Paper published in its final form in the journal Ratio, vol. 23, 2, 2010.

A PERSPECTIVAL DEFINITION OF KNOWLEDGE

Knowledge is not simply justified true belief, but it is justified

true belief justifiably arrived at.

Robert Fogelin

Abstract

In this paper an improved formulation of the classical tripartite view of knowledge is proposed and defended. This formulation makes explicit what is concealed by the symbolic version of the tripartite definition, namely, the perspectival context in which concrete knowledge claims are evaluated. Once we have done this, Gettier’s problem disappears smoothly, without the gratuitous generation of new difficulties.

Analytic philosophers have dissected the classical tripartite view of propositional knowledge as justifiedtruebelief with the following definition:

(i) (ii) (iii)

(Df.k1) aKp ≡ paBpaEBp (where p = proposition,

a = person, B = belief,

E = reasonable justifying

evidence).

It is well-known that this and similar formulationsof the old view have given rise to a challenge to the rationality of our knowledge which isknown as Gettier’s problem: there appear to be counterexamples in which all three conditions of knowledge are satisfied, even though theknowledge claimera has in fact no real knowledge of the proposition p.[1]It is also well-known that counterexamples of the Gettier-type have lead to amultiplicity of answers which have typicallygenerated new difficulties, evensuggesting that the conceptual analysis of knowledge is akind of degenerative research program withoutany good prospect.

Our overall diagnosis of the situation is much more optimistic: the classical view of propositional knowledge, as presented in the formulation above, though not incorrect, is an oversimplification of conceptual structures that have always belonged tothe praxis of our natural language; this formulation conceals a perspectival and potentially dialogical dimension of our knowledge evaluationswhichcan leadto misunderstandings of the Gettierian kind. This diagnosis calls for a therapy which consists inimproving the tripartite definition of knowledge in such a way that it becomes reflexive of thepossibly dialogical dimension of our knowledge evaluations. Once we have achieved this, we will not only have alleviated the symptoms, as most solutions to Gettier’s problem do, but actually cured the disease by treating its real cause. Gettier’s problem will then vanish without a trace, while the analysis of propositional knowledge will achieve its full pragmatic dimension. In order to arrive at these results, we need to begin by reviving an old discussion.

The Internal Link Between the Conditions of Evidence and Truth:

Almeder’s Attempt

A natural way to solve the problem without abandoning or substantially changing the tripartite definition of knowledge was defended in the seventies by Robert Almeder.[2] His solution emerged from the observation that in Gettier’s counterexamples the justifying evidence given by adoes not have anything to do with what makes proposition ptrue, while our epistemic evidence always makesp true.

To clarify this point, consider the following Gettier-type counterexample. Aknowledge claimera believes he sawb stealing a book in the library this afternoon. This is the justification for a’s belief that the statement p is true, namely, ‘b stole a book from the library today’. However, what a really saw wasc, b’s identical twin, stealing a book.Yet statement p is nevertheless true, for b actually was in the library earlier today and also stole a book, even though a did not see him do this. According to the tripartite definition of knowledge, a knows p because all three conditions are satisfied: p is true, a believes that p is true, and a has a reasonable justification for this. However, it is clear that a does not know p.But why is this so? The most intuitive answer seems to be that a’s lack of knowledge is due to the fact that the evidence given by a does not make p true, whichis necessary for a to know p. Therefore, we need to introduce the requirement that the evidence given by a for p must be sufficient for the truth of p, which for Almeder can be expressed in logical terms by saying that adequate epistemic evidence must entailp. As he notes, this requirement appears to be consistent with our linguistic intuitions: it seems odd to deny this with assertions such as: ‘Your evidence (justification) is sufficient for your knowledge of p, but it does not make p true’.[3] Using the sign ‘=>’ for entailment, we can restate the tripartite definition in an extended form which includes Almeder’s requirement:

(i) (ii) (iii)

(Df.k2) aKp ≡ p aBp (aEBp & (E => p)).

