Friday 15 May 2020

Tacit knowledge

Introduction

The main promoter of the idea of tacit knowledge (or ‘tacit knowing’, as he preferred) in twentieth century philosophy was the chemist turned philosopher of science Michael Polanyi. His book The Tacit Dimension starts with the manifesto:

I shall reconsider human knowledge by starting from the fact that we can know more than we can tell. [Polanyi 1967b: 4]

But, as he is quick to acknowledge, it is not easy to say exactly what this means. It does, however, suggest a via negativa. What is tacit is what is not ‘tellable’ or explicit under a suitable understanding of that.

The manifesto accords with some of the phenomena that are sometimes called ‘tacit knowledge’ in the popular adoption of the label: recognising someone’s face, or a few hastily-drawn lines as a face; throwing and catching a ball; riding a bicycle; touch typing; skilfully playing the piano; reading a book or map; immediately diagnosing a patient; navigating the shoals of interpersonal relationships; understanding a language. These phenomena seem to involve normative, intentionally directed activities that express some form of knowledge but also something that cannot be fully, at least, put into words.

Two less everyday examples are worth setting out because they are often used as paradigmatic examples in more academic discussions of tacit knowledge.

The first relates to poultry farming, in which there is economic advantage in being able to determine the gender of chicks as soon as possible after they hatch. In the 1920s, Japanese scientists came upon a Chinese method by which this could be done based on subtle perceptual cues with a suitably held one day old chick [Martin 1994: 3]. It was, nevertheless, a method that required a great deal of skill developed through practice. After four to six weeks of instruction and practice, a newly qualified chick-sexer might be able to determine the sex of 200 chicks in 25 minutes with an accuracy of 95% rising with years of practice to 1,000 - 1,400 chicks per hour with an accuracy of 98% [Gellatly 1986: 4].

The second example is that of skilled Polynesian navigators who were found to be able to navigate small out-rigger canoes ‘across two or three hundred miles of open sea; and do so in almost any weather, and even when less than fully sober. How is it done?’ [ibid.: 5]. Investigation suggested that the skill took years to master and was context specific: they were only able to navigate the seas and in the wind conditions of their familiar part of the world and that they were unable to put into words on dry land.

In the first case, although the theory of chick sexing by genital differences was simple, the nature of the recognitional skill involved was elusive. According to R.D. Martin’s history, having read about the theory, Mr Kojima, a poultry farmer from Nagoya, reversed engineered the skill using first 60 day, then 30 day, then younger and younger chicks [Martin 1994: 4]. Dreyfus and Dreyfus’ 1986 account seems to imply that not even the chick-sexers could explain how they did it [Dreyfus and Dreyfus 1986: 197-8]. Their own knowledgeable ability was opaque even to them and hence doubly ‘untellable’. But this claim risks distorting the fact that it was necessary to make an immediate perceptual judgement as chick-manipulation changed the key visual cue. Chick-sexers also often learnt their judgements aided by diagrams later ‘outgrown’ once the ability was second nature [Martin 1994].

The very idea of tacit knowledge presents a challenge, however: it has to be tacit and it has to be knowledge. But it is not easy to meet both conditions. Emphasising the tacit status, threatens the idea that there is something known. Articulating a knowable content, that which is known by the possessor of tacit knowledge, risks making it explicit. What limits can be placed on what can be said still leaving something that can be known?

Given his central role in discussing tacit knowledge, I will turn first to Polanyi, though as one Polanyian scholar concedes:

Now we are in a position better to understand why Polanyi’s notion of the tacit is unclear. Since he uses the term in different contexts to embrace all in human cognition that is not explicit, it is a comprehensive term that includes processes and contents from many ontological levels and different disciplines. Tacit processes and components include: (1) all the autonomic physiological processes that support at lower levels an act of knowing at any given moment; (2) plus the embodied skills, learned and perhaps innate, that contribute to one’s intentional actions (including cognitive actions); (3) plus all the psychological dynamics (integrations, judgments) involved in this knowing; (4) plus all the background presuppositions and beliefs that shape the prevailing personal framework of interpretation; (5) plus the immediately preceding thoughts and actions still active in working memory; (6) plus the network of sensitivities, moods, and feelings salient at the moment of analysis; (7) plus the influx of sensations, all vying for attention, relayed by the central and peripheral nervous systems, including sensory data from the body’s receptors; (8) plus the interests, goals, and expectations pushing thought and action toward certain satisfactions; (9) plus the words and grammar evoked as the transparent means to express and evaluate the meaning of this concatenation of influences. [Guilick 2016: 303]

My aim is to suggest a coherent person-level notion of tacit knowledge influenced by Polanyi rather than to attempt to make sense of his wider encyclopaedic ambition. One consequence is that not all potential instances of tacit knowledge in philosophy – such as of the axioms of a theory of meaning for a language – will fit [Evans 1981].

