Chapter Five of LINES OF THOUGHT
A Perspectival Definition of Knowledge
Knowledge
is not simply justified true belief, but it is justified true belief
justifiably arrived at.
—Robert Fogelin
Analytic
philosophers have disassembled the classical tripartite view of propositional
knowledge as justified true belief into its components in
the following definition:
(i) (ii) (iii)
(Df.k1) aKp ≡ p & aBp & aEBp
(where p = proposition, a = person, B = belief, E = reasonable justifying evidence).
It is well-known that this and similar formulations of the old view
have given rise to a challenge to the rationality of our knowledge called
Gettier’s problem: There appear to be counterexamples in which all three
conditions of knowledge are satisfied, even though the knowledge claimer a has
in fact no real knowledge of the proposition p.[1] It is also well-known
that counterexamples of the Gettier type have led to a multiplicity of answers
which have typically generated new difficulties. They even suggest that the
conceptual analysis of knowledge is a kind of degenerative research program
lacking any good prospects of success.[2]
Our overall diagnosis of the situation is much more optimistic: The
classical view of propositional knowledge, as presented in the formulation
above, is not wrong, but it nonetheless oversimplifies conceptual structures
that have always belonged to the praxis of our natural language. This
formulation conceals a perspectival and potentially dialogical dimension of our knowledge evaluations that can
lead to misunderstandings of the Gettierian type. This diagnosis calls
for a therapy that consists in improving the tripartite definition of knowledge
in such a way that it becomes reflexive of the possibly 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 underlying causes. Gettier’s problem
will then vanish without a trace, while the analysis of propositional knowledge
will achieve its full pragmatic dimensions. In order to arrive at these
results, we need to begin by reviving an old discussion.
Internal Link between the Conditions of Evidence
and Truth: Almeder’s Attempt
A sensible way to solve the problem without abandoning
or substantially changing the tripartite definition of knowledge was advocated
by Robert Almeder in the seventies.[3] His solution emerged from
the observation that in Gettier’s counterexamples the justifying evidence given
by a does not have anything to do with what makes proposition p true,
while our epistemic evidence always makes p true.
To clarify this
point, consider the following Gettier-type counterexample: A knowledge claimer a believes he
saw b 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’. In fact, what a really
saw was c, 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. It is nonetheless 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, which is 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 entail
p. 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’.[4] Using the sign ‘=>’
for entailment, we can restate the tripartite definition in an extended form
that includes Almeder’s requirement:
(i) (ii) (iii)
(Df.k2) aKp ≡ p & aBp & (aEBp &
(E => p)).
Adding the condition that E must in some sense imply the truth
of p should eliminate Gettier’s counterexamples. In these cases, it is
only a coincidence that the conditions of truth and justification are
conjunctively satisfied: in none of these cases does E actually entail
the truth of p.
Unfortunately, Almeder’s proposal has always seemed too strong, making
inductive justification impossible. For in these cases the truth of proposition
p does not necessarily follow from the truth of proposition E,
which states the justifying evidence, as should be the case with entailment.[5]
There is a rejoinder to this kind of solution that has been proposed by
W. E. Hoffmann, who restates the problem in a striking way.[6] Compare the following two
cases: (i) Having nothing better to do, Jones sits in a hotel lobby for some
hours watching some very large people crossing a certain spot carrying heavy
suitcases. Then, concluding inductively that the floor at this spot can
obviously also support his weight, he 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 since proposition p – ‘The
floor will support me’ – and the justifying evidence E are similar in
both cases, and since E does not make p true 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 also does not know p, which
is surely false.
Epistemic Link: Fogelin’s Solution
In the nineties, Robert Fogelin offered a more
convincing solution to Gettier’s problem by relating the conditions of
justification and truth. His approach, unlike Almeder’s, already places the
problem in a dialogical context. According to his view, the justifying evidence
given by anyone claiming knowledge must provide both a personal justification
and an epistemic justification. 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. When
introducing the tripartite definition, I called this reasonable evidence.
The evidence stated 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 proposition p for us – which no Gettierian
counterexample is able to do. In all of the Getterian cases, Fogelin claims, we
have ‘wider information’ than person a, and because of this we can see
that the justification given by a, although personally justified, cannot
make 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.[7]
So, returning to the counterexample, we see that the
evidence given by a, that a knows b stole a book from the
library today because he saw this happen, is epistemically inadequate. And the
reason for this inadequacy is given by our wider information, for we know that c,
b’s identical twin, also stole a book, and that this is what a
really saw this afternoon.
According to this view, the condition 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 by a
establishes the truth of p.
