From Pure to Pragmatic Physicalism

In a talk given on the Greenland Cruise conference on consciousness in 2014 Philip Goff describes two bitter pills which must, he argues, be swallowed by anyone who subscribes to ‘pure physicalism’, according to which “completed physics will give us one day the complete fundamental picture of reality” [4:19], an ontological view which Goff sees as the natural elongation of the weaker epistemological view that “we should look to and only to the physical sciences to tell us what fundamental reality is like” [2:55].

Those bitter pills are:

  1. Fundamental entities lack an intrinsic nature. [7:43]
  2. Consciousness can be accounted for in entirely causal terms. [11:05]

Goff argues that both of these are entailed by something he calls ‘dispositional essentialism’, which is in turn entailed by pure physicalism. Dispositional essentialism is the view according to which “there is nothing more to the nature of a fundamental property than what it disposes its bearer to do.” [6:40]

The thread Goff uses to link pure physicalism and dispositional essentialism is the oft-noted fact that all theories provided by the physical sciences, and all characterisations of the entities referred to in physical theories, are made in terms of dispositional properties. Physical theory doesn’t tell us what things are so much as what they do. (Goff gives the example of an electron: it is characterised as something having a certain mass and a certain charge, but those properties of mass and charge are themselves characterised in terms of what their bearers will do in the presence of other things.) And when it does tell us what something is, it does so by appealing to what other things do—heat is molecular motion, storms are systems of air currents moving in certain patterns, atoms are aggregates of quarks bonded to each other in various configurations, and so on. So if physical science can supply only theories concerning dispositions and relations, but nevertheless can supply a complete fundamental picture of reality (as the pure physicalist reckons), then it follows that a complete fundamental picture of reality will be purely dispositional in content.

Seeing that the second pill follows from this is just a matter of noting that a fundamental picture of reality should include everything that occurs in reality, including consciousness. Whether or not the pill really is bitter is, of course, subject to much dispute, and I will not get into it here (though I have done quite a lot recently—see here, here, here & here). Instead, in this post I shall talk a little about the first pill.

A thing’s instrinsic nature is what it is in and of itself, i.e. independently of how it relates to other things. Since dispositional properties concern a thing’s capacity to affect other things, dispositional properties are relational, i.e. extrinsic properties, and so dispositional essentialism certainly does entail that at the fundamental level there are no intrinsic natures, or, to put it another way, that insofar as there are any things with intrinsic properties, those properties are in some sense derivative of the extrinsic properties of other things (typically the things that constitute them).

(To clarify the terminology before things get messy: a relation holds of a certain number of things, called its arity. The relation ‘being greater than 7’ has arity 1, because it can only be applied to one thing (11 is greater than 7) whereas ‘being equal to’ has arity 2, because it is applied to two things (1+4 is equal to 2+3). An intrinsic property is just a relation with arity 1, and an extrinsic property is a relation with arity >1.)

Fair enough, but what’s wrong with this pill? By way of trying to convince his audience of its bitterness, Goff offers a few variations on a theme. He first points to a problem of regress in chains of analysis. Say we want to understand some property P. A successful analysis of P will have been reached when some other property Q (or properties—if so let Q be their conjunction) has been found which can be taken as defining P, i.e. such that the following holds:

Necessarily, P(x) if and only if Q(x)

Goff notes that any complete theory will, in addition to providing an analysis of P, have to provide an analysis of Q in terms of some other property—R—and then of R in terms of some other property, and so on. If this process is to come to an end, then it seems there must be at least some unanalysable (i.e. fundamental) properties at the end of the chains.

I will return to this inference later on in the post, but for the moment let’s agree with it and ask what it implies. Goff seems to think that it makes mischief for dispositional essentialism, presumably on the basis that only intrinsic properties could ground the chain. But why should this be so? Why could such a chain not end with an unanalysable extrinsic property?

Consider, to help make this clear, the property of being above 0 degrees Celsius. Applying what we know about heat being molecular motion, something is above 0 degrees Celsius when (and only when) the average kinetic energy of the molecules that compose it is above some value. This analysis represents one step down the chain of explanation, but even this simple example reveals an oversimplification in the equivalence above, namely that the property to be explained—being above 0 degrees Celcius—which holds of a single thing (i.e. it is an intrinsic property), has been analysed into a property—having an average kinetic energy above some value—which holds of a collection of things (i.e. it is an extrinsic property). This adds some nuance to the picture, indicating that there are some links in the chain of explanation which are going to look more like this:

Necessarily, P(x) if and only if Q(f(x))

Where f is the function that maps wholes onto their parts. But if this is the case, then Q may very well be a relation which holds of a collection of things, rather than of a single thing. The point here—perhaps I’m labouring it a little—is just that as we step over the biconditionals, moving through the list of properties along the chain of explanation, the arity of the explaining properties may grow. But if this is the case, why should we expect the property at the end of it to be instrinsic, rather than extrinsic?

So the problem of regress in chains of explanation is ambivalent about whether chains end in extrinsic or intrinsic properties. But perhaps there’s independent reasons to believe that extrinsic properties cannot end them (as they must if dispositional essentialism is true). Goff musters a few such reasons, all to the effect that the fundamental properties of reality being extrinsic would entail craziness.

At this point it’s worth stepping back to review the various possibilities. It must be confessed that a world in which all the fundamental properties are extrinsic would be a strange one indeed. All sorts of toothy metaphysical problems would no doubt emerge, in particular to do with what this picture of fundamental properties implies about fundamental entities. One tactic might be to say that strictly speaking there are no fundamental entities, that at bottom all there is is relations without relata. Another might be to argue that the fundamental entities necessarily come as multitude, and are inconceivable alone. Still another might be to argue that the fundamental entities are conceivable independently of their having any properties—intrinsic or extrinsic—at all. Or perhaps we could just give up on dispositional essentialism altogether (and pure physicalism with it), and believe that at bottom reality is composed of fundamental entities with intrinsic properties.

