Ways Modality Could Be

Cross-posted at Scholardarity: Click Here

In this post I want to introduce the idea of a higher-order modal logic—not a modal logic for higher-order predicate logic, but rather a logic of higher-order modalities. “What is a higher-order modality?”, you might be wondering. Well, if a first-order modality is a way that some entity could have been—whether it is a mereological atom, or a mereological complex, or the universe as a whole—a higher-order modality is a way that a first-order modality could have been. First-order modality is modeled in term of a space of possible worlds—a set of worlds structured by an accessibility relation, i.e., a relation of relative possibility—each world representing a way that the entire universe could have been. A second-order modality would be modeled in terms of a space of spaces of (first-order) possible worlds, each space representing a way that the entire space of (first-order) possible worlds could have been. And just as there is a unique actual world which represents the way things really are, there is a unique actual space which represents the way that first-order modality actually is.

Why, though, should we adopt a framework like this? To motivate it, consider the fact that people have mutually conflicting intuitions about what the space of all (first-order) possible worlds is like. Does God exist in all, none, or only some worlds? Or consider the famous dispute between Platonists and nominalists concerning predication. Platonists think that at least some predications can be true only if objects exemplify properties, and nominalists deny this. They think that there are no properties, but that predications can still be true. For the one party, some predications essentially involve properties, and for the other none do. Platonism, if true, is necessarily true, and if false, is necessarily false. The same goes for nominalism. Either some predications essentially involve properties or none do. On the face of it, this is problematic for the view that conceivability implies possibility: Platonism and nominalism have both been believed, and by many very able philosophers at that. What is believed is conceivable in some sense, otherwise such “beliefs” would have no content. So both positions are conceivable, but only one is possible. Either way, conceivability doesn't imply possibility.

But maybe that's not quite true. Perhaps, though only one of these positions is actually true, and hence first-order possible, both views are second-order possible. So maybe conceivability does imply possibility—at some order or other. Related considerations might apply to semantic content and possibility: If we can coherently mean something, it can be the case—at some order or other.

And what is the accessibility relation itself like? Presumably it is reflexive, but is it also symmetric, or transitive? And whichever of these properties it may or may not have, could that itself have been different? Could at least some rival modal logics represent ways that first-order modality could have been?

To be clear, the claim is not just that some things which are possible or necessary might not have been so, but rather that the nature or structure of actual modality could have been different. Even if the accessibility relation is actually both symmetric and transitive, maybe it could have (second-order)  been otherwise: There is a (second-order) possible space of worlds in which it is different, where it fails to be symmetric, or transitive. We must, therefore, introduce the notion of a higher-order accessibility relation, one that in this case relates spaces of first-order worlds. The question then arises as to whether that relation is symmetric, or transitive. We can then consider third-order modalities, spaces of spaces of spaces of possible worlds, where the second-order accessibility relation differs from how it actually is. I can see no reason why there should be a limit to this hierarchy of higher-order modalities, any more than I can see a reason why there should be a limit to the hierarchy of higher-order properties.

The accessibility relation is not the only thing that might be thought to vary between spaces of worlds: Perhaps the contents of the spaces can vary as well. While I presume that the contents of the worlds themselves remain constant—it makes doubtful sense to suppose that in one space an object o exists in w_1 and in another space o doesn't exist in w_1—we may suppose that the spaces differ as to which worlds they contain. Thus we might have a higher-order analogue of a variable-domain modal logic.

I do not expect this kind of framework to settle the issue of how modality at any order actually is—no more than I expect ordinary first-order modal logic to settle (aside from first-order necessary truths) what is actually the case. What goes for the actual world goes for the actual space of worlds, and for all higher-order spaces of spaces. What I do hope for is that it will, if it proves to be coherent, help to clarify the terms of the debate about the way modality is—to help us to state the issues, and to see their interrelations, as clearly as we can.

I think that's enough for this time. I'll leave the further development of such a framework for another occasion--or occasions—provided that you, my readers, think it merits further development.

