Monday, August 30, 2021

Divine simplicity and responsibility for creation

Libertarians believes something like this:

  1. If an agent has primary responsibility for a state of affairs A, then the agent gained that resposibility by intentionally indeterministically causing A.

Here, primary responsibility is distinguished from the kind of derivative responsibility that someone who freely got drunk (and hence has primary responsibility for getting drunk) has for the accident caused while drunk.

Next, add this plausible thesis:

  1. If an agent gains primary responsibility for a state of affairs A by intentionally causing A, then the agent has primary responsibility for an intention relevantly connected to A.

Now, combine (1) and (2). Suppose Alice has primary responsibility for A. Then she had an intention I = I1 relevantly connected to A that she had primary responsibility for. Applying (1) and (2) to I1, we conclude that Alice had primary responsibility for an intention I2 relevantly connected to I, and primary responsibility for an intention I3 relevantly connected to I2, and so on, ad infinitum.

But of course we don’t have an infinite chain of intentions. So we must break out of the chain. I think there is only one way to do so: at some point, In = In + 1. In other words, the intention relevantly connected to In just is In once again: there is no further intention. Rather, one’s intention to produce In is just constituted by In.

This means that it is possible for one to be primarily responsible for a state of affairs A—say an intention In—when the intention with which one caused A is itself at least partly constituted by A.

Now, I take it that something like this is what happens when a simple God creates something: God’s intention to create horses is partly constituted by horses, rather than simply by some inner state of God’s.

There is a lesson here: The primary worry that one has about a simple God’s contingently creating things—namely, that a simple God cannot have contingent inner states—is mirrored by a parallel worry about a libertarian agent’s production of intentions.

Absence of evidence

It seems that the aphorism “Absence of evidence is not evidence of absence” is typically false.

For if H is a hypothesis and E is the claim that there is evidence for H, then E raises the probability of H: P(H|E)>P(H). But then (as long as P(E)>0, as Bayesian regularity will insist), it mathematically follows that P(∼H|∼E)>P(∼H). Thus the absence of evidence is evidence for the falsity (“absence”) of the hypothesis.

I think there is only one place where one can challenge this argument, namely the claim:

  1. If there is evidence for H, then the fact that there is evidence for H is itself evidence for H.

First, let’s figure out what (1) is saying. I think the best reading is that it presupposes some kind of notion of a body of first-order evidence—maybe all the stuff that human beings have ever observed—and says that if the actual contents of that body of first-order evidence supports H, then the fact that that body supports H itself supports H.

Here is a way to make this precise. We suppose there is some random variable O whose value (not real valued, of course) is all first-order observations humans ever made. Let W be the set of all possible values that O could take on. For simplicity, we can take W to be finite: there is a maximum number of observations a human can make in a lifespan, a finite resolution to each observation, and a maximum number of human beings who could have lived on earth. Let o0 be the actual value that O has. Let WH = {o ∈ W : P(H|O = o)>P(H)}.

Assuming we have Bayesian regularity, we can suppose O = o has non-zero probability for each o ∈ WH. Then the claim that there is evidence for H is itself evidence for H comes to this:

  1. P(H|O ∈ WH)>P(H).

And it is easy to check that this follows by finite conglomerability from the fact that P(H|O = o)>P(H) for each o ∈ WH.

There might be cases where we expect infinite conglomerability to be lacking. In those cases (1) would be dubious. Here is one such case. Suppose Alice and Bob each get a ticket from a fair infinite jar with tickets numbered 1,2,3,…. Alice looks at her ticket. Bob doesn’t look at his yet, but knows that Alice has looked at hers. Bob notes that whatever number Alice has seen, it is nearly certain that his number is bigger (there are infinitely many numbers bigger than Alice’s number and only finitely many smaller ones). Thus, Bob knows that the evidence available to humans supports the thesis that his number is bigger than Alice’s. But Bob’s knowing this is not actually evidence that his number is bigger than Alice’s, for until Bob actually observes one or the other number, he is in the same evidential position as before Alice looked at her ticket—and at that point, it is obvious that it’s not more likely that Bob’s ticket has a bigger number than Alice’s.

But apart from weird cases where conglomerability fails, (1) is true, and so absence of evidence is evidence of absence, assuming we have enough Bayesian regularity.

Perhaps a charitable reading of the aphorism that absence of evidence isn’t evidence of absence is just that absence of evidence isn’t always significant evidence of absence. That seems generally correct.

