A virtuous evidential regress

Could this ever be the case: p₂ is evidence for p₁, p₃ is evidence for p₂, p₄ is evidence for p₃, and so on ad infinitum?

I don't think we can rule this out on epistemological grounds alone. For suppose that there are infinitely many unicorns in the universe, none of which you've observed, but there are also infinitely many experts. Expert number n happens to inform you that there are at least n unicorns in the universe. Now, let p_n be the proposition that there are at least n unicorns in the universe. Then obviously p₁ is evidence for p₂, p₃ is evidence for p₂ and so on. But there is nothing vicious about this regress. For you have independent evidence for each p_n. This is a case where although there is an infinite evidential regress, all the ultimate evidence is outside of the regress—for ultimately all the evidence about the unicorns comes from the experts.

But note that despite the fact that the ultimate evidence is all outside the regress, the evidential relations within the regress are important. For while you have some evidence for p₁ directly from the first expert, you also have some additional evidence for p₁ deriving from p₂, and hence from the second expert.

Infinite dependence regresses and set theory

Given the Axiom of Dependent Choice, the Axiom of Regularity in set theory is equivalent to the statement that there are no backwards infinite membership regresses, i.e., no cases where we have a backwards infinite sequence of sets ...,A₋₃,A₋₂,A₋₁,A_-0, where each set is a member of the next. Why think this is true? Well, intuitively, a set depends on its members. That suggests that the reason to believe the Axiom of Regularity is that there cannot be an infinite dependency regress. And that in turn has all sorts of other consequences (including that there is a first cause).

Infinite causal histories and causal loops

As I was thinking about causal finitism, the view that nothing can have an infinite causal past, I realized that there were structural similarities between the arguments for it on the basis of paradoxes like the Grim Reaper and Grandfather-like arguments against causal loops. And that led me to thinking whether there wasn't some way to generalize causal finitism so as to rule out both infinite causal pasts and causal loops.

There is. Here is one way. Say that a causal nexus is a network of nodes with partial-causation arrows between them, such that there is an arrow A→B if and only if A is a partial cause of B (or causally prior to? I think that's the same thing, but I'm not sure; or, if there is such a thing, directly causally prior to). Say that a monotonic sequence in a causal nexus is a finite sequence A₁,A₂,...,A_n of nodes such that each node is joined with an arrow to the next: A₁→A₂→...→A_n. The sequence culminates in A_n. Note that if there are causal loops, then a monotonic sequence can contain the same node multiple times.

The generalization of causal finitism now says:

• No metaphysically possible causal nexus contains a node that is the culmination of infinitely many monotonic sequences.

This rules out three kinds of causal nexuses:

1. Infinite regresses: longer and longer monotonic sequences of distinct nodes culminating in a given node.
2. Infinite cooperation: infinitely many arrows pointing to a single node (and hence infinitely many monotonic sequences of length two culminating in it).
3. Causal loops: longer and longer repeating monotonic sequences culminate in a given node (e.g., A→B, B→A→B, A→B→A→B, ...).

The possibility of handling infinite causal histories and causal loops--which I've long thought absurd--in the same framework makes me even more confident in causal finitism.

Visual programming for Minecraft

One of my hobbies is computer science education for children. Over the past year or so, I've been developing Raspberry Jam Mod (requires Forge and Minecraft 1.8), a Minecraft mod that implements the Raspberry Pi Minecraft API and allows one to write Python code that connects with Minecraft (this isn't that original: there are two other projects that do that). I taught some Python to gifted middle- and high-schoolers in the summer using this setup.

Over the last couple of days, I decided it would be nice to make something like this available for younger kids, using Google's Blockly graphical programming environment in place of Python. It's nothing very sophisticated, but you can use 3D turtle graphics commands to draw stuff in Minecraft. If interested, install Forge for Minecraft 1.8, then Raspberry Jam Mod version 0.50 or higher, start a single-user Minecraft world, and point your browser to robotblocks.appspot.com to get the Blockly code editor in-browser. The in-browser Blockly editor should then talk to your Minecraft.

Source code for the Blockly stuff is here.

An argument against heavy-weight Platonism

Heavy-weight Platonism explains (or grounds) something's being green by its instantiating greenness. Light-weight Platonism refrains form making such an explanatory claim, restricting itself to saying that something is green if and only if it instantiates greenness. Let's think about a suggestive argument against heavy-weight Platonism.

It would be ad hoc to hold the explanatory thesis for properties but not for relations. The unrestricted heavy-weight Platonist will thus hold that for all n>0:

1. For any any n-ary predicate F, if x₁,...,x_n are F, this is because x₁,...,x_n instantiate Fness.

(One might want to build in an ad hoc exception for the predicate "instantiates" to avoid regress.) But just as it was unlikely that the initial n=1 case would hold without the relation cases, i.e., the n>1 cases, so too:

2. If (1) holds for each n>0, then it also holds for n=0.

What is the n=0 case? Well, a 0-ary predicate is just a sentence, a 0-ary property is a proposition, the "-ness" operator when applied to a sentence yields the proposition expressed by the sentence, and instantiation in the 0-ary case is just truth. Thus:

3. If (1) holds for each n>0, then for any sentence s, if s, then this is because because of the truth of the proposition that s.

