Geological reductionism

One way for a naturalist to respond to arguments from, say, morality (such as this argument) is to either deny that our moral perceptions are veridical or to reduce the moral to the non-moral, say to a sentiment.

One should see moves that deny the veridicality of a large class of our perceptions (illusionism), or that reduce apparently objective truths to subjective ones, as epistemically costly. One way to see this is to consider parallel responses that a straw man young earth creationist might make to geological arguments:

1. Illusionism: Of course, the earth looks like it's billions of years old, but that appearance is non-veridical, being the result of Satan's work at deceiving us into thinking creationism is false.
2. Reduction: If t is more than 10000 years ago, to affirm that a geological state S of affairs occurred at t is just to affirm that right now it looks as if S occurred at t.

On the correct epistemology, moves such as these should be quite costly. (The above are only straw man versions of young earth creationist responses. In fact, apparently the Satan response is in disrepute among young earth creationists and I have never heard anybody make the reduction response.)

Counterfactuals

Lewis's account of a subjunctive conditional is that "if p were to hold, q would hold" is true if and only if

1. p holds in no worlds; or
2. some world in which both p and q hold is closer than every world in which both p and not-q hold.

But, plausibly:

3. No natural concept has a disjunctive account.
4. The concept of a subjunctive conditional is natural.

Therefore Lewis's account of a subjunctive conditional is not right. (Fortunately, there is a non-disjunctive modification of Lewis's account that has additional merits—see this paper and a reference therein.)

Is this a good argument against Lewis? I am not sure. If no disjunctive account of a natural concept is good, then no account of a natural concept in terms of the material conditional is right. Do we want to say that?

And, after all, the concept of a disjunction seems itself quite natural to us (certainly, much more natural than the connective nor, and probably at least a little more natural than nand). However, this answer may equivocate on "natural". Subjunctive conditionals, perhaps, are natural not in the sense that they are natural ingredients of our language, but in the sense that, unlike disjunctions, they are appropriate ingredients to have inside laws of nature.

[Edited]

Observing log: April 14, 2009

Scope: Odyssey 8 (I am now thinking of buying one of the early blue-tube Odyssey 13.1's—do any of my readers have one?). Darkness rating: Yellow. Weather conditions: Flitting light filmy clouds. Seeing: Decent (could see gap between Saturn's rings and Saturn, which I've never seen before).

Observed: Saturn, M 5, M 13, M 49, M 51, M 58, M 59, M 60, M 61, M 68, M 83, M 92, M 99, M 100, M 101, M 102, NGC 3242, NGC 4526, NGC 4535, NGC 4638, NGC 4567, NGC 4568, NGC 5139 (very low on horizon, did not resolve—just a slightly grainy ball, but it was still cool to see Omega Centauri), NGC 5907.

I've now seen 83% of the Messier catalog (I've done all the galaxies and nebulae, and most of the open clusters), 12% of the Herschel 400, and about 20% of the Best of the NGC. Lots of fuzzies to go.

Righting wrongs

The following argument is sound:

1. (Premise) All injustices are righted.
2. (Premise) If God does not exist, some injustices are not righted.
3. Therefore, God exists.

Of course, an argument can be sound but no good. Recall Plantinga's example, which was basically: "God exists or 2+2=5; but not 2+2=5; therefore, God exists", the logic is impeccable, and all the premises are true, but ordinarily only someone who is already a theist will accept the first premise. Is the present argument like this?

Well, I think (2) is fairly plausible. Think of someone innocent who is murdered. Who is there to right that injustice, unless it be God? Of course, one might posit other supernatural hypotheses than that of the existence of God that would suffice to ensure that injustices are righted, but the other hypotheses just do not strike me as very plausible—finite beings like the Furies aren't likely to be able to know and right all injustices.

Of course, premise (1) is not going to be at all plausible to the typical atheist. However, it may well be that some people have an intuition to the effect of (1). This intuition may be related to intuitions about how everything has a purpose, how bad things come to good, etc. These intuitions are ones that even an atheist can have (I once had an atheist student who had such an intuition about her own life—she wondered if the intuition was compatible with her atheism, and I told her that was something she'd need to figure out herself). So the argument need not always be question-begging.

