2. Point-based mastery of concepts

The ambition of point-based explanations to be informative seems to be in tension with the thesis, which has been defended in a variety of forms in twentieth-century philosophy, Footnote ⁴ that mastery of at least certain concepts is itself already point-based. This thesis can be articulated more precisely as follows:

Aspects of MPB that call for scrutiny include the notion of mastery or ability to apply concepts correctly, the standard of correctness involved therein, and the extent to which this mastery comes in degrees. In this paper, however, I shall treat these as given and focus entirely on the notion of the point of a concept. Distinguishing between different senses we can give to this widely used but far from transparent phrase will shed light on different versions of MPB and their relation to point-based explanation.

The historical roots of MPB reach at least as far back as Wittgenstein, in whose later work the point of language games is a recurring concern.Footnote ⁵ We later find the thesis lucidly articulated (in what we shall see is a variety of different versions) by Michael Dummett. Echoing Wittgenstein (Reference Wittgenstein, Anscombe, Hacker, Schulte, Hacker and Schulte2009, §§564–68), Dummett lends intuitive plausibility to MPB by drawing an analogy between concept use and the game of chess. He suggests that in order to be a competent chess player, it is not enough to know the rules by which the pieces move; one cannot be a competent chess player without understanding that the point of the game is to checkmate the king. Analogously, Dummett suggests, merely describing the usage of a concept is not enough to master it; one has to grasp the point of the concept.Footnote ⁶

MPB has also been prominent among advocates of the idea that the extensions of thick concepts – concepts which are both world-guided and action-guiding due to their combining descriptive and evaluative aspects – would be shapeless were it not for some grasp of the concepts’ points: without grasping a thick concept’s point, one would be at a loss to decide, on the basis of past applications of the concept, whether some new item should be seen as one more instance of that concept or not.Footnote ⁷ As Bernard Williams puts the key idea, which he traces via John McDowell, Philippa Foot, and Iris Murdoch to Wittgenstein (Williams Reference Williams2011, 263n7): ‘to understand how such a concept can be applied to a new sort of situation it is likely that one will have to grasp its evaluative point’ (Williams Reference Williams, Altham and Harrison1995b, 206).Footnote ⁸ Jonathan Dancy elaborates: ‘A person from another culture who failed to see the evaluative point of a thick concept would not be able to predict local use of it on the basis of descriptive similarities alone’ (Dancy Reference Dancy1995, 263).

It is clear already from this brief discussion that there is a need for disambiguation here, for how can exhibiting the point of a concept tell competent concept-users anything new if they already need to have grasped that point in order to be competent concept-users? In some respects, this problem of how a point-based explanation can be informative given that one already needs to have grasped the point to begin with is akin to the paradox of analysis, the problem of how a successful definition or conceptual analysis can be informative given that the definiens/analysans must be identical with the definiendum/analysandum.Footnote ⁹ One might speak here of the ‘paradox of point-based explanation, ’ were it not for the fact that the problem all too obviously calls for resolution through disambiguation (and thus fails to present us, as a paradox worthy of the name would, with intuitively plausible premises that jointly entail an unacceptable conclusion). However, it is precisely because it so obviously calls for disambiguation that this tension is useful in motivating the present project. Clearly, what Williams and Dancy mean by ‘the point of the concept’ is not the same as what Dummett means by it, Footnote ¹⁰ and we therefore need a typology of points.

3. Four types of points: practical, evaluative, animating, and inferential

According to the typology I want to propose in this paper, talk of the ‘point of concepts’ is ambiguous between at least the following four senses: the practical, the evaluative, the animating, and the inferential point. Let us consider each in turn.

(1) The Practical Point of a Concept: the salient practical consequence of using a concept at all, i.e. the salient useful difference which the concept actually makes to the lives of concept-users. Jane Heal nicely articulates the most general motivation for focusing on the practical point of concepts:

But what should we treat as a ‘realization of one or more of our interests’? The characterisation of a concept’s practical point as the salient useful difference it actually makes to the lives of concept-users will be too broad if anything useful about a concept qualifies as its point. But we can understand it more narrowly by (a) cashing out usefulness in terms of the extent to which using the concept serves the needs and interests of concept-users; and (b) cashing out saliency in terms that tie the relevant needs and interests to the particular explanatory purposes of the theorists in any given case. To say that a useful difference is salient, on this view, is not to say that it is salient to the concept-users themselves – a concept’s practical point need not be part of what motivates its use or guides its application; it is not necessarily something which participants are aware of at all. Rather, to say that a useful difference is salient is to say that among the many causal effects that use of a concept in a conceptual community actually produces, one or several are worth singling out in light of the purposes we theorists bring to the concept. Together, (a) and (b) narrow down the notion of a practical point, and do so in a manner that is in fact quite familiar. If one walks into a house, the totality of causal effects is unsurveyably vast; if one asks which effects serve the needs and interests of the house’s human inhabitants, one can narrow the field to effects that have a practical point for them – keeping out humidity, letting in the light, bringing in electricity, and so on; and if one has walked into the house to repair the heating system, one has further guidance as to what kind of practical point one is looking for.

As with any broadly functionalist description, describing something in terms of its practical point highlights a select few in a vast network of causal effects, and the merits of the selection depend on our purposes in so describing them.Footnote ¹¹ If we as theorists seek an explanation of why something like the concept of knowledge spread and endured in just about every human society, as E. J. Craig (Reference Craig1990) does, the fact that using that concept helps satisfy such a highly generic and basic human need as the need to gain information about one’s immediate environment will be a salient useful difference made by the concept. If, by contrast, we are trying to understand the concept with a view to offering a feminist critique of it, as Haslanger (Reference Haslanger1999) does, other useful differences made by the concept will become salient.

This last example also indicates that the proposed understanding of ‘practical point’ should not necessarily be taken to be individualistic, as it would be if a concept’s usefulness were restricted to the respects in which it proved useful to the individual who used it. On the contrary, a concept’s usefulness may reside in its tendency to serve social needs, i.e. needs possessed by the community over and above the needs of the individuals it encompasses (Queloz Reference Queloz, Hufendiek, James and Raphaelforthcoming-d); or a concept’s usefulness may reside in its tendency to serve the needs of a powerful group at the expense of the individual concept-user, a theme I come back to in §4.

Thus understood, the notion of a practical point can be found to be at work in many different areas of the literature. It can be found in the ‘paradigm-based explanation’ of Miranda Fricker, for example, who is clearly talking about the practical point when she writes that the ‘point of blame’ is ‘to increase the alignment of the blamer and the wrongdoer’s moral understandings’ (Reference Fricker2016, 165); or in the ‘genealogy’ of Bernard Williams, who is concerned with the practical point of the concepts and dispositions involved in cultivating and valuing truthfulness when he concludes that truthfulness ‘gets its point ultimately from the human interest, individual and collective, in gaining and sharing true information’ (Reference Williams2002, 126)Footnote ¹²; or in the ‘teleosemantic explanations’ of Ruth Millikan, according to whom linguistic forms survive and are stabilised because their effects are of interest to hearers and/or speakers (Reference Millikan2005, 54–63, Reference Millikan2017)Footnote ¹³; or in the ‘Cambridge Pragmatism’ advocated notably by Simon Blackburn (Reference Blackburn1993, Reference Blackburn1998, Reference Blackburn2013a, Reference Blackburn and Price2013, Reference Blackburn, Misak and Price2017a, Reference Blackburn2017b) and Huw Price (Reference Price2011, Reference Price, Blackburn, Brandom, Horwich and Williams2013, Reference Price, Misak and Price2017), who seek to naturalise such things as morality and modality by replacing questions about the nature of morality or modality with questions about the function or point of thinking and speaking in moral and modal terms. All these projects are concerned with the actual useful effects of particular conceptual practices on concept-users’ lives, effects which may be of a very different sort from those that the practices aim at (if they aim at any), and which may or may not be transparent to participants in the practices.Footnote ¹⁴

(2) The Evaluative Point of a Concept: the needs, interests, and values that together form an evaluative viewpoint which informs and is betrayed in the application of the concept. A viewpoint is betrayed in the application of a concept when no such concept application could have been produced by a concept-user that did not share or at least imaginatively inhabit that viewpoint.Footnote ¹⁵ What drives the insistence on the part of McDowell, Williams, Dancy, or Scanlon that one needs to ‘grasp the evaluative point’Footnote ¹⁶ of thick concepts in order to apply them correctly is the conviction that, in virtue of the way in which thick concepts combine the evaluative and the descriptive, evaluation feeds into the determination of the extension of such concepts, which is why one needs to occupy, at least in imagination, a certain evaluative stance in order to apply them correctly. Scanlon unpacks the idea thus: ‘In order to trace the contours of the ethical concept’s applicability we have to understand its evaluative point … we must be guided by the evaluative perspective of a thick concept in order to apply it’ (Reference Scanlon2003, 276). Williams glosses the ‘evaluative point of the concept’ as ‘the outlook of those who use it’ (Williams Reference Williams, Altham and Harrison1995b, 206). Elsewhere, he elaborates on this as follows:

The key idea in these debates is that the application of a thick concept is informed or guided by evaluation on the part of the user of the concept. Talk of the ‘evaluative point’ of a concept is slightly misleading in this respect, because what it refers to is not so much the point of that concept as the set of needs, interests, and values forming the evaluative viewpoint that informs and is betrayed in the application of the concept.Footnote ¹⁷ To grasp the ‘evaluative point’ of a concept is thus to grasp what sort of evaluation on the part of its user goes into its correct application.

(3) The Animating Point of a Concept: the aim, goal, or ideal concept-users consciously pursue in applying the concept, and in terms of which concept-users make sense of the practice of using the concept. The animating point of chess, which Dummett refers to, is to achieve a checkmate position (or, more allegorically, to kill the king).Footnote ¹⁸ Mastering games generally involves having a clear sense of what the game’s animating point is – of what, in playing the game, one is trying to do, where this is and needs to be distinct from the aim of winning the game.Footnote ¹⁹ This suggests that for a concept to possess an animating point, it is a condition on counting as a competent participant in the practice that one have a fairly clear sense of what the animating point of the conceptual practice is. This requirement admits of degrees, of course, but so does competence in participating in a practice: the animating point of soccer or football, for example, is to score more goals than your opponent, and since every move in the game is animated by that aim and must contribute to its attainment in order to count as a competent move, someone who failed to grasp the animating point of the game will quickly betray that fact.Footnote ²⁰ Evidently, not all concepts have a well-determined animating point in this sense. But as Ingo Brigandt has argued, for example, when a scientific concept such as the concept of a gene is introduced by scientists with fairly specific scientific aims in mind – what Brigandt calls their ‘epistemic goal’ (Reference Brigandt2010) – these aims animate the conceptual practice, motivating use of the concept and guiding its application and perhaps even its change over time. While this is unlikely to generalise to all concepts (Brigandt and Rosario Reference Brigandt, Rosario, Burgess, Cappelen and Plunkettforthcoming; Cappelen Reference Cappelen2018, 185), there are some concepts where the conscious aims, goals, or ideals of concept-users determine a task and thereby set a standard for the use of the concept to meet. This task may differ from the concept’s practical point; it is a task which may not in fact be fulfilled, and which the concept may in principle even be unfit to fulfil; but it is still naturally called ‘the point’ of the concept – in my terminology, its animating point.

Regicide in chess aside, it is for example the animating point which is at issue when Elizabeth Anderson presents the point of (the concept of) equality as being ‘to end oppression’ and ‘to create a community in which people stand in relations of equality to others’ (Reference Anderson1999, 288–89). The animating point of concepts is also central in certain legal practices, where authoritative decisions need to be made even in hard cases. Here it is part of the practice that its continuation is secured in part by its being based on and guided by the animating point of the concept.Footnote ²¹ Another example – which is more contentious, but which helps focus the notion of an animating point – is that of concepts involved in religious practices: consider the initially religious person who comes to believe that religious concepts serve a variety of immanent social and psychological functions, and who thereupon ceases to think in religious terms altogether; one explanation might be that this person thinks that the animating point of these concepts involves something more than the fulfilment of such immanent functions – that their animating point is to achieve correspondence to or with a transcendent realm, perhaps. Here the animating point, together with the realisation that what the concepts actually do in no way contributes to attaining it, helps explain why someone would give up certain concepts despite being convinced that they have social and psychological value in virtue of their practical point.