A tension in some of my recent work

Here is a tension in some recent work of mine. In Chapter 6 of Infinity, Causation, and Paradox, I argue that (a) the Axiom of Choice for countable sets of reals (ACCR) is true, and (b) this version of the Axiom of Choice plus causal infinitism implies a nasty paradox, so we should accept causal finitism instead. The argument for ACCR makes use of the premise that mathematical entities exist necessarily. But in “Might All Infinities Be The Same Size?”, I argue that for all we know, some mathematical entities exist contingently. Thus, the latter paper undercuts the argument of Chapter 6 of the book.

Fortunately, the argument of Chapter 6 of the book looks like it might be fixable. The argument for ACCR proceeded as follows:

  1. For any set of non-empty countable sets of reals, it is metaphysically possible that there is a choice function.

  2. If possibly there is a choice function, then necessarily there is a choice function.

The argument for (1) is elaborate, but it is (2) that the considerations in my article block.

But we can try to proceed as follows. The paradox in Chapter 6 of the book requires a choice function for a particular collection of non-empty countable sets of reals (reals generatable by a certain infinitary coin-tossing process). By (1), there is a possible world w′ where that particular collection of sets does have a choice function. So it seems all we need to do is to run the paradox in w′, and we should be done.

There are probably other areas in Chapter 6 where some tweaking (or more than that!) is needed to make things work with mathematical contingentism, and hence my cautious wording.

Friday, August 27, 2021

A superpower

Imagine Alice claimed she could just see, with reliability, which unprovable large cardinal axioms are true. We would be initially sceptical of her claims, but we could imagine ways in which we could come to be convinced of her having such an ability. For instance, we might later be able to prove a lot of logical connections between these axioms (say that axiom A12 implies axiom A14) and then find that Alice’s oracular pronouncements matched these logical connections (she wouldn’t, for instance, affirm A12 while denying A14) to a degree that would be very hard to explain as just luck.

Suppose, then, that we have come to be convinced that Alice has the intuitive ability to just see which large cardinal axioms are true. This would be some sort of uncanny superpower. The existence of such a superpower would sit poorly with naturalism. An intuition like Ramanujan’s about the sums of series could be explained by naturalism—we could simply suppose that his brain unconsciously sketched proofs of various claims. But an intuition about large cardinal axioms wouldn’t be like that, since these axioms are not provable.

Now as far as we know, there is no one exactly like Alice who just has reliable intuitions about large cardinal axioms. But our confidence in the less abstruse axioms of Zermelo-Fraenkel set theory—intuitive axioms like the axiom of replacement—commits us to thinking that either we in general, or those most expert in the matter, are rather like Alice with respect to these less abstruse axioms. The less abstruse axioms are just as unprovable as the more abstruse ones that Alice could see. Therefore, it seems, if Alice’s reliable intuition provided an argument against naturalism, our own (or our experts’) intuition about the more ordinary axioms, an intuition which we take to be reliable, gives us an argument against naturalism. Seeing the axiom of replacement to be true is just as much a superpower as would be Alice’s seeing that, say, measurable cardinals exist (or that they do not exist).

Thursday, August 26, 2021

Counting good and bad things

People sometimes wonder, perhaps in connection with the problem of evil, whether there is in total more good than evil in the world. The connection with the problem of evil is somewhat tenuous, of course. Even if it were agreed there is more good than evil, it could still be argued that there is gratuitous evil, inconsistent with the existence of God. And even if there is a God, there could presently be more evil than good, if, say, the evil is justified in connection with future good.

All that said, here is a question related to the question whether there is more good than evil:

  • Are there more good things than bad things in the world?

I will argue that on two different takes on “things”, there are vastly more good things than bad—or even bad or neutral—things in the world as we know it. Even if we can generalize from the world as we know it, this still does not show that there is more good than evil: perhaps there are more goods, but the bad things are so very bad that the total evil is greater than the total good. Nonetheless, I think the answer has evidential bearing on the existence of God, because it would intuitively be at least a little bit more likely for there to be vastly more good things than bad or neutral things in the observed part of the world if God existed than if God didn’t exist.

On to the argument. On a first take, “things” are substances. Now, I think the best story about substance is a neo-Aristotelian one on which in the part of the world we collectively know, the substances are the organisms and the fundamental physical entities.

Now, our three best theories as to what the fundamental physical entities are is that they are:

  1. particles,

  2. global entities like fields and the wavefunction of the universe, or

  3. particles and global entities.

