Thursday, April 17, 2014

Reference magnetism and anti-reductionism

According to reference magnetism, the meanings of our terms are constituted by requiring the optimization of desiderata that include the naturalness of referents (or, more generally, by making the joints in language correspond to joints in the world, as much as possible) and something like charity (making as many real-world uses as possible be correct).

Suppose we measure naturalness by the complexity of expression in fundamental terms—terms that correspond to perfectly natural things. (In particular, we can't talk of what cannot be expressed in fundamental terms, since reference magnetism would presumably not permit reference to what is infinitely unnatural.) Consider the reductionist thesis that the vocabulary of microphysics is the only fundamental vocabulary about the natural world. If this thesis is true, then our ordinary terms like "conscious" or "intention" or "wrong" are going to be cashed out in terms of extremely complex sentences, often of a functional sort. But I suspect that once these expressions are sufficiently complex, then there will be many non-equivalent variants of them that will fit our actual uses about as well and are about as complex. Consequently, we should expect that the meaning of terms terms like "conscious", "intention" and "wrong" to be highly underdetermined.

If we have reason to resist this underdetermination, we need to embrace an anti-reductionism on which the terms of microphysics are not the only fundamental ones, or else have another measure of naturalness.

Wednesday, April 16, 2014

Another argument for universal love

A part of the phenomenology of healthy full-blown love is that one sees that the beloved is such that one would have been remiss not to have recognized her lovability by loving her. The phenomology of healthy full-blown love is not misleading. But it is possible to have a healthy full-blown love for any person. So one should love everyone. For consider some person, say Sam. If one did have the healthy full-blown love for Sam, one would have correctly seen that one would be remiss in not loving Sam. But whether one would be remiss in not loving Sam doesn't depend on whether one in fact loves Sam. So, it is true that one would be remiss in not loving Sam.

In my previous post, I started the argument by noting that if you have full-blown love, you should continue loving, and yet I concluded that the conditional can be dropped—you should love (and continue loving) everyone. But why is it that the conditional had a special plausibility? I think it's because of the above phenomology of love. It's not that only the people you love are such that you should love them. But it's that by loving them that you best come to see that you should love them. Healthy love isn't blind: it sees our neighbor as she really is.

An argument for universal love

If you have full-blown love (not just be slightly fond of, but really love) someone, you should continue to love her. It is a serious moral defect to be open to discontinuing one's full-blown love. This can be discerned from the phenomenology of full-blown love.

But a failure to continue loving someone shouldn't get one out of the obligation to love her. It would be "too convenient" if simply by doing the wrong of ceasing to love one were to get out of the obligation to love our beloved.[note 1] So our principle that if you have a full-blown love then you should continue to love can be strengthened:

  1. If you had a full-blown love for someone, you should love her.

But why is (1) true? I propose that the best explanation for (1) is:

  1. You should love everyone you can love.

The best alternate explanation of (1) is that love is relevantly like a promise: by acquiring full-blown love for someone one commits to an obligation to love. But this view is not plausible. Think of the way that children come to deeply love their siblings. This love can grow on them early, before they have the kind of moral responsibility that would make them fit subjects for undertaking lifelong commitments.

Now, we could stick with (2) as the conclusion. But everyone is in principle lovable. But perhaps not lovable by me? But an inability to love someone who is in principle lovable is a moral defect in me, though perhaps not one that I am culpable for. And moral defects shouldn't get one out of moral obligations. So:

  1. You should love everyone.

And that completes the argument. Definitely not a knockdown argument, but still something that should give some credence to the conclusion.

Tuesday, April 15, 2014

Popper functions, uniform distributions and infinite sequences of heads

Paper forthcoming in the Journal of Philosophical Logic, now posted. I argue that Popper functions don't solve the problems of uniform probabilities in infinite spaces. Yet another in a series of highly technical papers.

