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Friday, 3 July 2009

‘Knowledge is true belief which …’ Can one satisfactorily fill in the dots?

For the purposes of this essay, I intend to look at some attempts to ‘fill in the dots’ most notably the tracking account developed by Robert Nozick, and contextualism as advocated by Keith DeRose. I intend to look at some of the difficulties faced by these accounts and consider whether they give any hope that a satisfactory resolution is possible.

Since the ancient Greek philosophers, a widely accepted definition of knowledge was as ‘justified true belief’. That is to say that:

S knows that p, if and only if:

1. It is true that p
2. S believes that p
3. S is sufficiently justified in believing that p.

On the face of it this seems straightforward enough and therein lays the problem. This tripartite account of knowledge went more or less unchallenged for over 2000 years and although there was perhaps disagreement over what qualified as sufficient justification (especially given the possibilities presented by radical scepticism) it enjoyed widespread acceptance. What happened next was as unexpected as it was overdue.

All was well until in 1963, Edmund Gettier published a three page long paper entitled “Is Justified True Belief Knowledge?” In this paper, it is widely agreed that Gettier provided two counter examples to the tripartite account of knowledge as justified true belief.

Gettier begins by stating three differing versions of justified true belief and formulates two counterexamples wherein p is true, S believes that p and is justified in doing so. Unfortunately, S does not know p because their reasons for believing p are wrong. Essentially, Gettier had shown that justification, truth and belief failed to be jointly sufficient and necessary criteria for knowledge attributions; something else was required. An explanation of knowledge that was generally accepted since Plato suggested it, had been shown to be flawed and was not easily repairable.

Many attempts to address the problem, address the question of what qualifies
as justification. One attempt to fill in the dots dispenses with justification entirely. In Philosophical Explanations Robert Nozick seeks to formulate conditions that are “jointly sufficient for knowledge so any case that satisfies all of them will be an instance of knowledge” (Nozick, 1981 p.23). What he argues for instead is the idea that when beliefs ‘track’ the truth they are instances of knowledge.

Nozick’s tracking account of knowledge is stated as follows:

S knows that p, if and only if:

1. p (it is true that p)
2. S believes that p
3. If not-p then S would not believe that p for the same reason
4. If p then S would believe that p for the same reason

Conditions 3 and 4 replace the traditional ‘justification’ requirement. In circumstances where all four criteria obtain, Nozick considers the subject, S’s belief to “track” the truth. ‘To know is to have a belief that tracks the truth’ (Nozick, 1981. pp.28). Part of Nozick’s intent here is to address the problem of scepticism and on this regard he has some sucesss, and in addressing Gettier’s counter examples the tracking account appears initially promising.

There are numerous Gettier-type counter examples and many versions of them are in circulation. For the purposes of this essay for the sake of convenience, clarity and my own familiarity I shall use the examples as quoted in Murali Ramachandran’s How Believing can Fail to be Knowing, mainly for the clarity of his presentation of these sample cases.

When testing such accounts against an array of Gettier-type counter-examples it becomes apparent that any such account of what it is to know needs to tread a fine line. On the one hand one wants to avoid ruling out cases in which a true belief that has been appropriately acquired, fails to qualify as knowledge; conversely, one wants to avoid classifying as knowledge those cases where an inappropriate belief has been inappropriately acquired, yet happens to be correct through chance. This is made clear in the case of NOGOT.


A colleague in S’s office, Mr Nogot, has given evidence which leads S to
justifiably believe (r) that Mr. Nogot owns a Ford, from which S correctly deduces (p) that someone in this office owns a Ford. But, unbeknownst to S, Nogot has been shamming and p is only true because another person in the office, Ms. Havit, owns a Ford.

In this situation Nozick’s tracking account fares well and produces the correct outcome. His first criterion is met because it is true that p (because, purely coincidentally someone in the office does indeed own a Ford) and the second also obtains because S believes p. Condition 3, however, is not satisfied because if no-one in the office owned a Ford then S would still believe p on the basis of r. It is obvious that since r is false, S’s belief that r is not adequate justification for knowledge that p. Because S’s belief in p is deduced from r, then we can conclude that whether or not p was true, S would believe p and so condition 3 does not obtain. The tracking account therefore produces the correct result. S does not know that someone in the office owns a Ford.

