8

SYNTHESIZING WITHOUT CONCEPTS

Peter Sullivan

This paper continues a discussion that Adrian Moore and I have had1 about the place of idealism in Wittgenstein’s philosophy. While there are several unresolved issues in that discussion I want here to pursue only one; and, to minimize the risk of repetition, I will shift the primary focus of discussion from Wittgenstein’s earlier to his later thought. I will, though, have to say something first to identify the point I have in mind from the earlier discussion, and second to indicate how the later issue corresponds to it. I’m afraid that will make for a longer than normal introduction.

I. General Background

The possibility of disagreement exists, according to Wittgenstein, only against a background of agreement, and that is certainly the case here. Moore and I share a view of Wittgenstein’s work as belonging to the Kantian, transcendental tradition; we are in agreement that the central requirement for a proper understanding of his thought is to make plain how it relates to the core ideas of that tradition, and in particular to transcendental idealism. But on just that issue we have disagreed. Suppressing niceties, and settling for what Adrian himself has called a “cartoon sketch,” Moore has held that in his early work Wittgenstein embraces transcendental idealism, while his later thought offers us ways of resisting it; whereas I have held exactly the reverse.

The easiest diagnosis of that would be to suppose that we understand the issue differently, but I don’t think that’s so. In both his early and his later work Wittgenstein is concerned with understanding the limits of thought. By the notion of a limit here is meant something set by, so essentially equivalent to, the essential nature or form of what it limits. It is the notion used when one says that a space is limited by its geometry (to take Wittgenstein’s favourite analogy from the Tractatus). This notion of a limit is not a contrastive one. There is nothing thought-like excluded by the limits of thought for lacking thought’s essential nature, just as there are no points excluded from space for being contra-geometrical. But thinking in general is contrastive: in general, that is, thinking something to be the case is thinking it to be the case rather than not. That is the broadest reason, if only the initial reason, why thought about limits is apt to portray them instead as limitations, boundaries that separate what has a certain nature from what does not. Moore and I are agreed that the crucial step in embracing or resisting idealism consists in succumbing to or resisting the construal of limits as limitations. This step is not enough on its own. Descartes construed the limits both of thought and of possibility as limitations, and he was no idealist. But having accepted that construal he did have to offer some account of how the limitations came to be what they are, and in particular of how the limits of thought and of possibility should so happily coincide. Kant mocked the explanation Descartes offered.2 And in this Wittgenstein was always with Kant: if there had to be any account of such things, then an idealist account was the only contender he could take seriously.

This is all common ground between Moore and me. And we further agree that Wittgenstein aimed, in both his early and his later work, at exposing the emptiness, or sheer senselessness, of any account one might be tempted to offer of these matters, hence the confusion there must have been in getting into the position of needing one. Our difference begins over whether the construal of limits as limitations only ever plays this negative role in Wittgenstein’s thought, or whether, at some other level, he embraces it, as contributing positively to whatever understanding working through his propositions is intended to induce.

II. The “Inner” Limit in the Tractatus

In a forthcoming paper3 Moore focuses this difference on what I tend to picture as the “inner” limit of language, the limit one runs up against in trying to articulate what some thought or statement amounts to. This is the limit of which Wittgenstein said, in Culture and Value, that it “is shown by its being impossible to describe the fact which corresponds to … a sentence, without simply repeating the sentence”; and he went on to remark about it, “This has to do with the Kantian solution to the problem of philosophy.”4 That is a typically unhelpful remark. Moore and I agree that it has somehow to do with that; it might have helped resolve the issue between us if Wittgenstein had said how.

In Wittgenstein’s early work this limit is reached in elementary propositions that present objects in immediate combination. In articulating what it is for things to be as such a proposition represents them as being, one can do no better, or no other, than to repeat it. But surely we want more than that. Our aim is to articulate our understanding of what it is for things to be as we represent them as being, and this includes our understanding that it is for these things to be that way. In merely repeating the proposition we of course exploit that understanding, but we do nothing to articulate it. To achieve that we should have to say, not just how these objects are, but what they are. And this we cannot do.

Objects I can only name … I can only speak of them. I cannot express them.5

Now Moore is certainly right to hold, in his remarks on this passage, that Wittgenstein deliberately conjures up here the sense of a real and intelligible aspiration that is necessarily frustrated. (Wittgenstein’s prose is so expressive that one would have to be deaf not to recognize this.) That Moore is also right in his suggestion that Wittgenstein has “something Kantian” in mind in doing this is proved by the uncharacteristic intrusion of Kantian terminology when the same limit is revisited later in the book: “Empirical reality is limited by the totality of objects.”6 But I think he underestimates (he does not in fact mention) the role that Wittgenstein’s doctrine of analysis is intended to have in dissolving this sense. This doctrine says to the aspiration alluded to, “Go ahead. Put into words whatever it is you think you want to articulate. There is no restriction here, no limitation, only the analytic triviality that, in whatever you say in doing that, you will speak of some things not thereby articulated. And those are objects.”

On Moore’s account the sense of a limitation here reflects our understanding of ourselves as finite, discursive thinkers, who must come to terms with reality by conceptualizing it, but cannot in that way fully possess it. This understanding survives through the realization that the aspiration to which it gives rise is confused, so that the expression of that recognition, in the statement that reality consists only in what we can thus possess—or more familiarly, that the world is the totality of facts, not of things—itself has to be heard as imposing a limitation. The effect of the doctrine of analysis, though, is to recast objects, from the presumed role of things we have to make sense of, to become elements in the sense we make. (The simplicity of objects, or the unanalyzability of names, then no longer signals some kind of surd restriction to conceptual thought, but instead is a mark of its transparency.)