I think the more jaded among us could be forgiven for speculating that this way lies a game of whose intuition is the least weird, the winner of which will be whoever can keep the straightest face while swearing blind that everyone else is talking nonsense while they make perfect sense. At any rate, I won’t pursue this line of thought any further here. I want to turn now to another take on all this, which seems to me to be far more promising.

Let’s return to the problem of regress in chains of analysis. The reasoning went that properties are analysed in terms of other properties, so if the resulting chains ever come to an end then there must be such things as fundamental, i.e. unanalysable properties. Picking it apart a little, we can see that this argument comes in two stages. A property, referred to by the predicate P, is defined by a new predicate, Q. Another such definition must be provided of Q, and so on. If these chains come to an end in a complete picture of fundamental reality, then the first cautious conclusion to be drawn is just that such a picture must contain primitive predicates, that is, predicates which cannot be defined non-vacuously in terms of others. To then reach the next conclusion—that reality contains fundamental properties—the further premise must be supplied that these primitive predicates will function in the complete picture by (truthfully) attributing properties. The rest of this post will be devoted to exploring what happens when this further premise is resisted.

To deny that primitive predicates attribute properties is just to hold that they function by doing something else. A predicate that often gets accused of this kind of non-attributive function is the truth predicate, which will serve as an illuminating example. The grimness of the prospects for finding a general definition of truth finds support from two directions. On the one hand, the common sensical correspondence theory of truth is difficult to unpack in a non-vacuous way (a fairly dated way of stating the correspondence theory is to say that a proposition is true if and only if it corresponds to a fact, but what is a fact if not a true proposition?). On the other hand, the Tarski equivalence (“p” is true if and only if p) seems to make clear that any definition of truth that fails to block the inconsistency of asserting a proposition’s truth while denying the proposition (such as that a proposition is true just when it is useful to believe, or when it coheres with other beliefs) has changed the subject.

But even if the truth predicate can’t be defined, perhaps something can be said about how it functions. The Tarski equivalence may not provide a definition, but it does (to pinch a phrase of Donald Davidson’s) represent our best intuitions about how the truth predicate is used. A lesson to draw from it could be that to say of a proposition that it is true is the same as to assert it. So rather than attributing a property to a proposition, perhaps the truth predicate functions by conveying the speaker’s belief in it—its function is expressive rather than attributive.

Now, it’s very difficult to imagine that the primitive predicates in a physical theory—in present theory these are things like having such and such an electrical charge, or spin, etc.—could be given an expressive treatment along similar lines, but the truth example does illustrate that property attribution may not be the only line of work available to a predicate. But what other options might there be, if neither attribution nor expression is appropriate?

One possibility, I would suggest, is that the function of primitive descriptive predicates is in an important sense null—devoid of any substantial content. Or, to put it another way, that being a primitive predicate is an important functional role in itself, independently of whether it does something else in addition, like attribute a property or express a belief. I have in mind that primitive predicates function like the simple pieces or tokens in a board game. In chess, for example, there’s nothing more to the concept of a ‘pawn’ than how it can be moved and what happens if it gets to the other end. (Well, there are some norms governing how it should look, but these are inessential to the game itself. If we had enough physical pieces we could permute all their roles, so that the front row was lined with queens, the rook moved diagonally, the object was to project the bishop, etc., and we’d still be playing chess, albeit in a very strange way.) Similarly, a primitive predicate can be thought of as having no semantic content aside from what other sentences it implies when predicated of a term. There is no additional need for it to be thought of as referring to a property out there in the world.

(To make a brief comment which ties in with the earlier discussion, there is no reason why the primitive predicates as they’re envisioned here couldn’t all be ‘extrinsic’, i.e. have an arity greater than one. In axiomatic set theory, for example, the only primitive predicate is a predicate relating two terms, usually symbolised as ∈, where “xy” is interpreted as true just when the set x is interpreted as referring to is a member of the set y is interpreted as referring to.)

Now, it may be objected at this point that the picture being drawn here—in which the primitive predicates are not ‘hooked on’ to fundamental properties—is going to lead to an implausible arbitrariness at the level of the whole system. To return to truth for a moment, if we assume that the expressive theory sketched above is more or less right, and that so is the classical theory of knowledge as being justified true belief, then the only difference between my saying of Jim that he is justified in believing that the Magna Carta was signed in 1215, and my saying of Jim that he knows that the Magna Carta was signed in 1215, is just that in the latter case I am additionally expressing my belief that the Magna Carta was signed in 1215. If this is the case then there is no fact of the matter about whether someone knows something or not. Knowledge is not an objective feature of the world, it is an ‘internal’ feature of human linguistic practice. In like fashion, the expressive function of truth will be inherited by any other concept whose definition or analysis it participates in.

Similarly, if primitive predicates in physical theory don’t hook on to properties, then neither will those that they participate in defining, directly or indirectly. And that’s everything, because these are the predicates which ground any and every chain of analysis. And if the web of theory doesn’t ‘hook on’ anywhere, what’s to stop it being completely arbitrary?

Responding to this objection will help clarify the picture. First let it be admitted that, according to this picture, ‘physical theory’ is indeed a massively holistic system. Since the meaning of a predicate is exhausted by what it implies when predicated of various terms, the meaning of any given predicate is dependent on all the others (sometimes directly, more often indirectly). No doubt there is also going to be a degree of contingency in the way the system is set up. Just as in a formalised logic only a couple of primitive operators are needed to define all the others (e.g. and and or can be defined from not and implies, or not and and can be taken as primitive and implies and or defined from them), there will probably be some degree of choice available as to which predicates are taken as primitive. What matters is the patterns of entailment between theoretical statements, not anything intrinsic to the predicates themselves (such as what outside the linguistic system they refer to), so long as there are at least some which are primitive. Which ones these are may change as theory is refined and expanded, with what were previously primitive predicates succumbing to analysis in terms of new ones which then serve as their explanans.

