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.