But I do not expect those few remarks to persuade. At points like this that my difference with Moore has tended to become horribly intractable. And it’s for that reason that I want to focus instead on the corresponding issue in Wittgenstein’s later work, where, I think, our disagreement is much more straightforward.

III. The “Inner” Limit in the Investigations

We run up against the same inner limit of language in Wittgenstein’s later work with the question, “How am I able to follow a rule?”7 The issue is the same, since to offer a “justification for my following the rule as I do”8 is to represent what I do as being what the rule requires. Wittgenstein has in mind particularly an articulation of my action as implementing some algorithm or procedure for applying the rule. Justifications of that kind are often available. But, as he says, they soon run out.9 When they run out the best I can offer is simply to repeat, in description of my action, the description the rule itself offers of what it requires: you asked me to bring a red flower, and the flower I have brought is red.

At any rate, that is what we might expect Wittgenstein to say, if the limit now reached is the limit mentioned in Culture and Value, and if it is genuinely a limit rather than a limitation. But it is not what he says. Instead we find,

How do I know that this colour is red?—It would be an answer to say: “I have learnt English,”10

or worse,

Then I am inclined to say: “This is simply what I do.”11

Of course, neither of these responses is a justification. Instead, they are allusions to all that could be found in the place where further justification might be sought. But if what we have reached is properly a limit, there is simply no such place, and only confusion can come from alluding to what is found there.

A “cartoon sketch” of my view of Wittgenstein’s later work is that this confusion is exactly what we find. Even to colour the sketch crudely I need to go back to the way the contrast of limits and limitations was introduced. I said, for instance, that there is nothing thought-like excluded by the limits of thought, or that there are no contra-geometrical points. The idea is not that limits exclude nothing at all, but that they exclude nothing of an appropriate kind, nothing that would qualify for inclusion if only it satisfied the condition the limit specifies. Here, too, if what we have met is a limit it excludes nothing of an appropriate kind, nothing that could further articulate or illuminate the rationality of my following the rule as I do. That is not to say that there are not lots of other true, and perhaps even interesting, things to say about how I am able to do that, for instance, about how I am such as to be able to learn English, or even how there could come to be any such thing as English for me to learn. Mention of shared reactions and whirls of organism and so on might be relevant in those connections. Excluding these things doesn’t turn the limit we are concerned with into a limitation unless they are taken to be of an appropriate kind, unless reflection on them is held to illuminate the rationality of my following the rule as I do. But that, I think, is how Wittgenstein, at least some of the time, does take them. His attempt to dismantle Platonism is altogether ineffective unless they can be taken that way. And the consequent construal of this limit as a limitation must be intended to contribute positively to the understanding his discussion induces, if freedom from the alleged “mythology” of Platonism is to be a component of it.

So, part of this sketch—the insistence on treating this “inner” limit as a limit—is simply a translation, into the terms of Moore’s and my discussion, of a familiar anti-reductionist response to the rule-following problematic. Some advocates of that response, notably McDowell, have endeavored to make it compatible with allowing to “sub-bedrock” considerations—such as the consideration that, had certain very general facts of nature been different, concepts other than those we employ might have been intelligible to us—enough force to dislodge Platonism. The rest of the sketch claims that these two cannot be made compatible without treating what one recognizes to be a limit simultaneously as a limitation, i.e. without idealism.12

IV. A Problem about “Intransitive Understanding”

That sketch is clearly too sketchy to entitle me to ignore all of the various ways in which philosophers have developed the Wittgensteinian idea that recognition of this “inner” limit of language somehow imperils the possibility of objective judgement. But it does set a problem for me in disentangling what I can accept in work pursuing that idea from what I must reject as symptomatic of the misconstrual of this limit as a limitation. This problem arises most sharply with what I think is the richest work to grapple with this idea, and to illuminate the connections between Wittgenstein and Kant that it suggests: David Bell’s discussion in his essay, “The Art of Judgement.”13 In the remainder of the paper I want to make a start on that problem. What makes this a suitable occasion is that, in another recent paper,14 Moore has expressed agreement with the spirit of Bell’s essay, and suggested how its core ideas can be seen as consonant with some of his own. So, although this is a really a problem for me, I can hope to turn it into a question for him. The form of the question will be this: whether what I can accept from Bell’s essay, and make out to be consistent with regarding this limit only ever as a limit, can begin to do duty to the extent of his agreement with Bell; or whether, on the other hand, doing duty to that must involve construing this limit as a limitation. (In the latter event I should then like to ask how the agreed position, with all the connections between Kant and Wittgenstein it sustains, can avoid attributing Kant’s idealism to Wittgenstein—for I’m sure that that is how Bell himself sees things.)