Regular probability comparisons imply the Banach-Tarski Paradox

Paper posted here (forthcoming in Synthese). Among goodies in the paper is a proof that the order extension principle (even in a weak form) implies the Banach-Tarski paradox, and a new argument against commensurability in decision theory. This is a very technical paper, so reader beware.

Monday, April 14, 2014

A curious thing about infinite sequences of coin tosses

Suppose that at locations ...,−3,−2,−1,0,1,2,3,... (in time or one spatial dimension) a relevantly similar independent fair coin is tossed. Let Ln be the event that we have heads at all locations kn. Let Rn be the event that we have heads at all locations kn. Let AB mean that event B is at least as likely as A, and suppose all our events Ln and Rn are comparable (i.e., AB or BA whenever A and B are among the events Ln and Rn). Write A<B when AB but not BA. Assume ≤ is transitive and reflexive. Then, intuitively, we also have:

  1. Ln+1<Ln
  2. Rn<Rn+1.
After all, Ln+1 and Rn require one more heads result than Ln and Rn+1, respectively.

Now here is a surprising consequence of the above assumptions. Say that n is a switch-over point provided that LnRn but Ln+1<Rn+1. When there is a switch-over point, it's unique (since for mn, we will have LmLnRnRm, and for m>n, we will have LmLn+1<Rn+1Rm). Then:

  1. Under the above assumptions, either (a) there is a switch-over point, or (b) Ln<Rm for all n and m, or (c) Rn<Lm for all n and m.
But each of these options is really rather absurd. Option (a) says that the probability distribution of our sequence of relevantly similar independent fair coins has a distinguished switch-over point. Option (b) implies that infinite sequences of heads stretching leftward (if we're talking about a spatial arrangement; backward, if temporal) are always less likely than infinite sequences of heads stretching rightward (forward, if temporal). And option (c) is just as absurd as (b). And of course in each of the three cases we have a violation of very plausible symmetry conditions on the story: in case (a), we have a violation of symmetry under shifts, and cases (b) and (c) we have a violation of symmetry under flips.

So something is wrong with the assumptions. Classical probability theory says that what's wrong are (1) and (2): in fact, all of the Ln and Rn events are equally likely, i.e., have probability 0. This seems a very plausible diagnosis to me.

Why does (3) hold? Well, suppose that (b) and (c) do not hold. Thus, Ln<Rm for some n and m. If mn, then we LmLn<Rm, and if m<n, then we have Ln<Rm<Rn. In either case, there is an b such that Lb<Rb. By the same reasoning, by the falsity of (c), there is an a such that La>Ra. As n moves from a to b, then, Ln decreases while Rn increases, and we start with Ln bigger than Rn at n=a and end with Ln smaller than Rn at n=b. This guarantees the existence of a switch-over point.

This result is basically a generalization of an observation about Popper functions for such infinite sequences in a forthcoming paper of mine.

Thursday, April 10, 2014

Theism and scientific non-realism

One of the major arguments for scientific realism is that the best explanation for why our best scientific theories are predictively successful is that they are literally true or at least literally approximately true. After all, wouldn't it be incredible if things behaved observationally as if the theories were true, but the theories weren't true?

While this is a pretty good argument, it's worth noting that theists have an alternate explanation: In order that intelligent beings be able to make successful predictions of a sort that lets them exhibit appropriate stewardship over the world, God makes the world exhibit patterns of the sort that human science is capable of finding, patterns that can be subsumed under theories that are sufficiently simple for us to find. And one sort of pattern is of the as-if sort: things behave as if there were photons, which lets us organize the behavior of macroscopic things into patterns by supposing (in a way that need not carry ontological commitment) photons.

That said, there is a value to science over and beyond its helping us exercise stewardship over the world—understanding of the world is valuable for its own sake—so even given theism, a scientifically realist theistic explanation seems better than a scientifically non-realist one.

