Consciousness and Sleep

 

 

Why do we say that a person is unconscious when asleep but conscious when awake? During sleep we often dream and dreaming is a conscious activity of mind, so why don’t we say that we are often conscious while sleep? Why do we speak as if sleeping and consciousness are opposed? Similarly, why do we suppose that being awake rules out being unconscious? It doesn’t rule out the existence of unconscious mental activity, so why should it rule out being simply unconscious—no conscious mental activity at all? Couldn’t a person be awake in the normal sense—mobile, eyes open, and alert—and yet there is a break in consciousness, a gap in the stream? Couldn’t wakefulness be punctuated by periods of unconsciousness, as sleep is punctuated by periods of consciousness? Couldn’t someone go into blindsight mode every once in a while and still be said to be awake?

            Part of the problem is defining what it is to be awake or asleep. The OED defines “sleep” as follows: “a regularly occurring condition of body and mind in which the nervous system is inactive, the eyes closed, the postural muscles relaxed, and consciousness practically suspended”; while “awake” is defined simply as “not asleep”.  [1] But couldn’t these conditions for sleep be met and yet the person (or animal) is still awake? What if I relax on my bed with my eyes closed and think only of sheep—aren’t I still awake? What if I take a drug that cuts off sense perception, paralyzes me, and leaves me with only the most minimal consciousness—could I not still be awake?  And what about the clause about consciousness being “practically suspended”? It doesn’t seem at all suspended during an intense nightmare or an ardent erotic dream. I suspect the editors mean “consciousness of the environment”, but that is neither necessary nor sufficient for being asleep: you can be asleep and aware of outside stimuli to some degree (hence the qualification “practically”), and you can be wide awake while having no awareness of the environment but only of yourself. Clearly, we have poor definitions of what sleep is, and likewise wakefulness. We don’t have a good analysis of what these states involve.

            The point remains that the logical connections between “asleep” and “unconscious” and “awake” and “conscious” are opaque at best. There seem in fact to be no logical connections here: we can experience states of consciousness during sleep, i.e. dreams, and we could go consciously blank while awake, i.e. not asleep. Being asleep is roughly a state involving being relatively unreceptive to the environment, but that doesn’t preclude a vivid inner consciousness such as occurs in dreams. Being awake is roughly being alert to the environment, immersed in it, but that doesn’t preclude moments of conscious blankness, as in blindsight. We say of simple organisms such as insects that they are awake, i.e. not asleep, but we don’t take this to entail that they are sentient beings. So there appears to be no analytic or necessary link between the awake/asleep distinction and the conscious/unconscious distinction. Indeed we could invert our usage and incur no charge of logical infelicity: we could say that we are conscious while asleep (though not all the time) and that we are unconscious while awake (though not all the time)—that is, we could say the latter if we actually had periods of conscious blankness while awake. Just as we are sometimes conscious during sleep, so that sleep is not necessarily a time of unconsciousness, so we could sometimes be mere zombies while awake, so that being awake is not necessarily a time of (uninterrupted) consciousness. You can be lying down in the dark fast asleep and have conscious experiences inwardly, and you could be moving around the world completely awake (“not asleep”) and be experiencing nothing consciously at all—you are in your robot phase. As things are, we are (apparently) conscious during the entirety of wakefulness—though there might be brief unconscious interstices—but we could be only intermittently conscious, perhaps so as to relieve the consciousness centers of our brain. Thus it would be arbitrary to say that we are unconscious while asleep and conscious while awake; rather, we are conscious and unconscious in both conditions (though not at the same time). I therefore recommend that we stop speaking as we normally do: we can be asleep or awake (whatever exactly these conditions amount to) and we can be conscious or unconscious, but there is no logical connection between these two dichotomies. Someone could in principle be continuously conscious during sleep by dreaming all the while, and could be continuously unconscious while awake by going into total zombie mode. Thus you could be completely conscious while asleep at night and completely unconscious while awake during the day—you could invert the normal human pattern. You could wake up to unconsciousness and go to sleep to consciousness. Your consciousness could be completely devoted to dream consciousness, while the banalities of waking life are handled by an unconscious brain system. For a possible species this might be an efficient way to apportion consciousness. Why waste your consciousness resources on fact when fantasy is so much more interesting? Sleeping is the time to let your consciousness roam free; being awake can be consigned to unconscious brain mechanisms.  [2]    

 

  [1] It is an interesting question whether there is any viable definition of “awake” that defines it more positively. The dictionary editors seem to be of the opinion that asleep is the more basic concept, with awake defined simply as its negation. This is to treat awake as what I elsewhere call an essentially negative concept. I suspect they are right to do so: our concept of wakefulness just is the concept of not being asleep.

