Naturalism and property dualism

It is generally taken that a view on which there are mental properties that do not supervene on the properties of physics is a non-naturalistic view: it is a form of property dualism.

But now imagine that we find out that:

1. There are chemical properties that do not supervene on the properties physics speaks of.

That would be a really exciting discovery, but it wouldn’t be a discovery incompatible with naturalism. The new chemical properties would presumably be just as natural as the physical ones.

So, why would we call non-supervenient mental properties non-natural, if we wouldn’t call non-supervenient chemical properties non-natural? It can’t be just because chemical properties are the province of a science, namely chemistry. For mental properties are the province of a science, too, namely psychology.

While we’re exploring this corner of logical space, consider this view:

2. Chemical properties do not supervene on physical properties, and mental properties do not supervene on physical properties either, but mental properties do supervene on, and even reduce to, physical and chemical properties.

I’ve never met an advocate of (2). It would be a very strange view. But here is one that, I think, is not actually all that strange:

3. Biological properties do not supervene on physical properties, and mental properties do not supervene on physical properties either, but mental properties do supervene on, and even reduce to, biological properties.

I think view (3) is worth thinking about. Most of the people who have tried to reduce the mental have tried to reduce it to the physical, but perhaps a reduction to an irreducible biological level would be more promising.

Ordinary language and "exists"

In Material Beings, Peter van Inwagen argues that his view that there are no complex artifacts does not contradict (nearly?) universal human belief. The argument is based on his view that the propositions expressed by ordinary statements like “There are three valuable chairs in this room” do not entail the negation of the Radical Claim that there are no artifacts, for such a proposition does not entail that there exist chairs.

I think van Inwagen is right that such ordinary propositions do not entail the negation of the Radical Claim. But he is wrong in thinking that the Radical Claim does not contradict nearly universal human belief. Van Inwagen makes much of the analogy between his view and the Copernican view that the sun does not move. When ordinary people say things like “The sun moved behind the elms”, they don’t contradict Copernicus. Again, I think he is right about the ordinary claims, but nonetheless Copernicus contradicted nearly universal human belief. That was why Copernicus’ view was so surprising, so counterintuitive (cf. some remarks by Merricks on van Inwagen). One can both say that when people prior to Copernicus said “The sun moved behind the elms” they didn’t contradict Copernicanism and that they believed things that entailed that Copernicus is wrong.

People do not assert everything they believe. They typically assert what is salient. What is normally salient is not that the sun actually moved, but that there was a relative motion between the rays pointing to the elms and to the sun. Nonetheless, if ordinary pre-Copernicans said “The sun doesn’t stand still”, they might well have been contradicting the Copernican hypothesis. But rarely in ordinary life is there occasion to say “The sun doesn’t stand still.” Because of the way pragmatics affects semantics (something that van Inwagen apparently agrees on), we simply cannot assume that the proposition expressed by the English sentence “The sun moved behind the elms” entails the proposition expressed by the English sentence “The sun doesn’t stand still.”

Something similar, I suspect, is true for existential language. When an ordinary person says “There are three chairs in the room”, the proposition they express does not contradict the Radical Thesis. But if an ordinary person says things like “Chairs exist” or “Artifacts exist”, they likely would contradict the Radical Thesis, and moreover, these are statements that the ordinary person would be happy to make in denial of the Radical Thesis. But in the ordinary course of life, there is rarely an occasion for such statements.

This is all largely a function of pragmatics than the precise choice of words. Thus, one can say: “Drive slower. Speed limits exist.” The second sentence does not carry ontological commitment to speed limits.

So, how can we check whether an ordinary person believes that tables and chairs exist? I think the best way may be by ostension. We can bid the ordinary person to consider:

1. People, dogs, trees and electrons.

2. Holes, shadows and trends.

We remind the ordinary person that we say “There are three holes in this road” or “The shadow is growing”, but of course there are no holes or shadows, while there are people (we might remind them of the Cogito), dogs, trees and (as far as we can tell) electrons. I think any intelligent person will understand what we mean when we say there are no holes or shadows. And then we ask: “So, are tables and chairs in category 2 or in category 1? Do they exist like people, dogs, trees and electrons, or fail to exist like holes, shadows and trends?” This should work even if like Ray Sorensen they disagree that there are no shadows; they will still understand what we meant when we said that there are no shadows, and that’s enough for picking out what we meant by “exist”. To put in van Inwagen’s terms, this brief ostensive discussion will bring intelligent people into the “ontology room”.