Bell aims in this essay15 to elucidate “the subjective, non-conceptual, spontaneous sense that experience must make to anyone capable of objective thought.”16 He is concerned, first, to shed light on what this sense is, or on what it is for experience to make this kind of sense to its subject. Following Kant, he counts it an aesthetic response to experience. And, to display what this response involves, he appeals to the process of coming to make sense of an initially recalcitrant painting, a process in which one can discern, as if in slow motion, its salient components:

At the most general level it has to do, for example, with the relation of parts to whole, and involves the feeling that the whole has an integrity, a point, in other words that its elements and limits are not arbitrary but comprise a mutually and internally self-determining unity.17

Bell takes from Wittgenstein a notion of “intransitive understanding” to emphasize that, while what I see now makes sense to me, there is no question of specifying, of putting into words in a sentence, the sense it makes. Moore, for his part, terms this aesthetic response the Feeling of Unity; and he too holds that it is a species of understanding, hence a species of knowledge, that cannot be put into words.18

Bell’s second concern is to explain the role of this kind of understanding or sense-making. It allows us, he says, to chart a middle path between “the pessimism of the belief that all human thought is ultimately ungrounded and arbitrary, and the incoherence of the belief that it can be given a final justification in terms of … objective rules for the application of which we would require further rules, and so on.”19 Bell, that is, takes Wittgenstein’s (and Kant’s) exposure of the latter incoherence to show that “when I follow a rule, … ultimately I do so blindly”; but he insists that this need not imply that I follow the rule “mindlessly, or merely mechanically.”20 Basic rule-following is “blind” in that it can be given no further grounding within the categories of objectivity and rationality. But it is saved from arbitrariness by a grounding of another kind. Objective thought is, and must be, “grounded in a spontaneous, blind, subjective awareness of intrinsic but inarticulable meaning.”21 Moore, too, holds that the inexpressible knowledge we have in exercises of the Feeling of Unity has a unique, grounding role22 as a “precondition of making rule-governed judgements.”23

Now the difficulty these thoughts of Bell’s pose for me is that of having a solution without a problem. For,

(1)  so long as we hold to the understanding of the “inner” limit of language as a limit, and do not misconstrue it as pointing to a place for further justification where no justification is to be found, then it is just plain wrong to hold that basic rule-following is blind. (I will argue this in the next section, in connection with a paper of Crispin Wright’s.)

This commits me to hold that

(2)  the “pessimistic” threat, that thought might be exposed as at bottom “mindless or mechanical”, is just an illusion created by that misconstrual. (In Section VI I will briefly indicate aspects of Bell’s discussion I take to confirm this diagnosis.)

Yet,

(3)  the intransitive understanding Bell characterizes is certainly a real phenomenon.

And I think it would be very hard, reading Bell’s essay, to doubt that

(4)  this kind of understanding has some role to play in explaining how thought can engage so smoothly, unhaltingly, with what we see. (In Sections VII–VIII I will try to indicate how this role can be acknowledged without endorsing Bell’s conception of the problem to which, in his work, it offers the solution.)

V. Basic Rule-Following Is Not Blind

Blindness is a deficit. If someone is”steering blind” they are steering without information they ought to have. This is not a description that applies to someone who knows their way well enough not to need a map. Anyone trying to make good the idea that basic rule-following is blind rule-following thus runs the risk of presenting it as something that properly speaking ought to be done by reference to a map, though in fact there is no map to be had. This section sets some markers by illustrating how, in “Rule-Following Without Reasons,”24 Crispin Wright succumbs to this risk. These markers will be helpful in the next, when we revert to Bell.

Early in this paper Wright makes the sound point that “the idea of an essential inner process—a cognitive routine—common to all cases of rule-following is mythical.”25 Wittgenstein made this point in the Blue Book with the example of the instruction, “Fetch me a red flower from the meadow.”26 His immediate target there was the notion that, to obey that order, one had first to summon up in one’s imagination a colour sample by reference to which one would select a flower of the right colour. That notion falls apart when we consider the instruction, “Imagine a red patch.” This example makes plain that the role the imagined intermediary was supposed to fill is one that in general nothing need fill (and that in the specific case nothing could fill). The effect of the example is thus to do away with, to expose as a confusion, the notion that there is any such theoretical place as the one that the imagined sample was supposed to occupy. So it would clearly not be right to represent Wittgenstein as showing here that there need be nothing in that place—as if the notion of there being such a place is all right, it’s just that there is in fact nothing there.

But that is what Wright does: “To express the matter dangerously, we need have nothing ‘in mind’ when we follow rules.”27 This is not just a dangerous way of putting the point, but a perverse one. By enclosing the phrase in scare-quotes Wright signals that “in mind” is to mean: “in the place the imagined sample was supposed to be.” But his formulation surrenders the phrase to that misconception, and so makes it unavailable to express the common-sense truth that to obey the order (intelligently, intentionally, not as a mere automaton) I must have in mind (i.e. I must know) the colour of the flower I am to bring. Wandering into the meadow with nothing in mind—not knowing what kind of flower one is to bring, or why—would indeed amount to applying the rule blindly. But to portray ordinary, intelligent compliance with an instruction in the light of a comparison with such abstracted or automatistic behavior would obviously be a disastrous misrepresentation of what Wittgenstein’s example was intended to show; and so we need to ask what, in spite of the danger he recognized, could attract Wright to it.

Wright’s forthright conclusion in this paper is that “in the basic case we do not really follow—are not really guided by—anything.”28 Basic rule-following is rule-following “without reason.” We count it rational in that it “involves intentionality, and a willingness to accept correction”; but it does not involve “responsiveness to the requirements of the rule …which can feature in thought and rationally inform one’s response.”29 In that precise sense it is “blind.”30

Wright reaches this conclusion by considering how rule-following in the basic case must contrast with what he terms “the modus ponens model”31 of a non-basic case:

RULE: if neither king nor rook has been moved … etc., one may castle.

PREMISE: neither king nor rook has been moved … etc.

VERDICT: one may castle.

In this consideration he is especially concerned with features of this model that have to do with the “extricability” of its several components.