  [2] It certainly seems as if we have more imaginative consciousness during sleep than during wakefulness, so why more of all kinds of consciousness?

                                               

 

 

Semantic Levels

 

 

Anyone interested in language and perception will recognize that there are different levels of analysis of the phenomenon in question. In linguistics we will distinguish phonetic, syntactic, and semantic levels (possibly others). In studies of visual perception we will distinguish the conscious percept, internal computations, the image on the retina, the proximal and distal stimulus, and the object of perception. If we compare the levels that concern the external object in the two areas, we notice a striking discrepancy: we speak of a single object of reference but several objects of perception. What did I refer to with “London”? I referred to a certain city and nothing else. What did I see when I flew over London? I saw the city, but I also saw a part of the city, the surface of the city, a facet of the city. In perception we readily speak of direct and indirect objects of perception—as when we say that I directly saw an elephant’s head but only indirectly saw the whole elephant, given that only the head was visible. We have the idea that you can see one thing in virtue of seeing another (one of its parts), as you can touch an object in virtue of touching a part of it (or the surface of part of it). Thus there are multiple perceptual objects in any visual encounter, but we suppose there to be only a single object in acts of reference. When I refer to London I don’t refer to its parts, surface, or facets. In the case of vision we might start out naively speaking of “seeing London”, but we quickly recognize that there is complexity here and that the objects of seeing are many—hence the talk of direct and indirect objects of perception. But we don’t think this way about reference: reference singles out a whole object not its parts of facets—hence there is no talk of direct and indirect reference analogous to the case of perception.

            We do suppose that the semantic level can be broken up into parts. In addition to the reference there is the sense, and sense itself can be broken into parts (character and content, say, or narrow and wide meaning). But we are not supposed to refer to sense—we express it. There is no dual reference, though the semantic level is composed of two sublevels. We might wonder whether the level of sense has all the complexity of the corresponding level in perception, i.e. the visual mode of presentation of the object. The latter divides into a central focal part and a peripheral part, but no one ever says that senses can be clearer at the center than at the periphery or that senses present many objects simultaneously. Senses seem simpler than percepts, as references seem simpler than perceptual objects. There is more structure in the one case than in the other. In particular, the semantic level concerned with reference to external objects is conceived as one-dimensional: we only refer to one thing at a time. Thus a theory of reference need only assign to words a single reference: the name “Saul Kripke” refers to Saul Kripke and to nothing else—not to his parts, surface, or facets. But the same is not true of seeing the man—here there are many objects of perception to be reckoned with. The obvious question is why the difference.

            Frege invoked the concept of an aspect in his classic discussion of sense and reference. The sense is said to contain an aspect–it presents or reveals or encodes an aspect. An aspect is an objective feature of the reference—something like the ensemble of properties apparent from a particular perspective. Objects can be seen from different perspectives and thus different aspects of the object are presented. This is what accounts for differences of sense (in central cases). A given object can present many aspects and sense can incorporate any of these. Now if we ask what relation a speaker has to an aspect, the answer will be that the aspect is presented to him, or perhaps that he apprehends the aspect. Maybe we can say that the name connotes an aspect—it somehow alludes to one. The aspect could be directly referred to, as in “the way the moon looks right now”: we can refer to the properties presented to us. The aspect belongs on the side of the world, along with the referent, not in the speaker’s mind. It is some kind of intentional object, in Brentano’s sense. So why not say that the aspect is referred to by the name? The name’s meaning identifies the aspect, alludes to it, specifies it—so doesn’t it refer to it? The sense of the name presents an object, but it also presents an aspect of the object; indeed, it presents the former by presenting the latter. I can be said to see an object and also to see an aspect of it, so why can’t I be said to refer to an object and also refer to an aspect of it? There is a kind of double denotation at work: the object and an aspect of the object are made objects of reference (intentionality). Even if the “folk theory” of reference doesn’t speak explicitly of this double denotation, closer analysis has revealed that there is more than just name and object; there is the aspect-presenting sense. So shouldn’t we revise the folk theory to take into account this further level of semantic structure? Wouldn’t that be good science?