(4) The Inferential Point of a Concept: the salient inferential consequence of applying a concept, that is, what properly and centrally follows from the fact that a concept’s application conditions are satisfied. Grasping the point of a concept in this sense is what Wilfrid Sellars and Robert Brandom think sets a bona fide concept-user apart from someone who just reliably responds differentially to the satisfaction of a concept’s application conditions.Footnote ²² It is constitutive of one’s mastery of a concept that one is able to draw at least the most salient among the proper inferential consequences of applying it – to understand, for example, that if an exercise of public power was the result of a democratic decision, this means that it was to that extent legitimate. Of course, applications of concepts have many inferential consequences. But among these consequences are some that strike us as particularly significant given our concerns, because they tie in with these concerns. This inferential sense of the point of a concept also figures prominently in Dummett’s writings, for instance when he considers a pupil who tries to master the concept of validity as applied to arguments while failing to grasp that an argument’s being valid is a reason to accept its conclusion if one accepts its premises:

As Dummett’s example suggests, the relevant notion of an inferential point does not simply correspond to the notion of an ‘inferential role’ as used in inferential role semantics.Footnote ²³ It is, rather, the notion of a particular inferential consequence worth singling out for its explanatory value, a value it possesses because it ties in with the concerns of concept-users in a way in which other inferential consequences do not. In Dummett’s example, the pupil’s problem is not simply that he has failed to master a sufficient number of the inferential moves characteristic of the concept of validity; he has failed to grasp the one move that makes the concept worth bothering with in the first place – the one inferential consequence that enables the concept to guide one’s reasoning and to improve one’s thinking. Without this inferential connection in particular, the remaining inferential intricacies of the concept of validity are no more than idle play or scholastic classification for its own sake, because they fail to link up with our needs and concerns as reasoners. Just as talk of a concept’s ‘point’ has its uses when we can profitably single out one among the various causal consequences of using a concept, so it has its uses when we can profitably single out one among the various inferential consequences of applying a concept. But as with causal consequences, which inferential consequence is worth singling out in any given case will depend on the particular explanatory interests and assumptions we bring to the concept – the inferential consequences worth picking out in an evolutionary psychologist’s investigation of how a concept contributes to biological fitness, say, will differ from those worth picking out in a Marxist’s investigation of how conceptual mystification serves capitalist interests.

Distinguishing these four senses of ‘the point of a concept’ thus brings out that the phrase is multiply ambiguous: it can refer to the practical consequences of using the concept, the evaluative point of view betrayed in applying the concept, the aims, goals, or ideals guiding and motivating the application of the concept, or the inferential consequences of applying the concept.Footnote ²⁴

4. Sharing without grasping: a non-intellectualist account of mastery

With these distinctions in place, we can now consider which type of point is at stake in point-based explanations, and for which type of point, if any, MPB holds. I shall argue in this section that the point at stake in point-based explanation is (1), the practical point of concepts, and that MPB is either false or misleading where (1) and (2) are concerned, even though it does hold, with qualifications, for (3) and (4). This will licence the conclusion that the version of MPB that is relevant for point-based explanation does not stand in tension with the ambition of point-based explanation to be informative. And it allows us to identify in more precise terms what the proper remit of MPB is, acknowledging its plausibility in two limited senses without overgeneralising it into an intellectualist account of concept use.

Which type of point is at stake in point-based explanations? A thorough answer to this question would require an extensive review and exegesis of the relevant literature. Though I have engaged in some of that exegesis elsewhere, Footnote ²⁵ I have no room for it here. I shall therefore confine myself to proposing an interpretive hypothesis and to drawing out its implications (the rest of this paper can be seen as an exploration of what would follow if this interpretive hypothesis were to prove correct). The interpretive hypothesis, which I take to be uncontentious enough, is this: the point at stake in point-based explanations is (1), the practical point. When E. J. Craig (Reference Craig1990) asks what the point of the concept of knowledge is, or Bernard Williams (Reference Williams2002) what the point of valuing the truth is, or Miranda Fricker (Reference Fricker2016) what the point of the practice of blame is, they are all primarily interested in identifying the useful practical differences which such concepts, values, or practices make to the lives of creatures like us, where usefulness is cashed out in terms of the actual tendency to satisfy the needs and interests of concept-users.

Assuming that point-based explanations are based on (1), the follow-up question is whether MPB holds true for (1). I contend that it does not: we are perfectly capable of mastering concepts without grasping their practical point. One can be in a position to deploy a concept correctly in virtue of sharing the needs, interests, and values that give the concept its practical point without grasping what that point is. Sharing the needs, interests, and values that give the concept its practical point secures the necessary guidance in the application of a concept to new situations by rendering certain features salient. Needs, interests, and values can shape what is salient to us the way our eyes shape our field of vision.Footnote ²⁶ The terminally thirsty person need not grasp the practical point of the concept of water in order to recognise water. Thirst will take care of rendering the more thirst-quenching features of the world salient. The same is true of thicker concepts: one need not grasp the practical point of the concept truthfulness in order to apply it correctly. The person who shares the needs, values, and interests that render it pointful to live by this concept will normally just see the relevant features of the situation that determine the applicability of the concept.Footnote ²⁷ It is concern with the features picked out by the concept, rather than some reflective insight into the practical value of thinking in these terms, that separates the competent concept-user from someone to whom the finite set of past applications of the concept leaves its future use underdetermined.