In the first place, PREMISE is extricable from RULE, in that someone could understand PREMISE and judge it to be true who had no inkling of RULE, or of the concept of castling that it governs. For that reason instruction in the model could serve as a means of explicitly introducing someone to this concept.

For the same reason, the model neatly parcels out what is required of someone to apply the rule correctly: he must grasp what, in general, RULE requires; and he must appreciate the specific circumstances that warrant a particular application of it, encoded in PREMISE. Someone could, then, be wrong about either of these without this impugning his grip on the other. This constitutes a rather different sense, to be explained by independence of commitment or knowledge, rather than of understanding, in which RULE and PREMISE are extricable from each other.

This in turn implies that VERDICT is, in that commitment or knowledge sense, extricable from both of them. For each of those components it holds that someone might be right about that component yet fail to reach a correct VERDICT because of ignorance or mistake about the other. I think it is the independence of VERDICT and RULE that matters most to Wright. It is what allows us to regard RULE as formulating knowledge by which one is guided in applying the concept of castling, and which particular VERDICTS must respect.

If we turn now to consider a case of basic rule-following it is obvious that many of these features will lapse.

RULE: if x is red, “red” is correctly predicable of x.

PREMISE: a is red.

VERDICT: “red” is correctly predicable of a.

But the core of Wright’s argument is that these features cannot lapse if there is to be any such thing as the requirements of a rule by which applications of it are guided. There can be, as he puts it, no “pure rule-following”, no “rule-following where a correct grasp of the rule itself guarantees correct performance.”32 So the parceling out so neatly effected in the non-basic case by the modus ponens model must be a feature of all rule-following, including basic cases. If there is to be any such thing as what a rule requires, this must be something grasp of which makes, in conjunction with whatever fills the role of PREMISE, its distinguishable contribution to correct performance. In the basic case, though, we cannot make the needed distinctions. PREMISE and RULE can no longer be extricated from each other. And, since PREMISE and VERDICT are now effectively identical,33 the same holds of the relation of RULE and VERDICT. Grasp of the rule, we are invited to conclude, dissolves into the verdicts we imagined it to inform.

At any rate, that is what I take to be Wright’s central argument. And, assuming that I have identified it correctly, I think it is clear where it goes wrong. In the shift to the basic case some of the features of the modus ponens model of non-basic cases must indeed lapse, but only some. The extricability relations that must lapse are (for the most part) those that were explained in terms of independent understanding: PREMISE can no longer be understood, let alone judged to be true, independently of RULE. But those that were explained in terms of independent commitment or knowledge remain. Specifically, one’s knowledge of the RULE governing “red” is not impugned if, through ignorance or mistake regarding the input PREMISE to an application of that rule, one fails to reach a correct VERDICT. Or, to put the same point less fancily, people who know what redness is sometimes wrongly call things red because they misperceive them. That is the only kind of extricability that the denial of “pure” rule-following entails.

Wright’s argument would have us hold that, in basic rule-following, the modus ponens model must lapse—for lack of rationally extricable premises—but also that it cannot lapse—since pure rule-following is impossible. It takes the pressure of a felt paradox to soften anyone for the conclusion that, in calling something red when one sees it to be red, one is acting blindly, or without reason. The less exciting truth is that some features of the model lapse, while others do not.

VI. Bell’s Paradox

Wright’s argument is not Bell’s. Bell’s essay is enormously ambitious, but, with the problems of expounding two Critiques already in hand, he reasonably enough takes pretty much for granted the Wittgensteinian considerations leading to the conclusion that “in the last analysis our discursive mental acts are performed blindly.”34 But Bell, too, presents the problem to which his notion of intransitive understanding offers a solution as a paradox, one to which we are immediately driven in halting a regress of rules. And this gives a needlessly paradoxical air to the solution itself. Somehow it is to explain how my basic judgements can be “characterized by a rule-governed spontaneity, that is, in Kant’s terms, by a ‘conformity to law without a law.’”35 That sounds, Bell concedes, “like an oxymoron.”36 And I think it is one. This brief section aims to remove some of the sense of paradox from the problem; the next will attempt the same for the solution.

Bell records the incoherence of a regress of rules, each one serving for the application of the last, in what he terms the Principle of Spontaneity. This principle requires that

The relation in which we stand to what we think or mean must be immediate and direct. If we are to avoid the incoherence of a regressive infinity of acts of judgement, … then at some point we must judge immediately, spontaneously—and this means without having already judged, identified, understood, or grasped a thought on the basis of a prior such act.37

This is entirely right. But we cannot hold onto this thought at the same time as holding that an act “is ‘blind’ [if] it remains necessarily inaccessible to prior rational and objective justification.”38 Together these two thoughts imply that immediate or basic judgements are “blind” judgements, and so not judgements at all—not acts in which we are rationally answerable to the requirements of the concepts we deploy. The two together imply, in other words, that there can be no such thing as a basic rational action; whereas the Principle of Spontaneity on its own entails that there must be.

This contradiction sets the central problem for Bell’s essay. In one formulation of it he asks, “When I apply a rule I may do so blindly—but that does not imply that I do so mindlessly. But, then, what role are we to ascribe to mind at precisely this point?”39

The question has no answer unless we settle and stick to a single understanding of what precisely “this point” is. Are we asking after the mind’s role in basic rule-following, when, as the Principle of Spontaneity requires, it applies concepts in unmediated recognition of their appropriateness? Or are we asking instead about some prior operation by means of which the mind accomplishes basic judgements, some operation that the second of the above thoughts insists has to be present if basic judgement is not to be exposed as a kind of mindless sounding-off? To put this reaction impressionistically (hence not in any way that amounts to reasoned criticism), I hear Bell’s question as asking: “What is the mind doing when it applies a basic rule? It is not following some instructions as to how to apply it. But it must reach the application somehow.” But really accepting the Principle of Spontaneity means accepting that there is simply no room for an issue of how a basic rule is applied.

