Evidence

The concept of evidence is crucial to epistemology and the philosophy
of science. In epistemology, evidence is often taken to be relevant to
justified belief, where the latter, in turn, is typically thought to
be necessary for knowledge. Arguably, then, an understanding of
evidence is vital for appreciating the two dominant objects of
epistemological concern, namely, knowledge and justified belief. In
the philosophy of science, evidence is taken to be what confirms or
refutes scientific theories, and thereby constitutes our grounds for
rationally deciding between competing pictures of the world. In view
of this, an understanding of evidence would be indispensable for
comprehending the proper functioning of the scientific enterprise. For
these reasons and others, a philosophical appreciation of evidence
becomes pressing. Section 1 examines what might be called the nature
of evidence. It considers the theoretical roles that evidence plays,
with a view towards determining what sort of entity evidence can be—an
experience, a proposition, an object, and so on. In doing so, it also
considers the extent to which evidence is implicated in justified
belief (and by extension, knowledge, if knowledge requires justified
belief). Then, section 2 considers the evidential relationship, or the
relation between two things by virtue of which one counts as evidence
for the other; and it explores the nature of their relationship, that
is, whether the relationship is deductive, explanatory, or
probabilistic. Finally, equipped with this theoretical background,
section 3 looks at some of the important problems and paradoxes that
have occupied those working in the theory of evidence.

1. The Nature of Evidence: What Is It and What Does It Do?

When we think about examples of evidence from everyday life, we tend
to think of evidence, in the first place, as consisting of an object
or set of objects. Consider evidence that might be found at a crime
scene: a gun, a bloody knife, a set of fingerprints, or hair, fiber or
DNA samples. The same might be said of fossil evidence, or evidence in
medicine, such as when an X-ray is evidence that a patient has a
tumor, or koplic spots as evidence that a patient has measles. Yet we
also consider such things as testimony and scientific studies to be
evidence, examples difficult to classify as "objects" since they
apparently involve linguistic entities. Possibilities proliferate when
we turn to philosophical accounts of evidence, where we find more
exotic views on what sort of thing evidence can be. In philosophy,
evidence has been taken to consist of such things as experiences,
propositions, observation-reports, mental states, states of affairs,
and even physiological events, such as the stimulation of one's
sensory surfaces.

Can all of these count as evidence? Few would think so, and basic
principles of parsimony seem to militate against it. But given all of
the possibilities with which philosophy and everyday life present us,
how would we go about making a decision? What kind of consideration
could determine the sorts of entities that can count as evidence? A
natural strategy to pursue would be to consider the role or function
evidence plays in both philosophy and everyday life. That is, perhaps
considering what evidence does affords the best clue to what evidence
is.

a. Propositional Evidence in Explanatory, Probabilistic and Deductive Reasoning

One way to approach the matter is to consider the role of evidence in
certain kinds of reasoning in which we engage. Recently, such a
strategy has led Timothy Williamson to the conclusion that evidence
must be propositional—that is, that it must consist in a proposition
or set of propositions (Williamson 2000, pp. 194-200). Although
Williamson declines to give any theoretical account of propositions,
minimally we may take propositions to be the bearers of truth and
falsity (what is true or false), the contents of assertions (what is
said or asserted) and the objects of propositional attitudes (e.g.
what is believed or known). More generally, propositions may be taken
to be the referents of that-clauses: for instance, I believe or know
that the house is on fire; it is true or false that the Orioles won
last night; I said or asserted that Jones is a thief; and so on.

To begin with, Williamson points out that evidence is often featured
in explanatory reasoning, in the sense that we tend to infer to the
hypothesis that provides the best explanation of the evidence.
Whatever else evidence may be, then, at the very least it is the kind
of thing that hypotheses explain. But what hypotheses explain,
Williamson contends, are propositions; we use hypotheses to explain
why such-and-such is the case, and so what is explained—the
evidence—is that such-and-such is the case. By contrast, it makes no
sense whatsoever to explain an object; we cannot explain this knife,
for example. What we might explain, however, is something true about
this knife, such as that it is bloody. Here, the evidence would be
that the knife is bloody—again, a proposition, not an object. Nor, on
Williamson's view, would it make sense to explain a sensory
experience. The hypothesis that I have a cold does not explain the
tickle in my throat, but would explain why I have a tickle in my
throat. Again, what is explained—the evidence—is that I have a tickle
in my throat, not the experience itself. Accordingly, if we consider
the role of evidence in explanatory reasoning, it seems that evidence
is propositional.

Additionally, Williamson claims that we use evidence to engage in
explicitly probabilistic reasoning, where such reasoning may or may
not be explanatory. For instance, we often compare the probabilities
of competing hypotheses H and H' on a common body of evidence, E. One
way to do so would be to consider the ratio:

P(H)P(E/H)
P(H´)P(E/H´)

(In general, the symbols P(X/Y) mean the probability of X given Y).
Here, we would compare the probability of the hypotheses, given the
evidence, only by considering the probability of the evidence, given
the hypotheses. It follows that evidence must be the sort of thing
that can have a probability. But again, Williamson claims that what
has a probability is a proposition; for example, it can only be
probable or improbable that such-and-such is the case. Even when we
speak loosely of the probability of an event, what we mean, says
Williamson, is the probability that the event will occur. And surely,
such things as objects or experiences cannot be probable or
improbable, although it could be probable or improbable that I have an
experience under certain conditions, or that an object has a certain
property. So again, granted that we engage in probabilistic reasoning
with evidence, the conclusion seems to be that evidence must be
propositional.

Finally, Williamson points out that we often think of evidence as
ruling out certain hypotheses. For instance, that I was in Cleveland
at the time of the murder rules out the hypothesis that I was the
murderer in Columbus. But evidence E rules out an hypothesis H only
when the two are logically inconsistent; in particular, one must be
able to deduce ~H from E. And, of course, the premises in a logical
deduction consist of propositions—the sort of thing that can be true
or false. Indeed, a valid deduction is one such that, if the premises
are true, the conclusion must also be true.

Yet, one may well remain unconvinced by these arguments. For example,
must the object of an explanation be a proposition, rather than, say,
an event? When Newton offered an explanation for the action of the
tides, one's first thought is that he was out to explain a physical
occurrence taking place on the surface of the earth, and not anything
like the content of an assertion or the referent of a that-clause.
Indeed, we might raise the same issue with Williamson's claim about
probabilities. There are well-known interpretations of probability
according to which events and event-types have probabilities, and not
propositions. For instance, on the standard frequency interpretation,
a probability is the limit to the relative frequency of an event-type
in a reference class; and on the propensity interpretation, a
probability is the disposition of a system—such as an experimental
arrangement— to yield a particular outcome, which is manifestly not a
proposition. In defense of Williamson, however, his strategy is to
consider the function of evidence is particular types of reasoning.
And as he frequently points out, if one is to reason with one's
evidence, either probabilistically, deductively, or explanatorily, the
evidence must be the sort of thing that one can grasp or understand,
namely, a proposition. (It makes little sense to grasp an event,
although we can grasp that an event took place). So, while there may
be theories of probability or explanation whereby events are
implicated, when we turn to explanatory, probabilistic or deductive
reasoning with the evidence, we are arguably dealing only with what is
propositional.

Whether or not we agree with Williamson, we shall see in the next
section, where we consider the important role evidence plays—namely,
as something that justifies belief—that we may have strong theoretical
ground for accepting, contrary to Williamson, that experiences can
also count as evidence.

b. Can Experiences Be Evidence? The Regress Argument

It seems almost a truism that whether a person's belief is reasonable
or unreasonable—justified or not—depends upon the evidence he
possesses. For instance, if I believe that my wife is having an
affair, but I have no evidence at all to think so, then such a belief
seems patently unreasonable. Given my lack of evidence, I am not
justified in holding the belief, and rationality would demand that I
relinquish it. If, on the contrary, I have overwhelming evidence in
support of my wife's infidelity, but persist in believing that she is
being faithful, then such a belief would be equally unreasonable. In
this situation, the only belief I would be justified in having, in the
light of my evidence, is that my wife is indeed having an affair.
Arguably, then, there is another important role that evidence plays:
evidence is that which justifies a person's belief. We shall examine
the matter in more detail below (§1c),

This being granted, suppose we were to accept, in addition, that
evidence consists only in propositions, as was urged in §1a. If so,
the natural conclusion would be that what justifies a subject's belief
are other propositions he believes (his evidence). More formally, we
would say that, for any proposition p that a subject S believes at a
time t, if S is justified in believing p at t, there must be at least
one other proposition q that S believes at t, which counts as S's
evidence for p. But if this is so, it seems we should also require
that S's belief in q itself be justified; for if S is groundlessly
assuming q, how could it justify his belief in p? Yet if S's belief
that q must be justified, then by the same reasoning S must possess
evidence for q, consisting in yet another proposition r that S is
justified in believing. And, of course, there shall have to be another
proposition serving as S's evidence for r. The question is: where, if
at all, does this chain of justifications terminate? We refer to this
as the epistemic regress problem. As we shall soon see, the regress
problem may support the conclusion that experiences can count as
evidence as well (see especially Audi 2003).