            We can call the object itself the “secondary reference” and the aspect the “primary reference”. I choose “primary” for the aspect because it is in virtue of referring to the aspect that the object is referred to, just as in the case of perception. If we think of the aspect as captured by a definite description, then the aspect is clearly primary, since the description contains it en route to picking out an object. There is nothing to prevent us talking this way and it clarifies the structure of the referential semantic level. The aspect exists objectively alongside the object, not in the speaker’s mind, and our words (according to Frege) pick the aspect out; saying there is “reference” to the aspect is a small step. Thus “the Morning Star” denotes both Venus and the aspect of it presented in the morning. The proposition expressed by sentences containing the name will thus include both the object and the aspect. This allows us to explain the difference between “the Morning Star” and “the Evening Star” at the level of reference: different aspects referred to. A direct reference theory therefore permits a solution to Frege’s puzzle. No individual concepts need to be introduced or anything of a psychological nature; we just need to allow that reference can function like perception. We can invoke the apparatus of direct and indirect intentionality: I see an object by seeing an aspect of it, and I refer to an object by referring to an aspect of it. Whether we talk that way in our folk theory of reference is beside the point; the structure is there and needs to be articulated.  There may be possible perceivers who speak of perception in the simple way, as if there is nothing involved but the perceiver and the object, forgetting about perspective; but they would be wrong to insist that the object is the only thing that is perceived. We see objects by seeing aspects of them (surfaces of parts, roughly). It is the same with reference: there are nested levels of reference. Frege convinced us to accept that words can mean two kinds of thing—reference or sense—and now we should accept that words can refer to two kinds of thing—primary reference and secondary reference. This is scientific progress, though it may seem counterintuitive at first, as Frege’s theory of sense and reference did (e.g. to Russell).

            Suppose that a group of speakers came to the subject of semantics already equipped with Frege’s apparatus—they know all about aspects and objects. They refer explicitly to aspects all the time and are well aware of their role in determining the reference of names. They might introduce names by linking them to expressions that denote aspects: “Let ‘Hesperus’ be the name of the planet with that aspect”. They might even stipulate that “Hesperus” is to mean “the planet with that aspect”. Then the sense will include a specific reference to an aspect, so that we can readily speak of the primary and secondary reference of the name. These speakers have never entertained a single-reference folk semantic theory but have always allowed for double denotation. Shouldn’t we follow their example now that we have clearly discerned the semantic structure of object and aspect? Given Frege’s analysis, it is simply true that sentences containing names pick out both objects and aspects, and what point is there in denying that this “picking out” is the same as reference? When we speak of “the” denotation of a name we should really mean the pair of object and aspect. A theory of reference for names will accordingly assign both sorts of entity to a name. A Millian about names can agree with this double assignment, because the object itself enters the meaning of the name; but he can also solve Frege’s puzzle by appealing to the (implicit) reference to an aspect. We don’t need to bring in individual concepts or some such psychological thing; all the work can be done at the level of objective reference. It is just that we refer to more things than we realized. A name can have sense and references.

            The theory of reference therefore divides into two theories: object reference and aspect reference. How do these types of reference work? Should we have a causal theory for both, and how will the theories be related? Or should we have a description theory for both? We can see how aspects might figure in a description theory of object reference, but what about reference to aspects—is this mediated by description too? Can aspects have further aspects that figure in a theory of reference for them? Won’t that lead to an infinite regress? Is it possible that the basic theory will apply to aspect reference, with object reference carried by a description like “the object with aspect A”? Will the two theories be independent in the sense that neither determines the other, because different objects can instantiate the same aspect and different aspects can belong to the same object? Are aspects primarily referred to by means of demonstratives, so that object reference is carried by something of the form “the object with that aspect”? When a baby is baptized is the reference of the name fixed by “the human being with the babyish aspect now before us”? Should we say that we know aspects by acquaintance and objects only by description? What about the radical idea that all real reference is to aspects, with objects not strictly referred to at all? Frege spoke of the sense as “illuminating only a single aspect of the reference”, but should we infer that the sense doesn’t illuminate the reference as such? Is sense a conduit for aspects not objects, with the latter coming along for the ride? Is aspect reference where all the semantic action is? Maybe the object comes into the picture because we need it to account for truth conditions, but the basic semantic work goes into aspect reference. Senses tell us a lot about aspects, but relatively little about the objects that have the aspects. If we knew all about reference to aspects, what further task would the theory of reference have? All we would need to add is that the object of reference is simply the one that has the aspect already referred to. The theory of reference might be mainly a theory of aspect reference—as with the theory of perception. In any case, double denotation calls for a doubling of theory.