(The quantification is substitutional.) For any sentence s, let <s> be the proposition that s. The following is very plausible:

4. For any sentence s, if s, then <s> is true because s.

But (4) conflicts with (3) (assuming some sentence is true). In fact, to generate a problem for (3), we don't even need (4) for all s just for some, and surely the proposition <The sky is blue> is true because the sky is blue, rather than the other way around: the facts about the physical world explain the relevant truth facts about propositions. Thus:

5. It is false that (1) holds for each n>0.

The above argument is compatible, however, with a restricted heavy-weight Platonism on which sometimes instantiation facts explain the possession of attributes. Perhaps, for instance, if "is green" is a fundamental predicate, then Sam is green because Sam instantiates greenness, but this is not so for non-fundamental predicates. And maybe there are no fundamental sentences (a fundamental sentence would perhaps need to be grammatically unstructured in a language that cuts nature at the joints, and maybe a language that cuts nature at the joints will require all sentences to include predication or quantification or both, and hence not to be unstructured). If so, that would give a non-arbitrary distinction between the n>0 cases and the n=0 case. There is some independent reason, after all, to think that (1) fails for complex predicates. For instance, it doesn't seem right to say that Sam is green-and-round because he instantiates greenandroundness. Rather, Sam is green-and-round because Sam is green and Sam is round.

Change and presentism

This post is an illustration of how widely intuitions can differ. It is widely felt by presentists that presentism is needed for there to be "real change", that the B-theory is a "static" theory. But I have the intuition that presentism endangers real change. Real change requires real difference between the past states and present states, and real difference requires the reality of the differing states. But if there are no past states, there are no real differences between past and present states, and hence no change.

Of course, a presentist can say that although a past state is unreal, there can nonetheless be a real difference between it and a real present state, just as there can be a real difference between the world of Harry Potter and our world, even though the world of Harry Potter isn't real. In a sense of "real difference" that's true, I agree. But not in the relevant sense. Change is a relation between realities.

The presentist can also insist that my line of thought is simply a case of the grounding problem for presentism, and can be resolved in a similar way. Supposing a window has just changed from being whole to being broken. Then while the past unbroken state doesn't exist, there does exist a present state of the window having been whole. I am happy to grant this present state to the presentist, but it doesn't affect the argument. For the relevant difference isn't between the window having been whole and the window being broken. For if no one broke the window, there would still have been a difference between the state of the window having been whole and the window being broken. There is always a difference between a state of something having been so and a state of its being so, but this difference isn't the difference that constitutes change.

(Incredible as it may seem to the presentist, when I try to imagine the presentist's world, I imagine an evanescent instantaneous world that therefore doesn't exist long enough for any change to take place. I am well aware that this world includes states like it was the case that the window was whole, but given presentism, these states seem to me to be modal in nature, and akin to the state of it is the case in the Harry Potter universe that magic works, and hence are not appropriate to make the world non-evanescent.)

Probably the presentist's best bet is simply to deny that real difference in my sense is needed for change. All that's needed is that something wasn't so and now is so. But if something's having been not so and its being so doesn't imply a real difference, it's not change, I feel.

Of course, the presentist feels very similarly about the B-theorist's typical at-at theory of change (change is a matter of something's being one way at one time and another way at another time): she feels that what is described isn't really change.

And this, finally, gives us the real upshot of this post. There are interesting disagreements where one side's account of a phenomenon just doesn't seem to be a description of the relevant concept to the other side--it seems to be a change of topic. These disagreements are particularly difficult to make progress in. Compare how the compatibilist's account of freedom just doesn't seem to be a description of freedom to the libertarian.

I don't have a general theory on how to make progress past such disagreement. I do have one thing I do in such cases: I try to find as many things connected with the concept in other areas of philosophy, like epistemology, philosophy of science, ethics and natural theology. And then I see which account does better more generally.

Platonism and Ockham's razor

One of the main objections against Platonism is that it offends against Ockham's razor by positing a large number of fundamental entities. But the Platonist can give the following response: By positing these fundamental entities, I can reduce the number of fundamental predicates to one, namely instantiation. I don't need fundamental predicates like "... is charged" or "... loves ...". All I need is a single multigrade fundamental predicate "... instantiate(s) ...", and I can just reduce the claim that Jones is charged to the claim that Jones instantiates charge, and the Juliet loves Romeo to the claim that Julie and Romeo instantiates loving. In other words, the Platonist's offenses against Ockham's razor in respect of ontology are largely compensated for by a corresponding reduction of ideology.

Largely, but so far not entirely. For the Platonist does need to introduce the "... instantiate(s) ..." predicate which the nominalist has no need for. On pain of a Bradley-type regress, the Platonist cannot handle that predicate using her general schema.