Now, granted that we cannot possibly entertain an infinite number of
justifying propositions, one possible way out of the regress would be
simply to reject an assumption used to generate it, namely, that only
propositions a person believes can count as his evidence. If we reject
this assumption, perhaps we can hold, on the one hand, that the
regress does terminate in what S is justified in believing, but on the
other, the evidence for these beliefs does not consist in other
propositions he believes. And aren't we perfectly familiar with such
cases? Consider beliefs we have about our own perceptual experiences.
I believe that I have a pain in my lower back. What justifies this
belief is surely not some other belief I have, but simply my
experience of pain in my lower back. Here, the belief is grounded
directly in the perceptual experience itself, and not in any other
proposition I believe. Or consider my belief that there is something
yellow in my visual field. Again, what justifies this belief is not
any other proposition I believe, but simply my experience of something
yellow in my visual field. Moreover, the point arguably need not be
limited to beliefs about our perceptual experiences (Audi, 2003; see
also Pryor 2000). For example, suppose I hear thunder and a patter at
my window, and come to believe that it is raining outside. That it is
raining outside is not a belief about my perceptual experiences, yet
seems to be grounded in them.

The idea, then, would be that the regress of justifications terminates
in a body of beliefs grounded directly in the evidence of the senses,
and not by any other beliefs that would themselves need to be
justified. This maneuver would terminate the regress, precisely
because—unlike a belief—it makes no sense to demand evidence for an
experience. Indeed, how can I give evidence for a pain in my lower
back? At the same time, experiences do seem to justify certain
beliefs, ostensibly making this an ideal solution to the regress
problem. It is worth noting that, since this view postulates a body of
beliefs that ultimately support all other beliefs without resting on
any beliefs themselves, it is an instance of a more general position
on the structure of justification known as foundationalism.

While this line of thought may give some reason for accepting that
experiences count as evidence, it still does not tell us anything
about the particular relationship between experience and belief by
virtue of which the former can constitute evidence for the latter.
Indeed, if Williamson's arguments from §1a are correct, we know that
experience can neither stand in an explanatory, nor probabilistic or
deductive relationship with a proposition believed. By virtue of what
sort of relationship, then, can a subject's experience count as
evidence for what he believes? Donald Davidson (1990) has argued that
experience can only stand in a causal relationship to belief. For
example, my hearing thunder and a patter at the window merely causes
me to believe that it is raining outside. For Davidson and others,
this is the wrong sort of relationship to account for justification;
what we need for the latter is not the sort of relationship in which
billiard balls can stand, but the sort of relationship that
propositions can stand—again, like an explanatory, probabilistic or
deductive relationship. Accordingly, like Williamson, Davidson claims
that only propositions a person believes can count as evidence for his
other beliefs, and opts for a coherence theory of the structure of
justification (and knowledge), rather than a foundationist theory.

Engaging further with Davidson's claim would take us too far afield.
For our purposes, it suffices to say that many philosophers still do
think that experience can count as evidence. Indeed, some, such as
John McDowell (1996), think that experiences have conceptual and even
propositional content—we can see, hear, feel that such-and-such is the
case—and thus that experiences can stand in rational relationships to
beliefs, and not just causal ones. Part of the urgency for McDowell is
that, in his view, the very survival of empiricism demands that
experiences count as evidence; indeed, Davidson, who denies this, is
perfectly happy to retire empiricism.

However, even those who deny that experiences count as evidence need
not think that a person's experiences are irrelevant to the evidence
he possesses. For instance, Williamson entertains the possibility that
there are some propositions that would not count as a person's
evidence unless he was undergoing some kind of experience. According
to Williamson, in such a case, experience may be said to provide
evidence, without constituting it. Whether this will be seen as
sufficient to save empiricism depends, of course, on how one
understands that doctrine.

c. Evidence And Justified Belief: A Closer Look

Recall that in order to start the regress in §1b, we assumed that
evidence is that which justifies a person's belief. This view can be
generalized to cover all so-called doxastic or belief-involving
attitudes—belief, disbelief, suspension of belief, and even partial
belief. The idea would simply be that S's doxastic attitude D toward a
proposition p at a time t is epistemically justified at t, if and only
if having D toward p fits the evidence S has at t. This view, known as
evidentialism, makes justification turn entirely on the evidence a
person possesses (Conee and Feldman, 2004). But is evidentialism
inevitable? Is having evidence sufficient for justified belief? Is it
even necessary?

Consider, first, whether possessing evidence is sufficient for
justified belief. Some think that justified belief is essentially a
deontological notion, involving the fulfillment of one's duties or
responsibilities as a believer. Hence, while having a belief that fits
one's evidence might be implicated in responsible belief, it seems
that responsibility also requires making proper use of one's evidence.
For example, suppose I am justified in believing p, and that I am
justified in believing that if p then q. Yet, I do notbelieve q on the
basis of this evidence, but believe it simply because I like the way
it sounds (Korblith, 1980). If I believe q on these grounds, I am
arguably not justified in my belief, even though it "fits" my other
beliefs; believing a proposition because of the way it sounds seems
like a patently irresponsible and therefore unjustified belief, no
matter what unused evidence for it I may possess. In defense of
evidentialism here, Conee and Feldman appeal to the auxiliary notion
of a well-founded belief: a belief that not only fits the evidence a
person possesses, but is properly based upon it. Thus, in the above
example, my belief in q is not well-founded, since I do not properly
use my evidence, even though the belief is justified by the evidence I
possess. This maneuver may do little, however, to placate those who
take justified belief to be inextricably related to responsibility.

Perhaps a more pressing challenge to the evidentialist is whether
evidence is even necessary for justified belief. Consider again
believing a proposition because of the way it sounds. Intuitively,
such a process or method of adopting beliefs is horribly unreliable;
that is, one is not at all likely to arrive at true beliefs in this
way. By contrast, consider the inference from "p" and "if p then q" to
the conclusion "q". If the former two are true, then believing q on
their bases is guaranteed to result in a true belief; indeed, sound
deductive reasoning is the very paradigm of a reliable or
truth-conducive process of inference. Accordingly, perhaps the central
notion involved in justified belief is not the responsibility or
possession of evidence per se, but how truth-conducive or reliable
one's belief-forming process or method is. If so, this opens up the
possibility that there are instances of justified belief in which
evidence is not implicated at all; for, while making proper use of
one's evidence is surely one way to form beliefs reliably, there is no
reason to suspect that it is the only way to do so. Indeed, consider
again beliefs formed on the basis of perceptual experience. Perhaps
the reason why such beliefs are justified is not because experience is
somehow evidence for such a belief; nor even because experience
provides evidence for other propositions, as in Williamson's view; but
simply because forming beliefs via experience is generally a reliable
or truth-conducive process of belief-formation. This view, which
relates justified belief to the reliability of the process by which it
is formed, is known as reliabilism (see especially Goldman, 1976,
1986).

It is far from clear, though, how far reliabilism can decouple
justified belief from evidence (see Bonjour 1980, but also Brandom
2000). As the view has thus far been described, a belief can be
justified even if one has no evidence whatsoever for believing that
the process by which the belief is formed isreliable; all that matters
is that the belief-forming process be reliable, not that the subject
has any reason to think that it is. Indeed, reliabilism is typically
thought to involve the thesis of epistemic externalism, or the thesis
that one need have no access to or awareness of what makes one's
beliefs justified. With this in mind, consider the well-known case of
the industrial chicken-sexer, who can reliably discriminate between
male and female chickens without having any idea of how he does so.
Suppose we take someone with that ability, but withhold from him
whether he is successfully discriminating chickens by sex; that is, he
not only has no idea how he reliably discriminates between chickens,
but does not even know whether he does so. Would such a person really
be justified in believing that a particular chicken is female, even
though he hasn't the slightest clue that he possesses the ability of
the chicken sexer? What if we told him that he gets it wrong the
majority of the time? Here, he would have evidence against his own
reliability. Would he be justified then? Even reliabilists such as
Alvin Goldman (1986) take heed here, requiring among other things that
a believer must not possess evidence against the reliability of the
belief-forming process. This, together with the notion that proper use
of one's evidence counts as a reliable process, ensures that the
concept of evidence will not be utterly irrelevant to justified
belief, even if we were to reject the strong thesis of evidentialism
in favor of something like reliabilism.