Justice and causation

Here's a valid informal argument. Again, soundness is the question. If I react to the shape of x, then x's shape plays a role in a causal explanation of my reaction. If I react to the injustice of situation, then, by parallel, the situation's injustice must be play a role (perhaps a privative one) in a causal explanation of my reaction. I do react to the injustice of some situations. But if naturalism is true, then justice and injustice do not enter into causal explanations. Hence naturalism is false.

Injustice

The following argument is valid:

1. (Premise) If there is no person who is causally responsible for an event E, then E is not an injustice, but at most a misfortune.
2. (Premise) There have been injustices (think of a child's dying after horrible suffering in an earthquake) for which no person was causally responsible by means of natural causal processes (in the sense of "natural" that naturalists talk about).
3. Therefore, some injustices were caused not by means of the natural causal processes of nature. (1 and 2)
4. (Premise) If naturalism holds, then all causal processes are the causal processes of nature.
5. Naturalism is false. (3 and 4)

There are two options in (3): either the injustices were caused by a supernatural person (e.g., a devil) or they were caused by a natural person but through processes that go beyond nature (e.g., Adam and Eve in causing the Fall).

The naturalist will likely deny (2). Thus, then naturalist is going to have to be an irrealist about a significant amount of human experience of the world—for people do experience various evils not that are not naturally caused by human beings as injustices.

A regress for bundle theory

According to bundle theory, each individual is a bundle of properties. But what is an individual? Presumably, individuals are existing entities that we can individuate, quantify over and predicate things of. Take that as a sufficient condition for being an individual. But then a property is also an individual. (If one balks at this, I expect that it is simply because one has stipulated this fact away, say by defining individuals as existing entities that we can individuate, quantify over and predicate things of which are not properties. If so, then the class of "individuals" is gerrymandered. But we needn't worry about words. Call something that we can individuate, quantify over and predicate things of an "individual*", and construe what I say below as about individuals*.)

But now the regress is obvious. Socrates, let us say, is a bundle of humanity, maleness, snubnosedness, smartness, hellenicity, etc. Fine. But humanity is also an individual. So, humanity is itself a bundle of properties. What properties? I don't know. Maybe properties like propertyhood, unchangingness, animal-kind-hood, rational-being-kind-hood, etc. Already it gets weird—we have no idea what to say. And then the problem returns for the properties that humanity is a bundle of. What, say, is propertyhood a bundle of? What is animal-kind-hood a bundle of? Obviously, a regress ensues. Is it vicious? I suspect so. We have bundles of bundles of bundles of .... If the bundling is done set-wise, then the sets will violate regularity.

And in any case if the individuation of bundles is by their members, that never bottoms out. On an abundant theory of properties, our non-property individuals all look like {{{...},{...},{...},...},{...},{...}},{...},...}, with exactly the same structure of braces. (That's for the set-theoretic construction. Otherwise, replace the braces by whatever bundling method we have.) On a sparse theory of properties, if it turns out that non-property individuals have finitely many properties, and that properties all have finitely many properties, maybe then we can differentiate these things by the structure of the rooted property-tree (individual x has 7 properties at the first level, the first of which branches has 19 properties, etc.) But that's as crazy as Pythagoreanism.

So maybe the bundle theorist will limit her theory of predication to individuals that are not themselves properties. But if she does that, she still needs a story about how we manage to predicate things of properties. For we do. Humanity is a universal. It is unchanging. It is non-spatio-temporal. It is different from hellenicity. And so on. And whatever non-bundle theory of predication that we give for the properties of properties, the opponent of bundle theory will say: Why not just simplify and give that for the individuals that are not properties?

Or one might take first-order properties to be bundles of individuals. But that's terrible. First, they'd have to be bundles of possible individuals. Second, we now have circularity in place of regress, which is worse.