But even if realism is in general the right policy, maybe theism could provide a tenable Plan B if there turn out to be cases where scientific realism is not tenable. For instance, one might think (incorrectly, I suspect) that there is no metaphysically tenable and scientifically plausible version of quantum mechanics. Then, one might retreat to a theistic explanation of why the world behaves as if the metaphysically untenable theory were true. Or one might think (because of Zeno's paradoxes, say) that it is impossible for spacetime to be adequately modeled by a manifold of the sort that mathematics studies (one locally homeomorphic to a power of the real number line). But why do things behave as if spacetime were such a manifold? Maybe God made them behave so because this lets us organize the world in convenient ways.

Wednesday, April 9, 2014

If casual sex is permissible, so is polygamy

If casual sex is permissible, so is premarital sex. Now, on a view on which premarital sex is permissible, marriage is a complex normative institution that removes the right to have sex with others and confers on the spouses various duties—such as of loving, cherishing, honoring and caring for—to the other, as well as makes for at least a ceteris paribus commitment that the couple will strive to have a sexual relationship. (If premarital sex is impermissible, then marriage has one more normative component: it confers a permission for sex.)

But there need not be anything morally wrong with x's promising y that she will not have sex with anyone other than y and z. Promises of loving, cherishing, honoring and caring for another are a great thing when taken really seriously, and are simply a higher and deeper form of the commitment that we all have anyway to our friends, and there seems nothing wrong with making such promises to multiple people, as long as there are implicit or explicit rules on how apparent conflicts of love and care are to be resolved (a problem that is already anyway present in the case of a monogamous marriage, since it can come up with respect to duties to spouse and to children, since these can be in tension). The only component possibly problematic in the normative complex is the ceteris paribus commitment to a sexual relationship with multiple people. But it is hard to see what is wrong with that if casual sex is permissible. If it would be permissible for Jane to have sex with Sid and Roman on alternate days, why would it not be permissible for her to make a ceteris paribus promise to do so? This is particularly unproblematic if one thinks of marriage as permissibly dissoluble, as most people who think casual sex is permissible do.

So it seems that if casual sex is permissible, then the normative complex of commitments that constitutes marriage can be permissibly modified to a plural form. One may ask whether the modified version would still count as a marriage. If not, then polygamy is misnamed: it's not a plural marriage (poly-gamy) but a plural marriage-like relationship. But either way, we get the conclusion: If casual sex is permissible, so is polygamy.

An interesting question is whether we can prove the stronger claim that if premarital sex is permissible, so is polygamy. Probably not, since someone could think that premarital sex is permissible only in the context of a relationship with an exclusive commitment to one person. But if one thinks that something weaker than an exclusive commitment is sufficient for permissibility, maybe love, or maybe mutual respect (Martha Nussbaum), then one may still get the conclusion that polygamy is permissible.

Of course, the right conclusion to draw is that casual sex is impermissible.

Tuesday, April 8, 2014

Self-inflicted sufferings, Maimonedes and anomaly

Suppose I know that if I go kayaking on a sunny day for two delightful hours, I will have mild muscle pains the next day. I judge that the price is well worth paying. I go kayaking and I then suffer the mild muscle pains the next day.

My suffering is not deserved. After all, suffering is something you come to deserve by wrongdoing, and I haven't done anything wrong. But it's also awkward to call it "undeserved". I guess it's non-deserved suffering.

It would be very implausible to run an argument from evil based on a case like this. And it's not hard to come up with a theodicy for it. God is under no obligation to make it possible for me to go kayaking on a sunny day and a fortiori he is under no obligation to make it possible for me to do so while avoiding subsequent pain. It is not difficult to think that the good of uniformity of nature justifies God's non-interference.

