Modal details in Unger's argument against his existence

Unger famously argues that he doesn’t exist, by claiming a contradiction between three claims (I am quoting (1) and (2) verbatim, but simplifying (3)):

1. I exist.

2. If I exist, then I consist of many cells, but a finite number.

3. If I exist and I consist of many but a finite number of cells, then removal of the least important cell does not affect whether I exist.

Unger then says:

these three propositions form an inconsistent set. They have it that I am still here with no cells at all, even while my existence depends on cells. … One cell, more or less, will not make any difference between my being there and not. So, take one away, and I am still there. Take another away: again, no problem. But after a while there are no cells at all.

But taken literally this is logically invalid. Premise (2) says that I consist of many but a finite number of cells. But to continue applying premise (3), Unger needs that premise (2) would still be true no matter how many cells were taken away. But premise (2) does not say anything about hypothetical situations. It says that either I don’t exist, or I consist of a large but finite number of cells. In particular, there are no modal operators in (2).

Now, no doubt this is an uncharitable objection. Presumably (2) is not just supposed to be true in the actual situation, but in the hypothetical situations that come from repeated cell-removals. At the same time, we don’t want (2) to be ad hoc designed for this argument. So, probably, what is going on is that there is an implied necessity operator in (2), so that we have:

4. Necessarily, if I exist, then I consist of many cells, but a finite number.

The same issue applies to (3), since (3) needs to be applied over and over in hypothetical situations. Another issue with (3) is that to apply it over and over, we need to be told that removal of the cell is possible. So now we should say:

5. Necessarily, if I exist and I consist of many but a finite number of cells, then removal of the least important cell is possible and does not affect whether I exist.

Now, I guess, we can have a valid argument in S4.

Is this a merely technical issue here? I am not sure. I think that once we’ve inserted “Necessarily” into (4) and (5), our intuitions may start to shift. While (2) is very plausible if we grant the implied materialism, (4) makes us wonder whether there couldn’t be weird situations where I exist but don’t consist of many but a finite number of cells. First, it’s not obviously metaphysically impossible for me to grow an infinitely long tail? That, however, is a red herring. The argument can be retooled only to suppose that I necessarily have many cells and I actually have a finite number. But, second, and more seriously, is it really true that there is no possible world where I exist with only a few cells? In fact, perhaps, I once did exist with only a few cells in this world!

Similarly about (5). It’s clear that right now I can survive the loss of my least important cell. But it is far from clear that this is a necessary truth. It could well be metaphysically possible that I be reduced to some state of non-redundancy where every cell is necessary for my existence, where removal of any cell severs an organic pathway essential to life. I would be in a very different state in such a case than I am right now. But it’s far from clear that this is impossible.

Perhaps, though, the modality here isn’t metaphysical modality, but something like nomic modality. Maybe it’s nomically impossible for me to be in a state where every cell is non-redundant. Maybe, but even that’s not clear. And it’s also harder to say that the removal of the least important cell has to (in the nomic necessity sense) be nomically possible. Couldn’t it be that nomically the only way the least important cell could be removed would be by cutting into me in ways that would kill me?

Furthermore, once we’ve made our modal complications to the argument, it becomes clear that of the three contradictory premises (1), (4) and (5), premise (1) is by far the most probable. Premise (1) is a claim about my own existence, which seems pretty evident to me, and is only a claim about how things actually are now. Premises (4) and (5) depend on difficult modal details, on how things are in other worlds, and on metaphysical intuitions that are surely more fraught than those in the cogito.

(One of the things I’ve discovered by teaching metaphysics to undergraduates, with a focus on formulating logically valid arguments, is that sometimes numbered arguments in published work by smart people are actually quite some distance from validity, and it’s hard to see exactly how to make them valid without modal logic.)

Consciousness and plurality

One classic critique of Descartes’ “cogito ergo sum” is that perhaps there can be thought without a subject. Perhaps the right thing to say about thought is feature-placing language like “It’s thinking”, understood as parallel to “It’s raining” or “It’s sunny”, where there really is no entity that is raining or sunny, but English grammar requires a subject so we through in an “it”.

There is a more moderate option, though, that I think deserves a bit more consideration. Perhaps thought has an irreducibly plural subject, and in a language that expresses the underlying metaphysics better, we should say “The neurons are (collectively) thinking” or maybe even “The particles are (collectively) thinking.” On this view, thought is a relation that holds between a plurality of objects, without these objects making up a whole that thinks. This, for instance, is a very natural view for physicalist who is a compositional nihilist (i.e., thinks that only simples exists).

It seems to me that it is hard to reject this view if one’s only data is the fact of consciousness, as it is for Descartes. What kills the three-dimensionalist version of this view, in my opinion, is that it cannot do justice to the identity of the thinker over time, since there would be different pluralities of neurons or particles engaged in the thinking over time. And a four-dimensionalist version cannot do justice to the identity of the thinker in counterfactual scenarios. However, this data isn’t quite as self-evident as what Descartes wants.

In any case, I think this is a view that non-naturalists like me need to take pretty seriously.

The cogito and time-delay

I’ve been thinking about how well Descartes’ cogito argument works given the following plausisble thesis:

1. Every perception, including introspection, has a time delay.

Consider:

2. I am in pain.

3. If I am in pain, then I exist.

4. So, I exist.

Supposedly, (2) is clear and distinct. But wait (!). By (1), I only introspect premise (2) with a time delay. In other words, by the time I introspect premise (2), the pain is over. It is one thing to be in pain—obviously, when I am in pain, I am in pain—but it is another to be aware that I am in pain.

In other words, at the present moment, if I am to stick to the indubitable, all I get to say is:

5. I was in pain.

6. If I was in pain, then I existed.

7. So, I existed.

Now, if eternalism or growing block is true, I still get to conclude that I exist simpliciter, but not indubitably so (since I need to rely on the arguments for eternalism or growing block).