Up to this point, we have merely been considering what might be called
the nature of evidence: what it is and what it does. And although it
has been suggested that evidence can stand in an explanatory,
probabilistic, or deductive relationship with a proposition it
supports, very little has been said about these relationships. That
is, we have yet to consider any theories on the evidential relation,
or the relation between two things by virtue of which one counts as
evidence for or against the other. It is to this topic that we now
turn.

In order to avoid biasing the question of what sort of entity evidence
can be, where possible, I will simply refer to the evidence as "E"
(although, if Williamson is correct, E will have to be a proposition
in each of the theories we shall consider).
2. Theories of the Evidential Relation

A theory of the evidential-relation provides conditions necessary and
sufficient for the truth of claims of the form

E is evidence for H.

Such a theory tells us, in philosophically enriched terms, what it is
for something, E, to constitute evidence for a proposition or
hypothesis, H. There are surely many ways to classify such theories,
but one intuitive way to do so would be to divide them into
probabilistic, semi-probabilistic and non-probabilistic or
quantitative theories; the first two types of theory feature
probabilities at least somewhere in their accounts of evidence, while
the latter type avoids reference to probabilities altogether. We will
look at probabilistic and semi-probabilistic accounts first.

a. Probabilistic Theories of the Evidential Relation

The most widely accepted probabilistic account of evidence is the
so-called increase-in-probability or positive- relevance account. The
idea is simply that E is evidence for H if and only if E makes H more
probable. In symbols, E is evidence for H if and only if

P(H/E) > P(H)

where this is to be interpreted as saying that the probability of H
given E is greater than the probability of H alone. Along similar
lines, we can say that E is evidence against H if and only if

P(H/E) < P(H).

Finally, we may say that E is neither evidence for, nor against, H iff

P(H/E) = P(H).

Of course, these definitions are purely formal, and will take on
deeper philosophical significance if we interpret the concept of
probability employed. Most prominently, subjective Bayesians interpret
a probability as a rational subject's degree of belief in a
proposition at a given time t, where the only condition necessary for
a subject to count as rational is that his degrees of belief to
conform to the axioms of the probability calculus. So, for example,
where H and H´ are logically incompatible hypotheses, the degree to
which a rational subject believes [H or H´] ought to be equal to the
degree to which he believes H plus the degree to which he believes H´,
since [P(H v H´) = P(H) + P(H´)] is an axiom of the probability
calculus. With this interpretation of probability in mind, the
positive-relevance definition of evidence says that E is evidence for
H, for a rational subject S at a time t, if and only if E would make S
believe H more, were he to learn that E is the case. Naturally, then,
evidence against H would make a rational subject believe H less, and
evidence that is neutral towards H would leave a rational subject's
degree of belief in H unchanged.

As intuitive as these definitions may seem, some think that these
simple probabilistic definitions are subject to serious
counterexamples, and either try to supplement the probabilistic
definition with other concepts, such as explanation, or reject the
quantitative approach altogether. Consider a simple counterexample to
positive-relevance offered by Achinstein (1983, 2001), devised to show
that a mere increase in probability is not sufficient for something to
count as evidence. Let E = On Wednesday, Steve was doing training laps
in the water; let H = On Wednesday, Steve drowned; and let our
background information include that Steve is a member of the Olympic
swimming team who was in fine shape Wednesday morning. Achinstein
claims that E increases the probability of H over the probability of H
alone; that is, swimming makes drowning more probable than when one is
not swimming at all. According to the positive relevance definition,
then, E ought to be evidence that H. But this is bizarre, for the mere
fact that Steve—an Olympian—is doing training laps on Wednesday seems
to provide no reason at all to believe that he drowned. Intuitively,
the idea behind the counterexample is that positive-relevance is too
weak to capture a notion of evidence; E can increase the probability
of H without being evidence for it at all. (For responses to this and
other counterexamples of Achinstein's, see Kronz (1992), Maher (1996)
and Roush (2005)).

Clark Glymour (1980) has offered a very widely discussed objection to
positive-relevance, specifically under its subjective Bayesian
interpretation, now known as the "problem of old evidence." According
to Bayesians, the first term in the positive-relevance definition,
P(H/E), is to be determined by way of a theorem of the probability
calculus known as Bayes' theorem, which in its simplest formulation
is:

P(H/E) = P(H) x P(E/H)
P(E)

With this in mind, Glymour points out that quite often scientists
advance an hypothesis to explain "old evidence," or some phenomenon
that is already known to obtain. For example, one known phenomenon
that Einstein's general theory of relativity was advanced to explain
was an anomaly in Mercury's orbit, known as the anomalous advance of
the perihelion of Mercury. In these cases, P(E) in the above theorem
would equal to 1; that is, since the phenomenon is already known to
obtain, a rational subject would believe that E obtains with
certainty. Assuming now that the theory (being an adequate
explanation) entails the phenomenon, then P(E/H) above would be 1 as
well. But note that if we plug these figures into the theorem above,
the theorem simply reduces to: P(H/E) = P(H). According to our
relevance definitions, then, old evidence could neither be evidence
for, nor against, an hypothesis. But clearly old evidence can be
evidence for, or against, an hypothesis, as was certainly the case
with the anomaly in Mercury's orbit: it was evidence for Einstein's
theory and evidence against Newton's. Considerations such as these
lead Glymour to eschew probabilities altogether in his own influential
theory of evidence (see §2c below). (For a subjective Bayesian
response to the problem of old evidence, see especially Howson and
Urbach (1996)).

One might think that we can easily devise a probabilistic definition
of evidence in order to circumvent these problems. Suppose, for
example, we say that E is evidence for H, if and only if the
probability of H given E is high (Carnap, 1950). Call this the
high-probability definition of evidence. In symbols, E is evidence for
H if and only if

P(H/E) > k

where k is some threshold of high probability. This would avoid
Achinstein's swimming counterexample, for while swimming does increase
the probability of drowning, it does not render it high. Moreover,
since it avoids making increase-and-decrease-in-probability a
criterion of evidence, it would not face Glymour's problem of old
evidence. But suppose E = Jones has regularly taken his wife's
birth-control pills over the last year, and H = Jones has not become
pregnant. Clearly, P(H/E) is as high as can be, but the fact that
Jones has taken his wife's birth-control pills is surely not evidence
that he has not become pregnant. The problem, of course, is one of the
evidence being relevant to the hypothesis, a problem that will surface
again with other accounts of evidence, as we shall see below (§§2ci,
3c).

b. Semi-Probabilistic Theories of Evidence

While an elegant probabilistic definition of evidence may be
desirable, these objections and others have suggested to some that
such an account might be unattainable. However, not all philosophers
who have been skeptical of a purely probabilistic approach have
abandoned probabilities altogether.

Achinstein (1983, 2001), for example, accepts the high probability
definition as a necessary but not sufficient component to an account
of evidence. In order to secure relevance between the evidence and the
hypothesis, Achinstein adds to the high-probability definition a
requirement that there also be a high probability of an explanatory
connection between E and H (given that E and H are true), where there
is an explanatory connection between E and H if H correctly explains
E, E correctly explains H, or some proposition correctly explains both
of them. (Here, probabilities are not subjective degrees of belief,
but are objective and have nothing to do with what any subject knows
or believes). Obviously, this account avoids the birth control
counterexample, precisely because there is no probability of an
explanatory connection between Jones' taking birth control and his
failure to become pregnant; and it continues to avoid the swimming and
the old evidence problems, for the same reason that the high
probability account did on its own. Also, the account seems to yield a
correct verdict in some cases. Suppose, for instance, that Jones' wife
is taking birth control pills and fails to become pregnant, but not
because of her contraception, but because she is no longer fertile. On
Achinstein's view we can still say, as it seems we should, that her
taking birth control pills provides evidence that she will not become
pregnant, even though the pills are not the real explanation, since
his view only requires there to be a high-probability of an
explanatory connection, as there seems to be in this case.

One might think, though, that Achinstein has simply traded one
somewhat manageable problem for two more difficult ones. For he is
cashing out the evidential relation in terms explanation and objective
probability, two notions that are perhaps more in need of
philosophical treatment than the evidential relation.

It should not be thought that one must employ either the
positive-relevance or high-probability accounts in giving a theory of
evidence. Deborah Mayo's error-statistical account (1996) is an
influential semi-probabilistic approach to evidence, that appeals to
neither account. Mayo' approach, like Achinstein's and unlike positive
relevance, is rather strong; her leading thought takes off from the
Popperian intuition that "any support capable of carrying weight can
only rest upon ingenious tests, undertaken with the aim of refuting
our hypothesis." Thus she proposes that E is evidence for H if and
only if H passes what she calls a "severe test" with E, where H passes
severe test T with E if and only if the following two conditions are
satisfied:

* E "agrees with" or "fits" H (which she leaves rather open-ended,
provided that P(E/H) is not low)
* There is a high probability that T would have produced a less
fitting result than E, if H were false.