And I suspect, though this is an empirical question and I could be wrong, once inducted into the discussion, most people will say that tables and chairs exist (and that they have believed this all along). But, van Inwagen should say, this nearly universal belief is mistaken.

This story neatly goes between van Inwagen’s view that ordinary people don’t believe things patently incompatible with the Radical Theory and Merricks’ view that ordinary poeple contradict the Radical Theory all the time. Ordinary people do believe things patently incompatible with the Radical Theory, but they rarely express these beliefs. Most ordinary “there exist” statements—whether concerning artifacts or people or particles—do not carry ontological commitment, and those of us who accept the Radical Theory normally aren’t lying when we say “There are three chairs in the room”. But the Radical Theory really is radical.

Creation and artifacts

Analytic metaphysics is widely thought a dry discipline. I want to show how it could be used to connect with some deeply devotional theological claims.

Here is a valid argument:

1. If artifacts exist, we created them.

2. Only God creates.

3. So, artifacts don’t exist.

This argument suggests that there can be a deeply devotional connection to the arguments of those metaphysicians, like Merricks and van Inwagen, who deny the existence of artifacts.

Here is another devotional line of thought towards this. Some radical theologians say that God doesn’t exist. They do this to emphasize the radical difference between God and creatures. But they do so wrong. The right way to emphasize this difference is to say that we don’t exist. (Recall how God is said to have told St. Catherine of Siena: “I am he who is and you are she who is not.”) Only God exists.

So, the things that God creates don’t exist—at least not in the same sense in which God exists. By analogy, it should be no surprise if the things we make don’t exist—at least not in the same sense that we exist.

Objection 1: We can create organisms in the lab, and organisms surely exist.

Response: Maybe we should say that their life comes from God.

Objection 2: The distinction between God’s creating and our making is sufficiently accounted for by noting that God creates ex nihilo and we make things out of preexistent stuff.

Response: God doesn’t always create ex nihilo. He made Adam out of the dust of the earth. And anyway the more differences we see between God and us, the more God’s transcendence is glorified.

Giant numerals stopwatch app

I do two activities where it is nice to have a stopwatch one can see from a distance: lap swimming and lap (indoor) rock climbing. I found one stopwatch app with large numerals, but they weren't large enough for my taste, so I ended up writing my own with the absolutely biggest digits I could (and lots of customizability and various extra features, like a start countdown).

For any Android users who want it, it's here. Source code is here. No ads, no in-app purchases. The app keeps track of the time even if it's navigated away from, and doesn't use any CPU time then. It should even continue keeping track of time if the device reboots or runs out of battery, though perhaps with some loss of precision. The lone permission in the app is to let it run on boot (to adjust the time in case it's running through a reboot).

For climbing, I leave my phone on the ground and easily read it from 50 feet up. For swimming, I put the phone in a freezer bag, and stand it up by the edge of the pool. In foggy dark goggles, I can read it from several yards away, which is good enough for pacing. (Our pool only has one analog wall clock which I can't read in foggy goggles.) Having time feedback as I swam encouraged me to improve two of my swim times (maybe it helped with pacing, too).

Curiously, in an early version I found that there is some bug in the font renderer on my phone: at maximum size, some digits were left blank on the screen (perhaps nobody anticipated drawing text so large that if it had descenders they wouldn't fit on the screen). So I wrote a python script that used a font library to convert digits, colons and minus signs to java code with the Android Path class.

The landscape screenshot shows it running in fullscreen mode with the classic German DIN 1451 highway sign font (and aspect ratio preservation turned off for even bigger digits). The second is with a standard Android Roboto font.

Anselm's ontological argument

Here is my favorite version of the “existence is not a property” objection to Anselm’s first ontological argument.

It makes no sense to talk of the greatness of a nonexistent being except hypothetically as the greatness it would have if it existed. When we compare the greatness of things, we compare what the things would be like if they existed. Thus, when we say that Thor is greater than Hermes, we mean something like this: if Thor existed, he would be greater than Hermes would be if Hermes existed. And to exist is to exist in reality.

But now take the crucial claim in Anselm’s argument that it is greater for x to exist in mind and in reality than just in mind. This claim is simply false when we understand it in the hypothetical way. For we need to compare the greatness of the x that exists in mind and reality to the greatness that the x that exists only in mind would have if it existed in reality. But that’s the same greatness!

Anselm’s second argument makes no such slip, for it is based on a comparison between contingent and necessary existence, and that comparison survives the criticism.