Suppose that the correct answer is (a) or (c). Then in the known universe, the vast majority of substances are particles. There may be a lot of organisms in the world, but there are way more particles. And the number of global entities, like fields and the wavefunction, on our best theories is in the single digits. But every particle is good: it perfectly fulfills its nature, which is to dance its dance according to the beautiful mathematical laws of the universe. So, on (a) and (c), the vast majority of substances are good. (Maybe good in a very minor way.)

Suppose that the correct answer is (b). Then the substances of the known universe consist of organisms and probably a handful of global entities like fields or the wavefunction. The organisms outnumber the global entities so much that we can neglect the global entities and, besides, the global entities are good, for the same reason the particles are. Among the known organisms there are some that are bad. The clearest cases are a sizeable proportion of humans.

Whether there are any bad non-human organisms on earth (essentialy the only place we know of with organisms) depends on whether we count instrumental value. For if we limit ourselves to intrinsic badness, plausibly all organisms that aren’t persons are good (and there are many good persons), and non-personal organisms vastly outnumber personal ones. If badness (and goodness), however, includes instrumental assessment, then there are bad organisms. But how many? There may be some species most of whose members are bad: perhaps some mosquito species are like that. But it seems very plausible that such species form a very small portion of the whole, and that the vast majority of species are such that the vast majority of their members are good. (Quick thought experiment: Suppose by pressing a button you could wipe out a randomly chosen non-human species? Surely it would be a very, very bad idea to press the button.) So, it seems quite plausible that the vast majority of organisms are good.

On a second take, “things” include events in addition to substances. Well, now, the vast majority of events in the known universe seem to be purely physical events that are neither good nor bad for living things, and they do no harm to non-living things either. But they are an intrinsically good part of the dance of nature according to beautiful mathematical laws. So, it seems, the vast majority of events is good.

Wednesday, August 25, 2021

Analog photography

For over a decade, all my photography has been digital, but this spring I finally pulled out the 1939 Voigtlaender Vito 35mm camera I inherited from my grandfather, checked with an oscilloscope (photo-detector on one side, flashlight on the other) that the shutter timer was still correct, loaded it up with 100 ISO black and white film, and took a bunch of pictures around Waco over several months. 

I had the pictures developed and scanned by OneStopDeveloping on Etsy.

Last years, Waco installed a bunch of animal-themed sculptures near the zoo. Though one of the pictures is of real animals.


"Despite" explanations

The phenomenon of contrastive explanations has been explored by a number of authors. There is another phenomenon in the vicinity, that of explanations of despite-claims, that has not received as much attention, even though it’s also interesting. Suppose Bob hates bananas and eats a banana.

  1. Why did Bob eat a banana? – Because he was hungry.

  2. Why did Bob eat a banana despite hating bananas? – Because he was very hungry.

A contrastive request for explanation, say

  1. Why did Bob eat a banana rather than an apple?

doesn’t so much ask for an explanation of a special contrastive proposition, but rather constrains what kind of answer is acceptable—an answer that provides a contrastive answer. Thus, saying that Bob was hungry is not an acceptable answer since it fails to be contrastive between the banana and apple options, while saying that Bob was hungry and a banana was closer at hand is an acceptable answer. However, whenever one constrains what kind of an explanation is acceptable, one runs the risk that—even without any violation of the Principle of Sufficient Reason—there is no answer. For instance, the question

  1. Who killed the mayor and why?

is a request for explanation that has no answer if the mayor died from a tornado, because (4) constrains us to agentive explanation, and in this case there is no agentive explanation.

Are requests for explanations-despite like requests for contrastive or agentive explanations, requests that constrain the type of explanation that is acceptable, rather than simply modifying the proposition to be explained?

I am inclined to think that the answer is negative. Here is a preliminary analysis for what is going on when we ask:

  1. Why p despite r?

First, the question carries a presupposition that the fact that r is antiexplanatory of p or that it has a tendency against p. If that presupposition is false, the question has no answer, being akin to one of the standard trick questions with false presuppositions (like “Have you stopped beating your spouse?”).

Second, what we are asking is something like this:

  1. How was the antiexplanatory force of the fact that r against its being the case that p countered such that p is true?

And this seems to be a straightforward request for an explanation of an admittedly complex proposition, without any constraints being placed on what explanations are acceptable.

If I am right about this, then while a failure to have a good answer to contrastive explanation question does no damage to the Principle of Sufficient Reason (PSR), a failure to have a good answer to an explanation-despite question, when the presuppositions of the question are correct, would be a violation of the Principle. This suggests that some of the attention focused on contrastive explanation in connection with critique of the PSR should be redirected towards explanation-despite. I think the PSR can survive such attention, but the investigation is worthwhile.