(But maybe Platonist can go one step further. She can eliminate single quantifiers from her ideology, too, using the Fregean move of replacing, say, ∃xF(x) with Instantiates(Fness, instantiatedness). Extending this to nested quantifiers is hard, but perhaps not impossible. If that task can be completed, then it seems that our Platonist has gained a decisive advantage over the nominalist: she has only one fundamental predicate and no quantifiers other than names (if names count as quantifiers). Not so, though! For this move needs to be able to handle complex predicates F, and the property Fness corresponding to such a complex predicate will probably have to stand in various structural relations to other properties, and we have complication.)

Necessary Existence

I forgot to post an update earlier in the month that my and Josh Rasmussen's book manuscript Necessary Existence was sent off to the publisher for review. This book contains a bunch of arguments, some of them developed on this blog, others by Josh alone, some in correspondence by the two of us, all of which contend that there is at least one concrete necessary being, where an entity is concrete if and only if it is possible that it causes something.

Colors and transsubstantiation

This is going to be very speculative, and I doubt it yields an orthodox account of transsubstantiation, but since there is some chance that it does yield such an account (and if it doesn't, we might get a deeper picture of transsubstantiation by thinking about why it fails), it's worth thinking about.

Let's say, as a first approximation, that an object is white at a spacetime region U provided that the object has a direct causal power of reflecting light incident on U diffusely and approximately uniformly across the visible spectrum. Observe that in this definition nothing was said about U being a region that is occupied by the object. It is logically possible for an object to have a causal power of action at a spatial and/or temporal distance, thereby diffusely and approximately uniformly reflecting light incident on a region unoccupied by the object. Now suppose that a white piece of bread is going to be destroyed, but just before it is destroyed the causal power of whiteness that it has is enhanced to work at a temporal distance, thereby diffusely and approximately uniformly reflecting light incident on a spatial region shaped like a piece of bread in the future after the destruction of the piece of bread. Then there is a sense in which the whiteness of the piece of bread persists after the destruction of the piece of bread.

It seems there are two senses in which we can say that the whiteness of an ordinary object is at a location V. One sense is that the relevant causal power is located at V and the other sense is that the object is directly causing light to be reflected whitely at V. The location of the accident of whiteness can be identified either with the location of the causal ground of the reflection or with the location of the immediate effect of that causal ground (the second matches how Aquinas understands the locations of angels: they are deemed present where they act). Normally, the two locations coincide or are very close together. So there is a a sense in which, in the scenario where the bread has the power of causing white reflections after its destruction, the accident of whiteness exists at the location where the reflection occurs, and hence continues to exist after the destruction of the bread.

Accidents outliving their substances

Thomas Aquinas's take on transsubstantiation supposes that the accidents of bread and wine can continue existing even after the bread and wine have perished, something that was heavily criticized by people like Jan Hus.

But here is an argument for the possibility of an accident outliving its substance. Consider a very long rattlesnake, stretching out to maybe ten million kilometers in length. The rattlesnake is rattling for one second. The rattling of the tail is an accident of the rattlesnake, call this accident R. Then the snake is near-instantaneously destroyed, e.g., by a series of synchronized explosive charges.

Well, near-instantaneously in one reference frame! This snake is long enough that there will be another reference frame in which the front half is destroyed 15 seconds before the back half is. In this reference frame, there will be a time when the rattling of the tail occurs even though the front half of the snake doesn't exist. But a snake whose front half has been destroyed is no longer existing. So in this reference frame the accident R exists even though the snake no longer does.

Granted, in the case of the snake it is only true in some reference frames that the snake doesn't exist while R does, while in the Eucharist the persistence of the accidents past the demise of the bread and wine takes place in all reference frames. But once we have seen that the principle that accidents must be contemporaneous with their substance is not generally true, I think some wind is taken out of the objector's sails.

Reality of change and change of reality

B-theorists are often accused of destroying the reality of change. That's a false accusation. B-theorists may have a reductive theory of change (to change is nothing but to have a property at one time and lack it at another), but they no more deny the reality of change than people who have a reductive theory of bachelorhood (to be a bachelor is nothing but to be a never-married marriageable man) deny the reality of bachelorhood.

However, there is a charge in the vicinity that does stick. While we B-theorists believe in the reality of change, there is an important sense in which we don't believe reality changes, since what is true simpliciter is always true simpliciter. Events don't become real or cease to be real. So we can say that we believe in the reality of change but not the change of reality.

Pursuing a goal because it's good to pursue the goal

A standard case of goal-directed activity is where I pursue a goal because the goal is worth achieving either intrinsically or in light of further ends. But not all cases of goal-directed activity are like that. Imagine (there may well be something like it) a parking system for a car that uses a variety of sensors to generate on a screen an animated 2D overhead view of the car, nearby obstacles and the parking space, so that you can park the car simply by looking at the screen. After I got used to the system, instead of thinking about moving my car, I would be thinking of moving the little animated car on the screen, much as in a video game. I would thus engage in end-directed activity whose goal would be that the little animated car move into its on-screen parking spot. As a result of my engaging in this activity, the real car would move into the real parking spot. But note that the on-screen movement of the animated car isn't a means to the movement of the real car. Rather, it is my pursuit of the goal of the on-screen car moving into the on-screen spot that accomplishes the movement of the real car, and it is the movement of the real car, not the on-screen movement, that has the relevant value. Moreover, in this system I would accomplish the movement of the real car more effectively by not thinking about the real car, and only focusing my goal-directed reasoning on the on-screen car.