Ethics and complexity

Here is a picture of ethics. We are designed to operate with a specific algorithm A for generating imperatives from circumstances. Unfortunately, we are broken in two ways: we don’t always follow the generated imperatives and we don’t always operate by means of A. We thus need to reverse engineer algorithm A on the basis of our broken functioning.

In general, reverse-engineering has to be based on a presumption of relative simplicity of the algorithm. However, Kantian, utilitarian ethics and divine command ethics go beyond that and hold that A is at base very simple. But should we think that the algorithm describing the normative operation of a human being is very simple? The official USA Fencing rule book is over 200 pages long. Human life is more complex than a fencing competition. Why should we think that there are fundamental rules for human life that can be encompassed briefly, from which all other rules can be derived without further normative input? It would be nice to find such brief rules. Many have a hope of finding analogous brief rules in physics.

We haven’t done well in ethics in our attempts to find such brief rules: the Kantian and utilitarian projects make (I would argue) incorrect normative claims, while the divine command project seems to give the wrong grounds for moral obligations.

It seems not unlikely to me that the correct full set of norms for human behavior will actually be very complex.

But there is still a hope for a unification. While I am dubious whether one can find a simple and elegant set of rules such that all ethical truths can be derived from them with no further normative input, there may be elegant unifying ethical principles that nonetheless require further normative input to generate the complex rules governing human life. Here are two such options:

• Natural Law: Live in accordance with your nature! But to generate the rules governing human life requires the further information as to what your nature requires, and that is normative information.

• Agapic ethics: Love everyone! But one of the things that are a part of love is adapting the form of one’s love to fit the the persons and circumstances (fraternal love for siblings, collegial love for colleagues, etc.), and the rules of “fit” are extremely complex and require further normative input.

Eleven varieties of contrastive explanation

In connection with free will, quantum mechanics or divine creation it is useful to talk about contrastive explanation. But there is no single generally accepted concept of contrastive explanation, and what one says about these topics varies depending on the chosen concept.

To that end, here is a collection of definitions of contrastive explanation. They all have this form:

• r contrastively explains why p rather than q if and only if r explains why (p and not q) and [insert any additional conditions].

They vary depending on the additional conditions to be inserted. Here are some options for these:

1. No additional conditions.

2. r makes p more likely than q.

3. r cannot explain q.

4. r wouldn’t explain q if q were true instead of p.

5. r wouldn’t explain q as well as it now explains p if q were true instead of p.

6. q wouldn’t be explained by r or by any proposition with r’s actual grounds if q were true instead of p.

7. q wouldn’t be explained by r or by any proposition with r’s actual grounds as well as r now explains p if q were true instead of p.

8. the conjunction of everything explanatorily prior to p makes p more likely than q.

9. r entails (p and not q).

10. r entails the truth of p.

11. r entails the falsity of q.

It is not possible to normally have contrastive explanations of indeterministic free choices or quantum events in senses 9–11, and probably sense 8, but it is possible (with an appropriately metaphysical theory of free choice or quantum events) in senses 1-7. As for the case of contingent divine creative decision, things depend on divine simplicity. Without divine simplicity, contrastive explanations are possible in senses 1–7. Interestingly, if divine simplicity is true, then it is not possible to have contrastive explanations of contingent divine creative decisions in senses 6 or 7.

In what I said above, I assumed that the explanandum cannot be a part of the explanans. If following Peter Railton one drops this condition, then contrastive explanation of all three phenomena (with or without divine simplicity) becomes possible in all the senses.

Lesson: When one talks about contrastive explanation, one needs to define one’s terms.

Acknowledgments: I am grateful to Christopher Tomaszewski for in-depth discussion that led me to recognize the important difference between 4–5 and 6–7. And the Railton point is basically due to a remark by Yunus Prasetya.

Substances are not parts of substances

Here is a quick and simple argument for the Aristotelian axiom that substances are not parts of substances.

1. The parts of substances are at least partly grounded in the substances.

2. Substances are not even partly grounded in other things.

3. Therefore, substances are not proper parts of other substances.

I suppose (1) is probably just as controversial as (3).

Aristotelian metaphysics and global physics

Too much of the contemporary ontological imagination is guided by the idea that the fundamental physical stuff in the world is discrete particles. Yet this is clearly dubious, since quantum mechanics (on non-Bohmian interpretations) suggests that the world is full of superpositions of states with different numbers of particles, while if discrete particles really exist, there had better be a well-defined number of them. Quantum mechanics instead suggests an ontology of the physical world where there is exactly one entity, “the Global Wavefunction”, whose physical state can be aptly represented as a vector in an infinite-dimensional vector space. And even if we didn’t have quantum mechanics’ vector-based approach on the table, we still wouldn’t be in an epistemic position to know that the right physics is based on particles rather than fields.