Tuesday, August 24, 2021

Theism and abundant theories of properties

On abundant theories of properties (whether Platonic universals or tropes), for every predicate, or at least every predicate satisfied by something, there is a corresponding property expressed by the predicate.

Here is a plausible sounding argument:

  1. The predicate “is morally evil” is satisfied by someone.

  2. So, on an abundant theory of properties, there exists a property of being morally evil.

  3. The property of being morally bad, if it exists, is thoroughly evil.

  4. So, on an abundant theory of properties, there exists something that is thoroughly evil.

  5. If theism is true, nothing that exists is thoroughly evil (since every entity is the perfect God or created by the perfect God).

  6. So if theism is true, an abundant theory of properties is false.

If I accepted an abundant theory of properties, I would question (3). For instance, maybe properties are concepts in the mind of God. A concept of something morally evil is not itself an evil concept.

Still, it does seem to me that this argument provides a theist with a little bit of a reason to be suspicious of abundant theories of properties.

An argument for nominalism

Assume theism. Then, there is nothing in existence that is intrinsically bad. For everything that exists is either God or created by God, and neither God nor anything created by God is intrinsically bad.

On radical nominalism, all that exist are substances: there are no relations, properties, tropes, accidents, essences, etc. And it is very plausible that no substance is intrinsically bad. The most plausible candidates for intrinsically bad things are non-substances, like properties (being in pain) or relations (being mistaken about something). Thus, radical nominalism has a neat and elegant way of preserving the theistic commitment to there not being anything in existence that is intrinsically bad.

This seems to me to be a significant advantage of radical nominalism over other theories.

Of course, this is not a decisive argument for radical nominalism: there are other ways of preserving the commitment to there not existing intrinsically bad entities, such as Augustine’s privation theory.

Monday, August 23, 2021

Anecdotal reasoning

Suppose I see a hypothetical click-bait article that says: “One thing you can do that science says doubles your chance of living past a hundred.” I foolishly click on it, and from the first paragraph find out that supposedly that thing is a serious photography hobby. Now, the idea isn’t crazy: having a serious hobby that can be pursued over a lifetime and that involves artistic and intellectual skills could well increase your lifespan. But I am reasonably sceptical.

Suppose for simplicity that after reading the first paragraph, I assign a credence of 1/2 to the null hypothesis N that there is no correlation between photography and living to a hundred and a credence of 1/2 to the hypothesis H that serious photography doubles the chance of living past 100.

Suppose I now tell my mother about the article, and she says: “Your great-grandma Alice was an avid photographer and she lived past 100!”

This is paradigmatically anecdotal evidence. But let’s do a quick and dirty Bayesian analysis. I just learned the fact E1 at least one of my eight great-grandparents was both a serious photographer and lived past 100. Let’s say for simplicity that each of my great-grandparents was born more than 100 years ago and had a 1% chance of living past 100 (some actual data is here), and that 15% of people are serious photographers. Then the conditional probability of my evidence E1 on the null hypothesis N is 1 − (1 − 0.01 ⋅ 0.15)8 or 1%, but on the doubling-chance hypothesis H it is 1 − (1 − 2 ⋅ 0.01 ⋅ 0.15)8 or 2.4%. Plugging these into Bayes’ theorem, I get a 67% posterior probability of H, and now I have a significant degree of credence in a photography-centenarianism link.

But suppose that instead of talking to my mother, I read further on in the article, and find after reading whatever scientific study spawned the article, the author found and interviewed a centenarian Bob who has been an avid photographer for half his life. What does that piece of anecdotal data do to my credence in the link between photography and a long life? Nothing! To a first approximation, the relevant fact I learned from the interview is the fact E2 that there exists at least one person in the world who was an avid photographer and lived past 100. And the conditional probability of E2 is very close to 1 on both H and N, so by Bayes’ theorem it doesn’t change my credences in H and N. (To a second approximation, I learned that the there was one person accessible to the author who was an avid photographer and lived past 100. And that is presumably slightly more likely on H and N. So I should get a slight boost in H, but only a slight one, since in the modern world we have access to lots of people.)