Bell’s paradox stands out still more clearly in a second formulation of his central problem. “How can I perform an act that is quite undetermined by the rules in question, but that somehow manages to conform to them?”40 The simple answer is that I cannot: there is no such act.

People sometimes speak of an action or its product as “merely conforming” to a rule, when, quite accidentally or coincidentally, it satisfies a description of what the rule requires (a slug-trail shaped like “68 + 57 = 125” is a typical example). That notion of “mere conformity” plainly has no relevance to Bell’s problem (if it did, there would not be a problem: there is, for instance, no mystery about how a slug-trail could take that shape). But once that notion of “mere conformity” is put aside, there cannot be the distance between being “determined by” a rule and “conforming to” it that Bell’s question supposes. No action is ever determined by a rule except in the sense that the action is correct if it conforms to the rule.

In non-basic cases an action conforming to a rule may be the causal upshot of putting into effect some procedure for following the rule; it may, for instance, be the result of a process of inference in line with Wright’s modus ponens model. This introduces a very different, causal sense in which a rule-governed action might be said to be “determined,” and this sense surely informs Bell’s question: it is because no procedure for following the rule is put into effect that he speaks of basic judgements as “quite undetermined”. But that sense is simply inapplicable in a case of basic rule-governed judgement, and is anyway generally misleading: using the same word for these different kinds of “determining” makes it too easy to forget that what does the determining, and likewise what is determined, is quite different in the two cases.

Wittgenstein suggested that his interlocutor’s remark, “All the steps are already taken,” serves to give symbolic or metaphorical expression to the difference between being causally determined and being logically determined.41 If that suggestion is right, then the interlocutor’s only mistake is not to have spelled out this difference more prosaically. Despite superficial grammar, “determining causally” and “determining logically” are not two ways of doing a single thing. What can determine logically (the rule) determines nothing causally: it is not an agent. What can determine causally (e.g. biology, or exposure to training) determines nothing logically. Conversely, what can be determined causally (e.g. the response I will in fact give, or how someone will carry on following exposure to certain examples or a given regime of training) is determined logically by nothing at all. And what can be determined logically (e.g. that continuing the series, … 1002, is correct) is the wrong kind of thing to have a cause. However it may be with Wittgenstein himself,42 much of the familiar rule-following problematic comes from making the difference between these two much too slight. Only in that way could commentators press, as if it were urgent or vexing, the question of what could determine, with a stronger-than-causal necessity, how someone will in fact continue a series; and only in that way could they present it as a discovery of Wittgenstein’s that there is no good answer to this evidently misbegotten question.

VII. Intransitive Understanding

Bell does not speak, as my title does, of “synthesizing without concepts.” The phrase he takes from Kant and aims to explain is rather “schematizing without a concept.” To do this is

to discover in the diversity of sensory experience a felt unity, coherence, order, which is non-cognitive and non-conceptual, but which is a necessary condition of the possibility of all rule-governed thought and judgement.43

I settled for the clumsier, non-Kantian phrase to make still more glaring the scope there is here for running into contradiction with the commitment that “all combination is … an act of the understanding.”44

That is hardly a prospect of which Bell is unaware. Schematism is in the business of harmonizing opposites,45 so it will not be surprising if paradox surrounds its description:

if, as I’ve suggested, schemata are to explain how it is possible to act spontaneously, blindly, and yet in conformity with the rules of rationality and objectivity, schemata will inevitably inhabit a non-man’s land between subjectivity and objectivity, between sensibility and understanding, between determinacy and indeterminacy, between passivity and activity, and so on.46

But I think we can see here two distinguishable reasons for Bell’s tolerance of apparent paradox in his description of the kind of intransitive understanding that is to yield this explanation. The first, with which I completely sympathize, is Bell’s concern to think himself thoroughly into the shape and motivations of Kant’s thought, to the extent that he can present the often-documented contradictions and equivocations of the schematism doctrine as “themselves indicative of Kant’s target.”47 The second, where I am sceptical, is a matter of homeopathy. Bell’s own sense that a real paradox threatens the rationality of basic rule-following makes him ready to accept a corresponding paradox in what averts that threat. The last section explained why I do not share that sense of paradox; in this section I aim to remove the correspondingly paradoxical aspects of Bell’s solution.

Bell is emphatic that the felt unity or significance that grounds conceptual judgement “cannot be the product of conceptual determination or conformity to rules”; stopping the regress requires at this point “a new model.”48 But when a model is needed to fill a threatening gap, and when this gap is conceived as one left by a regress that has been brought to a stop rather than satisfyingly resolved, it is surely very likely that what we are offered will be modelled in part on a further step in the regress.

Schematism … is precisely this process of introducing into [or discovering in] the diversity of experience a unity that is not conceptually determined, but that makes possible the subsequent application of concepts to it.49

That this unity is “not conceptually determined”—that it “owes nothing to concepts … or rules”50—is what makes this a new model, capable of stopping the regress. But with those words omitted from its description, it appears that this process achieves something very like what the understanding, the faculty of rules, achieves. That is, it seems that schematism is designed to achieve, at a level below the last step in a regress of rules, just what a further step in that regress would have achieved. This appearance is an aspect of Bell’s solution that comes from his conception of the problem, and as such it is an aspect I want to do without.

