Wednesday, October 7, 2015

Fundamental chaos

By fundamental chaos I mean a violation of the Principle of Sufficient Reason, a situation that occurs for no cause at all, something brute. What would we expect fundamental chaos to look like? Suppose that for no cause at all a world made of a variety of blocks came into existence. Intuitively, we'd expect it to look something like the first image.

But there is no reason why it wouldn't instead look like the second image. After all, by hypothesis, there is no reason for it to look one way than another.

One might think that because most world look messy, we would expect the brutish world to look messy. But there are two problems with this argument. The technical problem is that while in my two images, the worlds were created out of a finite variety of blocks within a finite universe, in reality there are infinitely many possible arrangements, and there are just as many neat-looking as messy-looking ones (after all, there are infinitely many worlds that look like the dragon world, differing in fine-scale details of what's inside the dragon).

But more seriously, even if there are more messy than neat worlds, it only follows that we should expect a messy world if the worlds are all equally probable. But when the worlds come about for no cause at all, in violation of the Principle of Sufficient Reason, there are no probabilities for the worlds, and so we cannot say that they are equally probable.

What this means is that the chaos hypothesis must be refuted a priori, not a posteriori. We need the Principle of Sufficient Reason.

Monday, October 5, 2015

The Principles of Indifference and Sufficient Reason

The Principle of Indifference says that we should assign equal probabilities to outcomes that are on par. Why? The thing to say is surely: "Well, there is no reason for one outcome to be more likely than another." But the equal probability of outcomes only follows from this remark if the Principle of Sufficient Reason holds so that when there is no reason for something, it doesn't happen. So it seems that the Principle of Indifference presupposes some version of the Principle of Sufficient Reason.

Personal identity, memory and fission

Suppose that (a) memory connections are constitutive of personal identity and (b) fission of memories destroys a person. If one accepts (a), then (b) is very plausible, so (a) is the crucial assumption.

Now consider this case:

  • At 4 pm, due to trauma, Sam suffers complete and irreversible amnesia with respect to events between 2 pm and 4 pm.

Then the 5 pm Sam has first-person memories of the 1 pm Sam, and it seems thus that:

  1. The 5 pm Sam is identical with the 1 pm Sam.
But the 3 pm Sam also has first-person memories of the 1 pm Sam, and by the same token:
  1. The 3 pm Sam is identical with the 1 pm Sam.
By symmetry and transitivity:
  1. The 3 pm Sam is identical with the 5 pm Sam.
There is as yet no absurdity here. There is, after all, a chain of memory connections between the 3 pm Sam and the 5 pm Sam, though the connections don't run in the same direction (3 pm Sam remembers 1 pm Sam who is remembered by 5 pm Sam). But I think there is a tension between (3) and (b), the claim about fission. For now imagine a different case:
  • At 2 pm, Sam's memories are copied into a spare brain, call it Bissam, and Bissam immediately time travels forward to 4 pm. (Forward time travel does not seem metaphysically problematic.) At 4 pm, Sam is killed.
This is clearly a case of fission, and so the 1 pm Sam no longer exists at 5 pm. But in terms of the structure of memories, this case is exactly the same as the initial amnesia case. The 5 pm Bissam remembers (or quasi-remembers, if we want to nitpick) the 1 pm Sam but not the 3 pm Sam. Likewise, in the original story, the 5 pm Sam remembers the 1 pm Sam but not the 3 pm Sam. In both stories the 3 pm Sam remembers the 1 pm Sam. So it seems that in both cases the 5 pm person and the 3 pm person are the results of the fission of the pre-2 pm person. Well, almost. Bissam exists for an instant at 2 pm while the memories are copied into him. But that isn't essential. We could imagine the copying process works such that the memories are only fully seated once Bissam arrives at 4 pm.

So the memory theorist who thinks that fission kills a person should think that total amnesia with respect to a short time period also kills one.

But if that's right, then we don't survive those nights where we do not remember our dreams upon waking up. For the dreaming person has memories (skill memories at least; but also temporarily inaccessible episodic memories) of the person who went to bed. But the waking person doesn't have memories of the dreaming person, though she does have memories of the person who went to bed. So the person who went to bed fissions into the person who dreams and the person who wakes up.