The addition of the condition that E must in some sense imply the truth of p should eliminate Gettier’s counterexamples, because in these cases it is only a coincidence that the conditions of truth and of justification are conjunctively satisfied: in none of these cases doesE entail the truth of p.

Unfortunately, Almeder’s proposal has always seemed too strong, making inductive justification impossible,forin these cases the truth of propositionp does not necessarily follow from the truth of the propositionEasserting the justifying evidence,as should occur in the case of entailment.[4]

There is a rejoinder to this kind of solution that has been proposed by W.E. Hoffmann, which poses the problem in a striking way.[5] Compare the following two cases: (i) Having nothing better to do, Jones sits in the lobby of a hotel for some hourswatching some very large people crossing a certain spotcarrying heavy suitcases and then, concluding inductively that the floor at this spot can obviously also support his weight, confidently walks across it. (ii) In the lobby of another hotel, Smith conducts an experiment identical to that of Jones in every detail, except that the floor caves in when he tries to walk across it. Comparing the two cases shows us that sincethe propositionp – ‘The floor will support me’ – and the justifying evidence Eare similar in both cases, and sinceE does not make ptrue in the case of Smith, then E does not entail the truth of p. However, if this reasoning is correct, Almeder’s acceptance of a requirement such as‘E => p’ leads to the conclusion that Jones does not know p too, which is surely false.

The Epistemic Link: Fogelin’s Solution

A more successful attempt to solve Gettier’s problem by relating the conditions of justification and truth was proposed by Robert Fogelin in the nineties. His approach, unlike Almeder’s, already placesthe problem in a dialogical context. According to his view, the justifying evidence given by anyone claiming knowledge must be both a personaljustification and an epistemicjustification. A personal justification is one that satisfies the condition of epistemic responsibility, being consonant with the right epistemic standards and the information available to the person; this is what I called reasonableevidencewhen introducing the tripartite definition. The evidencestated in Gettier’s cases satisfies this requirement. On the other hand, an epistemic justification must also be evidence (a ground, a reason) that establishes the truth of the proposition pforus – which no Gettierian counterexample is able to do. In all of them, Fogelin says, we have‘wider information’ than person a,and because of this we can see that the justification given by a, though personally justified, cannotmake proposition p true, as it fails to satisfy the standard of epistemic justification. As he states:

We are given wider information than a possesses, and in virtue of this wider information see that a’s grounds, though responsibly invoked, do not justify p. I think this double informational setting – this informational mismatch between the evidence a is given and the evidence we are given – lies in the heart of Gettier’s problem.[6]

So, returning tothe counterexample, we see that the evidence given by a, that b stole a book fromthe librarytoday because a saw this, is epistemically inadequate. And the reason for this inadequacy is given by the wider informationthat we have, for we know thatc,b’s identical twin, also stole a book, and that this is what areally saw this afternoon.

According to this view, thecondition of justification in the tripartite definition of propositional knowledge should be split into a condition of personal justification (iii-p) and a condition of epistemic justification (iii-e), and based on this we obtain the following definition of propositional knowledge:

a knows that p ≡ (i) p is true,

(ii) a believes that p is true,

(iii-p) a justifiably came to believe p,

(iii-e) the justifying evidence given bya

establishes the truth of p.

This formulation immunizes the tripartite definition against counterexamples of Gettier’s type because,although they satisfy (iii-p), they do not satisfy (iii-e);hence they are correctly identified as cases that fall short of knowledge.

Although this version of the tripartite definition is intuitively acceptable, as it already reflects the perspectival andoftendialogical dimension of our knowledge evaluations, itstill leaves unsolved the logical problem addressed by Almeder, namely, the question of what kind of logical or internal link exists between conditions (iii-e) and (i), between justifying evidence and truth. If the word ‘establishes’ in (iii-e) means the same thing as ‘entails’, then we are reverting back to the same difficulties.

Next I will develop a more perspicuous symbolic formulation of our epistemic intuition, one that is able to reflect the dialogical context in which mostconcrete knowledge claims are evaluated, as in the case of Fogelin’s solution, but thatalso solves the logical problem defectively addressed by Almeder, enabling us to bypass objections like Hoffmann’s.