 

Colin McGinn 

 

 

 

                                               

 

 

 

Knowledge By Necessity

 

 

We can know that a proposition is true and we can know that a proposition is necessary, but can we know that a proposition is true by knowing that it is necessary? Consider a simple tautology like “Hesperus = Hesperus”: don’t you know this is true by seeing that it is necessary? If someone asks you why you think it is true, you will answer, “It couldn’t be otherwise, so it has to be true” or words to that effect. The sentence is clearly necessary, so you can infer that it must be true. You treat the modal proposition as a premise to derive the non-modal proposition. The former proposition acts as the ground of your knowledge of the latter proposition. You can tell just from the form of the proposition that it must be true, and thus it is true. You derive an “is” from a “must”. You really can’t help seeing that the sentence expresses a necessity, given that you grasp its meaning, and truth trivially follows. We can call this “necessity-based” knowledge: knowledge that results from, or is bound up with, modal knowledge. How else could you know the proposition to be true—not by empirical observation, surely? You know it by analysis of meaning: the meaning is such as to make the sentence necessary. The sentence has to be true in all possible worlds, given its meaning, and so it is true in the actual world—truth is a consequence of necessity. It is immediately obvious to you that the sentence is necessary—and so it must also be true. If someone couldn’t see that “Hesperus = Hesperus” is necessary, you would wonder whether he had understood it right. Maybe someone could fail to see that necessity entails truth and hence not draw the inference; but how could he fail to see that “Hesperus = Hesperus” is a trivial tautology, in contrast to “Hesperus = Phosphorous”? The sentence is self-evidently a necessary truth.

            It thus appears that some knowledge of truth is necessity-based: knowledge of the truth involves knowledge of the necessity, with the latter acting as a premise. Sometimes people believe things to be true because they perceive them to be necessary. You know very well that Hesperus is necessarily identical to Hesperus—how could anybody not?—and so you are entitled to believe that “Hesperus is Hesperus” is true. For analytic truth generally the same epistemic situation obtains: you can see the sentence has to be true given what it means, so it follows that it is true. Even if the move from necessity to truth is not valid in every case (e.g. ethical sentences), it is in some cases. We can thus derive non-modal knowledge from modal knowledge. But clearly not all knowledge is like this—mostly you can’t come to know truths by perceiving necessities. You can’t come to know the truth of “Hesperus = Phosphorus” that way: here you have to investigate the empirical world. The sentence is necessary, but you can’t use this necessity to decide that the sentence is true. You may know that if it is true then it is a necessary truth, but you don’t know that it is true just by understanding it, so you can’t use its necessity as a premise in arguing that it is true. You need to appeal to observation to show that the sentence is true—as you do for any other empirical proposition. Here your knowledge is observation-based not necessity-based—observable facts about planetary motions not the analysis of meaning. You won’t cite tautology as a reason for truth in this case, but you will in the other case. You won’t argue that there is no alternative to being true for “Hesperus = Phosphorus”. Clearly you can’t argue that “Hesperus = Phosphorus” follows from “Possibly Hesperus = Phosphorus”, but that is the only modal truth you have at your disposal in your current state of knowledge, unlike the case of “Hesperus is Hesperus”. So you can’t take a short cut to knowledge of truth by relying on an evident necessity—you have to resort to arduous empirical investigation. You may wish you knew that the sentence is necessary, so as to spare yourself the epistemic effort, but that is precisely the knowledge you lack in this case, since the expressed proposition in question refuses to disclose this fact. We resort to observation when our modal sense cannot detect necessity, which is most of the time. Necessity-based knowledge is quick and easy, unlike the other kind.