On Imagination and Conception -- Possibility and the Phenomenology of Imagining

Cross-posted at Scholardarity's Diablog

 

A Note to the Reader:

What follows is the text of an (unpublished) essay that I wrote back in 2002. I was 16 at the time, and because of that this essay contains some misunderstandings, is a bit simplistic, and–to put it in way that’s kind to my past self –“overconfident” both in its ambition and its style. Nevertheless, in spite of that and the fact that I have changed my views on quite a few points since then, I still think there is some value in it, and so I’ve decided to post it here.

~ On Imagination and Conception ~

Jason Zarri

If I may be allowed to borrow your attention for a moment, I will explain to you a thought that occurred to me one day: Philosophy has gone on for thousands of years with logic, that is, the rules for correct reasoning. Logic is useful, to be sure, but oughtn’t philosophy have another implement in its tool-bag? One that tells it, for example, what the correct rules are for imagining and conceiving something?

It seems this new implement would be a sister-science to logic. Not, of course, that I mean to develop such a science myself. That is not the purpose of this essay. What I want is not to create this new science, but rather give something of a rough outline of it.

First of all, it shall be necessary for us to define what we mean by “imagine” and “imagination”. By “imagination”, we mean that class of mental phenomena which involves the production of sense images that are not given in actual perception; whether they are visual , audial, tactile, etc. By “imagine”, we mean the production of one of these images voluntarily. Secondly, for the “reference frame”. By “reference frame”, we mean what is usually termed the visual or phenomenal field. Specifically, we shall be interested in the phenomena of imagination as they relate to philosophical arguments for or against the conceivability or possibility of something. Fallacies of imagination I shall call abuses of the reference frame.

Since the time of Hume and Locke, not much has been said by philosophers concerning the nature of imagination, and I suspect that many still unconsciously subscribe to such an empiricist ‘cut and paste’ theory. Thus, the first thing we need to do is disabuse ourselves of such a notion, and especially of the idea, if any still have it, that such phenomena could be the product of a tabula rasa mind. 

Once hearing a tune, I may change its tempo, add to or subtract from the background layers of sound, and even completely change its instrumentation, say, from a violin to a clarinet; all the while retaining the ability to recognize it as ‘the same’. Here’s an interesting question: “How do I change the tempo of the song to make it faster or slower?” It is not accomplished by a mere verbal mental command, but in what it positively consists we never observe, nor do I think we can. 

Once hearing a voice speak for a short while, I may retain its sound, and so imagine it to to speak words I have never heard it say. One finds that one does this sort of thing very often, though usually thinking of how some friend or relation is going to respond to something.
To say I read a text means this: My eyes scan the page, while my mind speaks the words to itself in the voice it thinks the author of those words would have. And if I type like this, why does your mind put extra emphasis on the words ‘like’ and ‘this’?

Before you build a house, you must have some idea of it. But what could you possibly have in your mind before you construct that idea? It will simply not do to say that you form it as if by painting or by piecing colors together: in all such cases you have some conception of what you are creating beforehand. Yet, if it were spontaneous and random, there would be no structure to the scene. So just how is it that any of these mental landscapes we concoct initially come to mind?

Simple images may be flipped on a horizontal or vertical axis. If I, for example, form an image of a triangle that I have never before seen, and decide to flip it upside down, how does my mind know, before flipping it, what this, which is right side up, will look like upside down, in order that It may create that image? Surely I am not reversing some object. This is rather the destruction of one image and the creation of another. 

I believe that we must allow the mind some inventiveness of its own, for all this seems completely unaccountable on any tabula rasa view. Philosophically, it makes sense to say that the mind is a tabula rasa, because no one knows what ‘the mind’ is. But if you say that the brain is a tabula rasa, everyone knows you speak nonsense. 