An ontology of material objects that composes these objects out of particles is held hostage to a particle-based physics that may well not be true. It would be best if one could work on the ontology of material objects without presupposing an answer to the question whether fundamental physical reality is field-like, vector-like or particle-like. I do not know if this is tenable. If it’s not, then the ontology of material objects needs to be done conditionally: If fundamental physical reality is of this sort, then material objects are like this.

Interestingly, some metaphysical problems may become easier given a non-particulate physical substratum. For instance, one of the hardest problems for a contemporary Aristotelian metaphysics has been the problem of what happens to particles that get incorporated into a substance, in light of the axiom that a substance cannot be composed of substances. But if we do not see fundamental physical reality as made of apparently substantial particles, the problem dissolves.

Today I want to sketch two Aristotelian approaches that take globalized vector- and field-approaches seriously. On the vector- and field-approaches, fundamental physical reality consists of a mere handful of entities: a single vector-like entity or several (hopefully no more than a dozen, and ideally only one) field-like entities. But being Aristotelian, we will think there are at least billions of substances: every organism is a substance. If these substances are to be related to fundamental physical entities, billions of them will have to be related to the same fundamental physical entities.

The ordinary substances on my stories will be organisms. There are billions of them. In addition to the ordinary substances, there are extraordinary substances: one for each of the handful of fundamental physical entities (fields or a vector).

My stories now diverge. On the first story, the billions of ordinary substances each encode and ground local features of the global fundamental physical entities. On a field version of the story, you encode and ground the features that the global fields have where you are located and your dog encodes and grounds the features that the global fields have where your dog is located (I am less clear on how to describe the vector version). This is not enough. For there aren’t enough organisms in the universe to ground all of the richness of the global fundamental physical entities: too much of the universe is lifeless. Thus, I propose that there are additional substances located where the organisms are not, and the features of these substances ground the rest of the features of the global fundamental physical entities. One way to run this story is to say that there is one of these additional substances per global fundamental physical entity, and each grounds the features of its corresponding global fundamental phsyical entity away from organisms. These additional substances are like swiss cheese, with the holes being filled with organisms like people and dogs.

On this version of the Aristotelian story—which can be varied in a number of ways—the global fundamental physical entities are not metaphysically fundamental. They are grounded in the many substances of the world.

On the second story, the global fundamental physical entities are substances. They are global substances. These global substances interact with the ordinary substances (there are many ways to spell out this interaction). We can now identify the matter of an ordinary substance x either with x’s powers and liabilities for interaction with the global substances or with the plurality of these global substances qua interacting with x.

There are many options here. Much detail to be worked out. Some options may be inferior to others, but I doubt in the end we will come to a single clearly best option.

A measure of sincerity

On a supervaluationist view of vagueness, a sentence such as “Bob is bald” corresponds to a large number of perfectly precise propositions, and is true (false) if and only if all of these propositions are true (false). This is plausible as far as it goes. But it seems to me to be very natural to add to this a story about degrees of truth. If Bob has one hair, and it’s 1 cm long, then “Bob is bald” is nearly true, even though some precisifications of “Bob is bald” (e.g., that Bob has no hairs at all, or that his total hair length is less than 0.1 cm) are false. Intuitively, the more precisifications are true, the truer the vague statement:

1. The degree of truth of a vague statement is the proportion of precisifications that are true.

But for technical reasons, (1) doesn’t work. First, there are infinitely many precisifications of “Bob is bald”, and most of the time the proportion of precisifications that are true will be ∞/∞. Moreover, not all precisifications are equally good. Let’s suppose we somehow reduce the precisifications to a finite number. Still, let’s ask this question: If Bob is an alligator is Bob bald? This seems vague, even though the precisifications of “Bob is bald” that require Bob to be the sort of thing that has hair seem rather better. But for any precisification that requires Bob to be a hairsute kind of thing, there is one that does not. And so if Bob is an alligator, he is bald according to exactly half of the precisifications, and hence by (1) it would be half-true that he is bald. And that seems too much: if Bob is an alligator, he is closer to being non-bald than bald.

A better approach seems to me to be this. A language assigns to each sentence s a set of precisifications and a measure m_s on this set with total measure 1 (i.e., technically a probability measure, but it does not represent chances or credences). The degree of truth of a sentence, then, is the measure of the subset of precisifications that are actually true.