But for all its contingency such a system need not be arbitrary, and the reason—it’s time to bang this old drum again, I’m afraid—is that the system as a whole, its construction and its modification, is constrained by various requirements of utility. The requirement that physical theory succeeds at predicting and controlling the environment—in a word, that it succeeds in dealing with it—mean that the world with which physical theory deals provides endless conditioning stimuli upon it. Its logical structure needn’t be any more arbitrary than the internal structure of a neural net that has been trained for pattern recognition. Like the neural net, there may be different internal structures that could perform the same task, and so long as they perform it equally well there may be no grounds to prefer any particular one of them. It may even be the case that through such utility-conditioning the logical structure of physical theory begins to mimic the structure of the world, in which case maybe we could begin tentatively to link predicates with real properties, though these links would now be mediated by the utility of the system as a whole and would carry no air of ontological necessity. Or to look at it a different way, perhaps the lesson we would draw would be that the very concept of a ‘property’ is parasitic on the syntactic functioning of predicates. Thus we could give up a bit of realism about properties, recognising them as products of language and not keystones of reality out there in the world, and just go back to talking about them as we were before. Except now we’d have no need to worry about their ontology.

The picture I’ve sketched in the second half of this post is by no means original, and owes a hell of a lot to both Quine’s ‘web of belief’ and Robert Brandom’s inferentialism, both of which I’ve been on kind of a trip with recently. But in the name of returning to some of the considerations that kicked off this great rambling hog of a post, what sort of a picture is it that has been sketched? Is it of a kind with what Goff calls pure physicalism? Not quite. It’s not that someone who subscribes to this picture would necessarily disagree that we should look to and only to the physical sciences to find out what reality is like, or even that a completed physics would give us the fundamental picture of reality. But they might feel queasy about the metaphysical seriousness suggested by this wording. It may be that physics will provide a unified theory, and it may be that once it has there will simply be nothing left to say about fundamental reality. But the next inference—the claim that this unified theory gives us the fundamental picture of reality—is likely to provoke interpretive quibbling.

If this isn’t pure physicalism, then let’s give it a name: pragmatic physicalism. I’ve portrayed pragmatic physicalism as stemming from a suspicion towards the inference from a unified theory containing primitive predicates to the world containing fundamental properties. The consequence is a large-scale inversion in the conception of the way physical theory relates to the world it theorises about. Direct reference of predicates in physical theory to properties in the world gets displaced in favour of the utility of the whole system, and returns only in an indirect and contingent sense. But what reasons might there be for making this inversion?

One thought, which I shall end with, is that making utility the master concept is exactly what we might expect of someone who is looking to take a naturalistic approach not just to the various things that humans talk about, like God and the Good, but to human linguistic practices as such. As one animal among many, humans and human language are the result of evolutionary processes, and so it makes sense for someone on this path to treat language first and foremost as something humans do things with. And insofar as it is something things are done with, the relevant consideration is how successful it has been at doing those things. Is this not then the natural direction of slide for all those liable to sign up for either of the positions Goff was quoted as describing at the beginning of this post? Is pragmatic physicalism not the place pure physicalism will find itself once it has followed its own rationale all the way to the bottom?


Sam Harris and his Mysterian Sympathies

Here’s a quote I’ve seen popping up a lot recently, taken from Sam Harris’ most recent book Waking Up (p116):

Consciousness—the sheer fact that this universe is illuminated by sentience—is precisely what unconsciousness is not. And I believe that no description of unconscious complexity will fully account for it. To simply assert that consciousness arose at some point in the evolution of life, and that it results from a specific arrangement of neurons firing in concert within an individual brain, doesn’t give us any inkling of how it could emerge from unconscious processes, even in principle. However, this is not to say that some other thesis about consciousness is true. Consciousness may very well be the lawful product of unconscious information processing. But I don’t know what that sentence actually means—and I don’t think anyone else does either.

I think there is something important and right about what Harris says in the final sentence here. But I also think that it is far from clear what exactly this something is, and what it might imply. Harris himself, wishing to resist the dualist direction that many insist this observation must push us, angles his sympathies towards mysterianism: the view that us humans are constitutionally incapable of explaining the existence of consciousness, or of being able to understand a correct explanation were it given to us.

(I say ‘angles his sympathies’—to be clear, he doesn’t ever quite fully endorse the view. But then there are very few card-carrying mysterians. It seems that rather than being a position held, mysterianism is the sort of thing one pays lip-service to, acknowledges as a real possibility, sympathises with, hints at darkly, etc. I hope that what follows may offer a partial diagnosis of this strange state of affairs.)

What don’t we understand? This identity:

consciousness = the lawful product of unconscious information processing

One thought might be that the reason we do not understand this identity is that there are conceptual limits on the sort of thing a ‘lawful product of unconscious information processing’ could be—limits which rule out its identity with consciousness.

But this line of thought cannot be right, and for reasons which have nothing to do with what is known about the limits of physical systems. If we do have reasons to believe that the lawful products of information processing are limited in ways that preclude their being consciousness, then we have reason to believe that the above identity is false. If we are not sure what sorts of things the lawful products of information processing might be, then in the further absence of reasons to believe or reject the identity we should be agnostic about it. In neither of these cases should we say that we do not understand it.

Back to the drawing board, then: why don’t we understand the identity? Why might we not understand an identity statement in general? One reason could be that we are uncertain about what one of the terms on either side refers to.

I think we know fairly well what we’re talking about when we talk about ‘information processing’ and its ‘lawful products’. This is not to say that we have a complete, transparent knowledge of information processing and its lawful products, just that we know enough (or enough is stipulated) to be able to agree on what we’re referring to. This would suggest that the problem lies on the other side of the identity, with ‘consciousness’.

Of course, this is the side we’d expect the problem to lie, since consciousness is the thing we’re trying to explain while ‘lawful product of unconscious information processing’ is an example of the sort of thing that gets advanced as an explanation. So consider this identity:

consciousness = x

Is there any term that could be put in place of x—physical, functional or otherwise—that would help explain consciousness? (There are, of course, plenty of terms that we could substitute for that would do nothing to help explain consciousness: subjectivity, qualia, awareness, raw feels, what-it’s-like-ness, the illuminating light of sentience, etc.) I think we shall have to say that there is not.