In Personal Knowledge, Polanyi examines how what can be said or, more broadly, articulated both leaves room for, and depends on, something outside what can be articulated [Polanyi 1962]. There are two key arguments which stress the tacit element. (I will return to a third suggestion that helps with the knowledge status later.)

One depends on limits on the kind of representation available to summarise explicit knowledge in science, thus indicating a space for tacit knowledge.

The other depends on an analysis of what is involved in recognition (an argument which promises to impact on diagnostic judgement), which also connects to Polanyi’s views of how linguistic representation in general is possible.

I will suggest that this latter argument is the fundamental argument but start with the former.

Polanyi on the limits of representation

Polanyi considers the understanding that a skilled surgeon has of the spatial configuration and orientation of organs in the body. He argues that this cannot be captured in a representation.

The major difficulty in the understanding, and hence in the teaching of anatomy, arises in respect to the intricate three-dimensional network of organs closely packed inside the body, of which no diagram can give an adequate representation. Even dissection, which lays bare a region and its organs by removing the parts overlaying it, does not demonstrate more than one aspect of that region. It is left to the imagination to reconstruct from such experience the three-dimensional picture of the exposed area as it existed in the unopened body, and to explore mentally its connections with adjoining unexposed areas around it and below it. The kind of topographic knowledge which an experienced surgeon possesses of the regions on which he operates is therefore ineffable knowledge. [Polanyi 1962: 89]

The claim here is that three-dimensional spatial knowledge is ineffable, which here stands for tacit, because it cannot be captured in a representation. Polanyi goes on to argue that even if human bodies were identical and there were a map comprising cross sections based on ‘a thousand thin slices’ of the body, that in itself would not articulate the knowledge of a trained surgeon. Someone knowing merely the former ‘would know a set of data which fully determine the spatial arrangement of the organs in the body; yet he would not know that spatial arrangement itself’ [ibid: 89]. An additional act of interpretation or imagination is needed. But because that act cannot itself be encoded in a representation, according to Polanyi, it remains tacit.

This is surprising. Polanyi concedes that the set of cross-sectional representations, presumably with further information about their inter-relations, ‘fully determine[s] the spatial arrangement of the organs’ and yet denies that this amounts to an articulation of the three-dimensional understanding. Without the further information the maps alone would not be an articulation of the skilled surgeon’s knowledge. But then neither would they fully represent the arrangement of bodily organs. With the further information, however, why would this not count as an explicit articulation of the surgeon’s knowledge and thus not tacit?

A further possible clue to Polanyi’s thinking runs thus:

The difficulty lies here entirely in the subsequent integration of the particulars and the inadequacy of articulation consists altogether in the fact that the latter process is left without formal guidance. The degree of intelligence required from the student to perform the act of insight which ultimately conveys to him the knowledge of the topography, offers here a measure of the limitations of the articulation representing this topography. [ibid: 90]

But there remains something strange about this line of thought. If the integration of the partial representations, eg. cross-sections, were left without formal guidance then it would be clear why they could not articulate the surgeon’s knowledge. But neither would they determine the arrangement of organs as Polanyi has previously asserted.

I think that the clue to its Polanyi’s argument is his claim that whether a symbol determines anything always depends on a tacit element. This is supported by a different argument concerning the distinction between focal attention and subsidiary awareness.

Recognition and the distinction between focal and subsidiary awareness

I may ride a bicycle and say nothing, or pick out my macintosh among twenty others and say nothing. Though I cannot say clearly how I ride a bicycle nor how I recognise my macintosh (for I don’t know it clearly), yet this will not prevent me from saying that I know how to ride a bicycle and how to recognise my macintosh. For I know that I know how to do such things, though I know the particulars of what I know only in an instrumental manner and am focally quite ignorant of them. [ibid: 88]

Polanyi suggests that the skill involved in recognising a macintosh is akin to the practical skill of cycle riding. In both cases, the ‘knowledge-how’ depends on something which is not explicit: the details of the act of bike riding or raincoat recognition. While one can recognise one’s own macintosh, in the example, one is ignorant, in some sense, of how. Thus, how one does this is tacit.