Now consider an intermediate case. Instead of talking to relatives, I share the article with a hundred people, and one of them writes back: “Wow! My tennis partner’s great-uncle Carl was an avid photographer and lived past 100.” Let’s over simplify by supposing that each of my hundred correspondents read the article and on average contributes ten people born more than 100 years ago to the sample. So from the first response, I have learned the fact E3 that in this sample of 500, there is at least one person who is a centenarian and a serious photographer. The probability of this on H is 95% and on N it is 78%. Plugging these into Bayes’ theorem, my credence in the photography-centenarianism link is 55%, which is a rather modest boost over my initial 50%. (The crucial point was that in the initial grandparents sample, the probability on H was double than on N, but now as both probabilities approach 100%, the ratio gets less impressive.)

There are some lessons here: If we are careful with our reasoning, anecdotal data can actually be quite relevant. Moreover, while it’s presumably been ingrained in us since high school science classes that larger sample sizes are better, for certain kinds of anecdotal data, smaller sample sizes are better. This is because the relevant information given by certain kinds of anecdotal data is positive: it is information that some sample contains at least one instance of some sort that is rare on both the null hypothesis and the alternate hypothesis (say, a photographer centenarian). In those cases, once the sample size gets large enough, the probability of the evidence on either hypothesis gets close to 1, and the evidential force disappears.

What this means is that for certain kinds of anecdotal data it makes perfect sense to be more impressed by an anecdote about oneself (a sample of one) than by an anecdote about a relative, and by an anecdote about a relative than by an anecdote about a friend’s friend, and to be essentially unmoved by an anecdote about a stranger on the Internet. And that is, I suspect, how most people actually proceed, notwithstanding blanket condemnations of anecdotal reasoning.

How can we do even better? Well, we should try to enrich our positive anecdotal data with other kinds of anecdotal data: Did I have centenarian relatives who weren’t photographers or photographer relatives who weren’t centenarians? All that would ideally be taken into account. But, nonetheless, if all I have is one positive anecdote, Bayesianism requires me not to dismiss it.

Thursday, August 19, 2021

A philosophical advantage of quantum mechanics over Newtonian mechanics

We often talk as if quantum mechanics were philosophically much more puzzling than classical mechanics. But there is also a deep philosophical puzzle about Newtonian mechanics as originally formulated—the puzzle of velocities—which disappears on quantum mechanics.

The puzzle of velocities is this. To give a causal explanation of a Newtonian system’s behavior, we have to give the initial conditions for that system. These initial conditions have to include the positions and velocities (or momenta) of all the bodies in the system.

To see why this is puzzling, let’s imagine that t0 is the first moment of the universe’s existence. Then the conditions at t0 explain how things are at all times t > t0. But how can there be velocities at t0? A velocity is a rate of change of position over time. But if t0 is the first moment of the universe’s existence, there were no earlier positions. Granted, there are later positions. But these later positions, given Newtonian dynamics, depend on the velocities at t0 and hence cannot help determine what these velocities are.

One might try to solve this by saying that Newtonian dynamics implies that there cannot be a first moment of physical reality, that physical reality has to have always existed or that it exists on an interval of times open at the lower end. On either option, then, Newtonian dynamics would have to be committed to an infinite temporal regress, and that seems implausible.

Another solution would be to make velocities (or, more elegantly, momenta) equally primitive with positions (indeed, some mathematical formulations will do that). On this view, that the velocity is the rate of change of position would no longer be a definition but a law of nature. This increases the number of laws of nature and the fundamental properties of things. And if it is a mere law of nature that velocity is the rate of change of position, then it would be metaphysically possible, by a miracle, that an object standing perfectly still for days would nonetheless have a high velocity. If that seems wrong, we could just introduce a technical term, say “movement propensity” (that’s kind of what “momentum” is), in place of “velocity”, and it would sound better. However, anyway, while the resulting theory would be mathematically equivalent to Newton’s, and it would solve the velocity problem, it would be a metaphysically different theory, since it would have different fundamental properties.

On the other hand, the whole problem is absent in quantum mechanics. The Schroedinger equation determines the values of the wavefunction at times later than t0 simply on the basis of the values of the wavefunction at t0. Granted, the cost is that we have a wavefunction instead of just positions. And in a way it is really a variant of the making-momenta-primitive solution to the Newtonian problem, because the wavefunction encodes all the information on positions and momenta.

Wednesday, August 18, 2021


If an explanation is a truth or hypothesis that removes or would remove mystery from the proposition to be explained, then an antiexplanation is a truth or hypothesis that adds or would add mystery to the proposition to be explained. Like in the case of explanations, we need to be sensitive to context with antiexplanations. That Alice dislikes bananas is, in typical contexts, antiexplanatory of why Alice ate the banana. But if we add to the background that it’s Lent and Alice wishes to do penance, then Alice’s dislike of bananas becomes explanatory.