This arguments seems to force the bundle theorist to say that eventually we get to properties that have no properties (what about their abstractness? their propertyhood? maybe we say that these are not genuine properties--maybe abstractness is just the denial of concreteness). Todd Buras then points out to me that these properties with no properties are just like the bare particulars avoiding which was one of the main motives for bundle theory!

Note: The argument works equally well if we have bundles of tropes instead of bundles of universals.

I know that these issues have been worked over, and regress-finding is a fun game for the philosophical family, so this regress is quite likely known. (If you have a reference, please let me know.)

Platonism

Jerry waltzes. According to the Platonist, this means that Jerry instantiates the universal waltzing. So, where initially we thought we had Jerry alone, we now have Jerry, instantiation and waltzing. But we also, equally, have Jerry, instantiation and waltzing when Jerry is sitting instead of waltzing. After all, instantiation and waltzing are universals, and so they exist necessarily, even when Jerry isn't waltzing. So, what is different between the situation where Jerry instantiates waltzing and the one where he does not? It won't help to say that the ordered pair <Jerry, waltzing> instantiates instantiation. For the same problem reappears. Whether Jerry waltzes or not, Jerry, waltzing, the ordered pair <Jerry, waltzing>, and instantiation necessarily exist. Going to further levels of the regress will get us more entities, but it will not help resolve the problem. For we will simply get more beings that exist even when Jerry isn't waltzing, and those beings don't help to differentiate betweent he case of him waltzing and him not waltzing. (Nor does this depend on time; we can distinguish between the case of Jerry's instantiating waltzing at some time or other and the case of Jerry's not instantiating waltzing at some time or other.)

So what can the Platonist do? Well, she could just say that it's simply a fact, a fact not analyzed in terms of further Platonic entities, that Jerry in fact instantiates waltzing, or that <Jerry, waltzing> instantiate instantiation. But then she says exactly the same sort of thing that the ostrich nominalist does. And if she says it in this case, why bring in instantiation at all? Why not just say that Jerry in fact waltzes, and be done with it? Or maybe the Platonist will say that there is a state of affairs of Jerry's instantiating waltzing or <Jerry, waltzing> instantiating instantiation. Fine, but why do that? Why not just say that there is a state of affairs of Jerry's waltzing, and be done with it? Or perhaps the Platonist will posit a trope of instantiating present in <Jerry, waltzing> or a trope of instantiating-waltzing present in Jerry. But why not, then, just posit a trope of waltzing in Jerry?

I do not think this kills Platonism. It just shows that if Platonism is to do something useful for us, it is something other than helping us understand the nature of predication. For if Platonism is seen as helping with predication, it does this by reducing all predication to predications of the form "x instantiates P" or "<x,P> instantiates instantiation". Now in some cases, it is helpful to ground all instances of a class in terms of a distinguished subclass. Thus, in my dissertation, I argued that all modal claims should be grounded in claims about the powers of things. The latter claims are, of course, modal. However, if such a grounding is to have any usefulness, the distinguished subclass must be somehow preferable, maybe epistemologically, maybe in terms of comprehensibility, or in some other way. But why should, say, the state of affairs of Jerry's instantiating waltzing be preferred to the seemingly simpler state of affairs of Jerry's waltzing?

Now it may well be that Platonism has other uses than helping with problems of predication. It may indeed.

Divine love and union

Is agapê just a benevolence, as on Nygren's view, or does it involve a seeking for unity? I think one way to an answer is to look at God's love as presented in the New Testament.

"For God so loved the world that he gave his only Son, that whoever believes in him should not perish but have eternal life." (John 3:16) Now, the damned live forever, too, and it is not this kind of life that the text is talking about. Rather, it is an eternal life of knowing God, of living in the Father and the Son (cf. John 17:21).

God;s love is manifested in his acting that we might be reconciled and united with God. Now we can understand God.s intentions in two ways, which can be conveniently expressed by imagining God telling us of his intention:

1. I intend your reconciliation and union with God.
2. I intend your reconciliation and union with me.

Of course, "me" and "God" in these imagined speeches has the same referent, but there is a crucial difference.