Now, we ask ourselves, what is it like to imagine something? How do mental images differ from those given to us in perception? They all seem to share a common characteristic, which I think can only be described as a kind of faintness. If I hear a sound, I am always aware that I hear it, even if I am completely unable to determine what it is. When I imagine a sound, on the contrary, I am always able to determine it, even though I never hear it for an instant. And though I am perhaps able to increase its pitch, I find myself quite incapable of raising or lowering its “volume”. An analogous thing happens with sight. I may form whatever image I please, but regardless of the detail, it never enters into my visual field, nor does it disturb any of its content. In these instances, it is as though a second reference frame were created, and that nothing which goes on in the one has any effect upon the other. I believe that the first shall be called the perceptual frame, and the second, the imaginal frame. Each has its own peculiarities. The perceptual frame may increase or diminish in size depending upon the focus of one’s attention. When reading a book, say, it will seem that the text is all that exists, everything beyond the page being relegated to obscurity. Though our perceptual frame never vanishes, there are certain occasions, such as absorption in a daydream, when we become completely oblivious to its content, and on reflection cannot decide whether we were truly conscious of it or not. The imaginal frame, unlike its counterpart, is in no way permanent. It is created as soon as something suggests an image, and vanishes as soon as one’s attention is withdrawn from it. Images are formed continuously during the reading of a novel, and rarely or never at all during the viewing of a film or television program. During the remaining time the pace of the flow of images is located somewhere in between these two extremes. 

Having explicated the nature of imagination sufficiently for our purposes, we shall now concentrate on the abuses that philosophers have made of this faculty. I believe these may be divided into three major categories: abuses of amphiboly, abuses of improper imputation, and abuses of misapplication.

1. The abuse of amphiboly: The confusion of the noumenal and phenomenal sense of a term, or the mistaking of an image or perception for the thing itself, as this relates to philosophical arguments.

Example: Hume said that a man, lacking in the requisite experience, could not deduce from the qualities of FIRE, that it would burn him. But fire of the sort Hume means has never burnt anyone, and never will. For the ‘fire’ he is thinking of is naught but a certain conjunction of sensory qualities, viz.; hot, red, semi-translucent, etc. Our mind may conjure as much in a dream, without us suffering any ill effects. But if we were to take a studious pupil, whose subjects were chemistry and physics, and ask him what effects would ensue, upon the excitation of the molecules in my hand past a certain point; I cannot help but think that his answer would be “ignition”, even though he had never experienced for himself such a thing as ‘flame’.

2. The abuse of improper imputation: When imagining, to think or tell yourself something that you have not made the sensory qualities adequately represent. Or, to not imagine what the definition of the object or concept would entail, either fully or partially.

Example: McTaggart’s B-series. Whenever we try and represent to ourselves a tenseless timeline [I.e., a view of time according to which there is no "passage of time" and that all times are equally real], we find that we always imagine the events as simultaneously given, and subsisting in time. But that completely fails the conception of a temporal series, for it is the essence of time that its moments are not simultaneously given, and its component parts do not subsist. And when McTaggart said that the poker would always be hot on Tuesday, it is evident that he was using this picture, viz., the still image of a glowing poker, because that image does indeed subsist temporally. But the instants of the actual day would not exist in such a manner, even though that is how he represented them to himself.

3. The abuse of misapplication: The taking of the standard of our ability to form mental images as the standard of the possibility of things.

This abuse consists of three subsections:

1. The first form of the abuse of misapplication consists in the belief that whatever is imaginable and non-contradictory is also, for that reason, possible. In recent years, this principle has borne the title of “analytic-synthetic dichotomy”. It seems a bit odd, if I do say so myself, that this doctrine should be advanced by the empiricists as self-evident, without any further argument or experiment. Is there a way to test this hypothesis, so that we may see whether or not everything imaginable and non-contradictory is possible? I believe there is.
Let us suppose, for our example, a crystalline sphere. Let us also suppose that this concept we have conjured up possesses a very special property: once thought, this magical sphere will cease to exist merely as a concept or mental image, but will instead manifest itself in physical reality. Now, let us conceive of the proposed object. We do so, and… nothing happens.

Why?

To any sensible person, the answer to this question should seem exceedingly obvious. But our goal here is to be rational, not sensible.