How far can a theodicy of this sort be made to go? Well, it extends to other cases where the suffering is a predictable lawlike consequence of one's optional activities. This will include cases where the optional activities are good, neutral or bad. Maimonedes, no doubt speaking from medical experience, talks of the last case at length:

The third class of evils comprises those which every one causes to himself by his own action. This is the largest class, and is far more numerous than the second class. It is especially of these evils that all men complain,only few men are found that do not sin against themselves by this kind of evil. Those that are afflicted with it are therefore justly blamed .... This class of evils originates in man's vices, such as excessive desire for eating, drinking, and love; indulgence in these things in undue measure, or in improper manner, or partaking of bad food. (Guide for the Perplexed, XII)

Maimonedes divides evils into three classes:

  1. evils caused by embodiment,
  2. evils inflicted by us on one another, and
  3. self-inflicted evils.
In the third class he only lists self-inflicted evils that are inflicted by bad activity, but we can extend the class as above. He insists that evils in the first and second classes are "very few and rare" and says that "no notice should be taken of exceptional cases".

The last remark is quite interesting. It goes against the grain of us analytic philosophers—exceptions are our bread and butter, it seems. But Maimonedes' insight, which mirrors Aristotle's remarks about precision in ethics, is deep and important. It suggests that the evils for which there is a plausible "problem of evil", namely the evils of the first and second classes, are an anomaly, and should be handled as such (for a development of this idea, see this paper by Dougherty and Pruss, in Oxford Studies).

Monday, April 7, 2014

Death and the Fall

It is an evil that we die. The badness of death is constituted by the cessation of the good of life. But not every cessation of a good is an evil. If I have a good conversation for several hours with a friend and then we go our separate ways, the cessation of the conversation isn't an evil. Only the cessation of a due good is an evil.

But how is it due to us not to die? Is it not a part of our very nature as human beings that we die?

Here's an argument:

  1. If the empirical manifestation of our nature matches our real nature, what we are supposed to be, then death as such is not an evil, just a cessation of a good.
  2. Death as such is an evil.
  3. So, the empirical manifestation of our nature does not match our real nature, what we are supposed to be.
Claim (3) is already on its own a kind of doctrine of the Fall. And it calls out for explanation. The story of the Fall of Humankind provides such an explanation. The naturalist, on the other hand, cannot provide an explanation for (3). I think the naturalist should perhaps deny (2), but that is quite an implausible move.

Sunday, April 6, 2014

Knowing that you can't do otherwise

Suppose as is very plausible (except for dubious interpretations of "can do otherwise") that you know that

  1. Determinism implies that you cannot ever do otherwise than you in fact do.
Suppose you also know that
  1. You will in fact do A,
say by induction from what you've done in similar circumstances. Finally, suppose that you know that
  1. Determinism holds.
Then you know premises sufficient to conclude that you cannot do otherwise than A. So, plausibly, you are in a position to know that
  1. You cannot do otherwise than A.

This is interesting. For while determinism does not by itself guarantee the possibility of knowledge of how you are determined to act, it turns out that with a bit of induction and reflection, if you know determinism to be true, you are in a position to know what you are determined to do.

It is also plausible that:

  1. When you know you cannot do otherwise than A, then you are not freely choosing A.
For take Locke's locked room example. You're having great fun at the party, and don't want to leave, but unbeknownst to you, the door is locked so you can't leave. Then maybe Locke is right that you're freely staying at the party. But as soon as you find out that the door is locked, surely you're no longer freely choosing to stay at the party. The same is plausible in more sophisticated Frankfurt cases. Note that (5) can be accepted by a compatibilist.

But now we get the interesting conclusion that if you know determinism to be true, that knowledge could very well undercut some of our freedom. For it could boost knowledge of what we will in fact do to knowledge of what we will have to do.

Objection 1: Knowledge of what we will in fact do does take away freedom, so knowing that we will have to do it doesn't take away any freedom that wouldn't already have been taken away.

Response: I know I will eat lunch today, but that doesn't take away my freedom.