This formulation immunizes the tripartite definition
against counterexamples of Gettier’s type, because while 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
and often dialogical dimension of our knowledge evaluations, it still leaves
unsolved the logical problem addressed by Almeder, namely, the question of the
kind of logical or internal linkage that 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. It reflects the
dialogical context in which most concrete knowledge claims are evaluated, as in
the case of Fogelin’s solution, but it also solves the logical problem
inadequately addressed by Almeder, enabling us to bypass objections like
Hoffmann’s.
Introducing Dialogical Equivalence
Before
reformulating Df.k1, it is useful to be more explicit about our dialogical
assumptions. For this purpose, I shall call the concrete person who evaluates a’s
knowledge claims the knowledge evaluator s. 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 to us’. The plural form indicates that the evaluation would be
accepted, or that we think it would be accepted, by any reasonable person
possessing the relevant information. This, of course, does not preclude that s
= a, where a intends to evaluate his or her own knowledge
claims in an internalized (non-proper) dialogue. Moreover, we will call ‘t’
the time of the judgment, which here is the time at which s evaluates
a’s knowledge claims. Equipped with these concepts, we can add to Df.k1
the following dialogical equivalence:
(DE) sKt(aKp) ≡sKt(p & aBp &
aEBp)
or
(which is the same thing)
sKt(p)
& sKt(aBp) & sKt(aEBp),
What
DE says is intuitively clear. Let us suppose, for example, that the knowledge
evaluator is the teacher s, who asks the schoolgirl a where the
city of Angkor is located, and that a (correctly) answers p:
‘Angkor is in Cambodia’. To judge that a 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 really is
in Cambodia), that a believes p to be true (perhaps based on a’s
belief-affirmative behavior), and that a has reasonable evidence
for her belief that p is true (a has presumably found this
information in a reference book).[8]
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 links 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 completely leaves aside what
makes p true and for whom. However, there is no way of
attributing truth-value to p independently of judging subjects and the
ways in which they arrive at this attribution. As the one who decides that p
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 evaluator s.
To understand the relevance of what should be an
obvious point, let us suppose that p is the proposition ‘The Earth
orbits the sun’. This proposition would have been considered true by s1,
the Greek astronomer Aristarchus, who proposed the heliocentric view in the
Third Century BC. However, a well-informed knowledge evaluator s2, such
as an Inquisitor judging Galileo’s astronomical conclusions in 1633 (and
representing his community of epistemic subjects), would undoubtedly consider p
to be false, while s3, a well-informed knowledge evaluator living in
Eighteenth Century Europe (and representing another epistemic community), would
again hold p to be true. The evaluation that s2 would make of a
knowledge claim of p by person a would unavoidably be negative, for
there can be no knowledge of false propositions. Therefore, this evaluation
would differ from the evaluations made by s1 and s3, which would
depend on different conditions. This is so
because s1 and s3 are distinct knowledge evaluators, ascribing a
different truth-value to p at different times. A definition of knowledge
as humble as Df.k1, suggesting that the truth-value of p might be
considered independently of the evidence accessible to s, gives no
account of any spatio-temporal variation in truth evaluation, and consequently
in knowledge evaluation. This definition does not take into account the fact
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 ultimate truth-value of p, even if it is
impossible to ascribe truth-value to p independently of a knowledge
evaluator and the ways in which he or she comes to know it. The answer is that
here this demand would lead us to epistemic skepticism, since our empirical
truth attributions are almost 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 not p is
true and, consequently, whether or not a 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 not appealing to God’s judgment of
the truth-value of p, but rather to our own 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-value ascribed by s to p and based on the evidential
support accessible to s at the time. This truth-value isn’t usually
regarded as the ultimate one, but rather as a mere candidate for this
status, arguably the one with the highest probability. Therefore, the
interpretation of ‘p’ as ‘p is true for s’ is the only
really sound alternative.[9]
After making explicit for whom p 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 sKt(p) or sKt(that
p is true). As s is a human epistemic subject, s must come
to know that p is true by drawing on evidence (which might be
regarded as truth-makers, as facts, etc.). Thus, one could express sKt(p)
more explicitly as sKt(that there is sufficient evidence to make p true)
or as sKt(that there is at least one piece of evidence E, such
that E is sufficient to make p true).
However, this is still not a fully explicit representation 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 evidence. To arrive at a more
complete account, we need to introduce the concept of a corpus of evidence
E*, understanding this as a set of pieces of evidence that individually
count decisively for or against the truth of a proposition p for some s
at some point in time t. Here is the definition:
(Df. E*) E* = a set of pieces of
evidence, each considered sufficient for the assignment of 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. Thus, 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 we might call
‘sufficiency’, defining it in the following way:
‘p ~> q' means that if the antecedent p is true, the consequent q must either be necessarily true (with a probability of 1 and logical certainty)
or probably true to a very high degree (with a probability near 1 and
practical certainty).