Consequently, when a concept answers to our needs, interests, and values, our use of it will be guided by these concerns, and a conscious grasp of how these concerns bestow a point on the concept will not be required to master the concept. On this account, it would be an intellectualist overstatement to maintain that the practical point of a concept needs to be accessible to competent concept-users – that a description of that point needs to be among the contents of their thought. It is only at a more reflective level, if we want to understand our concepts better, that we have an incentive explicitly to represent to ourselves the practical point of our concepts and the concerns from which that point derives. Consequently, and crucially for the purposes of point-based explanation, to tie the unreflective mastery of a concept to the grasp of its practical point would be to over-intellectualise concept use.

When explicated in terms of (2), the evaluative point, MPB is not so much false as misleading: ‘grasping the concept’s point’ then turns out to mean inhabiting or imaginatively occupying the evaluative point of view from which the concept’s extension can be made out, something that is required whenever a concept’s extension is a function of one’s evaluative stance. Here also the decisive factor is whether one shares, or can imagine sharing, certain needs, interests, and values. Talk of ‘grasping the concept’s point’ then suggests something more cognitive and reflective than what is actually at stake. A less misleading formulation is the one Williams uses in Ethics and the Limits of Philosophy when he writes that ‘it might be impossible to pick up an evaluative concept unless one shared its evaluative interest’ (Reference Williams2011, 263n7).

Although MPB is either false or misleading when spelled out in terms of (1) and (2), it can rightly be said to hold for other types of points. Cashed out in terms of (3), the animating point, it seems perfectly reasonable: if it is a condition on counting as a competent participant in a conceptual practice that one have a fairly clear sense of the animating point of the conceptual practice, then someone who wanted to master the relevant concept would necessarily have to grasp its point in that sense. When application of a concept is guided and motivated by an aim in this way, someone who failed to grasp what that aim was would be as far from genuinely using the concept as someone who moved the pieces on a chess board without grasping the aim of the game would be from genuinely playing chess. But even in this sense, MPB only holds for a limited range of concepts, because not all concepts involve such an animating point in the first place.

Finally, MPB has some plausibility also when cashed out in terms of (4), the inferential point. Here, mastering a concept is explicated in terms of understanding what follows from the concept’s applicability, i.e. what inferences it licenses and what one commits oneself to by applying it. But not all inferences licensed by a concept are on a par. Many of the inferences licensed by the applicability of the concept silver are inferences that no-one but a few experts are able to draw, and yet it would be awkward to say that most people had failed to master the concept silver (at least in the undemanding sense of mastery used in this paper, which equates it with the competence to apply the concept correctly in everyday circumstances). To the extent that some of these inferences are plausibly seen as crucial or central to the concept – so that someone who failed to draw them could be said not to have mastered the concept – it is true that mastering the concept requires grasping its inferential point. But in this sense, mastery is not an all-or-nothing matter. It comes in degrees. And which among a concept’s inferential consequences strike one as particularly significant will again depend on one’s concerns and reasons for using the concept. Together, these two considerations suggest that the inferential-point version of MPB is true but context-sensitive (mastery among laypeople may not count as mastery among experts), and that MPB should be amended to articulate not a necessary condition, but rather the thought that mastery and inferential capacities progress in lockstep.

In sum, the version of MPB that is relevant for point-based explanation does not threaten its ambition to be informative, and while MPB does hold with qualifications for (3) and (4), it is false or misleading when spelled out in terms of (1) and (2). In these latter two senses, mastery of concepts is a matter of sharing the concerns that give a concept its point rather than a matter of consciously grasping that point in any strict sense. Hence, if we advocate MPB without restricting the meaning and scope of this thesis accordingly, we interpret MPB too broadly and over-intellectualise concept use. But thanks to the typology proposed above, we can trace out MPB’s proper remit.