The mysterian might not have to care about this. After all, couldn’t they just say that consciousness being inexplicable in not just physical-functional terms, but in any terms only adds further support to the view that consciousness is, as it were, intrinsically inexplicable to us?

However, once the issue has been put this way two other possible sources of our incomprehension emerge. One is that consciousness might be a base, unanalysable component of reality. This is the view taken by many panpsychists, the idea being that consciousness should be treated in roughly the same way that electrical charge is treated in physics: as a primitive posit that is not itself explained, but is used to explain everything else. On this view consciousness is just a brute fact. (It should be mentioned that mysterians may also refer to consciousness as a brute fact—Harris does—but the usage is different. According to the mysterian we have no choice but to treat consciousness as brute, because this is the best we can do given what we are. For a panpsychist of the type I’ve described consciousness is brute in and of itself, independently of who and how we are.)

The other possibility—the one I am more interested in pursuing here—is that the apparent hopelessness of explaining consciousness may simply come down to the fact that we are not clear enough about what ‘consciousness’ refers to. If this is the case then when we talk about consciousness we are not sure what it is that we’re talking about, and so it is unsurprising that purported explanations never quite seem to even touch the issue.

It’s worth noting that if this is right then mysterianism is a very strange position to hold. If the reference of consciousness is unclear, then the problem of consciousness has an undetermined content. And if the problem has an undetermined content, it’s hard to see what to make of claims about its solvability.

Do we know what consciousness refers to? Is there enough agreement about this to fix the content of the problem? I would submit that the answers to these questions are “no” and “hell no”. But regardless of what I think, what’s really important is that for vast swathes of philosophical debate on the mind, it is these questions that represent the point at issue. When the various arguments that aim to show what is problematic about the relationship between mind and body are put forward, they typically take the form of an attempt to isolate items of conscious experience via some special property. It is a curious feature of the mind-body problem that the very same features which identify its content are those which are used to stake out certain positions on it. The flip-side of this is that those who reject these arguments—physicalists, usually—are not just disputing an answer to a question whose content has been independently agreed on, they are disputing the content of the question itself.

In summary, then, there are two ways we can interpret Harris’ claim (in my view his correct claim) that we do not understand what it would mean for consciousness to be the lawful product of unconscious information processing. One is that we are not yet clear about what we are talking about, so we don’t know how to recognise a correct answer to the question “what is consciousness?”, and so our incomprehension comes as no surprise. But if this is the case then Harris’ mysterian sympathies are not supported, and ultimately are hard to even make sense of. On the other hand, perhaps Harris believes the questions which fix the content of the problem have been settled, in which case his mysterian attitude is more plausible. But this is a substantive belief, and thus a substantive claim that we will have to swallow if we are to take his original statement in the way he seems to want us to. We might wonder: what are his justifications? If they are the same arguments that dualists and panpsychists make against physicalists, then again we might wonder: why isn’t he a dualist or a panpsychist?

The Mind, First-Person Authority, and Tennis

Richard Rorty’s position on the mind-body problem can be approached via two intermediate claims:

1. What is problematic about the relationship between mind and body is fully captured by the idea that we are incorrigible about our own mental states.

2. This incorrigibility is best understood as a kind of social-linguistic convention.

Together these claims yield the deflationary thesis that the mind-body problem is an artefact of social-linguistic practice. In this post I want to expand on the second of these claims by discussing an analogy of Rorty’s, though in order to get there I must begin by saying a few words about the first claim.

Recent attempts to pin down the mind-body problem have focused on the phenomenal or qualitative aspects of the mind, gathered under the general heading “consciousness”. These attempts usually take one of two forms. The first argues that to be in a phenomenal state is to be in a special kind of cognitive state. This strategy is exemplified by Frank Jackson’s knowledge argument [1], which aims to show that being conscious involves knowing a special kind of fact that is not included in or derivable from any amount of the corresponding bodily, i.e. physical, knowledge.

The second argues that phenomenal entities (like pains and visual impressions) are identified by properties sufficient to preclude their identity with physical entities. This strategy finds perhaps its best expression in Saul Kripke [2], though it is also deployed by John Searle when he describes phenomenal entities as having a “first-person ontology” [3], i.e. as existing only insofar as they’re experienced (in contrast with physical entities whose existence presumably does not depend on whether or not they are experienced).

In Rorty’s view both of these strategies stem from a deeper intuition about what makes the mind special: incorrigibility. Incorrigibility pertains to the authority we each have with regard to our own mental states—if it seems to me that I am in pain, then I am in pain. I can’t be wrong about that, though I can be quite wrong about whether someone else is in pain or not. Incorrigibility is thus a kind of infallibility with regard to beliefs or reports about one’s own mental states.

If Rorty is right, and incorrigibility represents our best intuition about the peculiarity of the mental, then the first strategy mentioned above (Jackson’s) makes a blunder by confusing a special epistemic relation to a normal fact—being incorrigible about whether I am in pain—with a normal epistemic relation to a special fact—knowing “what pain is like”.

The Kripke-Searle strategy fares slightly better, but gets pushed back a step. If incorrigibility encapsulates the mind-body problem, then it does so without appeal to exotic entities (qualia, raw feels, etc.) which ‘appear’ to a ‘subject’ (and all the imagery that comes with this obscure mechanism: inner space, the eye of the mind, etc), and so this whole framework is sustainable only when seen as being posited to explain the incorrigibilty of first-person reports. This framework may or may not succeed in explaining incorrigibility, but even if it does there may be a better way of explaining it. Rorty reckons he has a better explanation, and this I shall turn to now.

Consider a tennis game: it’s match point, and what is potentially the winning shot has just been struck. It dips over the net and lands close to the edge of the court, but is moving too fast for the crowd to see whether it lands in. They turn to the umpire to call it [4].