Consider a simple example. Suppose we give a patient a test T to test
the hypothesis (H) that he has a disease D, and suppose (E) the test
comes out positive. Suppose further that when a patient has D, T
yields a positive result 95% of the time, and when the patient does
not have D, T yields a negative result 99% of the time. Clearly,
conditions (i) and (ii) are satisfied: E not only "fits" H, but T very
probably would have yielded a less fitting (i.e. negative) result if H
were false. Accordingly, since H passes a severe test T with E, E is
quite strong error-statistical evidence that the patient has disease
D. Intuitively, T is a very good test to use if we want to rule out
that H is the case, and so a result of T that instead passes H is
impressive evidence in its favor.

On the other hand, if we were to suppose that T yields false positives
95% of the time, the epistemic status of E would look quite different.
While condition (i) is still satisfied, condition (ii) would not be:
since the test almost as frequently produces false positives, there is
a very low probability that T would have produced a less fitting
result if the patient did nothave D. Accordingly, T would not count as
a severe test of our hypothesis H, and so E would fail to constitute
error-statistical evidence for H.

Needless to say, the error-statistical approach has been adapted to
cover much more complicated testing situations, and interested readers
are invited to consult Mayo (1996). Another severe-testing account of
evidence can be found in Giere (1983).

c. Qualitative Theories of the Evidential Relation

Not every approach to evidence has employed probabilities. In this
section, we shall look at three of the better-known qualitative
theories of evidence. In one way or another, these theories appeal
only to deductive relationships between evidence and hypothesis.

i. Hypothetico-Deductivism

Perhaps the best-known non-quantitative approach to evidence would be
hypothetico-deductivism, which is popularly thought to constitute the
scientific method (see Braithwate in Achinstein (ed.), 1983 or Hempel,
1966). According to the simplest version of this approach, one invents
an hypothesis and draws out its observational consequences. One then
checks to see whether these consequences turn out to be true, and if
so, one is said to have obtained evidence in favor of one's
hypothesis. If the consequence turns out to be false, then one has
refuted one's hypothesis. On this approach, then, evidence for an
hypothesis is a true observational consequence of that hypothesis,
while evidence against an hypothesis is a false observational
consequence.

We consider two well-known objections to hypothetico-deductivism here
and another one in §3c below. The first objection is the so-called
irrelevant-conjunction objection. If an hypothesis H logically entails
E, then so does the hypothesis H & H´, where H´ can be any hypothesis
whatever. If E turns out to be true, then, according to this approach,
it is evidence for both H and H´, which is unacceptable. The
irrelevant conjunction objection shows, as we shall see again in §3c,
that hypothetico-deductivism offers a much too indiscriminate an
account of the evidential relationship. The second well-known
objection to hypothetico-deductivism is the competing- hypothesis
objection (see e.g. Mill, 1959). Suppose H entails a body of evidence
E1…En, and suppose the evidence comes out true. Still, H is not the
only hypothesis from which we can derive E1…En; in fact, there may be
indefinitely many such hypotheses, even perhaps some that—as Mill puts
it—"our minds are unfitted to conceive." According to
hypothetico-deductivism, then, E1…En would support those hypotheses
equally well, and the evidence would never be sufficient to accept one
hypothesis among the others. One common reply is that we ought to
choose the simplest among the competing hypotheses. But first, this
simply shifts the problem to defining simplicity, which has proved to
be a difficult task; and second, there seems to be no reason to
believe that the simpler theory is more likely to be true. These
problems and others have led some philosophers to seek alternatives to
hypothetico-deductivism, which we will now examine.

ii. Evidence as a Positive-Instance

One influential alternative to hypothetico-deductivism is offered by
Carl Hempel (1965). On this approach, an observation-sentence E is
evidence for a universal hypothesis H, just when E describes a
positive instance of H—or as Hempel puts it, just when E says of the
items mentioned within it what H says of all items. Intuitively, in
such a case E would "instantiate" H, thus would be evidence for it.
While this is hardly groundbreaking, what is novel about Hempel's
approach is that he marshaled the resources of basic predicate logic
to give his account of a positive instance, thereby construing the
evidential relation, like deduction, as being a syntactical relation
obtaining between sentences. That is, on this approach E is evidence
for H not by virtue of the specific sorts of objects E and H describe,
but by virtue of the formal features of the manner in which they
describe them.

For instance, suppose we are psychological researchers entertaining
the "psychological hypothesis", H, that everyone loves someone. The
logical form of this hypothesis is ALL:x y Lxy. This simply says that,
for anything x, there is some y such that x stands in relation L to y,
which is a logical form shared with great many hypotheses (e.g. that
everyone hates someone). Suppose further that we have observed in our
psychological practice that person, a, loves himself, and that person
b loves a. Again, on a purely formal level, our observation-sentence E
would be "Laa & Lba". This says that a stands in relation L to itself,
and b stands in relation L to a (again, there are great many
observation-sentences that would share this form). Now, to determine
whether E describes an instance of H (and whether it is evidence for
it), we introduce the notion of the development of H with respect to
the individuals mentioned in E. Intuitively, the development of the
hypothesis is simply what the hypothesis would assert if there existed
only those individuals in E. Thus, purely formally, the development of
H for the individuals in E is:

(Laa v Lab) & (Lbb v Lba)

With this in hand, Hempel claims that a statement is evidence for an
hypothesis when it entails the hypothesis' development. Now, since
[Laa & Lba] does entail the above development, it follows that E is
evidence for our hypothesis H; that is, the observation-report that
person a loves himself and b loves a is evidence for the hypothesis
that everyone loves someone. Since it is clear that the
observation-report says of a and b what the hypothesis says of all
individuals, Hempel has captured the notion of a positive instance
using basic predicate logic. Moreover, since the criterion involves
only the logical form of the evidence-statement and the hypothesis,
any statements with those forms stands in the exact same evidential
relation.

As ingenious as this may be, one obvious shortcoming of Hempel's
approach is that an observation sentence E can be evidence for an
hypothesis H, only if E and H are formulated in the same vocabulary
(in this case, both must employ the predicate "L"). Thus this approach
cannot be used as a general theory of scientific evidence, since
scientific hypotheses often employ theoretical predicates referring to
unobservable entities and processes, while observation-sentences
employ a strictly observational vocabulary. In the next section, we
shall see that Clark Glymour—who, if you recall, raised "the problem
of old evidence" against the Bayesians—developed his bootstrapping
approach to evidence in part to remedy this shortcoming, while still
adhering to Hempel's basic idea that evidence is a positive instance
of an hypothesis.

iii. Bootstrapping

The basic idea of Glymour's bootstrapping theory (1975, 1980) is quite
simple: to test an hypothesis in a theory consisting of several
hypotheses, all of which contain theoretical terms, we can use those
other hypotheses in the theory, together with observational evidence,
to derive a positive instance of the hypothesis we are testing and
obtain evidence for it. By repeating this process for each hypothesis
in the theory, we can obtain evidence for (or against) the theory as a
whole, even though the theory employs a theoretical vocabulary, while
the evidence is couched in an observational one. In such a case, we
are "pulling ourselves up by our own bootstraps", in the sense that we
are using certain bits of a theory to obtain evidence for other bits
of the same theory, in the service of obtaining evidence for (or
against) that theory as a whole.

To fill-in this abstract characterization, consider one of Glymour's
historical examples. Newton's law of universal gravitation asserts
that all bodies exert an inverse square attractive force upon one
another. As evidence for this, he used Kepler's laws of planetary
motion. Yet none of Kepler's laws contains the theoretical term
"force"; they merely describe observable regularities in the planets'
orbits without offering any theoretical explanation for them. How,
then, do we link the observable evidence—Kepler's laws—to an
hypothesis that contains the term "force", so that the former can
become evidentially relevant to the latter? The evidential link is
supplied, of course, by other parts of Newton's theory, namely his
second law of motion relating the force on a body with the measurable
quantities of mass and acceleration. Newton used the second law and
the evidence of Kepler's laws to derive instances of the law of
universal gravitation for planets and their satellites. He eventually
generalized this law to all bodies in the universe. Despite being the
briefest sketch of Newton's argument, this illustrates Glymour's
point: here Newton is using observational evidence and other
hypotheses in a general theory under test to derive instances of—and
thus evidence for—a particular hypothesis in that theory, even though
the evidence and the hypothesis employ different vocabularies. This is
precisely what Hempel's instantial approach cannot achieve.

But the worry haunting Glymour's approach, as might be expected, has
surrounded the problem of circularity. A great deal of literature has
been devoted by Glymour and others to deal with this and other issues
(see Earman 1983).