            I have been leading up to the following thesis: a priori knowledge is knowledge by necessity while a posteriori knowledge is not knowledge by necessity. Here we define the a priori positively and the a posteriori negatively, unlike the traditional definition in terms of knowledge by experience versus knowledge not by experience. This gives us a result for which we have pined: a positive account of the nature of a priori knowledge. The two definitions map onto each other in an obvious way: knowledge by necessity is not knowledge by experience, and knowledge by experience is not knowledge by necessity. That is, we don’t come to know necessities by experiencing them, and necessities are no use to us in the acquisition of empirical knowledge. Necessity plays a role in acquiring a priori knowledge, but it plays no role in acquiring a posteriori knowledge. To have a crisp formulation, I shall say that a priori knowledge is “by necessity” and a posteriori knowledge is “by causality”—assuming a broadly causal account of perception and empirical knowledge. We can also say that a priori knowledge is knowledge grounded in our modal faculty, while a posteriori knowledge is knowledge grounded in perception and inference—thus comparing different epistemic faculties. But I think it is illuminating to keep the simpler formulation in mind, because it directs our attention to the metaphysics of the matter: modality in one case and causality in the other. The world causally impinges on us and we thereby form knowledge of it, and it also presents us with necessities that don’t act as causes—thus we obtain two very different kinds of knowledge. The mechanismis quite different in the two cases—the process, the structure.

            Is the thesis true? This is a big question and I shall have to be brief and dogmatic. There are two sorts of case to consider: a priori necessities and a priori contingencies. I started with an example of a simple tautology because here the necessity is inescapable—you can’t help recognizing it. Hence knowledge of necessity is guaranteed, part of elementary linguistic understanding. But not all a priori knowledge is like that, though tautology has some claim to be a paradigm of the a priori. What about arithmetical knowledge? If it is synthetic a priori, then we can’t say that knowledge of mathematical necessity results from linguistic analysis alone. Nevertheless, it is plausible that we do appreciate that all mathematical truths are necessary; we know that this is how mathematical reality is generally. When we come to know that a mathematical proposition is true we thereby grasp its necessity: a proof demonstrates this necessity. Mathematics is arguably more about necessity than about truth: we can doubt that mathematical sentences express truths (we might be mathematical fictionalists), but we don’t doubt that mathematics cannot be otherwise—it has some sort of inevitability. We might decide that mathematical sentences have only assertion conditions, never truth conditions, but we won’t abandon the idea that some sort of necessity clings to them (though we may be deflationary about that necessity). Modal intuition suffuses our understanding of mathematics, and this can function in the production of mathematical knowledge. I see that 3 plus 5 has to be 8, so I accept that 3 plus 5 is 8. Mathematical facts are inescapable, fixed for all time, so mathematical truths are bound to be true: I appreciate the necessity, so I accept the truth. The epistemology of mathematics is essentially modal and this plays a role in the formation of mathematical beliefs: in knowing necessities we know truths—and that is the mark of the a priori.  [1]

            Much the same can be said of logic, narrowly or widely construed. You cannot fail to register the necessity of a logical law, and you believe the law because you grasp its necessity. Nothing could be both F and not-F, and so nothing is. The necessity stares you in the face, as clear as daylight, and because of this you come to know the law—the knowledge is by necessity. Accordingly, it is a priori. It isn’t that you can believe in the truth of the law and remain agnostic about its modal status (“I believe that nothing is both F and not-F, but I’ve never thought about whether this is necessary or contingent”). Your belief in the law is bound up with your belief in its necessity; thus logical knowledge is a priori according to the proposed definition. The same goes for such propositions as a priori truths about colors: “Red is closer to orange than blue”, “There is no transparent white”, etc. Here again the necessity is what stands out: we know these propositions to be true because we perceive their necessity—not because we have conducted an empirical investigation of colors. Accordingly, they are a priori. In all the cases of the a priori in which the proposition is necessary this necessity plays an epistemic role in accepting the proposition; it is not something that lies outside of the epistemic process. It is not something that is irrelevant to why we accept the proposition. We recognize the necessity and that recognition is what leads us to accept the proposition. If we accepted the proposition for other reasons (testimony, overall fit with empirical science), then our knowledge would be a posteriori; but granted that our acceptance is necessity-based the knowledge is a priori. Being known a priori is being known by necessity: the involvement of modal judgment is what defines the category.  [2] By contrast, a posteriori knowledge does not involve modal judgment—you could achieve it and have no modal faculty at all. The basis of your knowledge is not any kind of modal insight, but observation and inference (induction, hypothesis formation, inference to the best explanation). You don’t have modal reasons for believing that the earth revolves around the sun, but you do have modal reasons for believing that red is closer to orange than blue—viz. that it couldn’t be otherwise. Since things couldn’t be otherwise, they must be as stated, and so what is stated must be true. The modal reasoning is not a mere add-on to knowledge of a priori truths but integral to it.