If this argument were successful it would be of general significance because it would also apply to all linguistic labelling. Polanyi makes this connection.

[I]n all applications of a formalism to experience there is an indeterminacy involved, which must be resolved by the observer on the ground of unspecified criteria. Now we may say further that the process of applying language to things is also necessarily unformalized: that it is inarticulate. Denotation, then, is an art, and whatever we say about things assumes our endorsement of our own skill in practising this art. [ibid: 81]

This connection between denotation and tacit recognitional skills appears to be the fundamental argument for the importance of tacit knowledge for explicit scientific accounts.

If, as it would seem, the meaning of all our utterances is determined to an important extent by a skilful act of our own – the act of knowing – then the acceptance of any of our own utterances as true involves our approval of our own skill. To affirm anything implies, then, to this extent an appraisal of our own art of knowing, and the establishment of truth becomes decisively dependent on a set of personal criteria of our own which cannot be formally defined.... [E]verywhere it is the inarticulate which has the last word, unspoken and yet decisive... [ibid: 70-71]

The argument for denotation being tacit seems to rest on an appeal to the clearer case of the recognition of particulars – such as a particular macintosh – which, Polanyi argues, depends on features of which one is focally ignorant. (The example concerns recognition of a particular macintosh as one’s own rather than merely that an object is a macintosh but nothing turns on this difference.)

To justify his claim about denotation he needs to defend the general claim that explicit recognition of something as an instance of a type is based on the implicit recognition of subsidiary properties of which one is focally ignorant. To recognise a feature (F, say) one must a) always recognise it in virtue of something else (subsidiary features G, H and I, eg.) of which b) one is focally ignorant. But it is not clear that either part of this claim is true.

Elsewhere, Polanyi uses the example of pointing to something with a finger to distinguish between focal and subsidiary awareness.

There is a fundamental difference between the way we attend to the pointing finger and its object. We attend to the finger by following its direction in order to look at the object. The object is then at the focus of our attention, whereas the finger is not seen focally, but as a pointer to the object. This directive, or vectorial way of attending to the pointing finger, I shall call our subsidiary awareness of the finger. [Polanyi 1967a: 301]

In attending from the finger to the object, the object is the focus of attention whilst the finger, though seen, is not attended to. The finger is not invisible. It could itself be the object of focal attention were it attended to. This suggests that the first part of the general claim that Polanyi needs itself faces an objection based on a regress. The recognition of an instance of a type depends on subsidiary awareness of something else which could have been the object of focal awareness and thus would have depended on subsidiary awareness of something else.

This is a potential rather than a vicious regress but, nevertheless, suggests something implausible about Polanyi’s general claim. It does not seem reasonable to think that it is always the case that recognition of the instantiation of a kind, for example a colour, depends on subsidiary awareness of something else. Polanyi seems to assume that the question of how one recognises something to be of an instance of a particular kind always has an informative answer and to cover cases where it is not obvious what this is, the defensive move he makes is to claim – implausibly – subsidiary awareness of ‘neural traces in the brain’ [Polanyi 1969: 147]. But whilst it sometimes may have an informative answer, there is no reason to think that it always has. This puts the first part of Polanyi’s claim – that to recognise a feature one must a) always recognise it in virtue of something else – under pressure. What of the second aspect: that one must be focally ignorant of the subsidiary features?

Even in cases where one recognises a particular as an F in virtue of its subsidiary properties G, H, I, and cannot give an independent account of those properties, it is not clear that one need be focally ignorant of them. It may be, instead, that the awareness one has of G, H, I is manifested in the recognition of something as an F or a particular F. One might say, I recognise that this is a macintosh (or my macintosh) because of how it looks here with the interplay of sleeve, shoulder and colour even if one could not recognise a separated sleeve, shoulder or paint colour sample as of the same type. Whilst it seems plausible that one might not be able to say in context-independent terms just what it is about the sleeve that distinguishes a macintosh from any other kind of raincoat (lacking the vocabulary of tailoring) that need not imply that one is focally ignorant of, or not attending to, just those features that make a difference. Recognition may depend on context-dependent or demonstrative elements, such as recognising shapes or colours for which one has no prior name. That suggests one has to be focally aware of them.

