such a coincidence if we are the product of naturalistic evolution, since it is unlikely that such a connection played a role in the survival of our species tens of thousands of years ago. If God exists, we can give an explanation: God gave us aesthetic preferences that guide us to truth.

The second story is that fundamental necessary reality is itself innately beautiful, and beautiful theories exhibit the beauty of their subject matter. And we recognize this beauty. It is puzzling, though: Why should fundamental necessary reality be beautiful? The best explanation of that which I can think of is again theistic: God is beauty itself, and all necessary truths are grounded in God.

Of course, one might simply reject the claim that our aesthetic preferences between theories lead to truth. But I think that would be the end of much of philosophy.

I think that in the order of knowing, aesthetics and ethics come first or close to first.

Thursday, April 6, 2017


Self-colocation is weird. An easy way to generate it is with time travel. You take a ghost or other aethereal object who time travels to meet his past self, and then walks into the space occupied by his past self--ghosts can walk into space occupied by themselves--so that he is exactly colocated with himself. If you don't like ghosts, time travel a photon--or any other boson--into the past and make it occupy the same place as itself. But time travel is controversial.

However, it occurs to me that one can get something a bit like self-colocation with an aethereal snake and no time travel. An aetherial snake can overlap itself. First, arrange the snake in spiral with two loops. Then gradually tighten the ring, so that the outer ring of the spiral overlaps the inner one, until the result looks like a single ring. Suppose that the snake exhibits no variation in cross-section. So we have a snake that is wound twice in the same volume of space. The whole snake occupies the same region as two proper parts of itself. [I'm not the only person in this room generating odd examples: Precisely as I write this, I hear our four-year-old remarking out of the blue that she wished she had two bodies, so she could be in two places at once. A minute or so later she is talking of twenty bodies.]

(The animation was generated with OpenSCAD using this simple code.)

So far it's not hard to describe this setup metaphysically: the whole overlaps two proper parts. But now imagine that our snake ghost is an extended simple. We can no longer say that the snake as a whole occupies the same region as a proper part of it does, as the snake no longer has any proper parts. But there seems to be a difference between the aethereal snake being wound twice around the loop and its being wound only once around it.

If we accept the possibility of aethereal objects that can self-overlap and extended simples, we need a way to describe the above situation. A nice way uses the concept of internal space and internal geometry. The snake's internal geometry does not change significantly as the spiral tightens. But the relationship between the internal space and the external space changes a lot, so that two different internal coordinates come to correspond to a each external coordinate. That's basically how my animation code works: there is an internal coordinate that ranges from 0 to 720 as one moves along the snake's centerline (backbone?), which is then converted to external xyz-coordinates. Initially, the map from the internal coordinate to the external one is one-to-one, but once things are completed, it becomes two-to-one (neglecting end effects).

The idea of internal and external space allows for many complex forms of self-intersection of extended simples. And all this is great for Aristotelians who are suspicious of parts of substances.