On the first version, we can understand this as follows. God, being omniscient, knows that Patricia's highest good is union with God. And being loving, he intends that Patricia achieve that highest good. In this, God has an intention we can all have in the same way. We can all seek Patricia.s highest good, and we can all pursue Patricia's reconciliation and union with God. As it happens, God is the one who can pursue it most effectively. But that does not imply a difference in intention.

On the second version, however, what God pursues is Patricia's union with him, best indicated by Castaneda's quasi-indicator "him*". When we pursue Patricia's union with God, we are pursuing something essentially different from what God is pursuing.

The distinction is easy to see in other contexts. There is a world of difference between drill sergeant who wants to train the soldiers to obey him, and the drill sergeant who wants to train the soldiers to obey their superior, which in this case happens to be the drill sergeant. (The distinction would remain even if the drill sergeant necessarily was their superior.) In the case of the drill sergeant, what is preferable is that he train soldiers to obey their superior.

However, love differs here from obedience. For there is something incomplete about a husband's love if he desires merely that his wife love her spouse, reasoning, perhaps, that it is a good thing for a married person to love the spouse, and his wife is a married person, hence it is good for her to love her spouse. Granted, that is a good, and so he should desire this good for his wife. But he should, over and beyond that, desire that his wife love him*. And if his wife does not love him, it is a sign of something deeply lacking in his love for her if he is merely saddened that his wife is not a spouse-loving person.

Our reconciliation and union with God is a good thing, and being good, it is something that God pursues. But he does not pursue it impersonally. God pursues it in love, in the way that a husband loves his wife, as Scripture emphasizes. He desires our reconciliation and union with him*. I do not have a proof text for this claim. But think what would happen if in all the texts in which God lovingly, often sadly, uses the phrase "my people". Now replace this with "God's people". For instance, in Zechariah, God says: "they shall be my people and I will be their God, in faithfulness and righteousness" (8:8). Consider the replacement: "they shall be God's people, and God (or haShem) will be their God, in faithfulness and righteousness." That would still be happy news, but the lover essentially speaks in the first person, except perhaps as a joke.

The beauty of mathematics

Consider the claims:

2. There is exquisite beauty in mathematics.
7. Mathematics is grounded in the existence of a maximally great being.

Then the following argument might be offered:

1. P(B|G) > P(B|~G).
2. Therefore, B is evidence for G.

It does not, however, follow from (2) alone that B is evidence for the existence of God.

Loss of faith

Sometimes, Christians worry whether they might not have lost their faith. Here is a line of thought that might be comforting, though it is probably only acceptable to Catholics. Faith being a gift of grace, it is not possible to lose faith without losing sanctifying grace. It is not possible, however, to lose sanctifying grace but by committing a (formal) mortal sin. Therefore, faith can only be lost through committing a mortal sin. But in a serious Christian, mortal sin is very unlikely to be something done casually—it is a free and conscious rejection of God's love, after all. Faith is not, then, something one can "just lose". It is something one can reject, but only by a mortal sin.

Infinite causal regress

Could everything in existence be explained by an infinite causal regress? I've argued in print that the answer is negative. Here is another thought in favor of the negative answer.

Suppose we have a world where there is an infinite regress of past states and that there is some numerical time-varying property Q(t) in the universe (say, entropy or temperature or charge or volume) that keeps on changing in such a way that the property's having one the value it does in one year determines the value it has in another. Now, consider the claim that the limit of Q(t) as t goes to minus infinity is, say, q₀. (Of course, Q(t) might not in fact converge to anything, but since we're stipulating, we can stipulate that it does.) If the regress explains everything, it explains why it was that the limit is q₀. But even if a regress explains something, it surely doesn't explain the boundary values at the beginning of the regress, and q₀ is precisely such a boundary value. It would be almost as absurd to say that the limit of the temperature in a room tended to 11.0 degrees as t approached noon from above because it was 11.1 at 12:10, and 11.06 at 12:05, and 11.05 at 12:05, and 11.01 at 12:01, and so on, as it would be to say that the temperature of the room was 11.0 degrees at noon because it had such-and-such values after noon.