In
this way, the symbol ‘~>’ respectively captures the force of formal
evidence (appropriate for
knowledge claims belonging to the formal sciences), and also the force of empirical
evidence (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 either p must
be false or p is very probably false. Considering this, with the concept
of E* we could render sKt(there is at least one piece of evidence
E, such that E is sufficient for p) as sKt(there is
an E* and E* ~> p), since E* is a set displaying
individually sufficient pieces 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 t the 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 evidence sufficient to make p1 true, and these
are the only two pieces of evidence that s has, then s has a
corpus of evidence E* for p1 constituted 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. This means that s knows at
time t that ‘E* & (E* ~> p)’, which means
that under these circumstances s knows (or believes he knows)
inductively, with practical certainty, that p1 is true.
Now let us assume that at time t a subject s believes in
the falsity of p2, a proposition stating that the Earth is flat, based
on at least one of the following pieces of evidence: E1 = ‘Photos taken
from space show that the Earth is round’; E2 = ‘There are many
historical accounts of the circumnavigation of the globe’; and E3 =
‘Ships seem to sink below the horizon when they sail out of view’. In this
case, for s ‘E* = {E1, E2, E3… En}’,
and each of these pieces of evidence is considered by s at t –
assuming the truth of his stock of beliefs at time t – to be sufficient
to falsify the proposition p2. This means that s knows (or
believes he knows) at time t that ‘E* & (E* ~> ~p2)’,
namely, that the probability of ~p2 being true is very high or that p2
is certainly false.
A third case is that in which s doesn’t know the truth-value of
the proposition. For example: Suppose that s doesn’t know whether the
proposition p3, ‘Aston Rowant is larger than Kingston Blount’, is true.
In this case, s’s corpus of evidence for p3 is
empty: E* = Ø.
Referring back to Df.E*, we conclude that a subject s can
access E* in three different ways:
(1) s does not attribute any truth-value to p;
in this case E* is seen by s as an empty set;
(2) s has cognitive
access to a non-empty set E* of justifications,
while (2) splits into two possibilities:
(2a) Each element of the set, each piece of evidence, is considered by s
as sufficient to make p true; in this case it is clear that s knows
that ‘E* & (E* ~> p)’, which means (deductively or
inductively) that s knows that p is true.
(2b) Each element of the set, each piece of evidence, is considered by s
as sufficient to make p false; in this case s knows that ‘E*
& (E* ~> ~p)’, which means (deductively or
inductively) that s knows that p is false.
One
could ask if there might be a further possibility, namely:
(2ab) E* contains at least one piece of evidence sufficient to
make p true and at least one piece of evidence sufficient to make p false.
However,
this would not be a real epistemic alternative. As E* is defined as a
set of individually sufficient conditions, in this case E* turns out to
be an inconsistent set, making p and ~p simultaneously
true for s at a certain point in time. We are often irrational in
our judgments, holding inconsistent beliefs, but insofar as we regard ourselves
as epistemic subjects, we are supposed to be rationally consistent. This means
that we should consider a single piece of evidence as sufficient for the truth
of a proposition p only when we do not possess any other evidence that
we consider sufficient to make p false, and vice versa. Assuming
the rationality of s’s judgment, the elements of E*, when
obtainable, must all be evidence for either the truth of p or its
falsity, but not for both.
The second point about Df.E* concerns a better understanding of
the concept of sufficiency expressed by the symbol ‘~>’. As was shown above,
this symbol must be understood as representing either something like a material
implication, in the case of formal evidence, or a strong inductive relation, in
the case of the usual empirical evidence. It is important to see not only that
‘E* ~> p’ must be true for s at a certain point
in time, so that when combined with E* it allows s to conclude
that p is true, but also that this conditional only works under the
assumption of the truth of the background beliefs and other relevant beliefs
belonging to the stock of beliefs held by s at this time, being insofar context-dependent.[10] To make this point
clear, let us consider the following cases of conditionals where the truth of
the antecedent is viewed by a subject s at a given time as sufficient
for the truth of the consequent:
(i) If my car’s gas tank is full, then there is
sufficient gasoline for my trip.
(ii) If the defendant’s fingerprints are found
at the scene of the crime, then we will have enough proof that he is
guilty.
(iii)
If
this is the result of the biopsy, then the surgeon can be sure that the
tumor is malignant.
In
all three cases, it is possible that the antecedent is true but the consequent
is nevertheless false. Let us suppose that the car’s gas tank has a leak, that
the fingerprints were planted, that the tumor is a benign one of an unknown
kind, indistinguishable in its histology from a malignant tumor. In all these
cases, the consequent will be false, although the antecedent remains true, which
would make the three conditionals false. Is this a threat to our understanding
of ‘being sufficient’? Certainly not, because in all three cases, if s becomes
aware of the facts that the gas tank has a leak, the fingerprints were planted…
then some of the beliefs belonging to s’s stock of beliefs will change,
which would on this basis lead him to disclaim his acceptance of the
conditionals. On the other hand, under the assumption that all the other
relevant beliefs held by s (such as the belief that his car’s gas tank
does not have a leak, that the fingerprints were not planted, that this is not
a new kind of tumor…) are consistent with the conditionals, it follows that if
the antecedent is true, the consequent should very probably also be true.