            It may be thought that the contingent a priori will scuttle the necessity theory, since the proposition known is not even a necessary truth; but actually it is not difficult to accommodate these cases with a little ingenuity. One line we could take is just to deny the contingent a priori, and good grounds can be given for that; but it is more illuminating to see how we could extend the necessity theory to cover such cases. Three examples may be given: reference fixing, the Cogito, and certain indexical statements. What we need to know is whether there are necessities that figure as premises in these cases, even if these necessities are not identical to the conclusion drawn from them. Thus in the case of fixing the reference of a name by means of a description (e.g. the meter rod case) we can say the following: “No matter what the length of this rod may be the name ‘one meter’ will designate it”. If I fix the reference of a name “a” by “the F”, then no matter which object is denoted by that description it will be named “a”. This doesn’t imply that the object named is necessarily F; it says merely that the name I introduce is necessarily tied in its reference to the description I link it to. Because we recognize this necessity we can infer that a is the F(no matter who or what the F is). We don’t need to undertake any empirical investigation to know that a is the Fsince it follows merely from the act of linguistic stipulation—and that act embodies a necessary truth (“the person designated by ‘a’ is necessarily the person designated by ‘the F’”).

In the case of the Cogito it is true that the conclusion is not a necessary truth (since I don’t necessarily exist), but there is a necessary truth lurking behind this proposition, namely “Necessarily anyone who thinks exists”. It is a necessary truth that thinking implies existence (according to the Cogito), but it is not a necessary truth that the individual thinker exists—he might not have existed. I know that I exist because I know that I think and I know that anything that thinks necessarily exists. Thus I use a modal premise to infer a non-modal conclusion: from “Necessarily anything that thinks exists” to “I exist”. That is my ground for believing in my existence, according to the Cogito, and it is a necessary truth. Thus the knowledge derived is a priori, according to the definition. I don’t make empirical observations of myself to determine whether I exist; I rely on a necessary truth about thought and existence, namely that you can’t think without existing. I know that I exist (contingent truth) based on the premise that anything that thinks exists (necessary truth), so my knowledge essentially involves the recognition of a necessity.

Thirdly, we have “I am here now”: this expresses a contingent truth whenever uttered but is generally held to be a priori. I know a priori that I am here now, but it is contingent that I am here now. But again there is a necessary truth in the offing, namely: “Anyone who utters the words ‘I am here now’ says something true”. By knowing this necessary truth I know that I must be speaking the truth when I utter those words, but my utterance expresses a contingent truth. So I rely on a necessary truth to ground my belief in a contingent truth. Without that necessary truth I would not know what I know, i.e. that my current utterance of “I am here now” is true. Again, the case comes out as a priori according to the definition; we just have to recognize that the modal premise need not coincide with the conclusion. We can have a priori knowledge of a contingent truth by inferring it from a distinct necessary truth. So we have found no counterexamples to the thesis that all a priori knowledge is knowledge by necessity.

            I have assumed so far that the type of necessity at issue is metaphysical necessity, not epistemic necessity. This is the kind of necessity we recognize when we come to know something a priori. But we could formulate the main claims of this essay using the concept of epistemic necessity. For simplicity, just think of this as certainty, construed as a normative not a psychological concept—not what people are actually certain of but what they ought to be certain of. Then we could say that when I am presented with a tautology I recognize that it is certain and infer from this that it must be true, and similarly for other cases of a priori knowledge. This approach converges with the account based on metaphysical necessity, because certainty and necessity correlate (more or less) in cases of a priori truth. But I prefer the metaphysical formulation because it connects an epistemic notion with a metaphysical notion—a priori knowledge with objective necessity. When I know something a priori I know it by recognizing the objective trait of necessity not a psychological trait of certainty (however normatively grounded). Thus the epistemological distinction has a metaphysical correlate or counterpart. To know something a priori is to know it by detecting an objective fact of necessity, though we may also be certain of what we thereby know. In contrast, to know something a posteriori is not to know it by necessity detection but by perception and inference (by causality). This is a deep and sharp distinction, and it at no point relies on a purely negative characterization of what we are trying to define. We really do know things in two radically different ways: by apprehending necessity or by registering causality.            

 

 

  [1] Perhaps part of the attraction of the view that mathematics consists of tautologies is that it comports with the idea that our knowledge of mathematics involves knowledge of necessities. The necessities occupy the epistemic foreground.