It is widely held, though still moderately controversial, that:

  1. The fact that a hypothesis p is explanatory of some known truth is evidence for p.

A parallel claim about antiexplanations would:

  1. The fact that a hypothesis p is antiexplanatory of some known truth is evidence against p.

This sounds even more plausible than (1). In a typical context, the antiexplanatoriness of a dislike of bananas to actual consumption of a banana provides evidence that Alice who ate a banana does not dislike bananas. Similarly, the fact that Bob is in perfect health is antiexplanatory of Bob’s death, and hence if Bob has died, we have evidence that Bob’s health was imperfect.

There are lots of explanatory arguments in philosophy based on (1). But it would be worth exploring whether one can’t also give antiexplanatory arguments based on (2).

In fact, I think some fairly intuitive arguments can be rephrased as antiexplanatory arguments. For instance:

  1. Materialism is antiexplanatory of consciousness.

  2. Consciousness is a known fact.

  3. So, we have evidence against materialism.

The thought behind (3) is simply that there is intuitively something particularly mysterious about a purely material thing having a conscious point of view.

C. S. Lewis’s version of the moral argument for theism can be taken to be in part an antiexplanatory argument.

  1. Atheism is antiexplanatory of moral law.

  2. Moral law is a known fact.

  3. So, we have evidence against atheism.

Further evaluation of such arguments would call for a deeper philosophical analysis of antiexplanation and an examination of (2). This is a task worth doing. Someone should do it.

Thursday, August 12, 2021

Does general relativity lead to non-locality all on its own?

A five kilogram object has the determinable mass with the determinate mass of 5 kg. The determinate mass of 5 kg is a property that is one among many determinate properties that together have a mathematical structure isomorphic to a subset of real numbers from 0 to infinity (both inclusive, I expect). Something similar is true for electric charge, except now we can have negative values. Human-visible color, on the other hand, lies in a three-dimensional space.

I think one can have a Platonic version of this theory, on which all the possible determinate properties exist, and an Aristotelian one on which there are no unexemplified properties. There will be important differences, but that is not what I am interested in in this post.

I find it an attractive idea that spatial location works the same way. In a Newtonian setting the idea would be that for a point particle (for simplicity) to occupy a location is just to have a determinate position property, and the determinate position properties have the mathematical structure of a subset of three-dimensional Euclidean space.

But there is an interesting challenge when one tries to extend this to the setting of general relativity. The obvious extension of the story is that determinate instantaneous particle position properties have the mathematical structure of a subset of a four-dimensional pseudo-Riemannian manifold. But which manifold? Here is the problem: The nature of the manifold—i.e., its metric—is affected by the movements of the particles. If I step forward rather than back, the difference in gravitational fields affects which mathematical manifold our spacetime is isomorphic to. If determinate position properties are tied to a particular manifold, it means that the position of any massive object affects which manifold all objects are in and have always been in. In other words, the account seems to yield a story that is massively non-local.

(Indeed, the story may even involve backwards causation. Since the manifold is four-dimensional, by stepping forward rather than backwards I affect which four-dimensional manifold is exemplified, and hence which manifold particles were in. )

This is interesting: it suggests that, on a certain picture of the metaphysics of location, general relativity by itself yields non-locality.

Wednesday, August 11, 2021

Free will and the PSR

Even though I think one of the biggest challenges to the Principle of Sufficient Reason (PSR) is the feeling that something is unexplained in the case of free actions. I think this can be answered: see Section 4 here. But in this post I want to make a very small and simple point that just occurred to me.

The puzzle of free actions is not the lack of reasons. It is a surfeit of reasons. Suppose I eat a donut rather than an apple. It is easy to give a reason: the donut is more delicious. If that’s all we had, there would be no felt difficulty about the explanation. But the felt difficulty comes from the fact that while the donut is more delicious, the apple is more nutritious, and hence while I have a reason for eating the donut rather than the apple, I also have a reason for eating the apple rather than the donut.

But while a shortage of reasons would be a problem for a principle like the PSR that affirms the existence of reasons, a surfeit of reasons is not a problem for it!

So whatever one might say about the puzzle of free will, it is not problem for the PSR.

Tuesday, August 10, 2021

The Theotokos and personhood

Catholics and the Orthodox insist that Mary is the Theotokos—the Godbearer. The child in her womb was God.