But there is an even more serious problem. Once we accept the time delay thesis (1), we no longer have indubitability in our introspection of pain. For suppose the time delay from being in pain to being aware that one is in pain is a microsecond. But now consider the half-microsecond hypothesis that the universe came into existence, fully formed, half a microsecond ago. If so, I would still have the introspective awareness of being in pain—without having had a pain! The half-microsecond hypothesis is crazy, but no crazier than the evil demon hypothesis that Descartes cares so much about. So now we don’t have indubitability about (2) or (5).

And what goes for pain goes for any other conscious state, i.e., for anything that Descartes calls “thought”.

We might now want to deny the time-delay thesis (1), and say that:

8. Whenever I have a conscious state Q, I am immediately thereby aware of having state Q.

But a bit of introspection shows that (8) is false. For being aware is itself a conscious state, and so if (8) were true, then whenever I have a conscious state, I have an infinite sequence of conscious states of meta-awareness. And I clearly do not.

Indeed, introspectively reflecting on the states of meta-awareness shows that sometimes the time-delay thesis is true. Let’s say that I am aware that I am in pain. It takes reflection, and hence time, to become aware that I am aware that I am in pain. So the time-delay thesis is at least sometimes true.

Now it might be that we are lucky and the time-delay thesis is false for introspection of first-order conscious states, like being in pain. I am a little sceptical of that, because I suspect a lot of non-human animals are in pain but don’t even have the first meta-step to perceiving that they are in pain.

So let’s grant that the time-delay thesis is false for introspection of first-order conscious states. Now it is no longer true that, as Descartes thought, his cogito could be run from any conscious states. It can only be run from the ones for which the time-delay thesis is false. But it’s worse than that. Even if the time-delay thesis is false for some introspective perceptions, it is not indubitable that it is false for them. The claim that these introspections lack time-delay is far from indubitable.

Yet all that said, isn’t it true that even in the half-microsecond world, I exist? Even if I didn’t have the pain that I think I had, surely to think that I had it requires that I am! Yes, but I only become aware that I think I had a pain with a time-delay from my thinking that I had a pain, because the time-delay thesis is empirically true at all the meta-levels.

This is all very strange. Maybe one can save something by supposing that awareness of a conscious state Q is always partly constituted by Q, and even with a time-delay we have indubitability. Maybe in the half-microsecond world, I couldn’t be aware of having had a pain when I didn’t have the pain, because the second-order awareness is partly constituted by the occurrence of the first-order awareness, be that occurrence past or present. Maybe, but the partial constitution thesis seems dubitable. And once we get to some meta-levels it seems implausible. Couldn’t I be mistaken in thinking that I aware that I am aware that I am aware that I am aware of Q, while in reality I only had two meta-levels?

I am feeling disoriented and confused now.

Preliminary notes on Cartesian scoring rules

Imagine an agent for whom being certain that a proposition p is true has infinite value if p is in fact true. This could be a general Cartesian attitude about all propositions, or it could be a special attitude to a particular proposition p.

Here is one way to model this kind of Cartesian attitude. Suppose we have a single-proposition accuracy scoring rule s(r, i) which represents the epistemic utility of having credence r when the proposition in fact has truth value i, where i is either 0 (false) or 1 (true). The scores can range over the whole interval [ − ∞, ∞], and I will assume that s(r, i) is finite whenever 0 < r < 1, and continuous at r = 0 and r = 1. Additionally, I suppose that the scoring rule is proper, in the sense that the expected utility of sticking to your current credence r by your own lights is at least as good as the expected utility of any other credence. (When evaluating expected utilities with infinities, I use the rule 0 ⋅ ±∞=0.)

Finally, I say the scoring rule is Cartesian with respect to p provided that s(1, 1)=∞. (We might also have s(0, 0)=∞, but I do not assume it. There are cases where being certain and right that p is much more valuable than being certain and right that ∼p.)

Pretty much all research on scoring rules focuses on regular scoring rules. With a regular scoring rule, is allowed to have an epistemic utility −∞ when you are certain of a falsehood (i.e., s(1, 0)= − ∞ and/or s(0, 1)= − ∞), the possibility of a +∞ epistemic utility is ruled out, and indeed epistemic utilities are taken to be bounded above. Our Cartesian rules are all non-regular.

I’ve been thinking about proper Cartesian scoring rules for about a day, and here are some simple things that I think I can show:

1. They exist. (As do strictly proper ones.)

2. One can have an arbitrarily fast rate growth of s(r, 1) as r approaches 1.

3. However, s(r, 1)/s(r, 0) always goes to zero as r approaches 1.

Claim (2) shows that we can value near-certainty-in-the-truth to an arbitrarily high degree, but there is a price to be paid: one must disvalue near-certainty-in-a-falsehood way more.

One thing that’s interesting to me is that (3) is not true for non-Cartesian proper scoring rules. There are bounded proper scoring rules, and then s(1, 1)/s(1, 0) can be some non-zero ratio. (Relevant to this is this post.) Thus, assuming propriety, going Cartesian—i.e., valuing certainty of truth infinitely—implies an infinitely greater revulsion from certainty in a falsehood.

A consequence of (2) is that you can have proper Cartesian scoring rules that support what one might call obsessive hypothesis confirmation: even if gathering further evidence grows increasingly costly for roughly the same Bayes factors, given a linear conversion between epistemic and practical utilities, it could be worthwhile to continue to continue gathering evidence for a hypothesis no matter how close to certain one is. I don’t think all Cartesian scoring rules support obsessive hypothesis confirmation, however.