5. Functional connections and the point of divergent points

I have been arguing that once we differentiate between four types of points, we can see that where there is a point one must have in mind in order to count as mastering a concept, that point is typically not the practical point. But this is itself somewhat puzzling. What is the point of taking something other than the actual practical point of a concept to be the point of that concept? In other words, why do we not always use our concepts with an eye on whether they are serving their practical point?

In this last section, I want to draw a more positive picture of the relations between the four types of points and point-based explanation which suggests an answer to that question. I shall argue that point-based explanation allows us to see the functional connections between different types of points, and that it can exploit these functional connections to explain why these points align or come apart in particular cases.

The explanatory power of point-based explanation derives from the fact that it initiates an aspect-shift in how we view our concepts and invites us to take a view of them we do not usually take: it invites us to take an instrumental view of our concepts and to regard them as tools or techniques that are more or less suited to our ends. This instrumental perspective also brings into view certain criteria of aptness by which to assess our concepts as tools according to whether they are, in the practical sense, pointful or pointless for us. For it to make sense to speak of a concept as having a practical point for a concept-user, certain conditions need to be fulfilled. To begin with, there must be certain needs, interests, or values to determine a task in relation to which the concept can be understood. Then, using the concept must have effects that tend to be conducive to the fulfilment of that task. And finally, the concept itself must be such as to be an apt tool for the production of these effects.

From this instrumental perspective on our concepts, the different types of points distinguished above all naturally fall into place. The practical point (1) is the pointfulness or instrumentality of the concept in fulfilling a certain task and serving certain needs, interests, and values. The evaluative point (2) is the set of needs, interests, and values that give the concept its practical point by determining a task for it to fulfil. The animating point (3) is the concept-users’ conscious representation of such a task, while the inferential point (4) is a key element of the concept’s inferential articulation which contributes to its being an apt tool for fulfilling that task.

From the instrumental perspective of point-based explanation, we can then inquire into the functional connections between these different points and, by showing how they contribute to the concept’s aptness as a tool, use these connections to explain why the concept combines these various points in the way it does: the practical point of a concept given its evaluative point can be used to explain why its animating point and its inferential point are as they are, and in particular why they diverge from the practical point – in the typology outlined above, (1) given (2) can explain (3) and (4).

At bottom, such an explanation works by revealing what the practical point is of taking something other than the practical point of a concept to be the animating or inferential point of that concept. The explanation shows that the concept’s having the animating or inferential point it does serves a practical point, and that this animating or inferential point either lines up with the practical point or differs from it the better to serve that practical point. In some cases, the practical point of a concept may be best served if its animating point aligns with its practical point, so that the practical point is overtly understood to be the ‘name of the game’ – this is the case if, assuming the practical point of the concept is to ϕ, we aim, in applying the concept, to ϕ. Similarly, the practical point of a concept may be best served if its inferential point aligns with its practical point, so that it follows from the concept’s applicability to x that x is a means of ϕ-ing.

But point-based explanation comes into its own where the animating or inferential point diverges from the practical point. We can distinguish three kinds of divergence: contingent divergence, deceptive divergence, and benign functional divergence.

First, contingent divergence is what we have when a concept’s animating or inferential point fails to line up with its practical point, but for what, from the instrumental perspective of point-based explanation, must appear as purely contingent reasons. For example, a concept originally picking out a food item as healthy (i.e. licensing the inference from x being such a food item to x being healthy) might be harnessed by a religious movement and come to have as its salient inferential consequence not that x is healthy, but that x is holy.Footnote ²⁸ In this case, assuming the practical point of the concept is to render concept-users suitably sensitive to the presence of a healthy food item, the inferential point would come to diverge from the practical point; but the divergence would be an accident of history, something to be explained in terms of causes rather than reasons. In cases of contingent divergence, point-based explanation is of interest because it directs our attention towards the practical dimension of concepts (e.g. their effects on health), which helps explain why we have them especially in cases where that dimension may be veiled by other concerns (e.g. concern with the holy). The category of contingent divergence allows for the fact that while our concepts may serve practical purposes in many respects, and those practical purposes may help explain why we have them, the fact that human beings live under culture means that there is also ample room for our concepts to acquire non-functional features reflecting the influence of cultural contingencies. Cultural variation between groups and cultures implies that even if certain functional features were the same across these variations, our concepts would nevertheless also be shaped by different contingencies in each case. Hume displays sensitivity to precisely this point when he writes that houses, though they share certain functional features and conspicuously ‘point all to a like end’ (EPM, 3.2), also vary from one culture to another in their non-functional aspects (or aspects that are functional only relative to more local concerns). Similarly, what our concepts instrumentally need to be is only a very partial guide to the form they actually take.