Introducing the Dialogic Equivalence

Before reformulating Df.k1it is useful to be more explicit about our dialogicalassumptions. In order to do this,I shall call the concrete person who is evaluating the knowledge claims of a the knowledge evaluators. Usually we speak about s allusively, using personal pronouns such as ‘we’ or ‘us’, as in ‘We are aware that a knows p’ or ‘a’s knowledge of p is known tous’, and the plural form indicates that the evaluation is accepted, or can be expected to be accepted by any reasonable personprovided with the relevant information. This, of course, does not preclude that s = a, wherea intends to evaluate his or her own knowledge claimsin an internalized (non-proper) dialogue. Moreover, we will call ‘tj’ the time of the judgment, which here is the timeat which s evaluatesa’s knowledge claims. Equipped with these concepts, we can add toDf.k1 the following dialogicalequivalence:

(DE) sKtj(aKp) ≡ sKtj(p aBp aEBp)

or (which is the same thing)

sKtj(p)sKtj(aBp)sKtj(aEBp),

What DE says is intuitively clear. Let us suppose for now that the knowledge evaluatoris the teacher s, who asks the schoolgirl a where the city of Angkoris located, and that a answers (correctly) p: ‘Angkoris in Cambodia’. To judge thata knows p, s must know that a knows p, and in order to know this, according to the tripartite definition, s must also know that p is true (that Angkor reallyis in Cambodia), that a believes p to be true (perhaps based ona’s belief-affirmative behaviour),and that a has reasonable evidence for her belief that p is true (ahas presumably found this information in the schoolbook).[7]Bearing in mind this dialogical assumption, my procedure will be to carefully reexamine what exactly is involved in the conditions of truth and justification, searching for the right link between them.

What Might be Dialogically Involved in the Condition of Truth

The condition of truth is usually formulated in the tripartite definition as p, or ‘p is true.’ This formulation completelyleaves aside what makes p true and for whom. However, there is no wayof attributingtruth value to p independently of judging subjects and the ways in which they arrive at this attribution. As the one who decides thatp is true is the person evaluating whether or not a knows p, the condition of truth assumes that p must be true for the knowledge evaluators.

To understand the relevance of what should be an obvious point, let us suppose that p is the proposition ‘The earth circles around the sun’. This propositionwould be considered true by s1, the astronomer Aristarchus, who dared to propose the heliocentric view in the Third Century B.C. However, a well-informed knowledge evaluators2, living in Antiquity or in the Middle Ages (and representing his community of epistemic subjects), would undoubtedly consider pto be false, whiles3, awell informed knowledge evaluatorliving in Europe in the Eighteenth Century (and representing another epistemic community), would again hold pto be true.The evaluation that s2 would make of a knowledge claimofp by person a would unavoidablybe negative,for there can be no knowledge of false propositions, and therefore this evaluation would differ from the evaluations made by s1 and s3,which would depend ondifferent conditions.This is so because the s’sare distinct knowledge evaluators,ascribing a different truth value to p at different times. A definition of knowledge ashumble as Df.k1, suggesting that the truth value of p might be considered independently of the evidence accessible to s, leaves any spatio-temporal variation intruth evaluation, and consequently inknowledge evaluation, totally unaccounted for.This definition does not take into account that what is held to be true or false (and for this reason to be knowledge or lack of knowledge) depends on the changeable standards of a given community of epistemic evaluators.