Cartesian-style ontological arguments

Cartesian-style ontological arguments run like this:

1. God has all perfections.

2. Existence is a perfection.

3. So, God exists.

These arguments are singularly unconvincing. Here is a simple reason they are unconvincing. Suppose we are undecided on whether there are any leprechauns and, if so, whether they have a king, and someone tells us:

4. The leprechaun king is very magical.

This sure sounds plausible in a certain frame of mind, and we may accept it. When we accept (4), while remaining undecided on whether there are leprechauns and, if so, whether they have a king, what we are accepting seems to be the conditional:

5. If the leprechaun king exists, he is very magical.

By analogy, when the agnostic accepts (1), it seems they are accepting the conditional:

6. If God exists, God has all perfections.

Given premise (2), we can conclude:

7. If God exists, God exists.

But every atheist accepts (7).

It seems to make little difference if in (2) we replace “existence” with “necessary existence”. For then we just get:

8. If God exists, God necessarily exists.

That’s not quite as trivial as (7), but doesn’t seem to get us any closer to the existence of God.

The above seems to perfectly capture why it is that Cartesian-style ontological arguments are unconvincing.

Even if the above is adequate as a criticism of Cartesian-style ontological arguments, I think there is still an interesting question of what sort of a conditional we have in (5)–(8)?

It’s not a material conditional, for then (5) would be trivially true given that there are no leprechauns, while (5) is non-trivially true.

Should it be a subjunctive conditional, like “If the leprechaun king existed, he would be very magical”? I don’t think so. For suppose that in the closest possible leprechaun world to ours, for some completely accidental reason, the leprechaun king is very magical, but in typical possible worlds with leprechauns, leprechaun kings are are actually rather a dud with regard to magicality. Then it’s true that if the leprechaun king existed, he would be very magical, but that shouldn’t lead us to say that the leprechaun king is very magical.

Perhaps it should be a strict conditional: “Necessarily, if the leprechaun king exists, he is very magical.” That actually sounds fairly plausible, and in light of this we would actually want to deny (4). For it is not necessary that the leprechaun king be very magical. But if we take it to be a strict conditional, we still have a triviality problem. Imagine an atheist who thinks that God is impossible. Then the strict conditional

9. Necessarily, if God exists, God has all perfections

is true, but so is:

10. Necessarily, if God exists, God has exactly 65% of the perfections.

But while it seems that our atheist would be likely to want to say that God has all perfections (indeed, that might be a part of why the atheist thinks God necessarily does not exist, for instance because they think that the perfections are contradictory), it doesn’t sound right to say that God has exactly 65% of the perfections, even if you think that necessarily there is no God.

I think the best bet is to make the conditional be a strict relevant conditional:

11. Necessarily and relevantly, if God exists, God has all perfections.

It is interesting to ask whether (11) helps Cartesian-style ontological arguments. Given (11), if all goes well (it’ll depend on the modal relevance logic) we should get:

12. Necessarily and relevantly, if God exists, God exists.

That sounds right but is of no help. We also get:

13. Necessarily and relevantly, if God exists, God necessarily exists.

Again, that sounds right, and is less trivial, but still doesn’t seem to get us to the existence of God, barring some clever argument.

Aquinas and Descartes on substance dualism

Roughly, Aquinas thinks of a substance as something that:

1. is existentially independent of other things, and

2. is complete in its nature.

There is a fair amount of work needed to spell out the details of 1 and 2, and that goes beyond my exegetical capacities. But my interest is in structural points. Things that satisfy (1), Aquinas calls “subsistent beings”. Thus, all substances are subsistent beings, but the converse is not true, because Aquinas thinks the rational soul is a subsistent being and not a substance.

Descartes, on the other hand, understands substance solely in terms of (1).

Now, historically, it seems to be Descartes and not Thomas who set the agenda for discussions of the view called “substance dualism”. Thus, it seems more accurate to think of substance dualists as holding to a duality of substance in Descartes’ sense of substance than in Aquinas’.

But if we translate this to Thomistic vocabulary, then it seems we get:

3. A “substance dualist” in the modern sense of the term is someone who thinks there are two subsistent beings in the human being.

And now it looks like Aquinas himself is a substance dualist in this sense. For Aquinas thinks that there are two subsistent beings in Socrates: one of them is Socrates (who is a substance in the Thomistic sense of the word) and the other is Socrates’ soul (which is a merely subsistent being). To make it sound even more like substance dualism, note that Thomas thinks that Socrates is an animal and animals are bodies (as I have learned from Christopher Tomaszewski, there are two senses of body: one is for the material substance as a whole and the other is for the matter; it is body in the sense of the material substance that Socrates is, not body in the sense of matter). Thus, one of these subsistent beings or substances-in-the-Cartesian-sense is a body and the other is a soul, just as on standard Cartesian substance dualism.

But of course there are glaring difference between Aquinas’ dualism and typical modern substance dualisms. First, and most glaringly, one of the two subsistent beings or Cartesian substances on Aquinas’s view is a part of the other: the soul is a part of the human substance. On all the modern substance dualisms I know of, neither substance is a part of the other. Second, of the two subsistent beings or Cartesian substances, it is the body (i.e., the material substance) that Aquinas identifies Socrates with. Aquinas is explicit that we are not souls. Third, for Aquinas the body depends for its existence on the soul—when the soul departs from the body, the body (as body, though perhaps not as matter) perishes (while on the other hand, the soul depends on the matter for its identity).

Now, let’s move to Descartes. Descartes’ substance dualism is widely criticized by Thomists. But when Thomists criticize Descartes for holding to a duality of substances, there is a danger that they are understanding substance in the Thomistic sense. For, as we saw, if we understand substance in the Cartesian sense, then Aquinas himself believes in a duality of substances (but with important structural differences). Does Descartes think there is a duality of substances in the Thomistic sense? That is not clear to me, and may depend on fine details of exactly how the completeness in nature (condition (2) above) is understood. It seems at least in principle open to Descartes to think that the soul is incomplete in its nature without the body or that the body is incomplete in its nature without the soul (the pineal gland absent the soul sure sounds incomplete) or that each is incomplete without the other.