Hence, it seems that the sign ‘~>’ gives s enough of a sense of
‘being sufficient’ or ‘being enough’ or ‘making true’, insofar as he interprets
it as making its consequent true with a very high probability, assuming the
truth of the relevant beliefs belonging to the stock of beliefs held by s at
the time of his evaluation.
Now that we have explained our concept of E*, it is time to
return to our task of restating sKt(p) in a precise and fully
explicit way. We have seen that sKt(p) can be rendered as sKt(there
is at least one piece of evidence E, such that E is sufficient
for the truth of p), where only the evidence and its rule were
mentioned. Now, using E* we can restate what is contextually assumed in
the condition of truth as it appears in the DE as:
(i’) sKt(E* & (E* ~> p)).
Indeed,
when s is aware of an E* at t, and when for him E*
has some element viewed as sufficient for the truth of p, then s
concludes either deductively (using the modus ponens) or
inductively (using the rules of induction) that p must be true. This
amounts to saying that it satisfies the conditions of truth! In this way, ‘E*
& (E* ~> p)’ only makes explicit what we (as
placeholders for s) implicitly mean by ‘p’ or ‘p is true’
in the condition of truth. As we will see, this analysis will suffice as a
restatement of what the conditions of truth presuppose, and it has the
advantage that it does not play down the role of the knowledge evaluator.
What Might Be Dialogically Involved in the
Condition
of Justification
What
about the condition of justification? Our proposal is to use a similar strategy
for its reconstruction. We must keep in mind the intuitive idea that the
justifying evidence given by a must in some way make p true
(which was misleadingly expressed by ‘aEBp & (E => p)’
in Df.k2), and also our perspectival analysis of the condition of truth. When
could E be sufficient for the truth of p, considering that what
is involved in the condition of truth might be rendered as ‘sKt(E* &
(E* ~> p))’? The answer is obvious: When the evidence E given
by a can be seen by s as belonging to E*! For if E
E*, and p is viewed by s as true, and if s is
reasonable, this means that all the elements of E* (E inclusive)
are viewed as making p true. To do justice to our intuition that E must
establish the truth of p in the context of the DE, we are led to
introduce what might be called a requirement of epistemic
adequacy for E, which can be stated as follows:
REA: The evidence E given by a for the truth of p
is considered epistemically adequate (and not just reasonable) iff the
evidence E comes to be regarded by s as belonging to his E*
when s evaluates a’s knowledge claim for p, insofar as E*
is held by s to make p true.
In
other words, REA requires that given the circumstances in which for s ‘(E
~> p) & (E E*)’ it should also be the case
that for s E makes p true under the assumption of
the truth of his stock of beliefs at time t. This is an assumption that
must be taken into consideration, since the content of the E* accepted
by s, as we have already seen, might easily change.
It is easy to assimilate REA into the analyzed form of DE. As we have
already adopted E* ~> p as part of the condition of truth, the
only thing we need to do is to add to aEbp, the condition that E
must belong to the evidence set E* which is accepted by s when
s evaluates a’s knowledge claim. In other words: instead of
Almeder’s condition E => p of Df.k2, which wrongly suggests
that E makes p true necessarily and in all contexts, what must
really be required is that for s at t, E E* and E* ~>
p. Therefore, what is assumed by the condition of justification in a
dialogical context of knowledge evaluation can be made sufficiently explicit as
follows:
(iii’) sKt(aEBp & (E E*)).
Accepting the reformulated conditions (iii’) and (i’), REA turns out to
be part of the DE, for which REA can be abbreviated as ‘(E E*)
& (E* ~> p)’, which already belongs to the conjunction of
the conditions (iii’) and (i’).
DE’ and the Perspectival Definition of Knowledge
The
next step is to improve DE, by substituting (i’) for (i) and (iii’) for (iii),
as follows:
DE’:(i’) (ii)(iii’)
sKt(aKp) ≡ sKt((E*
& (E* ~> p)) & aBp & (aEBp & (E
E*)))
DE’
clearly displays the logical or internal link between the conditions of
justification and truth, as shown by the arrows.[11] We are now able to give
expression to the perspectival and often dialogically reflexive formulation of
the tripartite definition of knowledge, insofar as we cancel sKt on both
sides of the equivalence as redundant, even if it is presupposed. Here is the definition:
(i) (ii)(iii)
(Df.k3)aKp ≡ (E*
& (E* ~> p)) & aBp & (aEBp & (E
E*)).