Nonetheless, one could still ask if what is meant by the condition of truth isn’t the ultimatetruth valueofp, even if it is impossible to ascribetruth value to p independently of a knowledge evaluator and the ways in which he or she comes to know it. The answer is thathere this demandwould lead us to epistemic scepticism, since our empirical truth attributions arealmost always dependent on fallible evidential support. Only God, the infallible evaluator, by knowing the ultimate truth value of any empirical proposition, would be able to apply the tripartite definition of knowledge in order to decide with absolute certainty whether or notp is true and, consequently, whether or nota really knows p. However, this is not what we mean when we say that knowledge is ‘justified true belief’. When we evaluate knowledge claims, we are notappealing to God’s judgment of thetruth value of p, but rather toourown present evaluation of this truth value, which is contextually contingent and based on our finite human cognitive powers.For this reason, what is at stake is the truth valueascribed by s to p and based on the evidential support accessible to s at the time. This truth valueisn’t usually seen as the ultimate one, but rather as a mere candidate for this role, arguably the one with the highest probability.Thereforethe interpretation of ‘p’ as ‘p is true for s’is the only really sound alternative.[8]

After making explicit for whomp must be true, we still need to make explicit what makes p true for s. In order to do this, we must again consider what is involved in the condition of truth as it appears in the DE. This condition appears as sKtj(p) or sKtj(that p is true). Ass is a human epistemic subject, s must come to know that p is true by drawing onevidence (which might beseen as truth-makers,as facts, etc.). Thus, one could expresssKtj(p) more explicitly as sKtj(that there is sufficient evidence to makep true) or as sKtj(that there is at least one piece of evidence E, such that E is sufficient tomakep true).

However, this is not yet a fully explicit presentation of what is involved in the condition of truth as viewed by the knowledge evaluator, since there is more to consider about the role of evidences. To arrive at a more complete account, we need to introduce the concept of a corpus ofevidenceE*, understanding this as a set of pieces of evidence that individually count decisively for or against the truth of a proposition p for somes at a certain time. Here is the definition:

(Df.E*) E* = a set of pieces of evidence, each considered sufficient for

the assignment of a truth value to a proposition p.

This definition means that if a piece of evidence E is an element of the set E*, then E must be sufficient to render p true or to render p false.

It is important to see that a piece of evidence E which belongs to E* can be composed of other pieces of evidence that in themselves are not sufficient for the assignment of truth value to p. The most common form of composition is by conjunction. So, for example, if I am sure that I am sitting in the same chair I sat in yesterday, because it has the same appearance and because it is located in the same place, the conjunction of these two pieces of evidence may be what I find to be sufficient evidence for the truth of the proposition.

In order to deal more precisely with the notion of being sufficient, I will introduce the symbol ‘~>’to represent what might be called ‘sufficiency’, defining it in the following way:

‘’ means that if the antecedentis true, the consequent must either be necessarily true (with a probability of 1 and logical certainty) or be probably true to a very high degree (with a probability near to 1 and practical certainty).

In this way the symbol ‘~>’ respectively captures the force of formal evidence (appropriate forknowledge claims belonging to the formal sciences) and also the force of empirical evidences (appropriate for inductive knowledge claims, such as those belonging to the empirical sciences,where the inference has strong inductive force and the consequent should be seen as practically certain).

Given that E is the case and that E~> p,then either p must be true or p is very probably true; and, given that E is the case and that E ~> ~p, then eitherp must be false or p is very probably false. Considering this, with the concept of E*we could render sKtj(there is at least one piece of evidence E, such that E is sufficient for p),assKtj(there is an E* and E* ~> p), sinceE* is a set displaying individually sufficientpieces of evidence as its elements. We will come to this conclusion shortly, but before this we need to make two explanatory points about E*.

The first point concerns the intuitive basis of the concept of a corpus of evidence for the ascription of truth value, as the following examples show.

Firstly, let us suppose that at time tthe subject s holds as true the proposition p1‘The temperature was below zero last night’, because of the evidence E1 ‘The snow didn’t melt’, and also because of E2, ‘p1 was stated in the weather forecast’. If s considers each of these pieces of evidencesufficient to make p1true, and these are the only two pieces of evidence that s has, then s has a corpus of evidenceE* for p1constituted by the set {E1, E2}. In this case, each of these pieces of evidence will also be considered by s(at this time, on the assumption that his stock of beliefs is true) as making the truth of p1 highly probable, which means that s knowsat time t that ‘E* & (E*~>p)’, which means thatunder these circumstances s knows (or believes he knows) inductively, with practical certainty, that p1 is true.