We ask ourselves: Is there any obstacle to our imagining this event? No, there certainly is not. We can quite clearly imagine ourselves thinking of the sphere, and then that the sphere appears in the space outside us. And we may be sure the the proposed event is not ‘logically impossible’, for the thought of such an occurrence engenders no contradiction. Since this magical concept is both imaginable and non-contradictory, it must, according to the principle, be a genuine possibility. But we have thought of the concept, and it has refused to manifest itself. Therefore, we must conclude that the proposed event was never really possible.
Allow me to clarify this line of reasoning:

p. Whatever is imaginable and non-contradictory is possible.

q. A concept which, when thought, will obtain in physical reality.

1. (q.) is imaginable and non-contradictory, and so according to (p.) must be possible.

2. (q.) is thought, but does not obtain.

3. (2.) creates a conflict between (1.) and (p.).

4. We cannot reject (1.), because (q.) is imaginable and non-contradictory.

5. Therefore, we must reject (p.)

Thus we must conclude that we cannot give to our concepts such a magical property, merely by thinking it, even though we can imagine ourselves doing so.

2. The second form of the abuse of misapplication consists in the violation of the the boundaries of the reference frame. For example, it has been argued by some (such as Kant, in his antinomy concerning space and time) that we must always think of space as being infinite, and cannot imagine that it comes to an end. From whence is this belief derived? I imagine it arises from a thought experiment like this: Imagine any colored shape, such as a square, or perhaps a tree. Regardless of the shape, you must always represent it as being against some background, whether black, or white, or blue, but it must always be some color. From this, you may come to the conclusion that for any colored area, there must be a colored border. The opposite you will decry as unimaginable, entirely inconceivable. Allow me to ask you a question. Does your visual field stretch on to infinity? No, I do not believe you can affirm that it does. Very well, then what lies outside it? Your very reference frame is a colored area outside of which there is no colored border! But if that is so, then your perceptual space comes to an end. So what’s going on here?

Everything that we see lies in our visual field, and thus within the borders of the reference frame. In order for us to see where the reference frame ends, we would have to drag its borders within themselves, which is absurd. Because we cannot “see” its boundary as we could the juncture of two colored areas, we feign it has no boundary at all. There arises a similar illusion regarding our perception of time. Whatever we perceive, we perceive at a certain moment in time. Because perception must occur at a given moment, we cannot technically experience its ‘beginning’ or ‘end’ (And, in my opinion, it is this that gives rise to the ‘specious present’ [The 'specious present' is the notion that our perception of time always involves extended intervals of time rather than durationless instants, and hence that what we experience as present is an interval of time.]). Here, as in the previous case, our experience terminates in a boundary that is itself unobservable. Because of this, we find that we cannot imagine a beginning or an end to time, though it is certainly possible in itself. When Kant plucked time from out the world, he dragged the antinomy the removal was supposed to efface in its train. It is all very well and good to say: “There is no time in the world, so there is no fact of the matter of time’s beginning or not.” But can one likewise affirm: “There is time in the mind, and there is no fact of the matter of time’s beginning or not”? The question comes down to this: “Is our past temporal history finite or eternal?” [In other words, what I meant was this: Consider the set consisting of all your past experiences. The set is either infinite in the "past direction" or not. If it is infinite, there was never a first moment at which you had a conscious experience, and so even if there is no fact about whether the physical world has existed forever, you and your experiences have always existed. If, on the other hand, the set is finite in the "past direction", there is a first conscious experience that you had, and so for you there is no time prior to that. In that case there is a beginning to your "experiential time", and if so, why should a beginning to time be inconceivable in the case of the physical world? Either way, I didn't see--and still don't, for that matter--any reason to think that Kant has established his antinomy.] If we are to take Kant’s first antinomy as proving its conclusion, then it is absolutely impossible for him to answer this question. Hence, there must be some defect in his conception of time. Therefore, I declare Kant’s first antinomy to be fallacious, for he has committed the abuse of misapplication.
3. The third form of the abuse of misapplication consists in the belief that whatever is unimaginable must, as a consequence, be impossible. This opinion, I suspect, is derived from a certain arrogance of the mind. Being naturally overconfident, it overestimates the power of its faculties, and if it finds that it cannot drag anything within its sphere, it must suppose the difficulty to arise from some defect in the thing, and so declares it to be nugatory and impossible in itself. 