This
is, I believe, the view of knowledge as justified true belief with its ‘missing
link’ relating conditions (iii) and (i). This definition may be somewhat
simplified. Since condition (ii) is already included in aEBp, we can
eschew it as redundant, formulating Df.k3 as:
(Df.k4)aKp ≡ aEBp & (E E*)
& E* & (E* ~> p)
By
means of these two formulas, knowledge is explicitly defined in a way that
reflects the epistemic perspective of the knowledge evaluators. The decisive
point for this definition is that it shows the correct internal link between
the justifying evidence E and the truth of p. The evidence E must
be sufficient for the truth of p, but in a contextually dependent way,
by means of its acceptance by person s as belonging to the set of given
evidence able to make p true under the assumption of the truth of other
beliefs belonging to his stock of beliefs at the time of his evaluation. But
would this definition solve our problems? To answer this question we first need
to see how it works.
Ordinary Cases of Applying the Definition
We
begin with the most common and unproblematic case. Suppose, for our first
example, that the knowledge claimer a states p, namely that
the temperature was below zero last night. I ask a how she knows that.
Her answer is E1: she has seen that the snow did not melt during the
night. In this standard case I am knowledge evaluator s, and I have the
evidence set E*, which, for example, consists of E1: ‘I saw that
the snow did not melt’ and E2: ‘I heard it on the weather report’. Thus,
my E* is made up of {E1, E2}, and because a
believes in the justification E1, which I accept as belonging to my E*,
and which at the time of my evaluation makes p true for me, I conclude
that a knows p.
Not all cases are so straightforward. There are others in which s
accepts a’s knowledge claim by expanding his E* in order
to include the evidence E in E* because of its coherence with
s’s previous beliefs. Imagine that I am s and
that person a tells me that she knows p: ‘Oxford is larger than
Whitney’, because of E1, namely, because she has heard this from a
tourist guide. Let us suppose that I know this for reason E2: ‘I have
spent some time in both towns’. Although her justification does not belong to
my E* for the truth of p, it is natural for me to expand my E*
in order to accept her justification (for if I hold E2 to be true,
assuming my stock of beliefs, which includes my belief in the trustworthiness
of a and of tourist guides, it follows that E1 also turns out to
be true for me). Thus, for me E* turns out to be {E1, E2},
both justifications making p true at the time of my evaluation, and from
this I conclude that a also knows p.
There are also examples showing that epistemic evaluation is very
dependent on the time at which s makes his evaluation. Let us
suppose that in a jury trial juror a concludes that b has
committed a murder, basing his conclusion solely on the sufficient evidence
given by E, which is the result of a DNA test... At time t1
judge s concludes that a knows that b is the murderer,
confidently including E in his E*. A few days later, at time t2,
it becomes known that the DNA test was performed incorrectly, which invalidates
the results. Nevertheless, new information, including b’s confession,
proves beyond any doubt that b was in fact the murderer. Aware of this,
the judge could not persist in his belief that juror a knew p
at t1, even by accepting the truth of p, for at t2 E has
ceased to belong to s’s E*. Indeed, judge s makes a new
evaluation with the expectation that juror a will accept p based
on evidence belonging to his present E*. Because the time at which
knowledge claims are evaluated is essential to the construction of E* by
s, the perspectival definition of knowledge explains spatio-temporal
variations in knowledge evaluations left unexplained by the usual formulations
of the tripartite definition.
Another important point is that by making knowledge claims relative to
the changeable belief stocks of knowledge evaluators, we are not compromising
ourselves with any relativist view concerning truth or knowledge. This
is show by the fact that the two opposite evaluations of the same knowledge
claim by judge s are asymmetrical: the old evaluation would be rejected
by any other rational evaluators possessing the new information. Most of our
perspectival and changeable epistemic evaluations are not incommensurable.
However, it is not the task of a theory of truth evaluation to explain the
structure of such variants, but rather that of a theory of verisimilitude or
truth approximation employing some normative concept of ultimate truth.
Finally, it is noteworthy to mention that sometimes the Df.k3 (or
Df.k4) seems to collapse into Df.k1. This is what occurs when we ask ourselves
whether we know something at the present moment. For
example: I wish to evaluate my present knowledge claim of p: ‘The
air-conditioning is on’. According to the traditional definition, I know p
because it is true that the air-conditioning is on and because I have
reasonable evidence for my belief, namely, the continuous humming sounds I
hear. According to the perspectival definition, I know this because I have
evidence E, namely, I can hear the sound of the air conditioner, and
because this evidence belongs to my presently accepted evidence set E*,
which makes p true. In this case, however, not only are s = a
and E = E*, but even the time of evaluation is the same (namely,
the present moment). It seems that here Df.k3 presupposes the identity DE’ in a
trivial way. But this does not necessarily render the application of our
definition superfluous, for it seems to require at least a meta-cognitive
awareness of s as a, and of E as E*.