The event of the ball landing can be described in two ways: physically, or in terms internal to tennis. On the physical description the ball landed at some particular location, either outside the box described by the court lines or not. On the description couched in ‘tennistic’ terms, the ball landed either in or out. Here we have two descriptions, in two vocabularies, of the same event. But here’s the rub: while the umpire can be wrong about where the ball landed in the physical sense, the umpire cannot be wrong about whether it landed in or out. If the umpire calls it out, it’s out; if he calls it in, it’s in.

That the umpire is incorrigible about whether the shot was in or out is no mystery. It is a consequence of the special role assigned to the umpire in this social practice, that is, to act as an ultimate authority who can override any quarrelling that may result from trying to determine exactly where the ball landed in relation to the line (particularly relevant in the days before slow-motion replays). And of course, that the umpire is incorrigible about whether a ball lands in but not about where exactly it lands is not a good reason to maintain that the ball landing in cannot be the same event as the ball landing in some physical location.

Here is the lesson to extract from this: whether or not a person is incorrigible with respect to an event is relative to the vocabulary in which the event is described. The direct application of this to the mind-body problem is that the fact that people are incorrigible about whether they are in pain, but not about what’s going on in their brain, does not imply that pains cannot be, say, firings of certain neural clusters. Furthermore, it hints that the authority we each have with regard to our mental states might be something like the authority a tennis umpire has with regard to whether shots land in or out. On this account, first-person authority is “built into” mentalistic vocabulary, and to treat another being as having a mind is to welcome them as participants (or potential participants) in a social-linguistic practice. This is the thought behind Rorty’s idea that having a mind is a moral (rather than metaphysical) matter.

I’m not sure if that’s going to convince anyone, but I do think it’s provocative. If you have read this and do not find this line of thought compelling, why not? Is there something wrong with the tennis analogy, or is it simply that incorrigibility does not represent our best intuitions about what the mind-body problem is? If it’s the latter, does the tennis example perhaps help to show that incorrigibility cannot pin down the mind-body problem?


1. See Frank Jackson – Epiphenomenal Qualia

2. See Saul Kripke – Naming and Necessity, Lecture III.

3. See, e.g., John Searle – Why I Am Not a Property Dualist

4. I tried to find the passage of Rorty’s I yoinked this example from, I really did, but it’s buried somewhere deep in Philosophy and the Mirror of Nature and the index—those bastards—did not contain an entry for ‘tennis’. Life is too short.

On mathematics: utility and necessity revisited

A few months back I wrote a rather messy post expressing some thoughts on the philosophy of mathematics, which I want to pick up again here (having been provoked by a few things I’ve read and listened to recently). In that post I ran together two distinct but related problems: the problem of mathematical knowledge and the problem of mathematical ontology. In doing so I managed to obscure what was, I think, a half-decent point by trying too hard to set it in opposition to platonism. In this post I shall do my best to ignore questions about the existence of mathematical entities and focus on the substantial point about mathematical knowledge.

The post began by suggesting that the difficulty of providing a plausible account of mathematical knowledge stems from the fact that mathematical truths are both necessary (i.e. they couldn’t be false) and useful, and that any successful account of one of these properties tends to encounter problems when faced with the other.

To illustrate: one clean way of explaining the necessity of mathematical truths is by positing that they are analytic truths, i.e. they are true in virtue of meanings (or ‘by definition’, as it were). Perhaps “2+1=3” is true just because it is part of the meaning of ‘+1’ that when applied to something it gives something different, and ‘3’ is just what we call the result of applying ‘+1’ to ‘2’. If this is the case then it couldn’t be false. But if so it is hard to see how arithmetic can be so useful for coping with the world. I could define a ‘rurble’ to be a kind of ‘gurdle’, and ‘durgle’ to be a kind of ‘rurble’, and get back the analytic (and hence necessary) truth that all durgles are gurdles—but this is trivial, and likely useless. All sorts of ‘formal systems’ like this could be defined which generate endless analytic truths, but there is no reason to suppose that they will in general be useful.

On the other foot, a good way to make sense of the utility of mathematical truths would be to posit that they originate in experience: if they are something like condensed abstractions of common encounters with the world, then it should come as no surprise that they are of great assistance in navigating it. But if this is the case then mathematical truths are not fundamentally different from other truths garnered from experience—they are just tremendously well confirmed empirical claims. But if this is the case then it is possible that evidence will one day be found that falsifies them. But then it is logically possible that arithmetical truths like “2+1=3” be false (i.e. they are not necessary), and this is hard to make sense of.

The core point I tried to make in my original post is that it is possible to bring together the benefits of both these views so long as it is remembered that even if a truth is both necessary and useful, it need not be necessarily useful. There is no reason why a necessary truth that is useful in this world shouldn’t be useless in a different possible world. (Since what is usually meant by ‘useful’ in the case of mathematics is ‘useful for formulating physical theory’, what this amounts to saying is that necessary mathematical truths that have proved essential to physics—those of group theory, for instance—might not have been so useful had the world had different physics, though they would still have been true.)

The ‘synthesis’ can perhaps be made vivid by considering the sort of thing that might count as evidence against a supposed arithmetical truth on the “originating in experience” account of mathematical knowledge. Imagine if it was found that under certain controlled, repeatable conditions, adding 2 marbles to a collection of 3 marbles gave a collection of 6 marbles. This would be very strange indeed, and it is tempting to think that the only paths open at this point would be either to admit that this counts against our belief that “3+2=5”, or that marbles are so beyond our ken that they can violate even mathematics—both of which seem like the nuclear option.

But I think this is an illusion. Consider the fact that adding two drops of water together leaves one, and that this doesn’t typically raise the worry that “1+1=2” might be false. More reasonable is to say that water droplets just aren’t the sort of things that combine additively when considered as discrete unities. What this hints at is that arithmetic (and, presumably, other parts of mathematics) have certain criteria of application, and that various portions of the world under various descriptions are under no obligation to meet them. So in the case of the mysterious marbles what is shocking is not that reason to reject arithmetic has been found, or that marbles are otherworldly beings, but just that marbles are not the sort of things previously thought, and do not meet the arithmetic criteria it was generally assumed they did.