So, here is where we are at this point: When discussing Aquinas, Descartes and substance dualism we need to be very careful whether we understand substance in the Thomistic or the Cartesian sense. If we take the Cartesian sense, both thinkers are substance dualists. If we take the Thomistic sense, Aquinas clearly is not, but it is also not clear that Descartes is. There are really important and obvious structural differences between Thomas and Descartes here, but they should not be seen as differences in the number of substances.

And here is a final exegetical remark about Aquinas. Aquinas’ account of the human soul seems carefully engineered to make the soul be the sort of thing—namely, a subsistent being—that can non-miraculously survive in the absence of the substance—the human being—that it is normally a part of. This makes it exegetically probable that Aquinas believed that the soul does in fact survive in the absence of the human being after death. And thus we have some indirect evidence that, in contemporary terminology, Aquinas is a corruptionist: that he thinks we do not survive death though our souls do (but we come back into existence at the resurrection). For if he weren’t a corruptionist, his ontology of the soul would be needlessly complex, since the soul would not need to survive without a human being if the human being survived death.

And indeed, I think Aquinas’s ontology is needlessly complex. It is simpler to have the soul not be a subsistent being. This makes the soul incapable of surviving death in the absence of the human being. And that makes for a better view of the afterlife—the human being survives the loss of the matter, and the soul survives but only as part of the human being.

Omniscience, omnipotence and perfection

Recently, I’ve been worried about arguments like this:

1. It is always more perfect to be able to do more things.

2. Being able to do impossible things is a way of being able to do more things.

3. So, a perfect being can do impossible things.

But I really don’t want to embrace 3.

It’s just occurred to me, though, that the argument 1-3 is parallel to the clearly silly argument:

4. It is always more perfect to know more things.

5. Knowing falsehoods is a way of knowing more things.

6. So, a perfect being knows falsehoods.

Once we realize that among “more things” there could be falsehoods, it becomes clear that 4 as it stands is false, but needs to be restricted to the truths. But arguably what truths are to knowledge, that possibles are to power (I think this may be a Jon Kvanvig point, actually). So we should restrict 1 to the possibles.

Beatific vision and scepticism

One way to think of the beatific vision is as a conscious experience whose quale is God himself. Not a representation of God, but the infinite and simple God himself. Such an experience would have have a striking epistemological feature. Ordinary veridical experiences are subject to sceptical worries because the qualia involved in them can occur in non-veridical experiences, or at least can have close facsimiles occurring in non-veridical experiences. But while everything is similar to God, the similarity is always infinitely remote. Moreover, there is a deep qualitative difference between God in the beatific vision and other qualia. No other quale is a person or even a substance.

Thus, someone who has the beatific vision is in the position of having an experience that is infinitely different from all other experiences, veridical or not. This, I think, rules out at least one kind of sceptical worry, and hence the beatific vision is also a fulfillment of the Cartesian quest for certainty—though that is far from being the most important feature of the beatific vision.

Priors, justification and rationalism

The rationalism of Leibniz and Spinoza worked like this: We figure out fundamental necessary metaphysical principles, and these principles determine everything else of necessity (with some qualifications on the Leibniz side as to the type of necessity).

But another rationalism is possible: We figure out fundamental necessary metaphysical principles, and these principles determine the basic probabilistic structure of reality. In Bayesian terms, the fundamental metaphysical principles yield the prior probabilities. A version of this was Descartes’ project in the Meditations.

And there is reason to engage in this probabilistic rationalist project. We cannot get out of the need to have something like prior probabilities. Moreover, priors need epistemic justification. Consider an empirical claim p that we assign a high enough credence for belief to, say 0.99, on the basis of total evidence e. Thus, P(p|e)=0.99. It follows by the axioms of probability that P(p ∨ ¬e)≥0.99. Hence we have a high enough prior credence for belief in p ∨ ¬e. Surely assigning a credence of 0.99 to something requires epistemic justification. Moreover, surely (though people who don’t like closure arguments may not like it) if we have posterior justification when we believe p, we have posterior justification when we believe the obviously entailed claim p ∨ ¬e. But this justification did not come from e. For P(p ∨ ¬e|e)=P(p|e)=0.99 and we have seen that P(p ∨ ¬e)≥0.99, so e is not evidence for p ∨ ¬e (in face, typically e will be evidence against this disjunction). Since e is our total evidence, the justification had to be there in the first place.

Thus we need epistemic justification for our priors. The priors encode genuine information about our world, information that we are justified in possessing. Where do we justifiedly get this information from? We don’t get it through logic, pace logical probability accounts. Metaphysics is one potential answer to this question and exploring this answer gives us good reason to engage in the probabilistic rationalist project. Another option is that the priors are a kind of innate knowledge built into our nature—my Aristotelian Bayesianism is a version of this.

Humean metaphysics implies Cartesian epistemology

Let’s assume two theses:

1. Humean view of causation.

2. Mental causalism: mental activity requires some mental states to stand in causal relations.

If I accept these two theses, then I can a priori and with certainty infer a modest uniformity of nature thesis. Here’s why. On mental causalism, mental activity requires causation. On Humeanism, causation depends on the actual arrangement of matter. If the regularities found in my immediate vicinity do not extend to the universe as a whole, then they are no causal laws or causal relations. Thus, given causalism and Humeanism, I can infer a priori and with certainty from the obvious fact that I have mental states that there are regularities in the stuff that my mind is made of that extend universally. In other words, we get a Cartesian-type epistemological conclusion: I think, so there must be regularity.

In other words, Humean metaphysics of nature plus a causalist theory of mind implies a radically non-Humean epistemology of nature. The most plausible naturalist theories of mind all accept causalism. So, it seems, that a Humean metaphysics of nature plus naturalism—which is typically a part of contemporary Humean metaphysics—implies a radically non-Humean epistemology of nature.

So Humean metaphysics and epistemology don’t go together. So what? Why not just accept the metaphysics and reject the epistemology? The reason this is not acceptable is that the Cartesian thesis that the regularity of nature follows with certainty from what I know about myself is only plausible (if even then!) given Descartes’ theism.