Suppose now that we add to our story a probability measure P representing credences. Then we can form the interesting quantity E_P(m_s) where E_P is the expected value with respect to P. If s is non-vague, then E_P(m_s) is just our credence for s. Then E_P(m_s) is an interesting kind of “sincerity measure” (though it may not be a measure in the mathematical sense) that combines both how true a statement is and how sure we are of it. When E_P(m_s) is close to 1, then it is likely that s is nearly true, and when it is close to 0, then it is likely that s is nearly false. But when it is close to 1/2, there are lots of possibilities. Perhaps, s is nearly certain to be half-true, or maybe s is either nearly true or nearly false with probabilities close to 1/2, and so on.

This is not unlikely worked out, or refuted, in the literature. But it was fun to think about while procrastinating grading. Now time to grade.

Credence and belief

For years, I’ve been inclining towards the view that belief is just high credence, but this morning the following argument is swaying me away from this:

1. False belief is an evil.

2. High credence in a falsehood is not an evil.

3. So, high credence is not belief.

I don’t have a great argument for (1), but it sounds true to me. As for (2), my argument is this: There is no evil in having the right priors, but having the right priors implies lots high credences in falsehoods.

Maybe I should abandon (1) instead?

The unavoidability of misleading evidence

Three definitional assumptions:

1. E is only evidence if there is some hypothesis H to which E makes an evidential difference, i.e., P(H|E)≠P(H).

2. E is incomplete if and only if it is evidence such that there is a hypothesis H such that 0 < P(H|E)<1, i.e., E doesn’t make everything certain.

3. E is misleading with respect to a hypothesis H if and only if either H is true and E is evidence against H (i.e., P(H|E)<P(H)) or H is false and E is evidence for H (i.e., P(H|E)>P(H)).

Then:

4. Every piece of incomplete evidence is misleading (with respect to some hypothesis).

[Proof: Suppose E is incomplete evidence. Either E is or is not true. If it is not true, it is misleading, since it lowers its own probability to zero. So, suppose that E is true. Let H₁ be a hypothesis such that 0 < P(H₁|E)<1. Replacing H₁ by its negation if necessary, we can assume H₁ is true. Note that the fact that E is evidence implies that 0 < P(E)<1. Let H be the disjunctive hypothesis: ∼E or (H₁&E). This is true as the second disjunct is true. Now, note that P(H₁&E)<P(E) as P(H₁|E)<1. Thus, (1 − P(E))P(H₁&E)<(1 − P(E))P(E). Thus, P(H₁&E)<P(E)P(H₁&E)+(1 − P(E))P(E). Thus: P(H₁|E)=P(H₁&E)/P(E)<P(H₁&E)+(1 − P(E)) = P(H₁&E)+P(∼E)=P(H). Thus, E is evidence against H even though H is true.]

In particular, we should not take misleadingness of evidence to be an evil. Misleadingness of evidence is a normal part of reasoning with incomplete information.

A hybrid view of laws

The big divide about laws of nature is whether the laws are pushy or descriptive.

It seems to me that a plausible view is that some are pushy and some are descriptive. This is what I think one gets on an Aristotelian view: there are laws describing which mutually harmonious natures are instantiated, and the instantiated natures then push stuff around in lawlike ways. For instance, there may be a descriptive law that says that all particles have natures of the quantum sort (rather than, say, of the Newtonian sort), and there are pushy laws that, say, prohibit two electrons from sharing the same state.

Dutch Books and update rationality

It is often said that if you depart from correct Bayesian update, you are subject to a diachronic Dutch Book—a sequence of bets you will have to rationally agree to that is sure to make you lose—and this is supposed to indicate a lack of rationality. That may be, but I want to point out that the lack of rationality is not constituted by being subject to a Dutch Book: being subject to a Dutch Book is merely a symptom. I expect most people working this stuff know this, but perhaps it’s worth giving an explicit argument for.

Here is why. Alice, Bob and Carl are observing a coin that is either double-headed (D) or fair (F). Their prior probabilities for the two hypotheses are 1/2, and they have the reasonable and consistent priors: they assign probability 3/4 to heads showing up, and so on. The coin is flipped and the result is observed. If the coin lands tails, all three correctly update their probability for D to 0. If the coin lands lands heads, Alice, Bob and Carl each follow a different rule for updating their credence for D. Alice updates to 2/3 in accordance with Bayes’ theorem. Bob updates to 3/4 as that intuitively seems right to him. Carl, on the other hand, initiates a process in his brain which randomly updates to a uniformly chosen credence between 1/2 and 1.