In summary, two general points can be drawn from this:

1. In the case that a phenomenon is encountered for which some mathematics expected to be applicable to it turns out not to be, it seems unlikely that this would ever be enough to motivate a revision of the mathematics—doing so would amount to changing the subject. The more reasonable thing to do would be to try some different mathematics, or, failing that, to develop some new mathematics. If right, this lends some credibility to the idea that mathematical truths are analytic truths—their truth depends on their meaning as it relates to other mathematical concepts and the logical relations between them, not on how they relate to the world. If some part of the world isn’t amenable to the mathematics, then all that tells us is that the mathematics is the wrong tool for job, not that it might be false.

2. Systems of necessary mathematical truths may or may not be useful in a particular domain, and there’s no guarantee that what is useful for dealing with one domain will be useful for dealing with another. The ‘criteria of application’ that determine whether a particular theory of mathematics will helpfully model some particular part of the world may even be completely opaque to us, only to be found by trial and error, but this doesn’t matter—success or failure is the only measure that does.

The picture emerging from this is one of constrained creation. It says something like: a mathematical theory is a system of logically related propositions built from concepts defined by stipulation, and so its truths are analytic, which is why they’re necessary. Any questions about the truth of various statements formed from its concepts have answers completely internal to the theory. These analytic systems are created by us in response to problems—both to practical problems formed through dealings with the world, and to theoretical problems formed through attempts to understand the world. The ones that are successful are the ones that stick around (and get funding), but which ones these are depends entirely on the contingent features of the world that shape, filter, and constrain the systems we end up building and exploring. If the world was different, different analytic systems would have been the useful ones.

I think this sort of picture goes a long to way to answering the question of how mathematical truths can be both necessary and useful. But there are questions it leaves unanswered, and several that it raises: what is it about the useful systems that makes them useful? Are they useful because they describe, or are they useful for some other reason? If they don’t describe, then why does their surface grammar suggest that they do? And if they do describe, what exactly do they describe?

Compatibilism and the consequence argument

Here is an argument for the incompatibility of determinism and free will given by Peter van Inwagen in his Essay on Free Will [1], followed by a few brief words about how one of the motivating insights behind compatibilism might be presented as an objection to it. The argument is a variation of the so-called “consequence argument”, and it formalises a familiar intuition.

Van Inwagen takes determinism to be the thesis that “if p and are any propositions that express the state of the world at some instants, then the conjunction of with the laws of nature entails q.” [2] (This depends on the assumption that at any given instant there is a proposition which expresses the state of the world at that instant. Van Inwagen builds this into his full definition, but here I will just assume it for the sake of simplicity.) This captures the idea that the state of the world at a given instant determines a unique future (and a unique past, for that matter, though this is not relevant here).

An agent S is said to be able to render a proposition p false if it is within S’s power to modify the world in some way that makes p false. (There are several caveats in van Inwagen’s full definition [3] which I have omitted, again for simplicity.) So for example, yesterday at 1pm I had lunch in town. According to the definition, we would say that I was able to render the proposition that I will have lunch in town at 1pm false only if at some earlier time it was within my power to influence the world in such a way that when 1pm came around I was not having lunch in town.

The argument aims to show that in an arbitrary example in which an agent — named, creatively, “J” — does something, determinism entails that J could not have done otherwise. So imagine that, after careful deliberation, J decides not to raise his arm at some time T. Let the proposition expressing the state of the world at T be called P. Now assume that J is uninhibited at T by physical or psychological pressures of any kind — if any sense at all can be made of someone having free will with regard to some action at some time, then J has free will with regard to raising his arm at T. So if J had free will with regard to raising his arm at T, then J could have raised his arm at T, even if in the end he did not.

Let T0 be some arbitrary time in the past (before J’s birth, say, to avoid any potential complications) and P0 be the proposition which expresses the state of the world at T0. Finally let L denote the laws of nature. The argument runs [4]:

1. If determinism is true, then the conjunction of P0 and L entails P.

2. It is not possible that J have raised his hand at T and P be true.

3. If 2 is true, then if J could have raised his hand at T, J could have rendered P false.

4. If J could have rendered P false, and if the conjunction of P0 and L entails P, then J could have rendered the conjunction of P0 and L false.

5. If J could have rendered the conjunction of P0 and L false, then J could have rendered L false.

6. J could not have rendered L false.

7. If determinism is true, J could not have raised his hand at T.

7 follows from 1-6. What is so clever about this argument is how little wiggling-room it leaves for those wishing to resist its conclusion. 1 applies the definition of determinism, 2 follows from the law of non-contradiction, and 4 is an application of modus tollens. That leaves premises 3, 5 or 6 open to challenge. Neither 5 nor 6 seems likely — denying 5 would mean denying that J couldn’t change the state of the world at a time prior to his birth, and denying 6 would mean denying that J couldn’t alter the world in a way that changed the laws of nature.

So it seems that the most hopeful strategy for a compatibilist would be to take aim at premise 3. Consider Austin’s golf putt, one of the most common illustrations of compatibilism. Austin imagines a golfer who tries to make a putt but misses, then asks whether he or she could have got it in the hole [5]. He notes that there is an important sense in which the answer to this question is independent of determinism. In such a situation there are a set of conditions which are relevant to the golfer’s ability to make the putt — the lie of the green, the weather conditions, the distance to the hole, etc — and another set of irrelevant conditions, such as the particular positions of each air particle above the green. There is a huge number of possible configurations of the irrelevant conditions corresponding to any given configuration of the relevant conditions. Austin argues that when we ask whether the golfer could have made the putt, what is important is how often, with all the relevant conditions fixed, does the golfer make the putt under variations of the irrelevant conditions? If this number is high enough to rule out flukes then we might reasonably say that the golfer could have made the putt. If it could be argued that these semantics of “being able to do otherwise” are paradigmatic, then it could be said that in matters of decision-making being able to do otherwise is not dependent on determinism being false.