A possible objection is that without p being true, it would have been impossible for Mr. Nogot to provide the evidence upon which S justifiably came to believe r. This ambiguity is avoided in the following variation and the results are not so good for the tracking account:


Mr Nogot is mad. He decides that he will fool his gullible colleague S into believing (p) that someone in the office owns a Ford if and only if someone in the office does own a Ford. (Let us suppose that Nogot has the means to find out if someone does.) Nogot finds out that Havit owns a Ford and embarks on his plan. The rest is history—S comes to believe truly (p) that someone in this office owns a Ford.

The line ‘if and only if someone in the office owns a Ford’ is analogous to the objection that it would only have been possible for Nogot to engender S’s justified belief in p if someone in the office owned a Ford. In this variant Nozick does not fare so well. All four conditions are satisfied, so Nozick would say that S’s belief in p tracks the truth. S knows that p but that belief has not been acquired appropriately and so the desired outcome should be that S does not know p. Clearly, something gets overlooked, because it appears Nozick is committed to saying that in the case of DEVIOUS NOGOT, S knows that p. The four criteria as they are, do not differentiate between sound and unsound justifications such as the false lemma (r). Nozick’s four points capture the importance of there being a causal relationship between the truth of p and S’s belief that p, however they do not account for the possibility of some deception resulting from a less direct chain of belief.

The rescue for Nozick seems to come from holding the criteria up to r. Conditions 1 and 3 do not obtain for r, because it is not true that r and because S would believe r even if it were false; because 1 and 3 do not obtain for r we can say that r is a false-lemma or false-belief. If we add a fifth condition that S’s belief that p cannot rest on any false beliefs, then the Devious Nogot case is no longer problematic.

One significant problem for the tracking account was proposed in a lecture by Saul Kripke. It goes along the following lines.


S is driving in a region of the countryside where, unbeknownst to her, there are many papier-maché facsimiles of barns (easily mistaken for genuine barns from the roadside—indeed, we may suppose that S has mistaken many of them for barns in the course of her journey).S does not know it but none of the fake barns are painted red. As it happens, S stops in front of a red barn and believes truly (p) that there is a red barn in front of her.

The problem here is that all four conditions obtain. (It is true that there is a red barn in front of her; S believes there is a red barn in front of her, she would not believe that there wasn’t a red barn in front of her if there wasn’t, and she would believe it if there was.) Even with the extra modifications S’s belief that p tracks the truth and is an example of knowledge. What is hard to believe is that S does not know (q) that there is a barn in front of her because condition 3 does not obtain for q – it is quite likely that if she had parked in front of a fake barn she would still believe that q.

How is it possible to know a specific without knowing the generality of which it is a part, namely how can you know that what is in front of you is a red barn, but not know that it is a barn? What Kripke’s Red Barn highlights, as well as a paradox that arises from the denial of closure, is an issue of context.

Context is an issue that is considered to be of particular significance, especially with regard to closure and entailment. Contextualists propose a semantic solution insofar as they argue that what it means ‘to know’ varies in meaning relative to context. A classic example of this is borrowed from Fred Dretske, wherein two people are at the zoo. The first one upon seeing stripy horse like creatures claims to know they are zebras. Quite a reasonable claim to make; they know they’re zebras, however the friend says “So you are sure they’re not just cleverly painted mules?”

Before that question was posed the situation seemed unproblematic; normally knowing that a certain creature is a zebra entails that you already know it’s not a cleverly painted mule. To ascribe knowledge suggests S has exhausted all reasonable alternate possibilities. The problem now is that one is less eager to say our subject knows. In raising alternate possibilities such as deception, we see how S might have believed p even if it were untrue and condition 3 of the tracking account would not obtain. This is similar to the problem of the red barn insofar as knowing you are standing in front of a red barn but not knowing something entailed by that (that it is a barn); the subject knows it’s a zebra but doesn’t know something which that should necessarily entail- that they know it’s not a painted mule.