Alice is not subject to a Dutch Book.

Bob is.

But Carl, once again, is not. [Proof: For any betting book, there is a non-zero chance that Carl would be rationally permitted to respond to that book in a way that it would be rationally permitted for Alice to respond. For Carl and Alice differ in their credences only in post-toss bets dependent on D in the special case that the first toss is heads, but the direction in which they differ in their credences is random: Carl has a non-zero chance of having a lower credence than Alice in D at this point and a non-zero chance of having a higher one. If at Alice’s credence of 2/3 the bet is rationally permitted to take, then either (a) for all credences lower than 2/3 it is rationally permitted to take, or (b) for all credences higher than 2/3 it is permitted to take, since the expected outcomes are linear functions of the credence. But there is a non-zero chance that Carl’s credence is lower than Alice’s and a non-zero chance that Carl’s credence is higher than Alice. Thus, there is a non-zero chance that Carl can permissibly take the bet, if Alice can permissibly take the bet. And the same argument applies if Alice can permissibly refuse the bet.]

However, Carl is not more rational than Bob, despite not being subject to a Dutch Book due to his unpredictability. Hence, not being subject to a Dutch Book is only a symptom of irrationality, not constitutive of it.

Functionalism and imperfect reliability

Suppose a naturalistic computational theory of mind is true: To have mental states of a given kind is to engage in a particular kind of computation. Now imagine a conscious computer thinking various thoughts and arranged around standard logic gates. Modify the computer to have an adjustment knob on each of its logic gates. The adjustment knob can be set to any number between 0 and 1, such that if the knob is set to set to p, then the chance (say, over a clock cycle) that the gate produces the right output is p. Thus, with the knob at 1, the gate always produces the right output, with the knob at 0, it produces the opposite output, with the knob at 0.5, it functions like a fair coin. Make all the randomness independent.

Now, let C_p be the resulting computer with all of its adjustment knobs set to p. On our computational theory of mind, C₁ is a conscious computer thinking various thoughts. Now, C_0.5 is not computing anything: it is simply giving random outputs. This is true even if in fact, by an extremely unlikely chance, these outputs always match the ones that C₁ gives. The reason for this is that we cannot really characterize the components of C_0.5 as the logic gates that they would need to be for C_0.5 to be computing the same functions as C₁. Something that has a probability 0.5 of producing a 1 and a probability 0.5 of producing a 0, regardless of inputs, is no more an and-gate than it is a nand-gate, say.

So, on a computational theory of mind, C_0.5 is mindless. It’s not computing. Now imagine a sequence of conscious computers C_p as p ranges from 0.5 to 1. Suppose that it so happens that the corresponding “logic gates” of all of them always happen to give the same answer as the logic gates of C₁. Now, for p sufficiently close to 1, any plausible computational theory of mind will have to say that C_p is thinking just as C₁ is. Granted, C_p’s gates are less reliable than C₁’s, but imperfect reliability cannot destroy thought: if it did, nothing physical in a quantum universe would think, and the naturalistic computational theorist of mind surely won’t want to accept that conclusion.

So, for p close to 1, we have thought. For p = 0.5, we do not. It seems very plausible that if p is very close to 0.5, we still have no thought. So, somewhere strictly between p = 0.5 and p = 1, a transition is made from no-thought to thought. It seems implausible to think that there is such a transition, and that is a count against computational theories of mind.

Moreover, because all the gates actually happen to fire in the same way in all the computers in the C_p sequence, and consciousness is, on the computational theory, a function of the content of the computation, it is plausible that for all the values of p < 1 for which C_p has conscious states, C_p has the same conscious states as C₁. Either C_p does not count as computing anything interesting enough for consciousness or it counts as imperfectly reliably computing the same thing as C₁ is. Thus, the transition from C_0.5 to C₁ is not like gradually waking up from unconsciousness. For when we gradually wake up from unconsciousness, we have an apparently continuous sequence of more and more intense conscious states. But the intensity of a conscious state is to be accounted for computationally on a computational theory of mind: the intensity is a central aspect of the qualia. Thus, the intensity has to be a function of what is being computed. And if there is only one relevant thing computed by all the C_p that are computing something conscious-making, then what we have as p goes from 0.5 to 1 is a sudden jump from zero intensity to full intensity. This seems implausible.