This is a fancy example, but whenever we use computers such things happen. For instance, when you send an email on a non-touchscreen computer, you think about how to click an on-screen "Send" button. Your means to that is to move a pointer on the screen to the button (say, with a mouse) and to click. So you have as your goal the movement of a pointer on the screen to a particular rectangular area on the screen. But in fact the movement of a pointer on the screen to a rectangular area on the screen does nothing to accomplish the sending of the email. The actual means to the sending of the email is the changing of a pair of behind-the-scenes coordinate variables to values in the intervals corresponding to the coordinates of the "Send" button, followed by the pressing of the mouse button. But you don't think about the coordinate variables. You may not even not know that that's how the system works. You think about moving the little arrow on the screen. But the little arrow is only a helpful visualization of the two coordinates. If the screen turned off, or the software stopped updating the displayed arrow, but the underlying coordinate variables continued to track the mouse position, you'd still send the email (but it would be hard to aim). In this case, people accomplish the goal of sending the email by aiming to move the on-screen arrow rather than by aiming to change the underlying coordinate variables. The pursuit of the goal of moving the arrow helps you send the email, but the fulfillment of that goal does not.

So we now have three kinds of goal-directed activity. In the first sort, the goal is pursued for its own sake. In the second, the goal is instrumentally valuable for the sake of something else. In the third, the one I want to think about, what is instrumentally valuable is not the goal that is being pursued but my pursuit of that goal. For it is the pursuit of that goal, rather than that goal itself, that promotes my further end.

The third case is actually a pretty common phenomenon. In the two cases I gave above, the way this worked was that the achievement of a goal that had no relevant instrumental or ultimate value (the movement of an animated car or a pointer) was correlated with the achievement of another goal that was valuable instrumentally or not. Another kind of case is where the the focus is not so much on the achievement on the first goal, but where the focus is on the pursuit of it. Games develop all sorts of human excellences. Some of these excellences are developed precisely through the pursuit of victory. Striving to win a race or climb to the end of a route provides one with healthy physical exercise, develops some aspects of strength of will, etc. In these cases, it isn't so much the achievement of victory that is correlated with the valuable things, as it is the striving for victory that gives rise to the valuable things.

Because of these considerations, it valuable for us to be able to set goals for ourselves, goals that are not otherwise valuable. The reasons why it is valuable that I have discussed so far are based in our cognitive and moral limitations. We can better focus on parking or clicking if we just think of moving the on-screen car or pointer. We are better motivated to exercise body or mind by pursuing victory (understood broadly to include non-competitive cases, like climbing to the end of a route or doing a jigsaw puzzle). I don't think all the goals achieved in this way, however, arise out of our limitations. For in the case of games, there are aesthetic goods that are achieved by the honorable pursuit of victory. (Note: some games have rules of honor that go beyond the rules adherence to which is logically necessary for one to count as having won rather than cheated.) The goods may be achieved whether or not one achieves victory, though they tend to be fuller when one does achieve victory. But, again, one may well be more effective--this may differ from game to game--at achieving these aesthetic goods when one's means-end reasoning isn't actually aiming at them, when one is aiming at victory (subject to side-constraints of honor, if applicable).

Are these cases an exception to the idea that we always act for the sake of the good? In one sense they're not, since one pursues the goal because pursuit of the goal is valuable in some way. But these cases seem to be an exception to the idea that when we engage in goal-directed action, the goal must be instrumentally or intrinsically valuable. Well, maybe not. Maybe the way this works is as follows. You see that it would be good for you to pursue a certain innately largely valueless goal (say, moving a pointer to a rectangle on the screen, or climbing over a sequence of holds marked with pink tape). Because it would be good to pursue the goal, you use your normative power to adopt goals, and when you use that normative power on the goal, fulfillment of it becomes valuable (it becomes, perhaps, a constitutive part of the basic human good of achievement), in something like the way that when you use your normative power to make promises, actions incompatible with what is promised become disavaluable.

Nonetheless, however, the focus with which you strive to fulfill the goal may legitimately be greater than would be explained by the good of achievement alone. For instance, suppose I need to park a car correctly in order to save a life (I am parking the dictator's car, and any scratch means death), and I have the parking system I described at the beginning of the post. To park well, I need to avoid distractions and focus on moving the little on-screen car into its on-screen parking spot. But the focus with which I should pursue this may exceed the focus that is legitimate simply for an instance of the good of achievement. I'm doing this to save a life after all, and so I should reject distractions from more minor goods which normally I should take into account. But I think when I reject distractions, I need to include among my reasons for rejecting the distractions not just the good of achievement, but the good of saving a life by parking correctly.

Aesthetics is epistemically central

Inference to best explanation is central to our epistemic lives. Aesthetic judgments about theories are central to inference to best explanation. Hence, aesthetic judgments are central to our epistemic lives. Thus we should be objectivists about at least a part of aesthetics.

No one can make you freely do a serious wrong

I've just been struck by the obviousness of this principle: It would be unjust for you to be punished for something that someone else made you do.