  [2] Given this account of a priori knowledge, it is doubtful that animals have it, because they lack modal sensitivity—they don’t perceive that propositions are necessary. If you present an animal with a tautology, it will stare at you blankly. They may have innate knowledge, but they don’t have a priori knowledge. Not even the most intelligent ape has ever thought that water is necessarily H2O or that the origin of an ape is an essential property of it. Animals have no knowledge of metaphysical necessity. This explains their lack of a priori knowledge.

 

 

Philosophical Originality

 

 

What produces philosophical originality? One answer is genius: from time to time a genius crops up and from his or her fertile brain originality flows. Then we have a golden age. No doubt the greatest philosophers were geniuses, so it is natural to suppose that this is what brings originality about. The trouble with this answer is that originality is too sporadic for this explanation to be plausible: geniuses will crop up in the population at a constant rate (assuming a genetic basis), but philosophical originality does not historically occur in this way—it comes in waves separated by arbitrary intervals of time. The best way to answer our question is to survey the history of philosophy (Western philosophy) and try to discern patterns and possible causes. Are there historical conditions that conduce to bursts of creativity?

            There are two possible types of explanation: internal to philosophy and external to it. Internal explanations say that the causes are internal to the subject of philosophy; external explanations say that the causes are external to the subject of philosophy. Thus either something about philosophy itself leads to innovation or something outside it does—or possibly both. I have come to the conclusion that the causes are principally external, and indeed that one type of cause is typical (which is not to say necessary). Obviously these are large historical and psychological questions, inherently difficult to assess, but a broad picture seems to emerge when we examine the history of the subject. Not to keep the reader in suspense, it appears that the prime cause of original thought in philosophy has been advances in mathematics. (I will restrict myself here to the parts of philosophy that don’t include ethics, aesthetics, and political philosophy—metaphysics, epistemology, logic, and related fields.)

Plato must be counted as a great original, and it is well known that he was much influenced by Pythagoras and his school. Greek geometry, later assembled by Euclid, formed the intellectual environment in which Plato forged his philosophical ideas. Thus we have the idea of a changeless perfect world of forms to be contrasted with what the senses reveal, where truths about this world can be established by rigorous proof. Geometry can be described as the mathematics of space, so it was the mathematical treatment of space that acted as a trigger to Plato’s originality. The objects of geometry supply the ontology and the method of proof supplies the epistemology—this is what a serious subject looks like. Aristotle continues in the same vein (substance and form) but reacts against it to some degree: he is less mesmerized by mathematics than Plato—but it forms the background to his thought. An intellectual stimulus can have either a mimetic or an antipathetic response. One can be creatively against something. Aristotle was against Plato’s excessively mathematical outlook and shaped his philosophy accordingly.

            There then followed a rather unoriginal period—the Middle Ages. During this time nothing comparable to Greek geometry occurred in mathematics and philosophy took no major steps forward (I am speaking broadly). Then we reach the Renaissance in which there was a great flowering: Descartes, Leibniz, Locke, Berkeley, Hume, and others. What happened? Physics is what happened—mathematical physics (Newton’s book is entitled Principia Mathematica). Calculus was invented and the mathematics of motion formulated. The physical world was conceived quantitatively, with mass, force, and motion mathematically measured. This new paradigm of knowledge led to a reinvigoration of philosophy—with adherents and dissenters  (notably Berkeley). It provides a framework for metaphysics (matter in motion) and an epistemology (observation and calculation), as well as a model of what a real science should look like. The question of materialism took on new life now that physics was in the ascendant. Thus a good deal of original philosophy was stimulated by the new mathematical physics—not from the insights of philosophers working on their own internal problems (worthy as that may be). The agenda was set, the map laid out—by a development in mathematics. Just as the major influence on Plato was a non-philosopher (Pythagoras), so the major influence on the philosophers of the Renaissance was a non-philosopher (Newton—also Descartes in his capacity as physicist and mathematician).

            Again, there followed a relatively static period in philosophy (though stirred somewhat by Darwin  [1]) until the dawn of the twentieth century. Then we have the spectacular rise of mathematical logic—the application of mathematics to logical reasoning. Frege, Russell, and Wittgenstein were philosopher-mathematicians impressed by the power of symbolic logic, with its formulas, proofs, and theorems. Russell and Whitehead’s Principia Mathematica was a mathematical treatise on the subject of valid reasoning (among other things), and it formed the shiny new object onto which philosophers could latch. Some saw it as the bright future of philosophy, others as its death knell. Again there is adherence and reaction: analytical philosophy versus continental philosophy (roughly), or the Tractatus and the Investigations. Mathematical logic played the historical role previously played by geometry and mathematical physics—a model and inspiration, or a threat to all that is holy. It was not the achievement of a professional philosopher qua philosopher that caused this ferment, but the achievement of mathematicians; the trigger was external to philosophy.