Some Unusual Cases: Gettier-Type Counterexamples
Arriving
finally at Gettier’s problem, it is not hard to understand why the proposed
analysis of the intuitive view disposes of this problem once and for all. By
assimilating REA into the formulation of the conditions of truth and
justification, the perspectival definition of knowledge brings to light the
real internal link between these two conditions. This internal link has
sufficient strength to neutralize all Gettierian counterexamples, since they
all arise from its absence, and at the same time it is sufficiently
flexible to circumvent objections such as Hoffman’s. In order to show this, we
must first adjust our eyes to the bright new light outside the cave of
Gettierian shadows, reconsidering some of these counterexamples.
Consider the following well-known Gettierian counterexample[12]: person b is an
employee in a’s office, and not only does a see b coming
to work in a BMW, b has also told a that the car belongs to him
and has even shown him his ownership documents. Based on this evidence E,
a makes the knowledge claim p: ‘Someone in my office owns a BMW’.
However, b has lied to a: the BMW actually belongs to his sister, the ownership
documents are forgeries, etc. However, p is still true, for without a’s
knowledge, another employee in his office, c, really does own a BMW.
Under such circumstances, it is obvious that a does not know p,
since there is no relationship between the truth of p and the evidence
given by a. However, according to the tripartite formulation of the
classical definition, a must know p, because (i) it is true that
someone in a’s office owns a BMW; (ii) a believes that p
is true; and (iii) a is able to offer the very reasonable evidence E
for the truth of p.
However, this is no counterexample to our dialogically conditioned
definition of propositional knowledge, for it is not able to satisfy it. To
make this clear, we need to follow the strategy of always viewing the supposed counterexamples
contextually, considering the whole of the concrete dialogical situation in
which a knowledge claim is evaluated by s, with all the relevant
independent information available to him. These counterexamples need to be
considered not just in their abbreviated form, like the examples used in books
on epistemology, but as fully concrete cases, similar to ones that could be
found in real life. In the case of the counterexample above, the question is:
How do we know all these facts about the employee in the office? Well…
let us suppose that, when considering who belongs to this elusive ‘we’, we are
led to a judging subject s, an older employee in the office who knows
all his colleagues very well and has told us this Gettierian story. He knows
that c owns an old BMW, and he also knows that b is a compulsive
liar who drives his sister’s BMW, pretending that it belongs to him. If a had
justified p by saying that c had told him this, giving him in
this way the evidence E1, s would judge that a knows p,
because s accepts this justifying evidence as belonging to his E*,
and because he thinks that on the basis of all he knows, this E* ~> p.
But taking into account that a justifies his claim to know p by
giving the evidence E that b has told him, s refuses to
accept this justification as an element of his E*. The knowledge claim
made by a is rejected by s because E E*, failing
to satisfy REA.
Now let us suppose that a justifies p by giving the true
evidence E2: ‘An employee in my office told me that he owns a BMW’.
Although this justifying evidence is true, it does not satisfy Df.k3 for s,
because in this case, anticipating that b and not c might be the
employee who reported this, s does not immediately accept E2 as
belonging to E*, asking a who told him p, which
brings him to the same result as before. A possible objection here would be
that a knowledge evaluator s might not be so well-informed, judging
falsely that a knows p… But in this case, we would need to
consider another well-informed knowledge evaluator in order to explain our
awareness of the fact that b is lying and that only c really owns
a BMW. Otherwise, how could this Gettierian story be grounded? The rejection of
a knowledge claim turns out to be unavoidable every time we replace the usually
abbreviated reports of Gettierian cases with a sufficiently detailed
explanation of how the evaluation of the knowledge claim was originated.
A second counterexample of the Gettierian type is based on perceptual
evidence.[13] Imagine that a is
a motorist who, glancing out of her car window, thinks she knows the truth of p:
‘There is a red barn in the field’. However, it is only by chance that what she
sees is a real red barn – for with the exception of this one, all the red barns
in the vicinity are really only façades that suggest red barns convincingly
enough to fool even the most observant traveler. Although a satisfies
the conditions of justified true belief as stated in the standard definition,
she does not satisfy these conditions as given in its dialogically conditioned
form. For in this form we need to consider the reasons for belief in the truth
of p, which always arises from a knowledge evaluator’s point of view. To
see whether the example satisfies our definition in a real case, we need to
consider the source of all this information! Here is a plausible story: we are
only reporting what the knowledge evaluator s has told us. This person
lives in the region and is well aware that all the red barns, with the
exception of this particular barn, are only barn façades… Motorist a has
given s a lift. As a drives away from a river, she directs s’s attention to a picturesque red barn she has noticed in a field.