A way of doing this is suggested by a comparison Bell makes51 between the aesthetic judgements that provide his principal model for pre-conceptual unity and the “judgements of perception” Kant speaks of in the Prolegomena. Pursuing resemblances of that kind might lead us to consider also the merely “subjective unity,” or a “relation of representations [having] only subjective validity”, mentioned in §§18–19 of the B Deduction; and then on again to the description of apprehension in the Analogies as “only a placing together of the manifold of empirical intuition.”52 A familiar exegetical difficulty presented by each of these cases is that Kant seems to be trading in a kind of combination prior to, and exploited by, the combination through concepts effected by the understanding—he speaks as if there were something akin to what is represented in an exploded diagram, some process like offering up the parts to one another before the bolts go in—when it seems plain that no such notion can play a positive role in his account. Now in at least some of these cases the difficulty is avoided by taking Kant to be speaking counterfactually: what he is describing is not a step on the way to categorial unity, but all there could be in its absence.53 Bell’s account of his solution creates the same kind of unease. So it is worth trying whether the same kind of approach to intransitive understanding will remove it: instead of asking how the sense of felt unity is forged, we should consider how things would be without it.

Bell’s central contention is that, if what I experience did not make to me the kind of sense he is concerned to characterize, I could not apply concepts to it. But then how would things be? In the analogy of the recalcitrant painting he speaks of things presenting themselves to me as “problematic,” or “perplexing.”54 Later he says that I could not “feel at home”55 in what I experience. Quoting Wittgenstein, he explains that to feel at home in this way is to have no need to interpret, and that what this amounts to can best be grasped through the contrasting scenario where, lacking this accommodation, the possibility of different interpretations is always an issue for me: “I see the thought symbol ‘from outside’, [and] … become conscious that it could be interpreted thus or thus.”56 If things generally were “opaque” to me in that way, then, Bell explains, the attempt to bring any particular concept to bear on them “would always require … some prior judgement as to its appropriateness, relevance, or warrantability.”57

From this it emerges that the counterfactual approach offers much more than a structural analogy. For what we find described here in Bell’s and Wittgenstein’s words is clearly recognizable as the etiolated (Humean) experience that Kant speaks of in that mode as “only a play of representations”, containing no ground of objective determination, and therefore nothing “to distinguish one appearance from another.”58 In the same explicitly counterfactual mode we can indeed conceive of a notion of what is really given in experience such that:

Now, if that is what it would be for experience not to make sense to its subject, can we recover a characterization of intransitive understanding simply by reversing these marks? I believe we can:

VIII. A Question to Moore

What this approach recovers is certainly nothing like all that Bell intended. Most obviously, what I have just described is not some species of awareness that underlies and grounds the possibility of conceptual judgement. It is the possibility of conceptual judgement.60 The unity we feel, on this approach, is not a precondition of combination through concepts. It is that. Adopting the counterfactual mode, this approach paints no positive picture of machinations below the limit of conceptual justification, of how things are arranged there so as to provide otherwise ungrounded judgement with some kind of foothold.

In some respects it would be possible for me to approach Bell’s view more closely than I have. For instance, he several times speaks of an “awareness … of … inarticulable meaning.”61 If the awareness in question is rightly termed “intransitive understanding,” then this cannot be awareness of a species of meaning. If it were, we should have to deal with the object of a kind of understanding that has no object, or with the sense that things make when there is no such thing as the sense that they make—and that is revelling in paradox rather than tolerating it. Even so, there would not be the same objection to speaking instead about the meaningfulness of experience. This would be a matter of its lending itself to articulate description. It would be inarticulable simply in that no articulation could begin to exhaust it. And then “awareness of intrinsic meaningfulness” could aptly characterize the smoothness and immediacy—the unhaltingness, the lack of arbitrariness, there being no need for hesitant and questionable interpretation to reach across some cognitive divide—with which we are able to articulate aspects of what experience presents us with. But even if this comes somewhat closer to what Bell intends, I am certain it does not exhaust it. (For one thing, it does not sustain the suggestive parallels Bell draws, following Wittgenstein, with the understanding of music.62)

What I think is much less clear is whether the approach I have recommended can accommodate as much of Bell’s view as Moore would himself want to agree with. A characteristic example of the grounding inexpressible knowledge that, on Moore’s account, I have “through exercise of the Feeling of Unity” is “my knowledge of what green things have in common; or … my knowledge of what it is for something to be green.”63 As above, this is, on the face of it, not a precondition or ground of my ability to make judgements about greenness. It just is that ability.

Moore expresses the hope that, despite some of his differences with the “letter” of Bell’s essay, a real convergence can be recognized in the spirit of their views. On many issues concerning the interpretation of the third Critique not touched on here, I am sure that this is right. But on those issues I have touched on, it seems to me that to converge fully with Bell would be to converge on the idealist position that he rightly takes to be shared between Kant and Wittgenstein. As to whether Moore intends that I am, as I said, much less sure. Perhaps Moore can put me right.64

Notes

1  Beginning in our Aristotelian Society symposium, “Ineffability and Nonsense.” See Adrian Moore, “Ineffability and Nonsense,” Proceedings of the Aristotelian Society, 2003, SV 77, pp. 169–193; and Peter Sullivan, “Ineffability and Nonsense,” Proceedings of the Aristotelian Society, 2003, SV 77, pp. 195–223.