Suppose that we still insist that the boundary value q₀ is explained by the regress. Now suppose that we find another explanation, say in terms of an atemporal being creating the universe. What should we say? That we have two explanations of the same phenomenon, each on its own sufficient? That can happen, but surely that's not what is happening here. The right thing to say is that the regressive explanation of the boundary condition is no explanation at all.

More on the Kalaam argument

Here is another counterexample to the claim that it is impossible to form a concrete and actual infinity through successive addition. Consider a gamma-widget. A gamma-widget is a stochastic critter that, once it is produced, produces at least one offspring. How many offspring it produces and how quickly is random. For every n>0, a gamma-widget has probability 2⁻ⁿ of producing exactly 2²ⁿ offspring in exactly 2⁻ⁿ years. The offspring are exact copies of the parent (this is a way in which the gamma-widget differs from the beta-widget). They, too, are gamma-widgets, and hence produce offspring. All the probabilities are independent.

Here is a mathematical fact (at least, it is a fact, if my scribbled calculations are right): There is a non-zero probability that if a gamma-widget comes into existence, it will be an ancestor of infinitely many gamma-widgets a year later. What has non-zero probability is also possible. Therefore, it is possible for this to happen. Here is another fact: The probability that there is a finite number n such that n years later there are infinitely many gamma-widgets is one. What is almost certain (i.e., has probability one) is a fortiori possible. Therefore, it is possible to have an infinite number of gamma-widgets arise through successive addition.

(If one is worried that the addition is not successive because multiple offspring are produced at the same time, we can stagger the productions in some way, and then not count the ones whose productions happen to overlap.)

Does this argument, and that in my previous post, destroy Craig's Kalaam argument? I think not yet. For there two ways that an infinity prima facie can be built up by successive addition. In one way, there is a first addition but no last one. In the other way, there is a last addition but not first one. What my examples show is that the first way is possible—there is a first addition but no last one. But I have not shown that there is no possibility of successive addition of the other sort.

However, the latter possibility follows from a modification of the case. Suppose that each gamma-widget that comes into existence before the year 2020 randomly and uniformly chooses a time during 2020, and completes a mug at that time. Then there is, almost surely, a subset of the mugs that has a last addition but no first one.

Craig can get out of these arguments by supposing that time cannot be infinitely divisible. Or he might just deny the possibility of my widgets. But what grounds would there be for that denial? Consider a variant on the gamma-widget, the delta-widget. It is just like the gamma-widget, except that it has probability 2⁻ⁿ of generating n² offspring in 2⁻ⁿ years. The delta-widget is just like the gamma-widget, except it is much less prolific: n² instead of 2²ⁿ. I am pretty sure (I haven't checked) that with probability one, delta-widgets do not have an infinite population explosion. So Craig can't object, it seems, to delta-widgets except by denying the infinite divisibility of time. But if delta-widgets are possible, why not the more prolific gamma-widgets?

Maybe my calculations are wrong. But I am pretty sure they're not. If they are wrong, replacing 2²ⁿ with an even faster growing sequence should fix things.

Infinite numbers of objects

Here is an argument that it is possible for an infinite number of objects to come into existence by successive addition, contrary to William Lane Craig. I am not sure how far I find this argument convincing, but it seems to me to be pretty strong. It's inspired by an idea of Wes Morriston.

An alpha-widget is an entity that has the following property. As soon as an alpha-widget x is made, it spends a year playing the violin, and doing nothing else. At the end of that year, x makes an almost-duplicate of itself in half of the time in which x itself was made: the almost-duplicate is just like x, except that if x has the information that it was made in t units of time, the almost-duplicate has the information that it was made in t/2 units of time. And alpha-widgets are never destroyed.