This means that the memory theorist shouldn't think that fission kills. (Another standard argument for this conclusion: If fission kills and identity is constituted by memory, then you can be killed by having your brain scanned and the data put into another brain; but you can't be killed by a process that doesn't affect your body.) But if fission doesn't kill, then it seems that the best view is that in cases of fission there have always been two persons. And that leads to various absurdities, too.

Friday, October 2, 2015

Thinking derivatively

In a lovely recent paper, Andrew Bailey has argued for the priority principle, that we think our thoughts not derivatively from another entity's thinking them--for instance, we don't think our thoughts derivatively from a brain's thinking them, or from a soul's thinking them, or a temporal part's thinking them, etc. I think this is all correct, but it seems to me that arguments of this sort don't go as far as they at first sight seem (this isn't a disagreement with anything Bailey writes).

For it has long appeared to me that the philosopher who is inclined to say that our thinking is derivative from the activity of a proper part of us should deny that the relevant activity of the proper part is thinking. Instead, there is some activity of the proper part which we might call "thinking*", and our thinking is derivative from the part's thinking*. For instance, a materialist might say that our brains think* (and analogously believe*, choose*, etc.), and that to think is to be a maximal organic whole that has a part that thinks*. This seems exactly right. For even if materialism is true, our brains don't think, but we think with our brains. And what our brains do when we think with them isn't thinking, and the materialist shouldn't say it is. (Likewise, when I nail something with a hammer, it is I who nail and not the hammer that nails. Nonetheless, the hammer does something which we can call nailing*, and I nail with a hammer if and only if I stand in the right kind of complex relationship to a hammer's nailing*.)

Once we see things this way, it unfortunately undercuts various arguments that otherwise I would be quite fond of. For instance, Trenton Merricks has a wonderfully clever argument against temporal parts on the grounds that if I have many temporal parts, then I don't know my age, since most of my present temporal parts are younger than me, and yet they think the same thoughts about age as I do. But wonderful as this argument is, and correct as its conclusion is (I don't have any proper temporal parts), the temporal part theorist should (though generally doesn't) say that my proper temporal parts have no opinions as to age, but only opinions*.

Could one strengthen Bailey's priority principle and say that my mental properties are fundamental? That's too strong. Plausibly some mental properties are not fundamental but are grounded in others. Maybe, though, we can say that some mental property is fundamental? That sounds right to me, but it's hard to argue for.

Thursday, October 1, 2015

Two ways of violating causal finitism

Causal finitism holds that the causal history of anything is finite. On purely formal grounds (and assuming the Axiom of Choice--or at least Dependent Choice), it turns out that there are exactly two ways that a world could violate causal finitism:

  1. The world contains an infinite regress.
  2. Some effect is caused by infinitely many causes.
Historically, a lot of attention has been paid to the first option, with arguments back and forth on whether this is possible. Not much attention has been paid to the second. But notice that in an infinite universe with Newtonian physics, we do have a type (2) violation of causal finitism, in that the motion of each object is instantaneously gravitationally caused by the pull of infinitely many objects. I suppose that insofar as that sort of a world seems logically possible, that's an argument against causal finitism, though not a decisive one.

But perhaps the last observation can be turned into an argument for causal finitism. For if it is possible to have infinitely many objects working together causally, it should be possible to haven an infinite Newtonian universe. But it would be strange to suppose that some but not all infinite arrangements of physical objects are compossible with the Newtonian laws. After all, we can imagine asking: "What would happen if angels shuffled stuff?" So it should be possible to suppose a universe that has nothing in the half to the left of me, but in the half of the universe to my right is an infinite number of objects arranged in a uniform density in space. If that happened, I would experience an infinite force to the right (think of the gravitational force of a solid ball of uniform density at the surface: the Newtonian law makes the force be proportional to the ball's radius as the cube-dependence of the mass beats out the inverse-square-dependence), and accelerate infinitely to the right. That's impossible.

Wednesday, September 30, 2015

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 pn 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 pn. 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).

Tuesday, September 29, 2015

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,...,An of nodes such that each node is joined with an arrow to the next: A1→A2→...→An. The sequence culminates in An. 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.

Thursday, September 24, 2015

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 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.

Wednesday, September 23, 2015

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,...,xn are F, this is because x1,...,xn 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:
  1. 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:
  1. 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:
  1. 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:
  1. 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.

Tuesday, September 22, 2015

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 thoght 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.

Monday, September 21, 2015

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.)

Friday, September 18, 2015

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.