This completes our survey of theories on the evidential relation. We
have not covered all such theories, of course, but have aimed
primarily at variety. In particular, we have examined theories that
feature probabilistic, deductive and explanatory relationships between
evidence and hypothesis. It is worth mentioning again that if
Williamson is right, these theories would testify to the propositional
nature of evidence.

Now that we are equipped with considerable background, in the
remainder of this entry we shall consider some well-known problems and
paradoxes in the theory of evidence.
3. Some Problems of Evidence

a. The Ravens Paradox

The famous ravens paradox was formulated by Carl Hempel in the very
paper in which he set out his own instantial approach to evidence
sketched in §2cii. The paradox arises by reflecting on the following
three seemingly uncontestable assumptions.

1. According to the first assumption, an instance provides evidence
for a generalization. So, for example, if our generalization is "All
ravens are black," then an item that is both a raven and black
provides at least some evidence for it. This certainly seems correct.
2. According to the second assumption, an instance that is evidence
for a generalization provides evidence for any generalization that is
logically equivalent to it, that is, any sentence that is true and
false in exactly the same circumstances. The idea behind this
assumption is simply that logically equivalent sentences make
essentially the same assertion couched in different words, and we
cannot have differential confirmation of sentences based simply on the
words they use. That seems correct as well.
3. The third assumption is simply that "All ravens are black" is
logically equivalent to "All non-black things are non-ravens," since
the latter is just the contra-positive of the former. This is just a
matter of simple deductive logic.

The paradox, then, arises as follows. Since, for example a green book,
is a non-black thing that is a non-raven, by assumption (1), it
provides evidence that all non-black things are non-ravens. By
assumption (2), the same green book provides evidence for any
hypothesis logically equivalent to it, which, by assumption (3), means
that it also provides evidence for the hypothesis that all ravens are
black. In fact, most of the things in a room provide evidence for
one's ornithological hypothesis without one having to look at any
birds or even leaving one's apartment. The paradox, then, is that
three ostensibly uncontestable assumptions lead to a consequence that
seems intolerable.

i. Hempel's "Solution"

Since Hempel was in the process of giving a positive-instance account
of evidence when he presented the paradox, perhaps we should not be
surprised that his own "solution" to the paradox was simply to accept
it, arguing that its paradoxical air was a psychological illusion. The
problem is that by picking some item or other in the apartment as an
example, we antecedently know that it will be a non-raven, and so the
outcome of the "observation" of the object seems irrelevant to the
confirmation of the hypothesis. When we are then told that, in fact,
the object does provide evidence for the hypothesis, this seems simply
unacceptable. But suppose that all we knew was that were there is a
non-black thing whose identity as a raven was still genuinely in
question. In this case, finding that it is not a raven would, says
Hempel, seem evidentially relevant to the hypothesis that all ravens
are black. In both cases, the non-black non-raven object supplies
evidence for the hypothesis, but whether this seems paradoxical or not
depends upon what information we include or suppress in stating the
example. Despite this, many have still found it intolerable that a
green book could provide evidence that all ravens are black.

ii. A Bayesian Solution

Interestingly, Bayesians (see §2a) tend to agree with Hempel that a
green book and a black raven each provide evidence for the hypothesis
that all ravens are black. However, they mitigate this seemingly
outlandish position by using Bayes' theorem and the positive-relevance
definition of evidence to show that one provides much stronger
evidence than the other. Consider again the simple version of Bayes'
theorem, which according to Bayesians is the theorem by which we are
to compute the conditional probability P(H/E):

P(H/E) = P(H) P(E/H)
P(E)

Now, it is easy to see from the theorem that as P(E) becomes larger,
P(H/E) becomes smaller. If we interpret this in light of the positive
relevance definition of evidence, this is to say that the more
probable the evidence, the less it increases the probability of the
hypothesis, and the weaker it is as a piece of evidence. Conversely,
the less probable the evidence, the more it increases the probability
of the hypothesis, and the stronger it is as a piece of evidence. This
result is said by Bayesians to capture the allegedly intuitive notion
that surprising evidence supports an hypothesis more. But note that,
since there are vastly more non-black things in the universe than
there are ravens, the probability of finding a non-black thing that is
also a non-raven is far greater than that of finding a raven that is
black. According to the theorem, then, finding a non-black, non-raven
ought to increase the probability of H (that all ravens are black)
much less than finding a black raven. Indeed, it ought to increase the
probability of the hypothesis hardly at all, since P(E) should be
close to 1. It follows that, while finding a black raven and a
non-black non-raven both provide evidence for the hypothesis that all
ravens are black, the latter provides much weaker evidence than the
former. Indeed, since the latter affords such weak evidence, we would
invariably overlook it as such, which may explain why it is so
surprising to be told that (say) a green book does provide evidence
that all ravens are black.

iii. An Error-Statistical Solution

Those who would regard as preposterous even the notion that a green
book could supply extremely weak evidence that all ravens are black,
may find some solace in an error-statistical solution to the ravens
paradox. Again, to yield evidence for an hypothesis on this view, a
testing procedure must severely test that hypothesis. With this in
mind, it is not difficult to see that examining all non-black items in
one's apartment would fail to be a severe test of the hypothesis that
all ravens are black. Again, appealing to Popper's dictum, this would
precisely not be "an ingenious test, undertaken with the aim of
refuting our hypothesis." For, while finding that all non-black items
in one's apartment are non-ravens may "agree with" the hypothesis that
all ravens are black (thus satisfying Mayo's requirement (i)), one
would very probably not obtain a less fitting result from such a
procedure if all ravens were not black (thus failing to satisfy
requirement (ii)). That is to say, we can be certain that this test
would yield the exact same results even if ravens were of a wide
variety of colors.

It is important to note, though, that even finding very many black
ravens may fail to provide evidence for the hypothesis on this
approach. One's testing procedure would have to ensure that one's
instances were sufficiently varied such that, if not all ravens were
black, one would very probably turn up one of those non-black ravens.
For example, one would at the very least have to select ravens from
different locales and of different ages and sexes. In short, employing
what one knows about the properties that make bird-coloration vary,
one would have to do one's best to obtain instances that would refute
the hypothesis that all ravens are black in order for one's results to
count as evidence for that hypothesis.

b. The Grue Paradox

Another famous paradox haunting the positive-instance approach to
evidence is Nelson Goodman's grue paradox. Indeed, Goodman's paradox
is often thought to have put an end to purely formal approaches to
evidence, such as Hempel's, and is of tremendous historical
significance.

Suppose that all emeralds examined so far have been green. Assuming
again that an observed positive instance of an hypothesis provides
evidence in support of it, then our observations of green emeralds
provide evidence for the hypothesis that all emeralds are green. So
far so good. But note that all emeralds examined so far have also been
grue, where the predicate "grue" applies to all things observed before
some future time t just in case they are green, or to things not so
examined just in case they are blue. Again, under the assumption that
an observed positive instance of an hypothesis provides evidence in
support of it, our observations of grue emeralds have also supplied
evidence that all emeralds are grue. Yet the two hypotheses are
genuine rivals. For example, they make incompatible predictions:
according to the green-hypothesis, the first emerald observed after t
will be green, while according to the grue-hypothesis it will be grue
(that is, blue). Thus, it seems our observations of emeralds provide
no more evidence to believe that the first emerald observed after t
will be green than to believe that it will grue (i.e. blue), which is
intolerable.

Note that the point of the paradox is not to undermine our confidence
that observations of instances can be evidence for a general
proposition expressing a law or uniformity of nature. Rather, the
paradox begins with that assumption, and asks the more penetrating
question of which propositions are apt to express the laws or
uniformities of nature, and thus which propositions are supported by
observations of its instances (or which propositions are "projectable"
in Goodman's terminology). Ostensibly, both the green and the grue
hypotheses are candidates here, since both assert that nature is
uniform in a certain respect: one says that emeralds everywhere and
throughout all time are green, while the other says they are grue. We
of course believe that only the green-hypothesis is lawlike, and thus
we believe only the green hypothesis can obtain support from the
evidence; but the paradox demands that we give a reason for this bias.

i. Goodman's Solution

Goodman's own solution to his paradox is rather startling. Goodman
thinks that the deep assumption generating the paradox is that an
account of the evidential relationship ought to look no farther than
the logical relationship between the evidence-statement and the
hypothesis alone (think of Hempel's account here). Thus, since the
green and grue hypotheses both bear the exact same logical
relationship to the evidence-statements—that is, since those
statements simply describe observed positive instances of the
hypotheses—both hypotheses are equally well supported by the evidence,
which is intolerable. Hence, Goodman's strategy involves rejecting the
underlying assumption that the evidential relation is a purely logical
one. While obviously the logical relation between evidence and
hypothesis will be relevant to their evidential relation; there is no
reason to think it is the only relevant factor. According to Goodman,
our linguistic practices must also play a role. Very roughly, our
observations of emeralds are evidence for the green hypothesis, and
not the grue hypothesis, because "green" has been used much more
frequently in hypotheses that have actually been accepted by us. On
this view, the evidence supported by our observations depends in part
upon how the world has heretofore been described in words. This, of
course, leaves open the possibility that, had "grue" been the
better-entrenched predicate, our observations would support the grue
hypothesis instead.