But it wouldn't be unjust for you to be punished for freely doing something seriously morally wrong. Hence, it is impossible for someone to make you freely do something seriously morally wrong. But if compatibilism is true, then it is possible for someone to make one freely do something seriously wrong: a powerful being could produce a state of the universe long before one's conception that determines one to do that wrong. (In principle a compatibilist could insist--as Ayer did--that it takes away one's freedom when an agent determines one to act a certain way. But this cannot be maintained. Whether I'm free shouldn't depend on ancient history.)

Educational institutions and football

In the light of the brain damage resulting from football, it is a serious question whether it's morally permissible to participate in or support the sport at all. Still, one can make a case that there are human excellences that this sport provides a particularly good opportunity for (I am grateful to Dan Johnson for this point), and the brain damage is an unintended side-effect, so there might be a defense of the sport in general on the basis of the Principle of Double Effect.

But I think it is particularly difficult to defend educational institutions supporting this sport among students. For the defining task of an educational institution is to develop the minds of the students. But brain damage harms the individual precisely in respect of mental functioning. And it is much harder for an organization to justify an activity that has among its side-effects serious harm to the goods pursuit of which defines the organization.

Randomness and compatibilism

The randomness objection to libertarian free will holds that undetermined choices will be random and hence unfree. Some randomness-based objectors to libertarianism are compatibilists who think free will is possible, but requires choices to be determined (e.g., David Hume). Others think that free will is impossible (cf. Galen Strawson). I will offer an argument against the Humeans, those who think that freedom is possible but it requires determinism for the relevant mental events. Consider three cases of ordinary human-like agents who have not suffered from brainwashing, compulsion, or the like:

1. Gottfried always acts on his strongest relevant desire when there is one. In cases of a tie between desires, he is unable to make a choice and his head literally explodes. Determinism always holds.
2. Blaise always acts on his strongest relevant desire when there is one. In cases of a tie between desires, his brain initiates a random indeterministic process to decide between the desires. Determinism holds in all other cases.
3. Carl always acts on his strongest relevant desire when there is one. In cases of a tie between two desires, his brain unconsciously calculates one more digit of π, and if it's odd the brain makes him go for the first desire (as ordered alphabetically in whatever language he is thinking in) and if it's even for the second desire (with some generalization in case of an n-way tie for n>2). Determinism always holds.

Gottfried isn't free in cases of ties between desires--he doesn't even make a choice. Our Humean must insist that Blaise isn't free, either, in those cases, because although Blaise does decide, his decision is simply random. What about Carl? Well, Carl's choices are determined, which the Humean likes. But they are nonetheless to all intents and purposes random. A central part of the intuition that Blaise isn't free has to do with Blaise having no control over which desire he acts on, since he cannot control the indeterministic process. But Carl has no control over the digits of π and these digits are, as far as we can tell, essentially random. The randomness worry that is driving the Humean's argument that freedom requires determinism is not fundamentally a worry about indeterminism. That is worth noting.

Now let's go back to Gottfried. Given compatibilism it is plausible that in normal background conditions, all of Gottfried's choices are free. (Remember that if there is a tie, he doesn't make a choice.) Suppose we grant this. Then there is a tension between this judgment and what we observed about Carl. For now consider the case of closely-balanced choices by Gottfried. Suppose, for instance, Gottfried's desire to write a letter to Princess Elizabeth has strength 0.75658 and his desire to design a better calculator has strength 0.75657. He writes a letter to Princess Elizabeth, then, and does so freely by what has been granted. But now notice that our desires always fluctuate in the light of ordinary influences, and a difference of one in the fifth significant figure in a measure of the strength of a desire will be essentially a random fluctuation. The fact that this fluctuation is determined makes no difference, as we can see when we recall the case of Carl. So if we take seriously what we learned from the case of Carl, we need to conclude that Carl isn't actually free when he chooses between writing to Princess Elizabeth and designing a better calculator, even though he satisfies standard compatibilist criteria and acts on the basis of his stronger desire.

What should the Humean do? One option is to accept that Gottfried is free in the case of close decisions, and then conclude that so are Carl and Blaise in the case of ties. I think the resulting position may not be very stable--if compatibilism requires one to think Carl and Blaise are free in the case of ties, then compatibilism is no longer very plausible.

Another option is to deny that Gottfried is free in the case of close decisions. By parallel, however, she would need to deny that we are free in the case of highly conflicted decisions, unless she could draw some line between our conflicts and Gottfried's fifth-significant-figure conflict. And that's costly.

Finally, it's worth noting that the objection, whatever it might be worth, against the incompatiblist that we shouldn't need to wait on science to see if we're free also works against our Humean.

New book started

Yesterday I started working on a new book (or possibly a very big paper, but probably a book). Title: Infinity, Causation and Paradox. Thesis: Nothing can be causally effected by infinitely many things.

Basic goods

Many Natural Law (NL) theorists center their exposition of NL around the concept of a basic good. They give lists of basic goods, such as: health, friendship, knowledge, religion, play, etc. The basic goods are incommensurable: each one provides a different aspect of fulfillment to the possessor.