Objection 2: Claim (5) is no more plausible than the disjunction of the following two principles:

  1. When you have a belief with knowledge-level justification that you cannot do otherwise than A and you think you know that you cannot do otherwise than A, then you are not freely choosing to do A
  2. When you cannot do otherwise than A, then you are not freely choosing to do A.
For the work in (5) is either done by the justified belief or by the factiveness of knowledge—it surely isn't done by anti-Gettier conditions or even by a combination of the constituents of knowledge. Now (7) begs the question against those determinists who grant (1), while (6) is false. Here's a counterexample to (6). You have knowledge-level justification that you cannot resist some temptation, and you think you know this. But being a fallibilist about knowledge you decide to try anyway, since you can try to do even what you know is impossible. And you succeed, because you didn't in fact know. So, the reason to accept (5) is a disjunction of two claims, one of which has been shown false and the other is dialectically unacceptable, so (5) is dialectically unacceptable.

Response: Maybe. But maybe the right way to reason is this. Clearly (5) is true. Now, there are two initially plausible explanations for (5), namely (6) and (7). Since (6) is false, that leaves (7). So we have an inference to best explanation from (6) to (7). And so, even though previously I was only arguing for the interesting conclusion that knowledge of determinism could take away some freedom, we have arrived at an argument for incompatibilism. The argument starts with (5), concludes to (7) by inference to best explanation, then adds (1), and concludes that freedom is incompatible with determinism.

Saturday, April 5, 2014

Responsibility and desires

Consider four cases. In each case, you know that Jones, an innocent person, is drowning and will survive if and only if you throw her a life preserver in the next two minutes. But in each of the four cases there are further facts that you know:

  1. The life preserver is locked down with a mind-reading device that will open if and only if you have a desire to eat a tarantula. You lack that desire and your character is such that you are unable to form that desire in two minutes.
  2. The life preserver is locked down with a mind-reading device that will open if and only if you have a desire to eat a tarantula. You lack that desire, as well as lacking a desire to rescue Jones, and your character is such that you are unable to form either desire in two minutes.
  3. Same as 2, but the the mind-reading device will open if and only if you have a desire to rescue Jones. You lack that desire and your character is such that you are unable to form that desire in two minutes.
  4. The life preserver is not tied down, but your character is such that you can only rescue Jones if you desire to rescue Jones. You lack that desire and your character is such that you are unable to form that desire in two minutes.

In case (1) you are not being directly responsible for failing to rescue Jones. You might, of course, be derivatively responsible, if, say, you had foreseen that the case would arise sufficiently early in the game you had foreseen that the case would come up and failed to make reasonable efforts to self-induce a desire to eat a tarantula. Such efforts could have involved reflection on the bragging rights one would gain from eating a tarantula, but it would take more than two minutes to succeed—it's too late now, anyway. With such a back story, you would be derivatively responsible for faiing to rescue Jones on the basis of your responsibility for being unable to have a desire to eat a tarantula. The case is no different from the life preserver being locked down with an ordinary lock that you have no key for and are unable to smash or pick. You have no direct responsibility, though you might have derivative responsibility if you were responsible for locking down the life preserver.

Now, in case (2), we will want to blame you. You wouldn't have rescued Jones even if you could. But while that does imply a defect of character, it is not a case of direct responsibility for failing to rescue Jones. Again, you may have derivative responsibility if you are responsible for having failed to get started earlier at self-inducing a desire to eat a tarantula. But if you're not responsible for your inability to have a desire to eat a tarantula over the next two minutes, you're not responsible for failing to rescue Jones. Though you might be responsible for failing to want to rescue Jones.

Case (3) isn't significantly different from case (2). If the mind-reading device requires you to have a desire that you are unable to form over the next two minutes, you're not directly responsible for failing to rescue, though again you may be derivatively responsible if you are responsible for your inability to have that desire.

But now consider case (4). Again, this is a case where you are unable to rescue Jones unless you form a certain desire to rescue her in two minutes, and you are unable to form that desire. The same thing as above should be true: you are at most derivatively responsible for failing to rescue Jones. And derivative responsibility requires that you be antecedently responsible for something else, in this case your inability to have over the next two minutes a desire to rescue Jones.