Since s knows that this is the only authentic red barn and that a is
only a visitor, s would not think that a really knows
that she is seeing a real
barn, as here the evidence E – which can be formulated as ‘I see
something like a red barn’ – does not belong to s’s E*. The only
evidence s would accept as belonging to E* would be a close inspection
of the barn by a, or a’s telling him that she already
knows about the façades and this one real exception, which is located after the
bridge. Such justifications would be accepted as belonging to or being implied
by his E*, and therefore as being sufficient to support the truth of p.
As the justification given by a was only that she had seen a red barn, s
concluded that a had said the truth only by chance, and that her merely
Gettierian justification does not belong to E*.
We can also consider a Gettierian counterexample that involves
self-evaluation, the interiorized form of dialogical evaluation. Let us suppose
that a looks at her watch and it indicates that the time is 11:15.[14] At this moment, a believes
that she knows p, namely, that it is 11:15. After this, a looks
at the clock on the church tower in the square, which indicates that it is
indeed 11:15. Then, however, a remembers that yesterday her watch was
running slow. Therefore, a examines her watch carefully and concludes
that its hands are not moving, and the watch had probably stopped the night
before. At this point, a realizes that she did not really know that it
was 11:15. the first time she looked at her watch: it was all just an amazing
coincidence. Here again, the three conditions for the standard version of the
classical definition are satisfied: p is true, a believes that p
is true, and a has a reasonable justification for her belief. But
for our improved statement of the classical view, a’s knowledge claim is
being evaluated in an internalized dialogical context by a knowledge
evaluator a’ (s = a’), who is the same a’ after she
realizes that her watch is not working. At this moment, the E* consists
in the evidence E1, given by the church clock, while the evidence E
which was given by a, that her watch indicates a time of 11:15, cannot
be accepted as belonging to the E* of knowledge evaluator a’. Once
again, no knowledge is acquired, as at the time the knowledge claim is
evaluated, E E*, leaving REA unsatisfied.
A nearly Gettierian counterexample is the following[15]: a reads in a
newspaper p: ‘The famous civil rights leader M. L. has been assassinated’,
which is based on E: an eyewitness report. Those close to a have
additional information from later reports that contradict this claim. However, p
is in fact true, since the later reports are false and were fabricated by
eyewitnesses. Df.k3 allows an improved answer to this: if s is someone
close to a, the additional information will make him reject E.
But if s also knows about the eyewitnesses’ conspiracy, s will
agree with a, for a’s E belongs to s’s E*,
and to fail to receive false information is no epistemic sin.
Indeed, it seems impossible to construct a Gettierian counterexample
that cannot be met by a sufficiently thorough application of the perspectival
definition of knowledge, since these counterexamples all suffer from a
detachment between reasonable evidence and truth.
Inductive Evidence and Defeasibility
Unlike
the old solutions, the perspectival understanding of the link between epistemic
evidence and truth allows us to deal satisfactorily with the problem of
inductive evidence. The given empirical evidence E must be seen by s
(and certainly also by a), as sufficient for the truth of p, that
is, as making p true with practical certainty. Moreover, this inductive
evidence belongs to a more complex inductive framework, for the empirical
evidence is viewed as being sufficient for the truth of p only on the
assumption of background information and other relevant beliefs belonging to
the whole stock of beliefs held by s at t, and for this reason it
is always susceptible to revision. That is: a change in a stock of
beliefs brought about by new experience and information can always undermine
evidential support, which fully conforms to what we expect from inductive
inferences.
We can illustrate the latter insights by answering Hoffman’s objection
that when we hold Df.k2, which requires that E => p, we must
accept that Jones does not have knowledge that the hotel lobby floor can
support him, since his evidence E, being fallible, does not entail the
truth of p. However, as we saw in the perspectival reformulation of the
tripartite definition, the link between the conditions of evidence and truth
should be expressed by a context-dependent inductive relation in which E ~>
p or not, depending only on whether E is accepted by the
knowledge evaluator at the time of his evaluation of a’s knowledge claim
as belonging to his E*, assuming that E* ~> p. In the
case of Jones, the knowledge evaluator s, being certain that the floor
could bear Jones’ weight, accepts his evidence E as being sufficient for
the truth of p, accepting that E E*, and that E* makes
p true, which is confirmed by his safely walking across the spot. Before
Smith’s accident the knowledge evaluator can conclude that both Jones and Smith
know p, as this conclusion is in conformity with his E* at the
time. But after the accident, because s already knows that the floor
could not support Smith’s weight, s drops his belief that the evidence E
given by Smith is sufficient for the truth of p, for at this point in
time he is aware that E E* such that E* ~> p,
having changed his assumptions about what evidence is sufficient for p.
However, s finds no reason to drop his view that Jones knows p.
The perspectival definition is flexible enough to overcome the possible
objection that the establishment of the truth of p by the evidence E
is too stringent a requirement, for it makes the inductive relation relative to
the context of evaluation of particular knowledge claims.