An NL theorist shouldn't, however, think of the theory as depending on the concept of a basic good. For the concept is a fishy one.

The basic goods are types of goods. Types come at many levels of generality. There does not, however, appear to be a non-arbitrary level of generality at which we get the "basic goods". Let me explain.

Here is a non-arbitrary level of generality: infima species of goods, types of good that there is no way of further subdividing into further subtypes that differ qua goods. Given NL's commitments about incommensurability, one might try to characterize an infima species of good as a type of good such that (a) instances of it are all commensurable and (b) it isn't a proper subtype of another type of good with that property. The basic goods are not infima species. For instance, knowledge can be subdivided into knowledge of necessary truths and knowledge of contingent truths, and we have incommensurability between the types. Knowledge of necessary truths can then be subdivided into mathematical knowledge and non-mathematical knowledge, and again there is incommensurability there. I suspect the infima species are going to be extremely specific, e.g., Smith's intellectual friendship with Kowalska focusing on fundamental political philosophy (and it will probably be more specific than that) or Jones's knowledge of Pythagoras' Theorem on the basis of proof P₁₇ (again, further specificity may be called for).

Here is another non-arbitrary level of generality: the highest genera. There might be just one highest genus, good. Or perhaps the highest genera are good of God and good of a creature. Or perhaps there is an infinite list of highest general but they are all instances of the schema good of N where N is a type of entity.

But the basic goods are neither infima species nor highest genera. They fall at some level of generality in between. And there seems to me to be no non-arbitrary way to delineate them. The best approach might be this: the basic goods (for humans) are the highest genera that fall properly under good of a human. (So if the good of a human is a highest genus, then the basic goods are second-highest genera.) But I doubt that there is a non-arbitrary way to define the highest genera under good of a human. There are many ways of subdividing good of a human, and the traditional subdivisions into basic goods are just one of them. For instance, one might subdivide good of a human into good of a human not in relation to other persons and good of a human in relation to God and good of a human in relation to non-divine persons (and maybe one or more hybrid categories). Or one might subdivide it into intellectual good and non-intellectual good. Etc.

Another option: an epistemic distinction. Perhaps the basic goods are the finest partition of the goods into genera with the property that one cannot fully grasp the distinctive value of any of the goods in any one genus on the basis of a grasp of the values of all the goods in the others. But I suspect that a distinction like this, if it can be made at all, would be liable to point to what is in at least some ways a finer level. Can one really grasp the distinctive value of aesthetic knowledge or friendship with Mother Teresa on the basis of other goods? Moreover, it may be that to grasp friendship one needs to grasp at least one other basic good, since friends promote each other's good not just in respect of friendship.

Fortunately, while the notion of incommensurable goods is important to NL, I do not think the NL theorist really needs a non-arbitrary concept of a basic good. The lists of basic goods are useful as heuristics, and they are a pedagogically valuable way to illustrate incommensurability. Moreover, it may be practically useful for guiding one's decisions and self-examination to have a division of goods that is sufficiently thick but not too fine-grained.

Justified belief and conditional evidence

Plausibly, a belief that p is justified only if one has good evidence that p. But what about a case where instead of having evidence for a belief, one has evidence that if one believes it, then it's be true? (I'll call this the Belief Conditional.) For instance, tonight Sam will decide whether to watch Battlestar Galactica or Deep Space Nine. But Sam hates being shown to be wrong. So if she now comes to believe that she will watch, say, DS9, then come evening she will watch, say, DS9 in order to make her earlier belief true. She knows all this. She also hates suspending judgment. So she makes herself believe that she will watch DS9. (She's not deciding what she is to watch. The decision will come tonight.) Once she realizes that she has succeeding in coming to the belief that she will watch DS9, she has evidence that she will watch DS9. But we may suppose that there is a short period of time during which Sam hasn't yet realized that she believes she will watch DS9. During that short period of time, she doesn't have evidence that she will watch it. Instead, she just knows the conditional that if she believes she will watch it, she will watch it. I am inclined to think that Sam's belief that she will watch DS9 is reasonable and justified.

But I am not happy to extend this to a general claim that having justification for a Belief Conditional suffices for justification of unconditional belief. Here's a case that worries me. Suppose that having read a lot of papers defending an error theory about folk psychology, and generally hanging about in unfortunate philosophical company, Fred is in possession of strong evidence that nobody believes anything. But despite the evidence, ingrained habits make Fred continue to believe that someone believes something. (I take it for granted that the error theory is mistaken.) Of course, Fred does know the obvious necessary truth that if he believes that someone believes something, then someone believes something. But nonetheless given the evidence against folk psychology, I am inclined to think that Fred isn't justified in believing that somebody believes something.

I don't know how to distinguish the cases of Sam and Fred. I feel pulled to assimilate one to the other, but I don't know which I should assimilate to which.

Against per se ordered infinite sequences of causes

Say that a sequence of events is per se causally ordered provided that each event not only causes the next but also causes everything in the next that is involved in causing the one after that (if there is one after that).