2  Immanuel Kant, Critique of Pure Reason, trans. N. Kemp Smith, London, Macmillan, 1933, B167.

3  “Was the Author of the Tractatus a Transcendental Idealist?,” forthcoming in P. Sullivan and M. Potter, eds., The Tractatus and Its History.

4  Ludwig Wittgenstein, Culture and Value, Oxford. Blackwell, 1980, p. 10.

5  Ludwig Wittgenstein, Tractatus Logico-Philosophicus, London, Routledge, 1922, 3.221.

6  Ibid., 5.5561.

7  Ludwig Wittgenstein, Philosophical Investigations, Oxford, Blackwell, 1953, §217.

8  Ibid., §217.

9  Ibid., §211.

10  Ibid., §381.

11  Ibid., §217.

12  Does this mean accepting “rails to infinity,” and all the associated “mythology” of Platonism? No. It means questioning the association. There are rails to infinity, if that claim is construed, as it naturally can be, as a general reminder of such truths as that any two numbers have a unique sum. But other, related imagery surrounding these truths can generate a very different position, reasonably called “hyper-Platonism”:

when [the mathematician] sees a peak he believes that it is there simply because he sees it. If he wishes someone else to see it, he points to it, either directly or through the chain of summits which led him to recognize it himself. When his pupil also sees it, the research, the argument, the proof is finished. The analogy is a rough one, but I am sure that it is not altogether misleading. If we were to push it to its extreme we should be led to a rather paradoxical conclusion; that there is, strictly, no such thing as mathematical proof; that we can, in the last analysis, do nothing but point; that proofs are what Littlewood and I call gas, rhetorical flourishes designed to affect psychology, pictures on the board in the lecture, devices to stimulate the imagination of the pupils.

(G.H. Hardy, “Mathematical Proof,” Mind, 1929, vol. 38, pp. 1–25; for Wittgenstein’s reactions to this article see Mathieu Marion, Wittgenstein, Finitism, and the Foundations of Mathematics, Oxford, Clarendon Press, 1998, p. 158n).

According to the view presented in the first part of this quotation the only role of proof is to bring someone who cannot do so without it to see the truth of what is proved. The end of proof is not that something be proved: it is an end that could be achieved, and, if only the learner were not short sighted, would be better achieved, without proof. This is hyper-Platonism, and there are good reasons for rejecting it. Hardy—who is, of course, nobody’s fool—identifies the most important of these reasons in the second part of the quotation, hyper-Platonism’s paradoxical consequence that the only method mathematics has is mere gas, something with no more than a flimsily contingent connection with mathematical knowledge. That amounts, as Hardy says, to there being no such thing as mathematical proof; and that leaves it entirely mysterious how, or whether, any mathematician can ever come to know anything.

Wittgenstein was fond—much too fond—of setting up Hardyesque imagery as his target. Many, many passages from the Remarks on the Foundations of Mathematics indicate that he supposed himself to be simultaneously targeting the Platonism of Frege. He aims to cast doubt on the idea that, in inferring one proposition from another, we are tracing an objective relation of consequence that independently holds between these propositions; and he suggests that this is fundamentally the same idea as that, in developing the series +2, we are, if we do it right, tracing steps that the rule itself determines to be the correct ones. My starting point is that neither of these ideas is remotely open to suspicion, and that they have no real connection with the fragments of hyper-Platonistic imagery that so often cling to them in Wittgenstein’s discussions. The effect of these adornments is that Wittgenstein’s discussion targets an amalgam of two positions that are more nearly contradictory than mutually entailing. This makes the discussion less effective than it might have been against one of them (hyper-Platonism), and wholly ineffective against the other (the sober Platonism of Frege).

13  David Bell, “The Art of Judgement.” Mind, 1987, vol. 96, pp. 221–244.

14  Adrian Moore, “Is the Feeling of Unity that Kant Identifies in His Third Critique a Type of Inexpressible Knowledge?,” Philosophy, 2007, vol. 82, pp. 475–485.

15  Bell’s main exegetical concern is with Kant’s third Critique, but I have to abstract completely from that: I have neither the space nor the expertise to do otherwise.

16  Bell, “The Art of Judgement,” p. 234.

17  Ibid., p. 237.

18  Moore, “The Feeling of Unity,” pp. 477 and 483.

19  Bell, “The Art of Judgement,” p. 241.

20  Ibid., p. 241.

21  Ibid., p. 241.

22  Moore, “The Feeling of Unity,” p. 485.

23  Ibid., p. 477.

24  Crispin Wright, “Rule-Following without Reasons: Wittgenstein’s Quietism and the Constitutive Question.” Ratio, 2007, vol. 20, pp. 481–502.