Two conceptions of matter

The philosophical tradition contains two conceptions of matter. One kind, associated with Descartes, connects matter with space: matter is what is responsible for spatial properties like extension or location. The other, associated with Aristotle, connects matter with passivity: matter is what makes an entity have a propensity to be the patient of causal influences. The spatial conception of matter has been the more popular one in recent times. But here is a reason not to go for the spatial conception of matter. The concept of materiality seems fairly close to the fundamental level. But it may well turn out--string theory is said to push in that direction--that at the fundamental level there is no such thing as space or time or spacetime. If that is a serious epistemic possibility, it would be good to do more work on the Aristotelian option.

Wanting to be even more sure

We like being sure. No matter how high our confidence, we have a desire to be more sure, which taken to an extreme becomes a Cartesian desire for absolute certainty. It's tempting to dismiss the desire for greater and greater confidence, when one already has a very high confidence, as irrational.

But the desire is not irrational. Apart from certain moral considerations (e.g., respecting confidentiality) a rational person does not refuse costless information (pace Lara Buchak's account of faith). No matter how high my confidence, as long as it is less than 100%, I may be wrong, and by closing my ears to free data I close myself to being shown to have been wrong, i.e., I close myself to truth. I may think this is not a big deal. After all, if I am 99.9999% sure, then I will think it quite unlikely that I will ever be shown to have been wrong. After all, to be shown to be wrong, I have to actually be wrong ("shown wrong" is factive), and I think the probability that I am wrong is only 0.0001%. Moreover, even if I'm wrong, quite likely further evidence won't get me the vast distance from being 99.9999% sure to being unsure. So it seems like not a big deal to reject new data. Except that it is. First, I have lots of confident beliefs, and while it is unlikely for any particular one of my 99.9999%-sure beliefs to be wrong, the probability that some one of them is wrong is quite a bit higher. And, second, I am a member of a community, and for Kantian reasons I should avoid epistemic policies that make an exception of myself. And of course I want others to be open to evience even when 99.9999% sure, if only because sometimes they are 99.9999% sure of the negation of what I am 99.9999% sure of!

So we want rational people to be open to more evidence. And this puts a constraint on how we value our levels of confidence. Let's say that I do value having at least 99.9999% confidence, but above that level I set no additional premium on my confidence. Then I will refuse costless information when I have reached 99.9999% confidence. I will even pay (perhaps a very small amount) not to hear it! For there are two possibilities. The new evidence might increase my confidence and might decrease it. If it increases it, I gain nothing, since I set no additional premium on higher confidence. If it decreases it, however, I am apt to lose (this may requiring tweaking of the case). And a rational agent will pay to avoid a situation where she is sure to gain nothing and has a possibility of losing.

So it's important that one's desire structure be such that it continue to set a premium on higher and higher levels of confidence. In fact, the desire structure should not only be such that one wouldn't pay to close one's ears to free data, but it should be such that one would always be willing to pay something (perhaps a very small amount) to get new relevant data.

Intuitively, this requires that we value a small increment in confidence more than we disvalue a small decrement. And indeed that's right.

So our desire for greater and greater confidence is indeed quite reasonable.

There is a lesson in the above for the reward structure in science. We should ensure that the rewards in science—say, publishing—do not exhibit thresholds, such as a special premium for a significance level of 0.05 or 0.01. Such thresholds in a reward structure inevitably reward irrational refusals of free information. (Interestingly, though, a threshold for absolute certainty would not reward irrational refusals of free information.)

I am, of course, assuming that we are dealing with rational agents, ones that always proceed by Bayesian update, but who are nonetheless asking themselves whether to gather more data or not. Of course, an irrational agent who sets a high value on confidence is apt to cheat and just boost her confidence by fiat.

Technical appendix: In fact to ensure that I am always willing to pay some small amount to get more information, I need to set a value V(r) on the credence r in such a way that V is a strictly convex function. (The sufficiency of this follows from the fact that the evolving credences of a Bayesian agent are a martingale, and a convex function of a martingale is a submartingale. The necessity follows from some easy cases.)

This line of thought now has a connection with the theory of scoring rules. A scoring rule measures our inaccuracy—it measures how far we are from truth. If a proposition is true and we assign credence r to it, then the scoring rule measures the distance between r and 1. Particularly desirable are strictly proper scoring rules. Now for any (single-proposition) scoring rule, we can measure the agent's own expectation as to what her score is. It turns out that the agent's expectation as to her score is a continuous, bounded, strictly concave function ψ(r) of her credence r and that every continuous, bounded, strictly concave function ψ defines a scoring rule such that ψ(r) is the agent's expectation of her score. (See this paper.) This means that if our convex value function V for levels of confidence is bounded and continuous—not unreasonable assumptions—then that value function V(r) is −ψ(r) where ψ(r) is the agent's expectation as to her score, given a credence of r, according to some strictly proper scoring rule.

In other words, assuming continuity and boundedness, the consideration that agents should value confidence in such a way that they are always willing to gather more data means that they should value their confidence in exactly the way they would if their assignment of value to their confidence was based on self-scoring (i.e., calculating their expected value for their score) their accuracy.

Interestingly, though, I am not quite sure that continuity and boundedness should be required of V. Maybe there is a special premium on certainty, so V is continuous within (0,1) (that's guaranteed by convexity) but has jumps—maybe even infinite ones—at the boundaries.

Another argument from Mersenne

In The Impiety of Deists, etc., Mersenne also gives this theistic argument:

And if there is no God, no independent being, it would be impossible that one exist, and thus our imagination would exceed all the beings of the word: and the being of our thoughts and our fantasies [phantasies] would infinitely exceed all real beings, and what would be imaginary would surpass the true, which cannot be. (p. 75)

There are a couple of interesting things. First, often Leibniz gets credited with noticing that if God possibly exists, then God actually exists. But here we see Mersenne claiming the contrapositive, almost two decades before Descartes' Meditations (in an objection to Descartes' Meditations, Mersenne also makes the point in the Leibniz form).