1. Any possible chunk of contingent reality is such that it is possible for something internally just like it to have a cause.
2. It is not possible to have a cause for an infinite per se causal regress of contingent causes.
3. Anything internally just like an infinite per se causal regress of contingent causes is an infinite per se causal regress of contingent causes.
4. So an infinite per se causal regress of contingent causes is impossible.

In the argument, (1) is a weak causal principle. The reason for the "something internally just like" phrase is that without the phrase the premise would immediately imply that every possible chunk of contingent reality has a cause given essentiality of origins. Premise (3) requires a non-Humean account of causation. I am going to ignore metaphysical questions about chunks of reality: perhaps we can reformulate in terms of pluralities, perhaps in terms of sets.

A crucial controversial premise is (2). Here's an intuitive line of thought that inclines me to (2). Suppose we have a backwards-infinite per se causal sequence of chickens and eggs, each chicken fully deterministically causing an egg with all of its relevant causal power, and each egg deterministically causing a chicken with all of its relevant causal power. And imagine this regress has a cause, say, G. How can G cause that whole sequence? Well, it couldn't do it by causing one particular chicken or one particular egg, for that wouldn't account for the chickens and eggs that came before that. The only picture I get of how something could cause the whole sequence would be if it caused each one of the eggs and chickens, or each one prior to some point in time, or more generally some backwards-infinite subsequence. The argument will be the same in each of the three cases, so I will just focus on the simplest.

So the cause G caused each of the eggs and chickens, and thereby caused the sequence. But of course each egg is caused by a chicken, too. So a given egg has two causes: it is caused by a chicken and by G. But the chicken caused the egg fully, with everything the egg needed to do its job of causing the next thing. So what did G contribute? Nothing really crucial to the sequence, since everything crucial to it was contributed by the chicken. Rather, it looks like it's going to be a case of overdetermination. The egg is caused by G and it's caused by the chicken. But G's causing of the regress as a whole isn't overdetermined (or so we may surely assume, modulo some technicalities), since in the absence of G the whole sequence wouldn't be caused. And if you take away a non-overdetermining cause, the effect disappears. So if you took away G, the whole regress should disappear. But why should taking away G matter, given that all of the causal influences by which G allegedly causes the regress are individually overdetermined?

If this is all right, then the critical attention will shift to (1).

Thomson's lamp and two counterfactauls

Thomson's lamp toggles each time you press the button and nothing else affects its state. The lamp is on at noon, and then a supertask consisting of infinitely many button presses that completes by 1 pm, and the question is whether the light is on or off at 1 pm. There is no contradiction yet. But now add these two claims:

1. The state of the lamp at 1 pm would not be affected by shifting the times at which the button presses happen, if (a) all the button presses happen between noon and 1 pm, and (b) we ensure that no two button presses happen simultaneously.
2. If we removed one button press from the sequence of button presses between noon and 1 pm, the state of the lamp at 1 pm would not change.

Given this intuition, we do have a problem. Suppose that our sequence of supertask button presses occurs at 12:30, 12:45, 12:52.5, and so on. Then shift this sequence of button presses forward in time, so that now the sequence is at 12:45, 12:52.5, 12:45.25,and so on. By (1) this wouldn't affect the outcome, but by (2) it would as we will have gotten rid of the first button press. That's a contradiction.

So if we think Thomson's lamp is possible--which I do not--we need to deny at least one of the two counterfactuals. I think the best move would be simply to deny both (1) and (2), on the grounds that the connection between the state of the lamp at 1 pm and the button presses must be indeterministic.

From a past-infinite causal sequence to a paradoxical lottery: A cosmological argument

Infinite fair lotteries are well-known to be paradoxical. Let's say that an infinite fair lottery is played twice with tickets 1,2,3,.... Then whatever number wins first, you can be all but perhaps certain that in the next run of the lottery a bigger number will win (since the probability of any particular number winning is zero or infinitesimal, so the probability that the winner is a member of the finite set of numbers smaller than or equal to the first picked number is zero or infinitesimal). So as you keep on playing, you can be completely confident that the next number picked will be bigger than the one you just picked. But intuitively that's not what's going to happen. Or consider this neat paradox. Given the infinite fair lottery, there is a way to change the lottery that makes each ticket infinitely more likely to win. Just run a lottery where the probability of ticket n is 2^-n (which is infinitely bigger than the zero or infinitesimal probability in the paradoxical lottery)

What makes the infinite fair lottery paradoxical is that

1. there is a countable infinity of tickets

and

2. each ticket has zero or infinitesimal chance of winning.

Let's stipulate that a lottery is "paradoxical" if and only if it satisfies (1) and (2).

Suppose now that a past-infinite causal sequence is possible (e.g., my being caused by my parents, their being caused by theirs, and so on ad infinitum). Then the following past-infinite causal sequence is surely possible as well. There is a machine that has always been on an infinite line with positions marked with integers: ...,-3,-2,-1,0,1,2,3,.... Each day, the machine has tossed a fair coin. If the coin was heads, it moved one position to the right on the line (e.g., from 2 to 3) and if it was tails, one position to the left (e.g., from 0 to -1). The machine moved in no other way.