While it is true that one is sometimes focally unaware of features that underpin one’s recognitional abilities and one cannot always say in general term on what features one’s recognition depends these facts do not support the general claim that (focal) recognition of one feature always depends on merely subsidiary awareness of something else. And if not, Polanyi has not offered a general reason to hold that recognition is a tacit skill by his own lights.

Contrary to Polanyian scholarship, it is thus better to sever an account of tacit knowledge from the focal versus subsidiary awareness distinction [contra Grene 1977].

A narrower Polanyi-inspired account of tacit knowledge

I suggested earlier that the very idea of tacit knowledge presents a challenge. Tacit knowledge is both tacit and knowledge and it is hard to meet both conditions. There is a second strand in Polanyi’s work which helps address this, though abstracting away from Polanyi’s own account. At the start of his book Personal Knowledge he says:

I regard knowing as an active comprehension of things known, an action that requires skill. [Polanyi 1962: vii]

In combination with the first slogan, this suggests a clue to tacit knowledge. First, it cannot be made explicit and, second, it is connected to action, the practical knowledge of a skilled agent. The latter suggests how tacit knowledge has content: as practical knowledge of how to do something. Taking tacit knowledge to be practical suggests one way in which it is ‘untellable’. It cannot be articulated except in context-dependent practical demonstrations. It cannot be made explicit in words alone.

In Tacit Knowledge, Neil Gascoigne and I set out an account of tacit knowledge as conceptually structured, context dependent, practical knowledge [Gascoigne and Thornton 2013]. We locate tacit knowledge at the level of the person, rather than the sub-personal, and within the ‘space of reasons’, the space of justifying and being able to justify what one says. [McDowell 1994: xiv, Sellars 1997: 76].

We motivate the account partly in response to ‘regress arguments’ offered by Gilbert Ryle and Ludwig Wittgenstein and defend the former against new intellectualist criticism [eg. Stanley and Williamson 2001]. But the support the regress arguments offer is nuanced. To take the latter, Wittgenstein considers teaching a pupil to continue a mathematical series correctly who ‘judged by the usual criteria… has mastered the series of natural numbers’ and is then taught to continue series of the form 0, n, 2n, 3n, etc. for arbitrary values of n

Then we get the pupil to continue one series (say “+ 2”) beyond 1000 – and he writes 1000, 1004, 1008, 1012. We say to him, “Look what you’re doing!” – He doesn’t understand. We say, “You should have added two: look how you began the series!” – He answers, “Yes, isn’t it right? I thought that was how I had to do it.” —– Or suppose he pointed to the series and said, “But I did go on in the same way”. – It would now be no use to say, “But can’t you see…?” – and go over the old explanations and examples for him again. In such a case, we might perhaps say: this person finds it natural, once given our explanations, to understand our order as we would understand the order “Add 2 up to 1000, 4 up to 2000, 6 up to 3000, and so on”. This case would have similarities to that in which it comes naturally to a person to react to the gesture of pointing with the hand by looking in the direction from fingertip to wrist, rather than from wrist to fingertip. [Wittgenstein 2009 §185]

The pupil reacts in a divergent way (from us) to explanations of how to continue. He appears to have acted under a divergent interpretation of the expression of the rule. But if to be successful an explanation of a rule has to be correctly interpreted then any expression of the interpretation might be subject to divergent understandings whether explicitly stated in a symbolism or by examples.

“But how can a rule teach me what I have to do at this point? After all, whatever I do can, on some interpretation, be made compatible with the rule.” – No, that’s not what one should say. Rather, this: every interpretation hangs in the air together with what it interprets, and cannot give it any support. Interpretations by themselves do not determine meaning. [ibid §198]

Since any interpretation has to be specified in some way, if understanding depends on an interpretation, no specification would be sufficient in itself. Hence the label ‘regress of interpretations’.

In an early work – Changing Order - on the role of tacit knowledge in science, the sociologist Harry Collins assumes that the regress argument shows that the correct way to continue, the correct notion of sameness, cannot be specified or said [Collins 1985].

[S]ince in spite of this we all know the correct way to go on, there must be something more to a rule than its specifiability’ [ibid: 14].