Second, we get an interesting argument:

1. If God doesn't exist, our imagination exceeds reality.
2. Our imagination does not exceed reality.
3. So, God exists.

We can also replace "exceed(s)" with "infinitely exceed(s)", which makes (2) even more plausible and (1) is still true. There are obvious connections between this and Descartes' infinity argument in the Meditations.

When thinking about this argument, I was initially puzzled why Mersenne starts the argument by arguing that if there is no God then the existence of God is impossible. After all, (1)-(3) doesn't seem to require the impossibility of God, just the non-actuality of God. My tentative interpretation is that Mersenne has in mind a fairly strong notion of "exceeds". Possibility has a certain foot in reality, and so for imagination to fully exceed reality, one would have to not only imagine something greater than what actually exists, but greater than what is possible. Now, God is greater than all non-divine possibilities. So if God is impossible, then the content of our thoughts outruns not just actuality but possibility, and that's what makes that content strongly outrun reality.

If this is right, then we can expand the argument as follows:

4. If God doesn't exist, it is impossible for God to exist. (Premise)
5. God is greater than all possibilities and actualities other than God. (Premise)
6. We can think of God. (Premise)
7. We cannot think of anything that exceeds all actualities and possibilities.
8. God doesn't exist. (Supposition for reductio)
9. God is not a possibility or actuality. (4 and 8)
10. We can think of something that exceeds all actualities and possibilities. (5, 6 and 9)
11. Contradiction! (7 and 10)
12. So, God exists. (By reductio)

Finally, it is rather interesting how Mersenne argues for the thesis if God doesn't exist, he can't exist. In the context of another argument, he says:

He isn't a being, as we supposed, he can't exist: since who would make him, and who would give him being [qui luy donneroit estre]? (p. 119)

My first thought on this was that Mersenne subscribes to the causal theory of possibility that I've defended. My second thought, however, was that his argument may be broader. The "who would give him being?" rhetorical question may work on any view on which possibility is grounded in actuality given the plausibility that God's possibility couldn't be grounded in anything other than himself, or else he wouldn't truly be an independent being (and notice the focus on independence in the first Mersenne quote).

By the way, while I am relying on my own translations in the above (partly for fun), professional translations can be found here.

Intensity of desire

Here are three things I would like:

1. Not to be kidnapped by aliens today for medical experiments.
2. To own the Hope Diamond.
3. To own a minivan.

My preferences go in this order. I'd choose not being kidnapped by aliens over the Hope Diamond and over a minivan, and I'd choose the Hope Diamond over the minivan, since I would sell the Hope Diamond and buy a minivan and many other nice things. But the intensity of my feelings goes in the other direction. I have a moderately intense feeling of desire to own a minivan. I have very little feeling of desire to own the Hope Diamond, and I find myself with even less in the way of feelings about being kidnapped by aliens, though imaginative exercises can shift these around.

So when we talk of the strength of a desire we are being ambiguous between talking of the intensity of the feeling and degree of preference. One might think of the degree of preference as something like a part of the content of the desire—the desire representing the degree to which one is to pursue something—while the intensity of the feeling is external to the content.

Those of us who think of emotions in a cognitive way, and who think there are many normative facts about what emotions one should have given one's situation, may be tempted to think that the intensity of the feeling should match the degree of preference. But that is mistaken. There are perfectly good reasons why my desire for the Hope Diamond and for not being kidnapped by aliens today should be less intensely felt than my desire for a minivan. The minivan is an appropriate object for my active pursuit, for instance, while I have little hope of getting the Hope Diamond and little fear of being kidnapped by aliens.

Maybe, then, the intensity of the desire should be proportional to the role that the desire should play in one's pursuits? That's an interesting hypothesis, but not clearly true. Let's say that you are told that you will be executed if and only if 2^9288389−1 is prime. At this point it seems quite right and proper to have an intense that this number not be a prime. But there is nothing you can do about it; barring Cartesian ideas about God and mathematics, there is no pursuit that you can engage in that can make it more or less likely that the number is a prime.

A better story would be that the intensity of the desire should be proportional to some kind of a salience. One way of the desire being salient is that it should play a heavy role in one's present pursuits. But there may be other ways for it to be salient.

There is, anyway, a spot of spiritual comfort in all this. Sometimes people worry that they do not desire God as much as they desire earthly things. But a distinction must be made. Preferring earthly things to God is clearly bad. But having a more intense desire for an earthly thing than for God may not always be a bad thing. For sometimes one must focus on an earthly task for God's sake, and a means can be more salient than the end.

We are fundamental entities

"I think therefore I am." It's hard to dispute either the argument or the conclusion. But while I undoubtedly exist, do I have to be one of the fundamental objects in the ontology?

Here is a line of thought to that conclusion, somewhat similar to some things I've heard Rob Koons say. Non-fundamental objects are entia rationis, at least in part creatures of our cognitive organization of the world. But we cannot be, even in part, mere creatures of our cognitive organization of the world on pain of circularity. So whatever non-fundamental objects there may be, we are not among them.

I think the controversial claim in the argument may be that non-fundamental entities are entia rationis, but I am not sure. This whole line of argument is difficult for me to think about.