It follows that this child she bore in her womb was a person. For the child was God by virtue of the Incarnation, and the Incarnation consists precisely of the union of two natures in one person. Moreover, the Incarnation is a process of God becoming a human being. So that person in her womb was also a human being.

Thus, the human being Jesus, while in Mary’s womb, was a person. Now, Jesus is like us in all things but sin. So, while we are in our mothers’ wombs, we already are persons.

A theory of personhood or personal identity that requires human persons to have developed human mental functioning—like Warren’s theory of personhood or Locke’s theory of personal identity—conflicts with the Catholic and Orthodox teaching on Mary the Mother of God.

My mother gave birth to me

  1. My mother gave birth to me.

  2. I have no memory connection, direct or indirect, to me at birth.

  3. Therefore, the memory theory of identity is false.

Eternalism and future non-existence

I go back and forth on whether this is a strong argument against eternalism:

  1. Given eternalism, it is guaranteed to be eternally the case that one exists simpliciter, even if one’s existence comes to an end.

  2. Given eternalism, one’s existence coming to an end is just finitude in the forwards temporal direction.

  3. If it is guaranteed to be eternally the case that one exists simpliciter, finitude in the forwards temporal direction would not be something to be dreaded.

  4. So, given eternalism, one’s existence coming to an end would not be something to be dreaded. (1–3)

  5. One’s existence coming to an end would be something to be dreaded.

  6. So, eternalism is false. (4–5)

(As a theist, I think our existence does not come to an end. Hence the hypothetical “would” in (5).)

The intuition behind (3) is that finitude in the forwards temporal direction, given that one exists simpliciter, is akin to finitude in the backwards temporal direction or along a spatial axis, and these are clearly not to be dreaded.

But, on reflection, I think the eternalist can make very good sense of the appropriate attitudes to an end of existence. Consider this: If I were threatened with amputation of the part of me below the head—i.e., with being reduced to a head in a life-support tank—that would be something to be dreaded. It would be something to be dreaded, because the kind of functioning that is natural to human beings requires the below-the-head portion of the body. On the other hand, we could imagine sessile aliens that are very much like human heads, and there is nothing dreadful about the life of these aliens. These aliens’ lack of the below-the-head functioning normal humans enjoy would not be a deprivation.

Thus, human flourishing has spatial requirements: we require all of our body to fully flourish. Similarly, human flourishing has a robust temporal requirement: it requires an eternal future. This is because of the nature of human flourishing. Plausibly, human flourishing has a drive to infinity, requiring endless growth knowledge of reality and relationship with others. (This is probably not the whole story, but it will do for this post.) But our flourishing does not require spatial unlimitedness—on the contrary, there is a maximum size along each spatial axis such that a human being that is too big along that axis is not a fully flourishing human being.

We are four-dimensional beings, and we require a specific four-dimensional shape to flourish: a shape that is not too small and not too large in the three spatial directions and that is infinite in the forwards temporal direction. A finite future is a terrible truncation.

Now not every animal is like humans. Brute animals do not require an eternal future to be fully flourishing: they can achieve complete flourishing in a finite life, say because the lack the drive to the infinite that humans have. If we were like that, it would not be appropriate for us to dread future non-existence. Not being inclined to dread future non-existence is hard for us to imagine, because the drive to the infinite arises from such deep features of our nature. But philosophically, it makes perfect sense to think that there could be beings that can complete their flourishing in a finite compass.

The eternalist’s seeing a future end of existence of a human as a terrible truncation, but as not necessarily a terrible truncation in a non-human, seems very compelling. On the other hand, I think it is harder for a presentist to make sense of the difference here. Future non-existence seems really bad, because future non-existence on presentism would imply that eventually one will not exist simpliciter, and that seems dreadful. But the dreadfulness of this seems to have to do with the value of existence simpliciter, and not with our nature. Thus, we may have a story as to why it would make sense for a presentist to dread an end to existence, but that story proves too much: for that story would apply even if the presentist were the kind of non-human that doesn’t need an infinite future for flourishing.

Wednesday, August 4, 2021

Second-order perception and the knowledge argument

Here’s something odd in the knowledge argument as usually formulated. According to the knowledge argument, Mary who was raised in a black and white argument but knew all of science came to know what it is like to see red by seeing red, despite having known all the physical facts first.