It has been alleged by many, though most famously by Hume and Berkeley, that the human mind has no power of conjuring up any image that is not fully determinate and particular in every degree. I shall advance no arguments against this position. Indeed, I heartily endorse it. But I shall not proceed with them in drawing their conclusion, viz., that an indeterminate image is impossible. For if they had been more attentive to their own perception, they would have realized that it is positively littered with indeterminacies! If you don’t believe me, you may try this experiment and see for yourself. Go into any room, preferably one that is brightly lit with a diversity of variously colored objects. Now, stare straight ahead, and focus your eyes on the very center of your visual field. While leaving your eyes where they are, focus your attention on the outermost periphery, preferably fifty degrees or more from the center. I believe you will notice that, though you can see that something is there, you cannot see it as being in a determinate shape, or having a determinate color. If you feign that you do, then try and tell yourself what its shape and color are without looking! This is especially evident in the case of text. Try focusing your eyes on one page of an open book, whilst focusing your attention on the page opposite it. Though you can discern the general shape that the words together form, it is quite impossible for you to honestly affirm that you see any individual character, or if you can, that you see what shape it is in. These experiences, though possible, are entirely unimaginable. Now, if our imagination cannot tell us about what it may be possible to experience, then a fortiori it applies even less to what is possible in reality. Thus, whenever a philosopher should henceforth proclaim something to be unimaginable, our reply shall be a resounding “So what?”
Finally, we shall draw our conclusions:

1. The mere fact that we can imagine something does not prove it to be possible, and the mere fact that we cannot imagine something does not prove it to be impossible.

2. Since we can have and now remember ‘unimaginable’ experiences, our inability to form such images stems not from a defect in their nature, but a defect in ours.

3. Hume, Berkeley, and innumerable others have committed the abuse of misapplication.

Our knowledge of nature, be it ever so great, has taught us but one thing throughout the ages, that humanity, through its blindness, refuses to learn: Reality is not quite so narrow as to be confined to our conception of it.

Conceivability, Consciousness and the Content of Belief

[Cross-Posted at Scholardarity's DiaBlog, here]

What follows is the text of my final paper for a philosophy of mind course that I took in the spring semester of this year. Due to constraints on length, the paper is much shorter than it needs to be. I would very much like to expand it to deal with David Chalmers' nuanced views on conceivability, among other things, and so I would be very grateful for any feedback that could help me to do that.  

Conceivability, Consciousness and the Content of Belief

1. Introduction

            In his article “Consciousness and Its Place in Nature”, David Chalmers presents an argument against materialism—the view that truths about consciousness and indeed mental phenomena in general are in some sense fixed by truths about physical entities—which is based on conceivability. If the argument is sound, the fact that one can conceive materialism to be false entails that materialism actually is false. In this paper I will argue that the argument is unsound, and I will do so by giving a parallel argument that is clearly unsound.

2. Sketching Chalmers’ Argument

            Let us say that something is metaphysically possible if it really could obtain, even if it actually does not. Let us also say that something is metaphysically necessary if it really has to obtain no matter what. In other words, if we say that a “possible world” is a way that absolutely everything—the entire universe—really could turn out to be, then something is metaphysically necessary if it obtains in every possible world. Now, Type-A materialists think that phenomenal truths—truths about “what it is like” to have experiences of various kinds—can be derived from physical truths via a priori reasoning. Type-B materialists, on the other hand, think that phenomenal truths are entailed by physical truths even though one cannot know a priori either that this is so or which physical truths entail which phenomenal truths. However, on both views phenomenal truths are fixed by physical truths as a matter of metaphysical necessity: There is no possible world in which the physical truths are as they actually are while the phenomenal truths are different.