Content externalist solutions to sceptical problems

A standard solution to general sceptical problems is to move to an externalist account of content. Grossly oversimplifying, if what makes a thought be about horses is that it has a causal connection with horses, then thoughts about horses can't be completely mistaken. This sort of move might be thought to be anti-realist, though I think that's a poor characterization. If this sort of move works, then we couldn't have thoughts and yet have our whole system of thoughts be completely mistaken. And hence, it seems, scepticism is dead.
But it just occurred to me that there is a hole in this argument. Why couldn't the sceptic who accepts the externalist story about content still say: "So, if I am thinking at all, then global scepticism is false. But am I thinking at all?" This may seem to be a completely absurd position—how could one doubt whether one is thinking? Wouldn't the doubt be a thought? Yes, the doubt would be a thought. Hence, the person who doubts whether she thinks would not be able to believe that she doubts. And, of course, the person who thinks she's not thinking has a contradiction between the content of her thought and the fact of her thought, but it's not so obvious that that's a contradiction in her thought (just as a contradiction between the content of an astronomical belief and an astronomical fact need not be a contradiction in the thinker's thought). Besides, the Churchlands think that they have no thoughts, and have given arguments for this.
If I am right in the above, then the content externalist move does not solve the problem of scepticism—it simply radicalizes it. But it raises the cost of scepticism—it forces the sceptic to stop thinking of herself as thinking. And as such it may be practically useful for curing scepticism if the sceptic isn't a full Pyrrhonian, in the way a rose or some other creature that has no thoughts is. However, if the motivation for the content externalism is to solve the problem of scepticism, rather than cure the sceptic, then the motivation seems to fail. (One difference between solving and curing is this. If a theory T solves a problem, then we have some reason to think T is true by inference to best explanation. But if believing a theory T would cure someone of a problem, inference to best explanation to the truth of T is not available. Though, still, I think the fact that believing T is beneficial would be some evidence for the truth of T in a world created by the good God.)

Yet another ontological argument

I've never heard the following version of the ontological argument put quite in this way, though there may be things in Anselm and Descartes that suggest it:

1. (Premise) An impossible being is imperfect.
2. A perfect being is possible. (By (1))
3. (Premise) Necessarily, a contingently existing being is imperfect.
4. A perfect being exists necessarily. (By 2 and 3)
5. (Premise) What exists necessarily also actually exists.
6. A perfect being actually exists. (By 4 and 5)

I don't know if (2) validly follows from (1). Or maybe there is a problem with (1), in that we simply cannot attribute about impossibilia?

Why believe (1)? Well, one line of thought is that impossibility is an impotence. Another is that an impossible property entails all properties, and in particular such properties as being imperfect, and no imperfect being is perfect.

A schema for theistic arguments

1. We think thoughts that are about Fness.
2. There is no good naturalistic explanation of how our F-thoughts manage to make claims about reality.
3. The best explanation of how our thoughts succeed in being about Fness, of how our F-thoughts have intentionality, involves God.

As far as I know, the first to give an argument of this form was Descartes, and he contributed the first two of the examples below. Examples of Fs that might fit in this argument schema include:

• God
• infinity
• duty
• truth
• reference
• metaphysical possibility
• good
• proper function
• normative
• numinous
• objectively beautiful

The point in this line of argument isn't that these properties depend on God. Rather, our grasp of these properties either is given to us by God, directly or not.

A related argument schema is to ask for the explanation of how we know F-facts.

[I may end up enlarging this list from time to time by editing this post. At least one of the entries is due to a commenter--see comments below.]

Introspection of judging

Consider the concept of a judging. A judging is a believing operating occurrently and consciously (this is stipulative). Sometimes, a judging comes at the beginning of believing: after weighing the evidence, I judge that p, and my judging that p is the beginning of my believing that p, a believing that soon slides from occurrence into dispositionality. Sometimes, perhaps, I have a belief dispositionally which I never acquired by means of a judging, but which belief comes to the mental foreground, and becomes a judging.

Let us suppose that for every believing there is a belief, namely a proposition that is believed. Then, since a judging is a kind of believing, every judging is associated with a proposition that is adjudged, a proposition that one might call the judgment. (Actually, "belief" and "judgment" are ambiguous in English between the proposition and the mental act; so I am here stipulating that I will use an "-ing" form for the mental act—e.g., "believing" or "making a judgment"—and "belief" and "judgment" for the propositional object of the mental act.) I shall also assume that a proposition, perhaps unlike a declarative sentence, is always either true or false.

Here is an anti-Cartesian thesis that I am going to offer an argument for, and then discuss whether one can get out of the argument:

1. It need not be possible to introspect whether a mental act is a judgment, and whether a mental act is a judgment is not an internal property of the mental act.

The argument is fairly simple. It is possible for me to judge that

2. Fred right now is not making a judgment that is true.

In judging (2), I might even be judging correctly—for instance, if Fred is asleep, or if Fred is judging that I do not exist. By exactly the same token, it is possible for Fred to judge that

3. Alex right now is making a judgment that is true.

Now imagine three possible worlds w₁, w₂ and w₃. These worlds are exact duplicates up to but not including t₀. In particular, prior to t₀, the distinctions between the three worlds are is not introspectible either to me or to Fred. Assume also that neither of us is within sensory range of the other at t₀. Now suppose that in w₁ at t₀, I make the judgment (2), and I am right, because Fred has just fallen asleep at t₀. In w₂ at t₀, I have just fallen asleep, and Fred makes the judgment (3), which judgment is thus wrong. Now, in w₃ at t₀, I have exactly the internal properties that I do in w₁, while Fred has exactly the internal properties that he does in w₂. But now observe that there is a very good argument that it is not the case that both I and Fred make a judgment at t₀ in w₃. For if I make a judgment at t₀ in w₃, it is surely the judgment (2). And if Fred makes a judgment at t₀ in w₃, it is surely the judgment (3). Let p₁ and p₂ be the respective judgments—the propositions adjudged. Then, plainly, p₁ is true if and only if p₂ is false, and p₂ is true if and only if p₁ is true. But that is a contradiction.

But introspectively, surely, w₃ at t₀ is just like w₁ for me, and just like w₂ for Fred. In w₁, I do make a judgment, and in w₂, Fred makes a judgment. Therefore, if I fail to make a judgment at t₀ in w₃, then whether I make a judgment is not introspectible, nor is it a matter of my internal properties, as I have the same internal properties at t₀ in w₁ and w₃, and hence (1) is true. Likewise, if Fred fails to make a judgment at t₀ in w₃, (1) is true. Since at least one of us fails to make a judgment at t₀ in w₃, it follows that (1) is true.