This stimulus received a boost later in the century, particularly from Turing, with the idea of a formal computation. This idea led not only to the computer but also to developments such as cybernetics, automata theory, and mathematical information theory. A new branch of mathematics supplied new tools with which to think about the mind and knowledge. The doctrine known as “functionalism” arose from these developments—a kind of mathematical theory of the mind (mental processes as functions from inputs to outputs, formally implemented). We are still living with Turing’s contribution in today’s cognitive science (including linguistics). And once again, there are followers and rebels—some who think we now have the key to understanding the mind, others who think the mind is quite other. It is the mathematical conception that sets the agenda and captures the imagination.  [2]Philosophy responded to computation theory as it did to the rise of mathematical logic. Nothing else has had this kind of impact on the field—not chemistry, biology, psychology, history, or whatever. Philosophy seems uniquely susceptible to the charms of mathematics. Not its slave, to be sure, but its keen observer, its ardent pupil–or its stern critic. You either love mathematical philosophy or you hate it.

            So now we have an interesting question: what is the next wave of mathematics that will drive the agenda of philosophy, shaking it up, reshaping the subject? We have had the mathematics of space, of motion, of logical reasoning, and of computation—what will it be next? I don’t think anything that now exists in mathematics can play the role played by these earlier innovations, so we need something new to get the ball rolling (whether we can achieve it or not). I suggest that what we need is a new mathematical theory of mind, especially of consciousness: we need a mathematical theory that does for the conscious mind what earlier mathematical theories did for space, motion, logical reasoning, and computation. I have no idea what such a theory might look like; my point is just that it would be likely to trigger a new wave of philosophical originality—perhaps greater than any seen heretofore. Think about it: a mathematical treatment of what lies at the center of human existence and human knowledge—what connects us to the world and to each other. Surely that would be an impressive body of mathematical thought with enormous implications. How would philosophy respond to it? What would it do to traditional philosophical problems? It would change the contours of the subject. Maybe we will have to wait a long time for a mathematical theory of consciousness to be constructed (look how long it took for the previous developments to come about), in which case we won’t see the degree of originality in philosophy that we saw in the earlier periods any time soon. Of course, I am speculating wildly and claim nothing more—it is an interesting idea to think about. There does seem to be an historical pattern here and a mathematical theory of consciousness would surely set the cat among the pigeons. It would set a standard of intelligibility and precision that isn’t even dreamed of today—a psychological Principia. The properties of consciousness would be as clear and exact as geometrical forms, motion through space, logical reasoning, and formal computation.

Mathematics crystallizes things, converts them into rigorous abstract patterns, and analyzes their structure, thus rendering them transparent to the intellect. This is why mathematical innovation impresses philosophers so much—it represents a distant ideal seldom if ever achieved in philosophy itself. We dearly wish that philosophy could achieve such clarity and precision—or we fear (some of us) that it would remove the charm of philosophical obscurity. Mathematics is like philosophy’s successful elder sibling, an inspiration and a rebuke. The affinity between mathematics and philosophy has often been remarked; it is no surprise, then, if philosophers keep a watchful eye on mathematics. When Spinoza wrote his Ethics in the style of Euclid’s Elements he was acknowledging the force of Euclid’s example. Empirical science can never exercise this kind of hold on the philosophical imagination because it is too caught up in the passing concrete empirical world; mathematics by contrast shares the abstract necessity of philosophy. Mathematics provides the kind of vision of things that philosophers (many of them) resonate to– so they are apt derive inspiration from it. Philosophers are mathematicians manqué.  [3]

 

Colin

  [1] Darwin’s theory has a mathematical aspect: a random process leads to the selection of organisms or traits that increase in frequency in a population. It is abstract and quantitative, a kind of algorithm; also statistical.

  [2] I should mention Godel’s results here—also mathematics with a large philosophical impact.

  [3] Philosophers who model their subject more on literature or history (such as Collingwood) recoil from mathematical philosophy; they cannot, then, use mathematics as a source of new ideas. Their philosophical tradition will be independent of mathematical innovations. But they are in the minority.