            Chalmers offers an argument against Type-B materialism based on our ability to conceive that the physical truths about the world could be just as they are while some phenomenal truths are different. Let P be some sentence expressing the complete truth about all things physical, and Q be some particular truth about someone’s phenomenology. Chalmers’ argument would then be:

1. It is conceivable that P ⋀ ¬ Q.

2. If it is conceivable that P ⋀ ¬ Q, then it is metaphysically possible that P ⋀ ¬ Q.

3. If it is metaphysically possible that P ⋀ ¬ Q, then materialism is false.

4. Materialism is false.

(Philosophy of Mind, p. 249). So if it is conceivable that P holds while at least one truth about someone’s phenomenology fails to hold, materialism, and hence Type-B materialism, is false. This argument is clearly valid, but I think it is unsound, and I propose to show this by giving a parallel argument that I take to be clearly unsound.

3. Presenting the Parallel

            Consider Platonism and nominalism about predication. Platonists think that the truth of sentences of the form “x is F” (or some restricted class of such sentences) require the further truth of sentences of the form “x exemplifies F-ness”, where ‘F-ness’ refers to the property expressed by ‘F’. Nominalists deny this. They would say that sentences of the form “x exemplifies F-ness” are (necessarily) false.[1] Nevertheless, for nominalists sentences of the form “x is F” are perfectly fine as they are.

            There are at least two different possible forms of Platonism. Type-A Platonists hold that sentences of the form “x exemplifies F-ness” can be derived from sentences of the form “x is F” via a priori reasoning. Type-B Platonists hold that sentences of the first form cannot be derived via a priori reasoning from sentences of the second form, although they do follow from them as a matter of metaphysical necessity. Nominalism has been upheld by many able philosophers over a long span of time, and since it is unlikely that this would be so if Platonism could be easily established a priori from the platitude that there are true predications, I think Type-B Platonism is more plausible than Type-A Platonism.

            Now for the parallel argument. Let R be some sentence expressing the conjunction of all sentences of the form “x is F”, and S be some particular sentence of the form “x exemplifies F-ness.” The argument would then be:

1. It is conceivable that R ⋀ ¬ S.

2. If it is conceivable that R ⋀ ¬ S, then it is metaphysically possible that R ⋀ ¬ S.

3. If it is metaphysically possible that R ⋀ ¬ S, then Platonism is false.

4. Platonism is false.

So if it is conceivable that R holds while at least one particular sentence of the form “x exemplifies F-ness” is false, it follows that Platonism, and hence Type-B Platonism, is false. I take it to be clear that Type-B Platonism cannot be refuted so easily. Something has gone wrong, but what?

4. Two Kinds of Conceivability

The second argument, like the first, is clearly valid. Thus, it must be unsound. Type-B materialists are committed to accepting premise (1) of first argument, and Type-B Platonists are committed to accepting premise (1) of the second. Also, in both arguments premise (3) appears to be necessarily true. This casts suspicion on premise (2) of each argument, though I will focus on premise (2) of the first argument.

I think premise (2) is questionable for two related reasons. The first reason is that I think the term ‘conceivable’ is ambiguous, and has two senses. Taking ‘thinkable’ and ‘comprehensible’ as technical terms, I will say that something is thinkable if one can understand it, and that something is comprehensible if, in virtue of understanding it, one can tell that it is possible.[2] So everything which is comprehensible is thinkable, but I think the converse is not true. Some expressions—nonsense strings like “!#?@”, and ungrammatical “sentences” like “Is and Caesar two” are not conceivable in either sense. On the other hand, sentences expressing logical or metaphysical impossibilities—e.g., “It’s true that Socrates was brave and it’s not true that Socrates was brave,” “Tyler is a married bachelor”—are, in my opinion, thinkable but not comprehensible. Some would take such sentences to be strictly meaningless, but I think that view is mistaken. For it seems that we can understand necessarily false sentences, because there are many cases where people have believed things which just can’t be true. Consider those who thought they could prove Euclid’s parallel postulate before the discovery of non-Euclidean geometries, or those who thought, before Gödel, that one could derive all the truths of mathematics within a single formal system. Once we grant that people have believed such things, we must also grant that necessarily false sentences are meaningful, and can thus be understood, for if they could not be understood they could not be the content of someone’s belief.