Can a Cartesian get out of the argument? I think the following are the main controversial premises (all of them purporting to be a necessary truth): (a) all judgments are propositional, (b) all propositions are true or false, (c) introspection depends on one's internal states, (d) one's internal states do not depend on what is simultaneously happening far away, and (e) if I or Fred make a judgment in w₃ at t₀, the judgment is (2) or (3), respectively.

If we're not Cartesians, perhaps we will happily embrace (1). But I think (1) has an unfortunate result, namely that it opens up the possibility of a sceptical hypothesis far more radical than any Descartes considers: the hypothesis that perhaps I am not actually making any judgments, and that this is true all the way down (I do not actually judge myself to be thinking, nor do I actually judge myself to be judging to be thinking, etc.)

The easiest way out for the Cartesian might be to deny (a). But then the Cartesian still has the unfortunate result that one cannot introspect whether there is a proposition that one is judging. That will, probably, be rather uncomfortable for the Cartesian, and the resulting sceptical hypothesis will still be nasty.

I myself am attracted to really crazy solutions, and in particular I think that each of (c), (d) and (e) is such that one can non-absurdly deny it.

As for (c), it might be trivially true. If it's trivially true, then (1) is less interesting. What is interesting is not whether we can always know by "introspection" whether we are judging, but whether we can always tell directly whether we are judging. The view under consideration would be one on which one has a non-natural way of recognizing what is going on far away, but perhaps one is unable to express it. This is weird, but not absurd.

The radical externalist will deny (d). The theist who believes in divine simplicity will have reason to deny (d) in the case of God. And one might have a weird non-naturalist view on which (d) is denied in our case. Again, not absurd.

As for (e), I think its denial is perhaps the most interesting option for the Cartesian. Spinoza thought all our judgments were true. A consequence of his view was that sometimes we can be unwittingly behaving as if we were judging that p, while in fact we are not judging that q. We behave as if we believed the stick in the water is broken. But in fact, what we are judging, according to Spinoza, is that our bodies are broken-stickly affected. It is only in the case, Spinoza insists, where we have conclusive and infallible evidence of the stick's being broken that we are judging that the stick is broken. This is weird indeed. But it may well indeed be where certain Cartesian thoughts taken to their natural conclusion lead. I do not want to go all the way with Spinoza to say that all our judgments are true, though I think his view can be defended more effectively than one might at first suppose. Rather, I want to focus on Spinoza's insight that the content of one's judgments may be belied by the words with which one expresses them, even in the case of someone who has mastered the language.

Knowing confusedly

Contemporary American philosophers tend to encounter the distinction between confused and distinct concepts in Descartes, and the distinction can be somewhat mystifying there—the "confused" seems a pejorative, for instance. It's interesting that the distinction is one that is already present in Aquinas. In Aquinas, the distinction is between knowing something confusedly and knowing it distinctly. There seem to be three paradigmatic ways one can know something confusedly:

1. Knowing the whole without knowing the parts. For instance, we may confusedly know our bodies without knowing the kidneys.
2. Knowing several individuals under a common description they all satisfy. For instance, in some sense we know all human beings—namely, we know that they are all human and hence have the properties that all humans have. But we know them under a common description here.
3. Knowing a nature (e.g., humanity) under an accidental rather than essential description. Thus, if I know humanity as my own species, I know humanity only confusedly (it is an accidental property of humanity that it is my own species—this is true in the Aristotelian sense of "accidental" and probably also in the modern, since were I not to have existed, then I would not have been human). But I know humanity distinctly when I know it as rational animality, Aquinas thinks. Aquinas uses this distinction to solve the puzzle of how we can perform the Socratic task of seeking a definition for something, since we allegedly need a definition to know what we are seeking the definition of. The answer is that we only need to know confusedly what we are seeking the definition of.[note 1]

Of these, the third seems best to match Descartes' usage and I think it is a reasonable hypothesis that this is what Descartes has in mind. What is interesting, though, is that Aquinas will not tolerate Descartes' claim that we have a clear and distinct concept of God. For the essence of God is beyond our knowledge in this life according to Aquinas. Aquinas and Descartes agree that if we had the concept of God clearly and distinctly, we would know that God exists. But Aquinas denies the antecedent of this conditional (while accepting the consequent but on other grounds).

I wonder if Descartes' discussion of the clarity and distinctness of the concept of God doesn't commit a certain fallacy. In Aquinas, the concept of confusion is not a pejorative concept. The philosopher knows all things—but confusedly, at least in sense (2) (the philosopher knows general descriptions under which all things fall). There is no cognitive failing in knowing things confusedly. In fact, knowing things confusedly can be a cognitive achievement. To see the trees is distinct knowledge, while to see the forest is confused knowledge in sense (1)—but this confused knowledge is an achievement. In sense (2), our ability to abstract things is what gives rise to confused knowledge, and this confusion is an achievement. In sense (3) it is a bit harder to see the confusion as an achievement, but it is. For it is one thing to know that humanity is rational animality, and another to know that it is my species (I am not sure Aquinas would see it this way). One can know the former without knowing the latter, and so the latter confused knowledge is an achievement in part independent of the distinct knowledge.

The fallacy I am thinking of is that I get the feeling at times that for Descartes "confusion" is pejorative (just as it is in 21st century English). Now, then, Descartes may be having the following intuition behind thinking that the concept of God is not confused: Were the concept confused, there would be something wrong in us for having it—but to have the concept is surely a positive intellectual attainment. But if we see that there is nothing negative about having a confused concept of God (though in some ways it would be better to have a distinct one), then it becomes much easier to just that our concept of God is confused.

One reason to think Descartes would take "confusion" in a pejorative sense is that apparently it did have that valuatively negative sense in 17th century French (at least the 1694 French dictionary I have on my PDA gives only valuatively negative examples under "confusion").