In relation to the given example this would work as follows. To say that J could have raised his hand at T is to say that there is a sizeable number of possible configurations of the world just prior to T with the same relevant conditions (whatever they may be) in which J raises his hand at T. This does not imply that under the actual conditions J had it within his power to change the uniquely determined future, that is, to render P false. So if Austin’s semantics can be justified, it could be plausibly maintained that premise three is false. There’s a lot of sketchiness in that account, of course, but it seems to me to represent the best line of attack on the consequence argument.


1. Peter van Inwagen – An Essay on Free Will (1983).

2. p65.

3. p68

4. p70

5. See J L Austin – Ifs and Cans.

Getting beyond non-cognitivism

The point of this post is to collect together a few big picture thoughts that have been creaking into place for me over the last few months. They concern the relationship between meta-ethics, truth, and the individuation of cognitive content. These thoughts are not original, though perhaps they’ve never been hacked together quite so shambolically before.

Consider the following two propositions:

1. Moral propositions (e.g. “murder is wrong”) are truth-apt.

2. Moral predicates (e.g. “is wrong”) do not refer to (or purport to refer to) moral properties of actions or people.

The first is the thesis known as cognitivism, the second is what I shall call non-descriptivism. It is often assumed that these propositions are mutually inconsistent. Thus expressivism — the thesis that moral predicates like “is wrong” express pro- or con-attitudes (and so do not describe properties) — is frequently taken to be a variant of non-cognitivism. Even Wikipedia says so. But as they stand it is not obvious why 1 and 2 should be inconsistent. It seems that what is being appealed to is a further premise:

3. If a proposition of the form P(x) is truth-apt then P references a property P’. (P(x) is true if x has P’ and false if x does not have P’.)

Clearly 1-3 form an inconsistent triad. So if 3 is true, then 1 and 2 can’t both be true. But equally, if 3 is false then perhaps 1 and 2 can both be true. So rejecting 3 clears some space for the possibility of a cognitivist non-descriptivism.

The sentiment expressed in 3 has strong links with the correspondence theory of truth. Specifically, rejecting the latter is a way of rejecting the former. Simon Blackburn has pursued this route by favouring a deflationary view of truth (which he dubs “minimalism”) over the correspondence theory. Like all variants of deflationism his starting point is the so-called ‘transparency’ property of the truth predicate as illustrated by Alfred Tarski’s famous equivalence:

“Snow is white” is true iff. snow is white

Saying of a sentence that it is true is to do no more than assert it. On Blackburn’s account the lesson to take from this is that we should adopt an attitude of quietism towards truth, i.e. a kind of pessimism about the prospects for a general theory of truth. If mathematicians establish that there is no greatest prime number then there is no further substantial question to be asked about whether this statement is really true, or what it might mean for that statement to be true beyond what the mathematicians mean by its being true. (There are philosophers who have proposed error theories of mathematics — Blackburn would likely say that these rely on a mistaken theory of truth.)

Similarly, to ask whether “murder is wrong” is true is just to ask whether murder is wrong. All meta-ethical questions about the truth of certain moral propositions collapse into first-order moral questions, and all questions about the truth-aptness of moral propositions become unintelligible except insofar as they are questions about what those moral propositions mean in the first-order sense.

This is not to say that there is no meta-ethical work to be done — we can still discuss whether moral predicates express pro-attitudes, or describe properties, or are used to issue imperatives, and so on. What gets rendered unintelligible on Blackburn’s view is the categorisation of these theories into “cognitivist” and “non-cognitivist”. According to Blackburn all questions of the truth or falsity of moral propositions (and so of their role in moral reasoning) belong to first-order ethics. This, as I understand it, is the essence of Blackburn’s ‘quasi-realist’ project.

A very different route to the decoupling of cognitivism from descriptivism can be found in Robert Brandom’s philosophy. Brandom is particularly concerned with developing a pragmatic account of propositional and cognitive content. The basic tenet of pragmatism is that linguistic utterances are to be thought of primarily as a kind of tool; the challenge is to describe what it is about a particular subclass of these tools (which we call “propositions”) that allows them to be asserted, believed, and denied — to be the sort of things which can be taken as true or false.

The key move made by Brandom is to argue that the semantic content of a proposition should be thought of in terms of inference, not representation. If you want to know what P means, don’t ask which state of affairs P represents but which other propositions P implies: the semantic content of a proposition is fixed by what can be inferred from it, not vice versa. On Brandom’s account this inferential structure is constituted by the practice of giving and asking for reasons of each other, conceived of as a kind of huge social game with emergent rules. Players in this game make moves by doing things — saying sentences, shaking their head, writing things down, screaming “bullshit!”, grimacing, table-thumping, nodding uncertainly, endorsing, committing — and the aggregate of these doings fixes the rules that govern which moves can be made and when, which moves can be made given which have already been made, and, in virtue of this structure, what the propositional contents of certain of those moves (the assertions) are.

That’s a too-brief summary of a painfully difficult concept, but its relevance to the present concerns can be illustrated by considering one standard objection to ethical non-cognitivism: if moral judgements were not truth-apt then moral disagreement and reasoning would be impossible; since we often disagree about moral issues, and frequently reason about them (occasionally with some success), non-cognitivism must be false.

If we think about this in Brandom’s terms the objection begins to look strange. The criticism is based on the premise that if we can disagree about a claim then it must be truth-apt, where the “truth-aptness” of the claim is considered to be independent of whether we disagree about it or not. But for Brandom this doesn’t quite make sense: the fact that we do disagree about it is part of what makes it propositional — that is, truth-apt — in the first place. It is the first-order practice of moral disagreement and reasoning that is constitutive of the truth-aptness and content of moral propositions. Whether the terms within them describe properties or do something else is an entirely different question. So when arguments of the above sort are put forward as objections to expressivism, say, Brandom can claim that they fail because they rely on an ass-backwards account of the individuation of propositional content. Just as Blackburn can claim that they fail because they rely on a mistaken theory of truth.