I now claim that it is possible for an alpha-widget to be made over the period of a year. If it were made, there would be a potentially infinite but never completed sequence of alpha-widgets coming into existence: the first at the beginning of year zero, the second at year 1.5, the third at year 2.75, and so on. Since the spacing between alpha-widgets is always more than a year, because of that year of violin-playing, we do not here have any counterexample to Craig.

It would be difficult, I think, for Craig to object to this possibility. It doesn't violate his strictures against actual infinities. It does require laws of nature different from those of our world, or perhaps divinely mediated miracles, in order to overcome speed of light limits on the production speed of an alpha-widget.

But now consider a beta-widget. Recall that an alpha-widget would first play the violin for a year, and then would make an almost-duplicate of itself in half the time that it itself was made. A beta-widget does the same thing, but in opposite order: it first makes the almost-duplicate in half time, and then plays the violin for a year. Since the alpha-widget is not doing anything in that year of violin playing other than playing the violin (it's not, for instance, setting up a production line for its almost-duplicate), there is no reason to suppose that it would be harder for God to make a beta-widget in a year than to make an alpha-widget in a year. (And, yes, God can make things non-instantaneously if he so chooses.)

So, it should be logically possible to make a beta-widget in a year. But if a beta-widget is made in a year, then half a year later, it makes another beta-widget. That one, then, makes another in a quarter of a year. And so on. By the time two years are up, we have an infinite number of beta-widgets produced by successive addition.

I should, of course, note that while I think there are problems in the Kalaam argument's a priori argument for the finite age of the universe, its a posteriori argument may well be fine, and in any case there are other cosmological arguments that work just fine.

Sexual orientation

Consider the following two claims that some people seem to accept:

1. Same-sex and opposite-sex sexual relationships are on par.
2. Heterosexuality, homosexuality and bisexuality are on par, and persons of one orientation do not have reason to try to change to another.

I don't know what exactly "on par" here means—I think it's some combination of morally on par, should be treated equally by society, equally valuable and equally normal.

I will argue that (1) and (2) are in tension.

Suppose that George is sexually attracted to people, male or female, of a particular ethnicity, and not at all towards anybody, male or female, of any other ethnicity. We would think this weird and maybe just a little perverted even if we accepted (1) and (2). After all, why should George limit his romantic options to members of a particular ethnicity? Indeed, his attitude would border on racism. Granted, if George hadn't done anything to choose his pattern of sexual attraction, and couldn't overcome it, we would not morally criticize George for his limiting his sexual interest to that ethnicity. But there would still seem to be something wrong with George.

I am not talking here of a mere preference. Perhaps there is nothing wrong with an Elbonian preferring Elbonians. But to be unable to be sexually interested in anybody but Elbonians is limiting, unfortunate, not quite right. And it is particularly odd if one isn't Elbonian oneself. It is certainly sub-optimal, given that sexual relationships with Elbonians are on par with sexual relationships with non-Elbonians, and it is not a good idea to have artificial limits in the difficult task of finding a suitable romantic partner. Furthermore, if George were not in a relationship, and there were a pill that had no side-effects and could remove the limitation, it would be reasonable for George to take the pill, at least assuming (1).

But the heterosexual or homosexual is in a similar state to George. The heterosexual man and homosexual woman is limited in sexual attraction to to women. The homosexual man and heterosexual woman is limited in sexual attraction to men. If same-sex and opposite-sex sexual relationships are on par (as per (1)), then there is something sub-optimal in value here—an odd limiting of possible partners on the basis of a quality, maleness or femaleness, that is basically irrelevant to sexual relationships according to (1). So, if (1) holds, then there is something not quite right with homosexuality and with homosexuality—it is a limiting of the relational options. Moreover, there would be reason to change one's orientation to bisexuality if one could do so easily and with no side-effects, thereby removing that restriction.

Thus, if (1) holds, bisexuality has a privileged status among sexual orientations, and, in particular, (2) is false.

One can, of course, contrapose the argument—and I think one should. If bisexuality does not have a privileged status among sexual orientations, then (1) is false.