The standard of justification for knowing you are standing in front of a barn, is higher in a fake barn scenario than it would be in a situation where there are no fake barns. In a zoo where they couldn’t afford real animals it would require a lot more evidence to persuade you that you knew what any given animal really was. The contextualist would argue that saying S ‘knows’ means something different in the dodgy zoo and kosher zoo situations. They argue furthermore that conversational factors affect what it means to say somebody knows. Contextualism, therefore, allows that prior to the question about mules, one can say he knew; but still accept the possibility that he does not know after the question.

For contextualists; ‘Attributor factors…affect how good an epistemic position the putatative knower must be in to count as knowing’ (DeRose, 1992)

When S’s friend raises the possibility of fake zebras, what occurs is a raising of the requirements to attribute knowledge. Duncan Pritchard refers to this as ‘epistemic ascent’; and its reverse, which occurs when one forgets the possibility of a scam and epistemic standards return to normal, ‘epistemic descent’.

Pritchard uses an everyday example to illustrate the problem. In everyday conversation it seems fine to say that S knows p –the table is flat. However when someone raises the possibility that the table is in fact not flat, due to microscopic bumps and irregularities, it becomes nonsensical to maintain that S knows p because with higher epistemic demands, and different context, the statement means something different.

What I hope to have shown is that the tracking account demonstrates that an account of knowledge should require that belief be truth-sensitive (as is shown by the successes with some problem cases) but as shown by the Red Barn example, this is not sufficient. The essential difference between S not knowing they are in front of a barn, yet knowing that they are in front of red barn, is not because of any information they possess.

It is an attributor factor which makes the difference (the attributor’s knowledge about which colour barns could be fake, etc). The context, such as the possibility of there being fake barns or not, is something that knowledge attributions need to be sensitive to. The problem is that this contextualist view is not straightforward to state clearly and precisely in the form of a sufficiency condition for instances of knowing.

Additionally it opens the door to the threat of scepticism once more. In the context of a discussion about Brains in Vats (BIV) the epistemic ascent is such that no knowledge claim becomes justifiable; furthermore it becomes unclear why the reverse should ever occur once some time has passed.

It seems counter-intuitive that S could later make the claim to know that the creatures were not cleverly painted mules without going and checking, just because time had passed since the possibility was raised. Similarly, in the BIV scenario, it seems wrong to lower epistemic standards just because the conversation moves on. As Duncan Pritchard puts it;

‘It seems highly counterintuitive that one should both assert and deny knowledge of the same proposition whilst consciously remaining in the same epistemic position.’ (Pritchard, 2000, pp19)

With this problem of justification for epistemic descent, contextualism is unable to claim to be any more context sensitive than sceptical invariantism, since there is no justification for ever considering the BIV hypothesis to be irrelevant once it has been raised. Ones epistemic position in relation to the possibility goes unchanged.

Issues such as these have led more recent thinkers to argue along different lines, suggesting that justification, (which is still undefined) may simply be a shorthand for what it means to know. Such thinkers reject the justified true belief account. Instead arguing that knowledge simply denotes a certain kind of relation; one between belief and truth, or in the case of Timothy Wiliamson (in Knowledge and its Limits,) go one step further to argue that knowledge is irreducible and whilst it consists of justification, truth and belief, it is itself conceptually unanalyseable, or sui generis. What is interesting about this is that such accounts of knowledge have moved beyond the old formulation of true belief plus something, and are looking at knowledge in new ways.


DeRose, K. (1992) Contextualism and Knowledge Attributions, Philosophy and Phenomenological Research, 52, pp. 1-51

Gettier, E.L. (1963) Is Justified True Belief Knowledge? (available online from accessed 19/11/2008

Nozick, R. (1981) “Knowledge and Scepticism”, extract from Philosophical Explanations. Reprinted in Dancy, J. (ed.) Perceptual Knowledge. Oxford University Press, (1988)

Pritchard, D. (2001) Contextualism, Scepticism and the Problem of Epistemic Descent, Dialectica 35, pp.327-49

Ramachandran, M. How believing can fail to be knowing, Theoria 56 (May, 2006) pp. 185-94

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