Second, deceptive divergence is what we get if a concept serves a practical point which, if it became transparent to concept-users, would lead many of them to give up the concept, because that practical point is in tension with the concept’s animating or inferential point. It is in this structure that we can situate the cases familiar from Critical Theory and ideology critique, where diagnoses of ideological functions can get a grip by showing that the practical point actually served by a concept radically differs from the aims that animate its use and the inferences we draw with it. In such diagnoses, the concepts in terms of which advocates of human rights, liberalism, or egalitarianism think and argue, for instance, are made out really to serve the practical point of promoting Western domination, imperialism, or inequality.Footnote ²⁹ These diagnoses identify a radical divergence between, on the one hand, the aims animating the use of such concepts and the salient inferences drawn from their application, and, on the other hand, the practical effects of thinking in these terms. The divergence is a deceptive one because the diverging points are in tension with one another: the use of the concepts is revealed to be counterproductive by the evaluative standards these concepts themselves encode. A point-based explanation identifying such a deceptive divergence can nevertheless be explanatory by revealing the practical point, for people with an interest in promoting Western domination, imperialism, or inequality, of deceiving other people – and perhaps even themselves – into taking the point of these concepts to be a loftier one than the practical point they actually serve. The animating and inferential points then serve the divergent practical point by concealing it. Here the functional connection between the different points is such that it cannot be entirely transparent to the concept-users if they are to use the concepts in a fully engaged, non-cynical manner.Footnote ³⁰

Third, the divergence may also be of a benign functional kind. This is the case when some outcome is not best achieved by having concept-users aim for that outcome, but rather by having them be animated by something other than the desire to achieve that outcome. When the practical point of a concept is to achieve some common good – such as the pooling of information, for example – the tragedy of the commons entails that the common good is under threat as long concept-users are animated by and conceive of the common good solely in terms of its instrumental value to them. The best way of reaping the benefits of the common good may then be for concept-users to be, in Williams’s phrase, bloody-minded rather than benefit-minded, for instance by having people think of the disposition to truthfully pass on information to others as something that is not just instrumentally valuable insofar as it contributes to the pooling of information (a consideration that may have little weight for me when I can deceive for gain), but as something that is valuable in itself.Footnote ³¹ On this picture, the practical point of thinking in terms of the concept of truthfulness is that it is conducive to the effective pooling of information; but the animating point of the concept that is on our minds as we discriminate and choose between truthful and untruthful behaviour is not this social benefit, but a concern with the goodness or rightness of truthfulness. Similarly, the salient inferential consequence we draw from something’s being an instance of truthfulness is not that it will have contributed to maintaining a system of epistemic division of labour, but rather that it is a good thing just because that is the kind of action it is. This divergence of points is functional because it renders the system of epistemic division of labour less vulnerable to the dynamics of the tragedy of the commons. But it is a benign functional divergence because the functional connection between the different points is such that it can become entirely transparent to concept-users without undermining the confidence with which they use the concept. On the contrary, the functional connection can be made explicit in the hope of strengthening their confidence in the concept.Footnote ³² A point-based explanation will then reveal why the points of the concepts need to diverge in the way they do, and why it makes good functional sense for them to do so, because the most effective way to ϕ by means of the concept of x is to take the animating and inferential points of the concept to be something other than ϕ-ing.

6. Conclusion

I have been arguing that we need a typology of points if we are to put point-based explanation on a clear and solid foundation and to navigate potential tensions and fruitful connections between different types of points. On the basis of the typology I have offered in this paper, I have shown how exactly point-based explanation can avoid presupposing a grasp of what it is supposed to reveal; I have argued that this typology allows us to put in its place the otherwise overly intellectualist thesis that mastering a concept requires one to grasp its point, and that its proper remit turns out to be fairly limited; and I have argued that point-based explanation can exploit the functional connections between the points of concepts to make sense of why we sometimes take the point of our concepts to be something other than the practical point they actually serve: a concept’s having a certain animating or inferential point that differs from its practical point may serve to conceal its practical point, or it may itself serve that practical point. It thus turns out that there is a point both to there being, and to distinguishing between, different types of points.

Funding

This work was supported by the Swiss National Science Foundation (CH) [P0BSP1_162025].