Finally, the perspectival definition of knowledge also allows us to
find a better place for the condition that epistemically adequate evidence must
remain ultimately indefeasible. When appended to a modest form of
the tripartite definition like Df.k1, the condition that the justifying
evidence must remain ultimately indefeasible imposes a much too heavy burden on
knowledge claimers, namely, that they must know the totality of
truths, for this is the only way to warrant that the given evidence is
truly indefeasible. The problem with this conclusion is that it leads to
skepticism, since no human epistemic subject can have access to the totality of
truths. However, this condition makes sense again when transformed into a
requirement that must necessarily be satisfied by each piece of evidence E given
by a in order to be accepted as belonging to E*. This requirement
(which is already implicit in Df.k3) states that E must remain
ultimately indefeasible by the totality of beliefs held by s at the time
of his evaluation, which is reasonable enough.
[1] Edmund L. Gettier, ‘Is Justified Belief Knowledge?’ Analysis,
23 (1963), pp. 121-123.
[2] Timothy Williamson: Knowledge and its Limits (Oxford: Oxford University Press, 2000).
[3] R. F. Almeder, ‘Truth and Evidence’, Philosophical
Quarterly, 24 (1974), pp. 365-68.
[4] R. F. Almeder, Blind Realism: An Essay on Human
Knowledge and Natural Science (Lanham, MD: Rowman & Littlefield, 1992),
p. 8.
[5] See, for example, G. S. Pappas and Marshall Swain on
regarding justification as entailing truth: ‘If the contention under question
were correct, then it appears that many inductive justifications would simply
not qualify as justifications at all, and this surely flies in the face
of accepted views about justification’. G. S. Pappas and M. Swain (eds.), Essays
on Knowledge and Justification (Ithaca, NY: Cornell University Press,
1978), p. 13.
[6] W. E. Hoffmann, ‘Almeder on Truth and Evidence’, Philosophical
Quarterly, 25 (1975), pp. 59-61.
[7] Robert Fogelin, Pyrrhonian Reflections on Knowledge
and Justification (Oxford: Oxford University Press, 1994), pp. 22-23.
[8] Knowledge evaluators must always assume previous
knowledge. This brings into play the danger of infinite regresses, e.g., ‘…sKsK(aKp)’
or ‘…sKsKp’. However, s can easily take the place of a in
further evaluations. Moreover, in cases like sK(aKp) and sKp,
where there is no possible distinction between evidence for truth and
justifying evidence, further evaluation turns out to be pointless (the step
needed to take the step beyond is a reason that is lacking).
[9] A common supposition is that our truth attributions
match the ultimate truth-values, and it seems that in this respect we can
compare our attempts using a normative ideal of ultimate truth.
However, this normative ideal is not what is at stake in our knowledge
evaluation.
[10] It is interesting to see that similar constraints can
be found in the more sophisticated views on hypothetical-deductive confirmation
in science, as they also deal with cases of inductive evidential support.
[11] I am assuming that empirical epistemic justification
should usually lead, if not to logical truth, at least to a highly probable
truth and, consequently, to a firm kind of belief, a practical certainty. There
are arguments against this. The most interesting for us at this point is the
lottery paradox, according to which a gambler has a very strong justification
for the truth of the assertion that he will not win, but does not know that he
will not win, because in this case he would not make any bets. The answer to
this seems to lie in the statistical, non-Humean nature of the inductive
inference involved. Using Humean inductive inferences, probability cannot be
determined by mathematical methods, as they rely solely on the uniformity of
nature. For this reason, the high probability achieved by most epistemic
justifications does not need to be that of logical truth. That is why I can say
that I know that the sun will rise tomorrow, even if I cannot attribute
a probability of 1 to this. But the probability of winning in a lottery can be
calculated a priori (for example, if there are 10,000 tickets, then any
one ticket has only a 0.0001 chance of winning). I suggest that the fact that
this is a statistically inductive inference raises the required standard of
epistemic justification to a probability of 1. This is that required by logical
or mathematical knowledge (where ‘~> = →’), and the difference in standards
may lead to confusion, if one equivocally assimilates the lower standards of
Humean inductive epistemic justification to the higher standards of statistical
epistemic justification, which should be those of logical probability.
[12] Keith Lehrer, Theory of Knowledge (London:
Routledge, 1990), p. 16.
[13] From Robert Nozick, Philosophical Explanations (Cambridge,
MA: Harvard University Press, 1981), pp. 174-5. This example was originally
introduced by Carl Ginet.
[14] Adapted from Bertrand Russell, Human Knowledge:
its Scope and Limits (London: Allen & Unwin,
1948), pp. 154-5.
[15] Gilbert Harman, ‘Knowledge,
Inference and Explanation’, American
Philosophical Quarterly, 5
(1968), pp. 164-173.
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