25  Ibid., p. 486.

26  Ludwig Wittgenstein, The Blue and Brown Books, Oxford, Blackwell, 1958, p. 3.

27  Wright, “Rule-Following without Reasons,” p. 486.

28  Ibid., p. 497.

29  Ibid., p. 498.

30  Ibid., p. 496.

31  Ibid., p. 491.

32  Ibid., p. 492.

33  To identify PREMISE and VERDICT—“a is red” and “‘red’ is correctly predicable of a”—is to hold that the quotation marks make no real difference. If one did take them to make an important difference, then the modus ponens model would apply to the “red” case exactly as it applies to the castling case. Someone—a monolingual German, for instance—could understand PREMISE and judge it to be true without any inkling of RULE; and that person could be introduced to the practice of applying “red” through instruction in this model. Wright, in effect, agrees with this, when he says (at p. 495) that a “stubborn” application of the modus ponens model enforces an “Augustinian picture” of language: “Augustine describes the learning of human language as if the child … already had a language, only not this one. Or again: as if the child could already think, only not yet speak” (PI §32). I have no disagreement at all with this important part of his discussion. But I will—because it anticipates conclusions reached in Section VIII—enter one reservation about the use to which Wright later puts its conclusion. The question at that point is what, in a basic case, knowledge of the rule governing an expression amounts to—or how we should, and should not, understand such claims as that so-and-so knows the rule(s) for the use of “red”. In such a case, Wright contends, “we should not think of knowledge of the requirements of the rule as a state which rationally underlies and enables competence”; instead, “The knowledge is the competence. Or so I take Wittgenstein to be saying” (p. 498). Now, the final claim here is surely right, and, since the previous claim follows from it, that too must be right. But it mistakes the issue. The issue was whether, even in a basic case, one’s understanding of an expression, or knowledge of the rule governing it, rationally underlies, not one’s “competence” with the expression, but one’s actual applications of it (the “VERDICTS” one issues). If “the knowledge is the competence,” then this knowledge rationally underlies one’s particular judgements about (e.g.) redness. We can, and should, accept with equanimity that nothing in turn underlies it.

34  Bell, “The Art of Judgement,” p. 227.

35  Ibid., p. 227.

36  Ibid., p. 227.

37  Ibid., p. 226.

38  Ibid., pp. 226–227, emphasis added.

39  Ibid., p. 227.

40  Ibid., p. 227.

41  Ludwig Wittgenstein, Philosophical Investigations, §§219–220.

42  Well, how is it, in fact, with Wittgenstein himself? It would of course be absurd to suggest that Wittgenstein is generally insensitive to the contrast between causal and logical connections, or to deny that unpicking causal from logical threads in the relation between understanding and performance is a central aim of his discussion of rule-following in the Investigations. (Specially relevant here is §183’s warning against supposing there to be some totality of conditions that would guarantee correct performance, since that supposition would inevitably fuse logical and causal factors.) But when those undeniable facts are acknowledged, we still need to ask how the threads got to be tangled up in the first place; and, in considering this question, we should bear in mind that one way of making the difference between causal and logical connections “too slight” is to represent the task of untangling them as more delicate than in fact it is. Does it, for instance, help us to become clear about the impression that “The steps are really already taken … as if they were in some unique way predetermined, anticipated—as only the act of meaning can anticipate reality” (§188), that Wittgenstein allows “the steps” to remain ambiguous between those I shall take and those I should, or that the notion that meaning anticipates reality is left to sink and drown in the muddle that “an act of meaning” might do so? The following section (PI §189), in which Wittgenstein considers the different things that might be meant by saying “The steps are determined by the formula …,” reveals more clearly the sources of such damaging non-interference. Here Wittgenstein first offers a causal reading, on which the statement might claim that, for certain people (in contrast to others), “the order ‘add 3’ completely determines every step” they will take. (It is wildly implausible that the statement would ever be used to claim quite that. What of distractions, blackouts, sudden illness, death? But let that pass.) Clearly contrasted with that causal understanding is a second, logico-mathematical usage, which distinguishes formulae (e.g. y = x2) which do “determine a number y for a given value of x” from others (e.g. y2 = x) which do not. But conspicuously absent from the section is another logico-mathematical sense, which applies to both sides of this second contrast: that the equation y2 = x has, for a given value of x, two roots, and what those roots are is as much determined, and determined in the same way, as is the unique root of y = x2. Wittgenstein’s suspicion of this general, unreduced notion of logical determination is responsible for its omission; and its omission opens the way to the confusions we are concerned with, since only the first, causal understanding has the breadth of application of required of anything one might be tempted to substitute for it.

43  Bell, “The Art of Judgement,” p. 239.

44  Kant, Critique of Pure Reason, B130, emphasis added.

45  Ibid., A138/B177.

46  Bell, “The Art of Judgement,” p. 229.

47  Ibid., p. 229.

48  Ibid., p. 238.

49  Ibid., p. 229, emphasis added. Bell speaks of discovering, rather than introducing, unity in the previous sentence. I’m sure he’s right that the difference between these two is not the important issue; for a similar view see Moore, Points of View, p. 185, on “imposing” and “finding.”

50  Ibid., p. 239.

51  Ibid., p. 235n.

52  Kant, Critique of Pure Reason, B219, emphasis added.

53  An especially clear example of this is the paragraph at A194–195/B239–2.

54  Bell, “The Art of Judgement,” p. 237.

55  Ibid., p. 239.

56  Ibid., p. 242, quoting Wittgenstein, Zettel, Oxford, Blackwell, 1967, §§234–235.

57  Ibid., p. 239.

58  Kant, Critique of Pure Reason, A194/B239.

59  On this, and indeed on everything said in this section, see Peter Strawson, “Imagination and Perception,” reprinted in his Freedom and Resentment and Other Essays, London, Methuen, 1974, pp. 45–65.

60  It is, I said, the possibility of conceptual judgement, and that possibility is not a judgement.

61  Bell, “The Art of Judgement,” pp. 241, 243, 245.

62  Ibid., pp. 242–243.

63  Moore, “The Feeling of Unity,” p. 484.

64  This paper was first written for a meeting in 2007 of Mark Sacks’s AHRC-funded project on Transcendental Philosophy and Naturalism. Thanks are due to those who raised critical points at that meeting; to Adrian Moore for taking the trouble to respond to it; but above all to Mark Sacks, for providing a context for this work and a model—inadequately followed, of course—for how to go about it.