We need one more reflection. If you are not directly responsible in case (4) when you know the facts about your character that are given in (4), you are also not directly responsible in case (4) when he is ignorant of these facts. (You might be responsible for failing to try to induce a desire, but not for failing to induce it or for failing to rescue.[note 1])

There is a lesson here. If you are unable to do something because you're unable to have a mental state, then you're at most going to be derivatively responsible for failing to do it. Moreover this principle should not be limited to failure but needs to be applied to positive action as well: if refraining from an action would take a mental state that you are unable to gain in the time required, you're at most going to be derivatively responsible. But derivative responsibility must ultimately come from direct, non-derivative responsibility. However, if compatibilism is true, then all the things we are responsible for are determined by our motivational states. In no case like that, though, can we have non-derivative responsibility. That was the lesson of the above cases. So if compatibilism is true, there is no non-derivative responsibility, and hence there is no responsibility.

Friday, April 4, 2014

Induction, naturalness and physicalism

Something is grue provided that it is now before the year 3000 and it is green or it's the year 3000 or later and it's blue. From:

  1. All observed emeralds were grue
we should not infer that all emeralds will be grue. But from
  1. All observed emeralds were green
we should infer that all emeralds will be green. A standard thought (e.g., Sider in his Book book) is that the relevant difference between (1) and (2) is that "green" carves reality more at the joints, is more natural, than "grue".

Suppose that we understand naturalness in a Lewisian way: a concept is more unnatural the longer its expression in a language whose bits refer to perfectly natural stuff. And suppose we think that among the sciences only the terms of fundamental physics refer to perfectly natural stuff. Now consider:

  1. All observed electrons were nesitively charged
where an object is nesitively charged provided it's negatively charged and it's before the year 3000 or it's positively charged and it's 3000 or later. We had better not infer that all electrons will be nesitively charged. But "nesitively charged" is an order of magnitude more natural than "green". Consider this beginning of an account of "green":
  1. in electromagnetic radiation of the 484-789 THz range, reflecting or transmitting primarily that in the 526-606 THz range.
And this account is not finished. To make this be in terms of the perfectly natural stuff, we'd need to specify the units (terahertz) in microphysical terms, presumably in terms of Planck times or something like that, and we'll get quite messy numbers. Moreover, we need an account of reflection and transmission. I suspect that we can more easily give an account of nesitive charge: "positive" and "negative charge" seem to already be perfectly natural or close to it; the year 3000 is a bit tricky, but we can count it (or maybe just some other "neater" date) in Planck times from the Big Bang.

If naturalness then correlates with brevity of microphysical expression, "green" is not more natural, and probably is less natural, than "nesitive charge". And so we had better not base induction on naturalness.

I think the lesson of this is that we either shouldn't think of degrees of unnaturalness as distance from the perfectly natural, or we shouldn't limit the perfectly natural (even in the concrete realm) to the microphysical. The latter gives us reason to accept some kind of antireductionism about the special sciences and ordinary language.

Thursday, April 3, 2014

The neural prosthetic argument against naturalism

While it is unclear whether my mental functioning could survive my getting getting a prosthetic brain, surely it could survive my getting a prosthetic brain part:

  1. For any 0.5 centimeter cube in my brain and any machine that functions in exactly the same way with respect to inputs and outputs on the cube boundaries as the neural matter did, it is possible that replacing the cube with the machine would not change my mental functioning.
Claim (1) strengthened by removing "it is possible that" is in fact a key argument for functionalism: roughly, one repeats application of the strengthened claim until the whole brain has been replaced by a functional isomorph. So claim (1) certainly doesn't beg the question against functionalism. And it's pretty plausible.