We can think of today's position of the machine as picking out a ticket from a countably infinite lottery. Moreover, this countably infinite lottery is paradoxical. It satisfies (1) by stipulation. And it's not hard to argue that it satisfies (2), because of how random walks thin out probability distributions. (And all we need is finite additivity for the argument.)

So if past-infinite causal sequences are possible, paradoxical lotteries are as well. But paradoxical lotteries are not possible, I say. So past-infinite causal sequences are not possible. So there is an uncaused cause.

Culpably mistaken conscience

It is plausible that we have duties of conscience arising from inculpable mistakes about what we should do. I shall assume this and argue that culpable mistakes also yield duties of conscience.

Here are two cases.

1. Fred hires a neurologist to brainwash him into a state which will make him think the next day that it is his duty to embezzle money from his employer. The neurologist succeeds. The next day Fred conscientiously believes he has a duty to embezzle money from his employer. But he refrains from doing so out of fear of being caught.
2. Sally hires a neurologist to brainwash her into which will make him think the next day that it is her duty to embezzle money from her employer. The neurologist fails. But that night, completely coincidentally, a rogue neurologist breaks into her home and while she's sleeping successfully brainwashes her into that very state the first neurologist failed to brainwash her into. The next day Sally conscientiously believes she has a duty to embezzle money from her employer. But she refrains from doing so out of fear of being caught. There are no further relevant differences between Sally's case and Fred's.

Fred is responsible for his conscience being mistaken. Sally is not responsible for that. Granted, Sally is culpable for trying to make her conscience be mistaken, but she is no more responsible for the mistaken conscience than the attempted murderer is responsible when her intended victim is coincidentally killed by someone else.

If inculpably mistaken conscience gives rise to duties, Sally has a duty of conscience to embezzle, and she fails in her duty. She thus acted immorally on both days: on the first day she acted immorally by asking to be brainwashed and on the second day she acted immorally by refusing to obey her conscience.

Thus:

3. If culpably mistaken conscience does not give rise to duties, then Fred has not violated a duty of conscience by refraining from embezzling, while Sally has.

If culpably mistaken conscience does not give rise to duties, then Sally is in a morally worse state than Fred, being guilty of two things while Fred is only guilty of one.

But on the other hand, Fred and Sally have made all the same relevant decisions in the same subjective states. The only possibly relevant difference is entirely outside of them--namely, whether the neurologist that they actually hired is in fact the neurologist who brainwashed them. But the whole point of the idea of duties of conscience is to honor the subjective component in duty, and so if Fred and Sally's relevant decisions are all relevantly alike, Fred and Sally will also be alike in whether they've violated a duty of conscience. Hence:

4. If Sally has violated a duty of conscience by refraining from embezzling, so has Fred.

It logically follows from (3) and (4) that:

5. Culpably mistaken conscience gives rise to duties.

Of course all of this argument was predicated on the assumption that inculpably mistaken conscience gives rise to duties, and perhaps a reader may want to now revisit that assumption. But I think the assumption is true, leaving us with the conclusion that mistaken conscience gives rise to duties whether or not the mistake is culpable.

Now let's turn the case about. Suppose that both Fred and Sally follow their respective mistaken consciences and therefore embezzle. What should we say? Should we say that they did nothing wrong? It seems we shouldn't say that they did nothing wrong, for if they did nothing wrong then their consciences weren't mistaken, which they were. So let's accept (though I have a long-shot idea that I've talked about elsewhere that might get out of this) that they both did wrong. Thus, as in Mark Murphy's account of conscience, they were in the unhappy position that whatever they did would be wrong: by embezzling they defraud their employer and by not embezzling they violate their conscience.

But what about their culpability? Since Sally's case is one of inculpable ignorance, we have to say that Sally is not culpable for the embezzlement. Let's further suppose Sally and Fred's reasons for having themselves brainwashed were to get themselves to embezzle. Thus Sally is guilty of entering on a course of action intended to lead to embezzlement--basically, attempted embezzlement. But she's not guilty of embezzlement. What about Fred? He is certainly responsible for the embezzlement: it was intentionally caused by his immoral action of hiring the neurologist. But I am inclined to think that this is an effect-responsibility ("liability" is a good word) rather than action-culpability. Fred is responsible for the embezzlement in the way that one is responsible for the intended effects of one's culpable actions, in this case the action of hiring a brainwasher, but he isn't culpable for it in the central sense of culpability. (Compare: Suppose that instead of hiring a neurologist to brainwash himself, he hired the second brainwasher in Sally's case. Then Fred wouldn't be action-culpable for Sally's embezzlement, since one is only action-culpable for what one does, but only responsible for her embezzlement as an intended effect of his action.) Sally lacks that responsibility for the effect--the embezzlement--because her plan to get herself to embezzle the money failed as the embezzlement was caused by the rogue neurologist.

In terms of moral culpability for their actions, in the modified case where they conscientiously embezzle, Fred and Sally are, I think, exactly on par. Each is morally culpable precisely for hiring the neurologist, and that's all. That may seem like it gets them off the hook too easily, but it does not: they did something very bad in hiring the brainwasher. So, if I'm right, they are on par if they both conscientiously embezzle and they are on par if they both violate their consciences by refusing to embezzle.