Thus there is a genuine gap between what is said in an explanation of a rule and what is understood when all goes well and something is needed to plug the gap so as to explain the otherwise mysterious ability to go on correctly.

The extra element is social entrenchment such that the sense of sameness in continuing in the same way is relative to a community. It underpins the ‘mysterious abilities that enable us to know when to continue ‘2,4,6,8’ with ’10,12,14,16’ and when with ‘who do we appreciate?’’ [ibid: 22, italics added].

Collins calls this ‘tacit knowledge’.

[T]he member of a social group who has the ability to continue the sequence ‘2,4,6,8’ with ‘10,12,14,16’ as a matter of course, without even thinking about it, also possesses something that the stranger to our culture and the newborn do not. This is sometimes referred to as ‘social skill’ but we can call it tacit knowledge without doing too much violence to the term. [ibid: 56 italics added]

According to Collins tacit knowledge cannot be put into words, is invisible in its transmission and capricious [ibid: 129]. This suggests a picture of rule following in which explanations are always inadequate but are patched by invisible and capricious tacit knowledge: the picture that Wittgenstein puts into the mouth of his interlocutor in order to reject it.

“But do you really explain to the other person what you yourself understand? Don’t you leave it to him to guess the essential thing? You give him examples a but he has to guess their drift, to guess your intention.” – Every explanation which I can give myself I give to him too. ¬ “He guesses what I mean” would amount to: “various interpretations of my explanation come to his mind, and he picks one of them”. So in this case he could ask; and I could and would answer him. [Wittgenstein 2009: §210]

There is, however, a different way to connect the regress argument to tacit knowledge. The moral of the regress of interpretations according to John McDowell is that:

We learn that it is disastrous to suppose there is always a conceptual gap between an expression of a rule and performances that are up for assessment according to whether or not they conform to the rule, a gap that is made vivid by saying the expression of the rule stands there… We must not acquiesce in the idea that an expression of a rule, considered in itself, does not sort behaviour into performances that follow the rule and performances that do not. [McDowell 2009: 100-1]

This, according to McDowell, is the moral of §201 of the Philosophical Investigations: ‘there is a way of grasping a rule which is not an interpretation, but which, from case to case of application, is exhibited in what we call “following the rule” and “going against it”’ [Wittgenstein 2009: §201]. For those who are party to the relevant practices, there is no gap between the expression of the rule and being told which way to go. A signpost, for example, not merely a signpost under an interpretation, points the way. On this account, the regress of interpretations is stopped before it can start. Hence, the expression of a rule is explicit in its directions.

But it is only explicit for those with the right eyes to see or ears to hear an explanation, for those, in Stanley Cavell’s phrase, who share the ‘whirl or organism’ of our form of life [Cavell 1969: 52]. This in turn grounds out in the applications of rules, which are context-dependent, conceptually structured and practical. The regress of interpretations argument shows that any informative explanation of what following a rule correctly, going on in the same way, comprises soon gives out. Any general account of the relation of rules or conceptual generalities to particular judgements falls prey to the regress of interpretations. What can be made explicit via the art of denotation – in Polanyi’s phrase – rests on the tacit, not because of a distinction between focal and subsidiary awareness but because going on in each specific way simply is accord with a rule or concept, is also context dependent and, by linking conceptual generalities to particular cases in judgements, is practical.

An ontology rather than epistemology of tacit knowledge?

Taking tacit knowledge to be person-level and conceptual (as well as practical and context specific) is not the only possible approach, however.

In his later Tacit and Explicit Knowledge, Collins also contrasts tacit knowledge with what is explicit [Collins 2010]. But the characterisation of the explicit is not as what can be expressed linguistically – as Polanyi and I assume – but rather with what Collins calls ‘strings’ [Collins 2010: 57]. Strings are ‘bits of stuff inscribed with patterns: they might be bits of air with patterns of sound waves, or bits of paper with writing, or bits of the seashore with marks made by waves, or patterns of mould, or almost anything’...’ [ibid: 9] The motivation for this is to avoid the ‘freight of inherent meaning that makes the notions of signs, symbols and icons so complicated’ [ibid: 9]. One repeated worry is that strings (and hence signs as kinds of strings) do not have an essential meaning: ‘strings are without meaning… a book is a physical thing, not a meaningful thing’ [ibid: 34]. So rather than presupposing meaning or mental content, Collins stresses the physical nature of strings: ‘a string is just a physical object and it is immediately clear that whether it has any effect and what kind of effect this might be is entirely a matter of what happens to it’ [ibid: 9].