ii. Achinstein's Solution

Goodman's solution seems rather shallow. It rests upon the obvious
fact that we have accepted hypotheses involving the predicate "green"
more frequently than those involving "grue", without offering any
rationale for our acceptance. Achinstein claims to be able to provide
such a rationale with his own theory of evidence (see §2b). First,
recall Achinstein requires that if E is to provide evidence for H,
then the probability of H, given E, must be high. Next he requires
that if observed instances are to bestow high probability on a
universal hypothesis, and thus be evidence for it, the observed
instances of the hypothesis must be sufficiently varied. In other
words, if one's instances are not varied, then it is hard to see how
they can make the probability of a universal hypothesis high. Finally,
note that grue is a disjunctive property; the predicate grue applies
to two different kinds of cases, green objects observed before t or
blue objects observed after t. Now, given that (1) evidence requires
high probability, (2) high probability requires varied instances, and
(3) grue applies to two different kinds of cases, it seems that our
observed instances could never be evidence that all emeralds are grue,
unless some instances of that hypothesis are of both kinds of cases.
That is to say, the only way for observed emeralds to be sufficiently
varied to provide evidence that all emeralds are grue, is if we
examine some emeralds before t and find them to be green, and some
after t and find them to be blue. Since one of the very conditions of
the paradox is that we have not done so, our observations of emeralds
could not provide evidence that all emeralds are grue. In general, the
disjunctive nature of "grue", and the consequent impossibility of
obtaining sufficiently varied instances of grue items, explains why
"grue" is not a well-entrenched predicate in our language—why we have
not frequently accepted hypotheses featuring that predicate in the
past. On the other hand, since "green" for us is not a disjunctive
property, nothing prevents "green" from being the well-entrenched
predicate that it is in our language, as Goodman observed.

c. Underdetermination of Theory by Evidence

There is no more pervasive problem in epistemology than the problem of
underdetermination of theory by evidence. Consider, first, radical
skepticism about the external world. Here, the skeptic proposes a
seemingly far-fetched competing hypothesis to account for all the
evidence that experience apparently provides about the
mind-independent world. For example, perhaps I am merely a
brain-in-a-vat, electrochemically stimulated by a supercomputer to
have the very experiences I am having at this moment, or all the
experiences I have ever had. This hypothesis is equally compatible
with, and indeed entails, that I will have the very same experiential
basis for belief that I would have if the world were as I have always
believed it to be. Indeed, any test that I could perform to decide
between the two competing hypotheses may simply be another set of
experiences fed into my brain from the supercomputer. On what grounds,
then, can I say that the hypothesis is "far-fetched"? Indeed, given
all the evidence I will ever possess, the skeptic's seemingly bizarre
story appears just as likely to be true as my ordinary beliefs.
Granted, I may prefer my ordinary beliefs out of familiarity, or even
simplicity, but neither of these is a reason for believing that my
ordinary beliefs are any more likely to be true; my preference would
be just a baseless prejudice. Accordingly, all possible evidence I
could have radically underdetermines which theory I ought to believe.

Other skeptical arguments, such as inductive skepticism and skepticism
about other minds, are designed to establish the same conclusion. In
the case of inductive skepticism, evidence from the past and present
course of nature allegedly underdetermines the shape of the future
course of nature.. In the case of skepticism about other minds,
evidence from what others say and do underdetermines not only what
their mental life might be like, but also whether they even have a
mental life. In both of these cases, the evidence stands in the exact
same logical relationships to the skeptical hypotheses as they do to
our favored ones. Accordingly, the evidence allegedly provides no
justification whatsoever for preferring one hypothesis to the other.

But it's not just skepticism that runs on underdetermination of theory
by evidence. Indeed, the grue paradox from §3c above does so as well:
none of our observations before time t favor the green hypothesis over
the grue hypothesis. As we saw, the problem forced Goodman to turn to
seemingly non-epistemic factors such as the sort of language we use.
And there are problems of underdetermination that are far less
esoteric as well, such the curve-fitting problem. Suppose we have a
graph on which very many data points are plotted; for instance,
suppose that the data points relate the pressure and volume of various
samples of gas. Now, it turns out that there are infinitely many
equations describing curves that can fit the evidence; in our case,
this means that Boyle's law of gases is merely one of an infinite
number of equations that can fit the data. Moreover, it does not
matter how many data points we add; while some curves will be ruled
out with the addition of new evidence, there will always be an
unending supply of equations that will fit. On what grounds, then, do
we accept Boyle's law? Once more, the idea is that the evidence itself
does not determine which of the equations we ought to prefer.

In all of these cases, the evidence allegedly fails to provide any
rational grounds for preferring one hypothesis over an indefinite
number of competing hypotheses.. To make a choice, we seem forced to
prefer an hypothesis on non-evidential and therefore non-epistemic
grounds. And this threatens to make a mockery of the very idea of
evidence. For is evidence not supposed to help us determine what we
ought to believe? If something can't do this, with what right do we
even speak of it as evidence?

These problems are far too numerous, and their solutions far too
involved, for us to discuss here. We would do best to concentrate on a
problem of underdetermination dealing with which the materials of the
previous sections have equipped us.. Hence, in the remainder of this
entry, we shall concentrate on underdetermination as it relates
specifically to thesis of evidential holism, or the thesis that
evidence never bears on a proposition in isolation from other
propositions we accept—and possibly all the propositions we accept. As
we shall see, the theories of the evidential relation already on the
table will not only help us set-up the problem, but also offer some
solutions.

i. Underdetermination and Holism: The Duhem-Quine Problem

Uncovering the problem of holism and underdetermination is usually
credited to Pierre Duhem, the late 19th and early 20th century French
physicist, historian of physics, and philosopher of science. Duhem
asks us to consider the hypothetico-deductive method of
theory-testing, sketched in § 2ci: again, from the proposition under
test we derive an observable prediction; if the prediction comes out
true, we are said to have evidence for the theory, while if not, we
are said to have evidence against it. Yet Duhem explains that, while
correct in outline, the account is much too simple: the scientist does
not derive testable implications from the proposition alone, but from
that proposition and "a whole group of theories accepted by him…" For
example, in order to obtain any observable predictions from Newton's
laws of motion and gravitation with respect to our Solar System, we
need take those laws in conjunction with a host of auxiliary
hypotheses and assumed facts, such as that only gravitational forces
act on planets; or assumptions about the relative masses of the
planets, their satellites and the sun; or information about planetary
velocities, which are, in turn, derived from instruments whose correct
functioning is based on the employment of still other theories; and so
on. Granted this, Duhem now asks us to suppose, as is often the case,
that the prediction generated by this body of statements does not turn
out true. Since no single hypothesis or theory entails the false
prediction, but only a whole web of theory and alleged fact taken
together, the evidence does not by itself indicate which member of
that web is refuted; nature is silent with respect to where the blame
lies. To put the point in starker terms, there simply is no fact of
the matter with respect to which the evidence is evidence against,
which is just to say that the evidence underdetermines which parts of
the body are to be believed and which parts are not. This much being
granted, the same should also go for evidence consistent with one's
theory: since in no case does that theory by itself entail a true
observable prediction, there would simply be no fact of the matter
with respect to which the evidence is evidence for. The conclusion,
then, seems to be evidential holism: evidence never bears on a
proposition in isolation, but only on a body of propositions taken as
a whole.