5. The Perilous Parallel

We now have the resources to see why my parallel to Chalmers’ argument is significant, and what its significance is. Regarding predication, either Platonism or nominalism is true. Now, either the truth of predications (or some restricted class of predications) requires that objects exemplify properties, or it does not. So either Platonism or nominalism is necessarily true, and if Platonism is necessarily true nominalism is necessarily false, and vice versa. Either way, one side thinks, but does not comprehend, something that is metaphysically impossible.

This brings us, at last, to the second reason why premise (2) is problematic. Let’s say that a world satisfies some sentence (or whatever one takes the ultimate bearers of truth to be) if that sentence is true at that world; or, alternatively, that that sentence would be true if that world were actual. If something is comprehensible then it is indeed satisfied by some possible world.  But either nominalists or Platonists think something which is metaphysically impossible, and which cannot be satisfied by any possible world. Despite that, both of these alternatives are epistemic “possibilities” in the sense that we cannot rule them out a priori given our current knowledge and limited inferential abilities. Thus some epistemic possibilities are not satisfied by any metaphysically possible worlds. If we nevertheless wish to count Platonism and nominalism as epistemic possibilities in the above sense, we will have to hold that some things are satisfied by impossible worlds—worlds in which some necessary truths may fail to hold. One could not say that such worlds are really misdescribed possible worlds or scenarios, as when a world in which water is purportedly XYZ is really a world in which the watery stuff is XYZ while water is still H₂O. A “world” in which predication essentially involves properties is not really a misdescribed world in which predication doesn’t essentially involve properties. Some work in semantics has shown that one can make sense of impossible worlds[3], but this is no help to Chalmers’ argument because the argument only works if worlds where P ⋀ ¬ Q holds are metaphysically possible. P ⋀ ¬ Q may be epistemically possible in the above sense, but that does nothing to show that it is metaphysically possible.

6. Objection and Reply

            Chalmers could try to question the idea that one could believe impossible things. If one cannot, my distinction between thinkability and comprehensibility threatens to collapse.

            I think, however, that the view that one cannot believe the impossible cannot be sustained. Consider the content of that very belief: If it is impossible to believe impossible things, it is impossible to believe that one can believe impossible things. What then could Chalmers make of his opponents’ position? He could not say that someone believes that someone can believe impossible things. Are sentences like “Wyman believes that P”, where ‘P’ is an arbitrary impossible sentence, meaningless? If so, “Wyman believes that someone believes impossible things” is meaningless. Could Chalmers maintain that his opponents are not mistaken, but simply confused? In that case he should not deny what they say, holding it to be false. He should instead claim that his opponents have an illusion of belief, and on pain of incoherence this illusion must not itself involve a false belief about the semantic status of certain of their apparent beliefs.  Vindicating that claim is no easy task, and I doubt it can be done.

7. Conclusion

We can now see why Chalmers’ argument against Type-B materialism fails. It fails because it does not distinguish two different senses of ‘conceivable’, namely thinkable and comprehensible, and while the falsity of materialism is thinkable we have no real evidence that its falsity is comprehensible. So we can conceive that materialism is false in one sense, but this does not entail that it is really possible that it is false. Maybe materialism is false anyway, but Chalmers’ argument does not show that it is.

References

Chalmers, David J. “Consciousness and Its Place in Nature,” Philosophy of Mind: Classical and Contemporary Readings, ed. David J. Chalmers. New York, Oxford University Press, 2002.

Chalmers, David J. Philosophy of Mind: Classical and Contemporary Readings. New York, Oxford University Press, 2002.

Restall, Greg. “Ways Things Can't Be”, Notre Dame Journal of Formal Logic, 38: 583–96. 1997.

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[1] There is one exception: “Trope” theorists do believe in properties, but for them properties are tropes.  These are particular properties like Socrates’ wisdom, not Platonic properties like wisdom in general which are thought to exist outside of space and time. In the main text I intend ‘property’ to be understood as referring to Platonic properties, not tropes.

[2] I think ‘conceivable’ is really an operator, not a predicate. Instead of saying, e.g., “Nominalism is conceivable,” one should say, “It is conceivable that nominalism is true.” The same goes for ‘thinkable’ and ‘comprehensible’.

[3] See for example Restall (1997)

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