But note that one cannot simply come to know what it is like to see red by seeing red. One knows what it is like to see red by having the second-order perception of oneself seeing red. When one has the first-order perception without the second-order one, one doesn’t directly know that one has the first-order perception. (One may be able to infer it, of course: Here is a tomato, my eyes are open and are pointed towards it, so I am seeing it.) Of course, typically when one has the first-order perception, one also has the second-order perception (but typically not the third-order one), but the point remains is that it is not by the first-order perception, but by the second-order one, that one learns what it is like to see red.

Presumably, any ordinary human perception can be mistaken: it can occur in the absence of its object. Thus it is possible to have the second-order perception without the first-order one. It follows that it is possible for Mary to know what it is like to see red without ever seeing red: all she needs is the second-order perception.

This does not seem to me to damage the knowledge argument as such, but merely to tweak it. For even after the above reflection, it still seems plausible that one doesn’t know what it is like to see red on the basis of physical facts, but by means of a second-order perception. Moreover, we now have an answer to the memory objection to the knowledge argument, namely that just as you and I can know what it is like to see red by having true memories of seeing red, so too someone could know what it is like to see red by having false memories of seeing red, and so actual perception of red is not needed. But this does not affect the argument once we have realized it’s about the second-order perception. For memories, true or false, of seeing red are a kind of temporally backwards second-order perception.

More on the non-causal dualist theory of perception

In a recent post, I offered a non-causal dualist theory of sensory awareness on which when I see a red cube, there is a state rb of my brain representing the red cube, and a relation V of perception between rb and my soul, which relation is external to the soul. As a result, there need be no intrinsic difference between my soul when I am perceiving red cube and my soul when I am not perceiving a red cube.

I want to make a few more notes on this theory, for it seems to me that it is worth taking seriously.

1. This theory is very close to Aquinas’. Aquinas thought that sensory awareness was constituted by the reception of sensory data (“phantasms”) by sense organs. The sense organs, and not the soul, are modified by the sensory awareness. Of course, it was crucial to this that the sense organs be informed by the form of the animal, and the form of an animal is the soul. So we have a similar structure: there is a relation of the soul and the sense organs, and the sense organs are then modified by the sensory data. If we neglect the difference between the brain in my theory and the sense organs in Aquinas’s, then Aquinas’s theory is just an expansion on my theory. The state rb is the state of the sense organs having their sensory data, and my external relation V of perception on Aquinas’s view is simply constituted by a pair of relations on Aquinas’s: the informing relation of the soul to the organ, and the sensory-data-possession relation between the organ and its sensory data.

Thus, the main difference between my theory and Aquinas’s is that I replace the sensory organs with parts of the brain. And there is good reason to think that if Aquinas had the empirical data we do, he would think of the phantasms as in the brain rather than in the eyes, ears, etc. For we have good reason to think direct neural stimulation of the visual center of the brain could produce the same visual experience as gazing upon a red cube. Thus, the only difference between Aquinas and the theory—apart from Aquinas offering more detail on the relation V—is that on the theory, the sensory organs in Thomas’s sense are all inside the skull.

2. What we should say about qualia on this theory? The analogue to the visual quale of my perceiving a red cube on this theory consists of V and rb. That’s a pair of things rather than one thing. One of these two things, the brain state rb, is physical, but the other thing, the relation V, is a non-physical relation between a non-physical thing, the soul and a brain state rb. Thus qualia are partly non-physical and partly physical.

3. It seems the theory contradicts the knowledge argument. Consider the brain state rb representing a red cube and the brain state gb representing a green cube. It seems that on the basis of seeing a green cube, I can get to know the relation V obtaining between my soul and gb. And on the basis of neuroscience, I can get to know rb. Thus, without ever seeing anything red, it seems I can know what it’s like to see red.

I am not strongly attached to the knowledge argument in its standard form. I kind of like the radical variant on which a never conscious person could never get to know what consciousness is like. And that variant fits with the theory, since a never conscious person has never experienced the relation V. (You might say: A never conscious person couldn’t know anything. I think it is a mistake to require consciousness for knowledge. First, one can have non-occurrent knowledge without consciousness—I know my multiplication tables even when asleep. Second, the unconscious vampires in Watts’ Blindsight clearly have knowledge.)

That said, I do not think it is obvious that just by knowing what the ingredients are like one knows what the whole is like. Thus, knowing what rb and V are like may not be enough to know what it is like to have one’s soul stand in V to rb. (Compare: Alice knows what it is like to be married to Bob, and she knows Carl, but it doesn’t follow that she knows what it is like to be married to Carl.)