Yesterday I argued that if functionalism is true, basic mental states are perfectly natural. In comments, Brian Cutter offered some excellent criticisms (though I responded back), but even if Cutter's criticisms are right, we still have:

  1. If functionalism is true, the realizers of basic mental states have to be at least fairly natural.
But if we replace a cube of neural matter whose state is a part of the functional realizer of a basic mental state M by a sufficiently complex prosthetic while keeping fixed edge interaction, we can make the corresponding realizer as messy as we like. By (1), mental functioning could be unchanged by this, while (2) tells us that if functionalism is true, we'd have to lose mental state M. So we've argued that
  1. If (1) and (2) are true, functionalism is false.

Now, it is actually pretty plausible that:

  1. If naturalism is true, functionalism is true.
The naturalistic alternatives to functionalism just don't seem great. So, we have an argument against naturalism based on the possibility of neural prostheses.

Anyway, probably any naturalistic alternative to functionalism will be heavily biological in nature. It will tie mental functioning to organic rather than functional features of our brains. And in so doing, it is apt to violate (1) as well. Or at least it will violate a strengthened version of (1) which says that (1) necessarily holds for any mental being whose cognitive organs have the same kind of functional density that our brains have. For the replacement of a cube by a prosthetic need not change functional density, and then one could do a second replacement, and continue. Finally, by S4 one would conclude that it is possible that mental functioning could continue after total prosthetization of the brain, which would violate the organicity of our naturalistic alternative to functionalism.

So, surprisingly, gradual replacement considerations may favor dualism, not functionalism.

Wednesday, April 2, 2014

Functionalism, biological antireductionism and dualism

According to functionalism, a mental state such as a pain is characterized by its causal roles. But if one physical state plays the causal role of pain, so do many others and so the characterization fails. For instance, if neural state N plays the causal role of pain in me, so does the conjunction of N with my having blue eyes. One could require minimality of the state, but that won't help. First, plausibly, there is no minimal state that plays the role: if a state plays it, so does that state minus a particle. Second, even if there is one, it is very unlikely to be unique. There is likely to be redundancy, and there will be many ways of getting rid of redundancy.

The solution to this problem in the spirit of Lewisian functionalism is to restrict one's quantifiers to natural states. There are two ways of doing this. First, we could restrict the quantifiers to states which are sufficiently natural, whose degree of unnaturalness is below some threshold. (An obvious way to measure unnaturalness is to measure the length of the shortest linguistic expression taht expresses the state in terms that are perfectly natural.) But this is unlikely to work. If mental states have degreed unnaturalness, presumably there will be a lot of variation in the degree of unnaturalness. Some mental states will, for instance fall far below the threshold. Those states could then be made slightly more complicated while still staying below the threshold, so once again we would have a problem.

So we better restrict quantifiers to perfectly natural states, at least in the case of the basic mental states (or maybe protomental states—I won't distinguish these) out of which more complex ones are built. Thus we have our first conclusion:

  1. If functionalism is true, basic mental states are perfectly natural.
This has an interesting corollary. Presumably no macroscopic state of a purely physical computer is perfectly natural. Thus:
  1. If functionalism is true, a purely physical computer has no basic mental states, and hence no mental states.
Thus, the only way a computer could have mental states is if it wasn't purely physical (Richard Swinburne once suggested to me that if a computer had the right functional complexity, God could create a soul for it.)

What about organisms? Well, if organisms are purely physical, then their mental states will be biological states (subject to evolution and the like). So:

  1. If functionalism is true, then some of the biological states of a minded purely physical organism are perfectly natural.
This is an antireductionist conclusion. Thus,
  1. Functionalism implies that all minded organisms have non-physical states (dualism) or some minded organisms have perfectly natural biological states (antireductionism) (or both).
Moreover, our best account of naturalness is that it is fundamentality. If that is the right account, then our antireductionism is pretty strong: it says that some biological states are fundamental.

Moreover, functionalism is the only tenable version of physicalism (I say). Thus:

  1. Physicalism implies biological antireductionism.