But since strings are just ‘bits of stuff inscribed with patterns’ their elaboration, transformation, mechanization and explanation are all counted by Collins as instances of what is explicit. Hence the focus of the book turns out not to be the nature of the knowledge that rational subjects possess but the worldly objects of knowledge: the processes or tasks or worldly patterns themselves.

One example of this is the way that Collins, as I have, attempts to demystify tacit knowledge by connecting it to what is practical:

We are just like complicated cats, dogs, trees, and sieves… Sometimes we can do things better than cats, dogs, trees and sieves can do them, and sometimes worse. A sieve is generally better at sorting stones than a human (as a fridge is better at chilling water), a tree is certainly better at growing leaves, dogs are better at being affected by strings of smells, and cats are better at hunting small animals… if we were to stop talking and just get on with things — that is, if the tacit was not made mysterious by its tension with the explicit — there would be no puzzle at all about the body, per se. That teaching humans to accomplish even mimeomorphic actions is a complicated business, involving personal contact, says nothing about the nature of the knowledge, per se. (ibid: 104-5)

The final claim reiterates the idea that what matters to Collins – ‘knowledge, per se’ – does not depend on how humans think of or conceptualise tasks, something in the realm of sense, but rather on the mechanical process, in the realm of reference. The passage does not explicitly equate tacit knowledge with the behaviour of cats, dogs, trees and sieves but it does suggest that thinking of sieves sorting stones is a good way to demystify human tacit knowledge. Whatever the independent merits of an ontology of strings, however, it is far from an account of knowledge itself. It is pitched at the level of reference rather than sense and ontology rather than epistemology.

Polanyi was right to stress the importance of a form of knowledge at the level of the person, expressive of human minds, tied to context and practical and presupposed by, but exceeding, linguistic codification. The challenge is to articulate it.

References

Cavell, S. (1969) Must we mean what we say?, Cambridge: Cambridge University Press

Collins, H. (1985). Changing Order: Replication and Induction in Scientific Practice, London: Sage

Collins, H. (2010) Tacit and Explicit Knowledge, Chicago: University of Chicago Press

Dreyfus, H.L. and Dreyfus, S.E. (1986) Mind Over Machine, New Youk: Macmillan

Evans, G. (1981) ‘Semantic Theory and Tacit Knowledge’. In Holtzman, S.H. and Leitch, C.M. (eds.). Wittgenstein: To Follow a Rule, London: Routledge and Kegan Paul

Gascoigne, N. and Thornton, T. (2013) Tacit Knowledge, Durham: Acumen

Gellatny, A. (ed) (1986) The Skilful Mind, Milton Keynes: Open University Press

Grene, M. (1977) ‘Tacit knowing: grounds for a revolution in philosophy’ Journal of the British Society for Phenomenology, 8: 164-71

Guilick, W. (2016) ‘Relating Polanyi’s Tacit Dimension to Social Epistemology: Three Recent Interpretations’ Social Epistemology, 30: 297-325

McDowell, J. (2009) The Engaged Intellect, Cambridge, MA: Harvard University Press

McDowell, J. (1994) Mind and World, Cambridge, MA: Harvard University Press

Martin, R.D. (1994) The Specialist Chick Sexer, Melbourne: Bernal

Polanyi, M. (1962) Personal Knowledge, Chicago: University of Chicago Press

Polanyi, M. (1967a) ‘Sense-giving and sense-reading’ Philosophy 42: 301-325

Polanyi, M. (1967b) The Tacit Dimension, Chicago: University of Chicago Press

Polanyi, M. (1969) Knowing and Being, Chicago: University of Chicago Press

Ryle, G. (1949) The Concept of Mind, London: Hutchinson.

Ryle, G. (1945) ‘Knowing How and Knowing That’ Proceedings of the Aristotelian Society, 46: 1-16

Sellars, W. (1997). Empiricism and the Philosophy of Mind. Intro. by R. Rorty and study guide by R. Brandom. Cambridge, MA: Harvard University Press.

Stanley, J. and Williamson, T. (2001) ‘Knowing how’ The Journal of Philosophy 97: 411-444.

Wittgenstein, L. (2009) Philosophical Investigations, Oxford: Blackwell