Where does this leave us? I’m not sure. At the very least I think it shows that the pigeon-holing of expressivism into non-cognitivism can be plausibly resisted. One way might be to reject the correspondence theory of truth (Blackburn), another might be to reject a representational theory of semantic content (Brandom). Of course, these two strategies are closely related.  If they succeed then some important traditional objections to non-cognitivism cease to be relevant for any carefully worded expressivism. Finally, we can raise some questions about the implications of all this for moral realism. What would it take for moral realism to be true? Is it (a) that some moral propositions are true? or (b) that there are real moral properties? What if the answers to a and b are independent of each other, as I think we can reasonably believe them to be? My view is that if they are then it is no longer clear what is at stake when it is asked whether moral realism is true or false.

Falsification, anomaly, and crisis

In my last post I discussed Karl Popper’s critical rationalism as illustrated by his interpretation of the ancient cosmological debate between Thales and Anaximander. Meanwhile I’ve been reading Thomas Kuhn’s classic 1962 work The Structure of Scientific Revolutions, which offers a rather different picture of the evolution of scientific theory. Near the end of the book Kuhn contrasts Popper’s view with his own, and raises the following objection [1]:

A very different approach to this whole network of problems has been developed by Karl R. Popper who denies the existence of any verification procedures at all. Instead, he emphasizes the importance of falsification, i.e., of the test that, because its outcome is negative, necessitates the rejection of an established theory. Clearly, the role thus attributed to falsification is much like the one this essay assigns to anomalous experiences, i.e., to experiences that, by evoking crisis, prepare the way for a new theory. Nevertheless, anomalous experiences may not be identified with falsifying ones. Indeed, I doubt that the latter exist. As has repeatedly been emphasized before, no theory ever solves all the puzzles with which it is confronted at a given time; nor are the solutions already achieved often perfect. On the contrary, it is just the incompleteness and imperfection of the existing data-theory fit that, at any time, define many of the puzzles that characterize normal science. If any and every failure to fit were ground for theory rejection, all theories ought to be rejected at all times. On the other hand, if only severe failures to fit justifies theory rejection, then the Popperians will require some criterion of “improbability” or of “degree of falsification.” In developing one they will almost certainly encounter the same network of difficulties that has haunted the advocates of the various probabilistic verification theories.

Popper emphasised falsification on the grounds that it provided a way around David Hume’s problem of induction. His insight can be illustrated by noting the asymmetry involved in justifying and refuting universal claims such as “all sheep are white”. If I believe this statement true, I could attempt to verify it by gathering observations of white sheep. But various probabilistic problems emerge as soon as it is wondered how many white sheep I will have to observe before I become justified in believing that all sheep are white. On the other hand, if I deny that all sheep are white all I will need to do to be justified is observe (e.g.) a single black sheep. Popper saw that since scientific hypotheses typically aim at generality, and so take the form of universal claims, a move that exploits this asymmetry can be made. If we view scientific theory not as requiring positive vindication by observation, but as a set of always-provisional conjectures whose acceptance depends on their robustness under attempts at refutation, then Hume’s problem can be dodged.

But as Kuhn notes, this account relies on one-off falsification events acting as conclusive refutations. If they don’t then judgements need to be made about the degree to which a theory is falsified by a given observation, which simply reintroduces all the probabilistic problems that the Popperian move was supposed to avoid. But if they do then every scientific theory ever conceived has already been definitively refuted, because there are always observations that are inconsistent with any given theory. For Kuhn as with Popper these inconsistencies prove to be critical, though not just in how they help to precipitate theory change, but also for the pivotal role they play in setting the agenda for scientific research in a particular field.

The notion most famously associated with Kuhn is that of a scientific ‘paradigm’. A paradigm is something more than a theory — it is what a theory becomes when it is universally or near-universally accepted by a scientific community, to the extent that it can no longer be thought of as answering a set of prior questions but rather as posing the questions to be tackled by the community. The space of all possible scientific problems is just too vast to be approached systematically, and so according to Kuhn a paradigm functions by identifying and isolating a small domain of relevant mysteries. This is why Kuhn sees it as not only unproblematic, but vital to scientific progress that observations which contradict the incumbent paradigm exist. Without them science would be akin to a random search through the Library of Babel, and equally as hopeless. Solving the problems posed by the current paradigm thus becomes the primary task of what Kuhn refers to as ‘normal science’.

Clearly, on Kuhn’s account observations inconsistent with the paradigm cannot be seen as falsifying it. In fact the working assumption of normal science is (indeed must be) that such inconsistencies can be assimilated by the paradigm. The task of normal science is to develop the resources to do so: creating new mathematical techniques to better articulate the theories which constitute the paradigm, working through more and more of its implications, improving the quality and quantity of observational data, building more elaborate technology to enable this, and so on. But sometimes an inconsistency will persist despite the efforts of normal science, and at this point it ceases to be a mystery and takes on the status of an ‘anomaly’. If the anomaly continues to persist despite the increasing resources directed at it by the scientific community then it may provoke members of the community to start questioning the foundational principles of the paradigm itself. At this point the field can be said to be in crisis. For Kuhn this is where normal science ends and ‘extraordinary science’ begins.

With its paradigm in tatters a field may become increasing fragmented, until in the end there are as many competing theories as there are experts, each trying to reconstruct the entire field from the ground up. At some point one of the competing theories will begin to dominate, ultimately becoming established as the new paradigm. The factors involved in the acceptance of the new paradigm may be varied — they will likely involve its ability to deal with the anomaly which led to crisis in the first place along with its successful interpretation of previous experimental results, as well, perhaps, of its ability to meet certain extra-scientific pressures (such as aesthetic standards). But one thing is sure: the new paradigm will come with its own set of mysteries, inconsistencies, and unexplained phenomena. Far from refuting the paradigm before it has even left the ground, these serve to define a new problem space, and in doing so to set the course for the next phase of normal science.


1. Thomas S. Kuhn – The Structure of Scientific Revolutions (50th Anniversary Edition) pp.145-146