Duhem thought that his problem could be solved by the "good sense" of
the practicing physicist, but it was Quine who unleashed the problem
of holism, by extending it beyond a theory and its auxiliary
assumptions, to an entire body of statements we accept. Quine's holism
is intimately related to his rejection of the analytic-synthetic
distinction in the philosophy of language. An analytic statement is
one that is true solely by virtue of its meaning (such as all
bachelors are unmarried), while a synthetic statement is one that is
true or false by virtue of both its meaning and how things turn out in
the world (such as all bachelors are less than five feet ten inches
tall). Accordingly, while synthetic statements are accepted as true or
rejected as false by virtue of what the world affords us in
experience, analytic statements are accepted as true come what may in
experience. Now Quine's rejection of the analytic-synthetic
distinction is far too involved to review here, and we only need
concern ourselves with its outcome: if there is no distinction between
a type of statement that is true in virtue of meaning and a type of
statement that is true in virtue of how things turn out in the world,
then, in principle, any statement can be accepted as true or rejected
as false in the light of experience, and any statement can be held
true come what may. The only constraints on what to accept or reject
given the evidence of the senses are consistency with what else we
accept, and pragmatic considerations such as conservatism and
simplicity. Otherwise, the evidence so radically underdetermines our
web of beliefs that there is an indefinite number of systems of the
world that can be made to square with it. Accordingly, whichever
picture of the world we choose is merely one of many, with no
evidential basis to decide between them. No one puts the point better
than Quine himself:

[It] becomes folly to seek a boundary between synthetic
statements, which hold contingently on experience, and analytic
statements, which hold come what may. Any statement can be held true
come what may, if we make drastic enough adjustments elsewhere in the
system… Conversely, by the same token, no statement is immune to
revision. Revision of even the logical law of the excluded middle has
been proposed as a means of simplifying quantum mechanics… The
totality of our so-called knowledge or beliefs…is a man-made fabric
which impinges on experience only along the edges. Or, to change the
figure, total science is like a field of force whose boundary
conditions are experience. A conflict with experience at the periphery
occasions readjustments in the interior of the field. Truth-values
have to be redistributed over some of our statements…But the total
field is so underdetermined by its boundary conditions, experience,
that there is much latitude of choice as to what statements to
reevaluate in the light of any single experience. No particular
experiences are linked with any particular statements in the interior
of the field, except indirectly through considerations of equilibrium
affecting the field as a whole…

i. A Bootstrapping Solution

Glymour's bootstrapping approach to evidence, if tenable, provides an
ingenious response to the problem posed by Duhem and Quine, for it
extracts a kernel of truth from the problem while rejecting what seems
most pernicious about it. First of all, we are urged by Glymour not
accept the problem, as Quine does, but instead take it as exposing the
key weaknesses in the hypothetico-deductive account of evidence that
generates it, namely, that such an approach makes the bearing of
evidence on the theory unacceptably indiscriminate. Indeed, the
irrelevant conjunction problem, as we saw in §2ci, reveals essentially
the same flaw. Accordingly, far from accepting hypothetico-deductivism
and the holism that comes along with it, we ought to reject the
hypothetico-deductive approach on the bases that it fails to meet a
crucial constraint on any acceptable theory of evidence, namely, how
an observation or test can be relevant to one part of a theory while
not to others.

Of course, the bootstrap approach is devised to satisfy exactly this
very constraint. Again, according to this approach, we use other
hypotheses in the general theory under test, together with
observational data, to derive a confirming or disconfirming instance
of a specific hypothesis in the theory; and we are enjoined to repeat
the same process for the other individual hypotheses composing the
theory itself. So while hypothetico-deductivism has the evidence
entailed by a mass of theory, leaving underdetermination and holism as
the inevitable consequences, bootstrapping has the evidence and a mass
of theory entailing an instance of an hypothesis within it, which
allows the evidence to bear specifically on a single hypothesis of
interest. Hence, we can see that, contrary to holism, evidence does
bear on specific parts of the theory, but, crucially, it does not do
so in isolation from other parts of the theory. Thus, what is correct
about holism is the notion that large parts of theory must always be
involved in theory-testing; what is not correct is to conclude from
this, as Duhem and Quine do, that a piece of evidence does not bear on
one part of the theory without bearing upon all of it. Of course, the
plausibility of this solution can be no greater than the plausibility
of the bootstrap approach as a whole, which as mentioned above, some
have questioned.

iii. A Bayesian Solution

To consider a different sort of approach, subjective Bayesians (see
§2a) use Bayes' theorem, the positive/negative-relevance definition of
evidence and their own subjective interpretation of probability, to
illustrate how evidence can indeed single out one hypothesis among
others for rejection. (Recall that, for the subjectivist, a
probability is a rational subject's degree of belief in a proposition
at a given time). While these illustrations are too complicated to
spell out in all their detail here, we will consider an abridged
account of an illustration offered by Jon Dorling, employing a case
from the 19th century physics. Our hypothesis H is Newton's theory of
motion and gravitation, and the auxiliary hypothesis A is the
assumption that tidal effects do not influence secular lunar
accelerations. We will suppose that H and A together entail the
expected observed acceleration of the moon E´, but what is observed
instead is the anomalous lunar acceleration E. Thus E tells us that H
and A cannot both be true, but the problem, again, is that it seems to
underdetermine which one of the two hypotheses we are to believe.

On the Bayesian view, what we need to consider are the separate
effects wrought by E on the probabilities of H and A. Accordingly, the
goal will be to compare P(H/E) and P(A/E), both of which can be
conveniently calculated by means of Bayes' theorem:

P(H/E) = P(H)P(E/H) P(A/E) = P(A)P(E/A)
P(E) P(E)

With this framework intact, we now need to assign a plausible
probability distribution to the right-hand sides of these equations
that would mirror the degrees of belief of a typical scientist at the
time. Since the typical scientist had much confidence in both H and A,
but somewhat less so in A, we can plausibly set P(H) to .9 and P(A) to
.6. Next, we need to determine the so-called likelihoods, P(E/H) and
P(E/A). Given some uncontroversial transformations, the details of
which we will pass over here, it turns out that

P(E/H) = P(E/A & H)P(A) + P(E/~A & H)P(~A)
P(E/A) = P(E/A & H)P(H) + P(E/A & ~H)P(~H)

Now, since the obtaining of E refutes the conjunction of A&H, we
already know that P(E/A&H) here would be 0. Thus the above reduce to:

P(E/H) = P(E/~A & H)P(~A)
P(E/A) = P(E/A & ~H)P(~H)

Since we already have P(A) and P(H), we can easily determine P(~A) and
P(~H), which will be 0.4 and 0.1, respectively. So the object, now, is
to determine P(E/~A & H) and P(E/A & ~H). It is plausible to suppose
that, while scientists at the time would believe E to be highly
unlikely given H and ~A (say, P(E/~A & H) = .05), it is clear that,
given the wide acceptance of Newtonian theory at the time, they would
take E to be virtually inexplicable if H were false. That is, the
typical scientist at the time would be highly skeptical that there is
a competitor to H that could account for E. Granted this, we can
plausibly set P(E/A & ~H) to a very low .001. Plugging in our figures
we obtain:

P(E/H) = P(E/~A & H)P(~A) = (.05) x (.4) = .02
P(E/A) = P(E/A & ~H)P(~H) = (.001) x (.1) = .0001

This gives us all the figures in the numerator of Bayes' theorem. We
still need to determine the denominator P(E). To expedite matters, we
will simply suppose, as was surely the case, that our scientist
believes E would be very unexpected, and will stipulate that P(E
)≈0.02.

Thus, we now have all of our figures to plug into the above Bayes'
theorem. Performing the calculations we find that P(H/E) ≈ .9, while
P(A/E) ≈ .003. Accordingly, while the probability of Newton's theory
would be virtually unchanged given E, the probability of A given E is
reduced to almost zero. But, according to the relevance definition of
evidence, this means that E is very strong evidence against the
auxiliary A, and not Newton's theory. Clearly, then, it was the
auxiliary A and not Newton's theory that should have been—and
was—discarded in light of E. Hence, what Bayesians offer is the
machinery with which we can work out exactly how evidence bears on one
hypothesis more than others. If this view is correct, the problem of
holism and underdetermination would be resolved.

Some have questioned whether this constitutes a solution at all (Mayo
1996, Earman 1992). While we are certainly given probabilities that
make the choice of hypothesis obvious, we are not told whether those
corresponding degrees of belief would be warranted, and thus whether
the choice to reject an auxiliary would be a good one. Indeed, the
flexibility of subjective Bayesianism would allow a different
probability distribution, according to which H rather than A would
bear the brunt of the evidence. But if it would be acceptable to blame
either A or H, it seems that, instead of a solution, we have a
re-description of the problem—namely, which hypothesis do we reject in
light of the evidence?

But for the subjective Bayesian, the objection is entirely specious.
Such probability distributions would be warranted, so long as they
conform to the axioms of the probability calculus. On the subjective
Bayesian view, there is simply more than one rational perspective on a
matter.
4. References and Further Reading

Achinstein, Peter (ed.) (1983) The Concept of Evidence (Oxford: Oxford
University
Press).

A short collection of essential reading on the evidential relationship.

Achinstein, Peter (1995) "Are Empirical Evidence Claims A Priori?"
British Journal for the Philosophy of Science 46: 447-73.

Discusses the question of whether claims to have evidence for an
hypothesis are themselves empirical, or known by mere calculation or
logic.

Achinstein, Peter (2001) The Book of Evidence (Oxford: Oxford University Press).

An extended presentation of Achinstein's own account of evidence,
as well as applications of that account to the paradoxes of grue and
the ravens, and the issue of scientific realism.

Achinstein, Peter (ed.) (2005) Scientific Evidence: Philosophical
Theories and Applications (Baltimore: Johns Hopkins University Press).

A collection of papers by various authors addressing Achinstein's
and other views of evidence (including the error-statistical view),
along with several papers on the nature of evidence in particular
sciences.

Audi, Robert (2003) "Contemporary Modest Foundationalism" in Louis J.
Pojman (ed.) The Theory of Knowledge: Classical and Contemporary
Readings. (Belmont, CA: Wadsworth).

Uses the epistemic regress argument to support a view of
foundationalism on which experiences count as evidence. Very clear and
accessible.

Bonjour, Lawrence (1980) "Externalist Theories of Empirical Knowledge"
in P.A. French, T.E. Uehling, Jr., H.K. Wettstein (eds.) Minnesota
Studies in Philosophy 5: Studies in Epistemology (Minneapolis:
University of Minnesota Press).

Classic critique of externalist/reliabilist theories of epistemic
justification, and whether one can have justified belief without
evidence of one's reliability, or with evidence against one's
reliability.

Brandom, Robert (2000) "Insights and Blindspots of Reliabilism" in
Articulating Reasons: An Introduction to Inferentialism (Cambridge,
MA: Harvard University Press).

Among other things, questions how far the notion of reliability
can separate justification from reasons for belief or evidence.

Carnap, Rudolf (1950) The Logical Foundations of Probability (Chicago:
University of
Chicago Press).

A quantitative approach to confirmation developing Carnap's own
logical or a priori theory to probability. Highly technical but very
influential.

Conee, Earl and Feldman, Richard (2004) Evidentialism. (Oxford: Oxford
University Press).

Collection of papers surrounding—and defending—the thesis of
evidentialism. See especially the papers "Evidentialism", "Having
Evidence", and "Internalism Defended".

Davidson, Donald (1990) "A Coherence Theory of Truth and Knowledge" in
A.R. Malachowski (ed.) Reading Rorty. Critical Responses to Philosophy
and the Mirror of Nature (and Beyond) (Oxford: Blackwell Publishers).

An argument for various coherence theories, relating essentially
to Davidson's influential views in semantics.

Duhem, Pierre (1954) The Aim and Structure of Physical Theory,
translated by P Wiener
(New York: Athenium).

Classic work in the philosophy of science presenting the problem
of underdetermination, among many other important positions.

Dorling, Jon (1979) "Bayesian Personalism, the Methodology of
Scientific Research Programmes, and Duhem's Problem" in Studies in the
History and Philosophy of Science 10: 177-87.

A Bayesian solution to the problem of underdetermination.

Earman, John (ed.) (1983) Testing Scientific Theories (Minneapolis:
University of Minnesota Press).

Contains critical papers on bootstrapping. Highly technical.

Earman, John (1992) Bayes or Bust? (Cambridge, MA: MIT Press).

An assessment of Bayesian confirmation theory. Highly technical.

Giere, Ronald (1983) "Testing Theoretical Hypotheses" pp. 269-98 in J.
Earman (ed.) Testing Scientific Theories: Minnesota Studies in the
Philosophy of Science, Vol 10 (Minneapolis: University of Minnesota
Press).

Presents a severe testing approach to evidence, somewhat similar to Mayo's.

Glymour, Clark (1975) "Relevant Evidence" Journal of Philosophy 72 pp. 403-420.

A short presentation of Glymour's bootstrapping approach to evidence.

Glymour, Clark (1980) Theory and Evidence (Princeton, NJ: Princeton
University Press).

An in depth presentation of bootstrapping, as well as an
evaluation of Bayesian, hypothetico-deductive and Hempel's approaches,
among others. Also presents the problem of old evidence. Technical in
spots.

Goldman, Alvin I. (1976) "What is Justified Belief?" in G.S. Pappas
(ed.) Justification and Knowledge (Dordrecht: D. Reidel).

A paradigm of a reliabilist theory of justified belief.

Goldman, Alvin I. (1986) Epistemology and Cognition. (Cambridge, MA:
Harvard University Press).

Goodman, Nelson (1955) Fact, Fiction and Forecast (Cambridge, MA: Harvard
University Press).

Classic presentation of the grue paradox, and Goodman's solution.

Hacking, Ian (1975) The Emergence of Probability. (Cambridge:
Cambridge University Press).

An historical account on the development of probability that
contains an account of the history of the concept of inductive
evidence.

Hempel, Carl G. (1965) Aspects of Scientific Explanation and Other
Essays in the Philosophy of Science (New York: The Free Press).

Contains "Studies in the Logic of Confirmation"—the less technical
presentation of Hempel's positive-instance approach—as well as several
other classic papers in the epistemology of science.

Hempel, Carl G. (1966) Philosophy of Natural Science (Upper Saddle
River, NJ: Prentice Hall).

A classic introduction to the philosophy of science that contains
a very clear description of hypothetico-deductivism.

Howson, Colin and Urbach, Peter (1996) Scientific Reasoning: The
Bayesian Approach,
3rd Edition (Chicago: Open Court).

A comprehensive presentation of the subjective Bayesian approach
to scientific reasoning. Contains Bayesian treatments of many of the
important problems in the epistemology of science, including old
evidence, grue, the ravens paradox and the Duhem-Quine problem.

Kornblith, Hilary (1980) "Beyond Foundationalism and the Coherence
Theory", Journal of Philosophy LXXII: 597-612.

Author criticizes foundationalism and coherence theory, arriving
at a kind of reliabilist theory of justified belief that combines
aspects of both, but which also involves the notion of responsibility.

Kronz, Frederick (1992) "Carnap and Achinstein on Evidence" in
Philosophical Studies 67: 151-167.

Contains a reply to Achinstein's objections to positive relevance.

Mayo, Deborah (1996) Error and the Growth of Experimental Knowledge (Chicago:
University of Chicago Press).

Mayo's error-statistical approach to scientific reasoning.
Technical in spots.

Maher, Patrick (1996) "Subjective and Objective Confirmation" in
Philosophy of Science
63: 149-174.

Contains a defense of positive-relevance against Achinstein, as
well as a presentation of the authors own objective theory of
confirmation, in opposition to the subjective Bayesian view.

McDowell, John (1996) Mind and World. (Cambridge: Harvard University Press).

Provocative work in which the author navigates between the
pitfalls of coherentism and traditional foundationalism, arguing among
other things that experience contains propositional content, and thus
can stand in rational relationship to belief. Not nearly as difficult
or obscure as it often made out to be.

Mill, John Stuart (1888) A System of Logic. 8th ed. (New York: Harper
and Brothers).

A classic work on inductive reasoning, among other things,
presenting Mill's criticisms of hypothetico-deductivism, as well as
his contribution to his famous debate with 19th century
hypothetico-deductivist William Whewell.

Nozick, Robert (1981) Philosophical Explanations, Oxford: Oxford
University Press.

Contains Nozick's "truth-tracking" account of evidence (and knowledge).

Pryor, James (2000) "The Skeptic and the Dogmatist", Nous, 34, pp. 517-49.

Argues for a modest foundationalism about perceptual beliefs on
which experience counts as evidence.

Quine, W. V. (1951) "Two Dogmas of Empiricism" in the Philosophical
Review vol. 60.

Quine's rejection of reductionism and the analytic-synthetic
distinction, with its attendant holism.

Quine, W. V. (1992) The Pursuit of Truth. (Cambridge: Harvard University Press.

A compressed and accessible presentation of many of Quine's
philosophical views, with the first chapter devoted entirely to
evidence.

Roush, Sherrilyn (2005) "Positive Relevance: a defense and challenge"
in Scientific Evidence: Philosophical Theories and Applications, P.
Achinstein ed. (Baltimore: Johns Hopkins University Press).

A paper co-written with Achinstein where Roush defends
positive-relevance, and Achinstein attacks it once more.

Roush, Sherrilyn (2006) Tracking Truth: Knowledge, Evidence and
Science (Oxford: Oxford University Press).

Updates Nozick's truth-tracking account of evidence (and knowledge).

Snyder, Laura J (1994) "Is Evidence Historical?" reprinted in
Philosophy of Science: The Central Issues, Curd and Cover (eds.) (New
York: Norton).

A contribution to the debate over whether knowing about evidence
prior to formulating a theory makes a difference to whether and to
what extent the evidence supports the theory.

Stalker, Douglas, ed. (1994) Grue! The New Riddle of Induction
(Princeton: Princeton University Press).

A large collection of papers on the grue paradox.

Williamson, Timothy (2000) Knowledge and its Limits (Oxford: Oxford
University Press).

An important work in recent epistemology that contains chapters
devoted especially to evidence. See especially chapters 8, 9 and 10.