Tim McGrew


[Forthcoming in an anthology from Routledge]


The concept of evidence pervades our lives. In science, history, law, medicine, and innumerable other areas, evidence plays a central, indispensable role. Yet both the analysis of the concept of evidence and the characterization of its role in our cognitive lives are matters of lively philosophical controversy. To understand how these philosophical controversies have arisen, it is helpful to start from non-philosophical concepts and uses of evidence and explore the questions they raise.


Some Characteristics of Evidence


In the common sense of the term, evidence may come in a wide variety of forms. In a case at law, evidence might include a fingerprint, bloodstains, testimony, or a will. In science the paradigm case of evidence is a set of experimental data, but sometimes (as in astronomy or paleontology) the principal data are not directly amenable to experimental manipulation, so observation plays the central role. In history, evidence is typically in the form of narrative documents, but it might also take the form of a coin, some fragments of papyrus, or a few bits of pottery. In medicine it could consist of anything from an x-ray or a test result to a subjective experience of a certain sort of pain. In a trip to the grocery store it might consist in the redness of a watermelon or the softness of a peach.


Although the examples from these different fields are diverse, they have certain common characteristics. First, evidence is always evidence for (or against) something: the guilt of the defendant, the truth of a hypothesis, the truth of a particular historical claim, the presence of a certain disease, or the ripeness and sweetness of fruit. Second, it comes in a range of strengths. Sometimes we are in a position to compare evidence, to say that some piece of evidence is better evidence for a hypothesis than some other piece is, or that a piece of evidence is better evidence for one hypothesis than it is for some alternative hypothesis. Third, and relatedly, evidence may be more or less direct. Testimony that the defendant expressed dislike of the victim is indirect; eyewitness testimony that the defendant assaulted the victim is more direct, and all else being equal we are inclined to take the latter more seriously. Fourth, small things may give us strong evidence for surprising, antecedently improbable facts. When Robinson Crusoe had spent over twenty years as a castaway without seeing any signs of another human being, he had excellent reason to believe that he was alone on his island; but the sight of a single footprint overturned all of his evidence to the contrary. Fifth, pieces of evidence can typically be combined or opposed. A clinical diagnosis may be confirmed or undermined by a histopathological examination; a will may be called into question by the presentation of written documents apparently revoking it. This is closely related to a sixth point. Pieces of evidence may be undermined in several distinct ways: by being opposed by contrary evidence (a second will), by being undermined (documents revoking the will), or by the introduction of new relevant alternatives. In Charles Dickens’s Tale of Two Cities, for example, Charles Darnay is falsely accused of treason on the testimony of a witness. The defense attorney’s assistant, Sydney Carton, stands up and removes his wig, revealing that he and Darnay are strikingly similar in appearance; the witness’s certainty that it was Darnay he saw is undermined by the sudden introduction of the possibility that he actually saw someone else of similar appearance.


Propositional Evidence, Internalism, and Foundationalism


Each of these characteristics gives rise to certain interesting philosophical questions and issues. Take the fact that evidence is always evidence for or against something. How can a fingerprint or a bloodstain be evidence for something? The question is more tricky than it looks. After all, fingerprints by themselves do not say anything, and the sense in which a bloodstain can be said to accuse the defendant is clearly metaphorical. Trying to parse this out, some philosophers have been attracted to the view that, strictly speaking, what counts as evidence is not physical objects or even experiences, but rather a set of believed propositions; the bloodstains, wills, and pains are relevant because somehow they underwrite or legitimate our belief in the relevant  propositions that this smudge is a bloodstain, or that the document is the will of the deceased, or even, in the first person case, that I am experiencing thus.


The position that evidence is, in the strict sense, always propositional has many attractions. Propositions can be believed or disbelieved, but fingerprints cannot; to say that one disbelieves a fingerprint seems to be a shorthand for saying that one does not believe that the fact that this fingerprint is present (a proposition) indicates that the defendant is guilty (another proposition). Propositions can stand in logical relations to one another, can entail each other, can be negated, conjoined, and otherwise logically manipulated. But we can no more create a disjunction between a proposition and a fingerprint than we can divide the number seven by a banana. Treating evidence as propositional provides us with a natural way to discuss the combination of evidence, which we noted above as one of the common features of evidence. And there are tremendous systematic advantages to treating the whole system of our beliefs as a set of propositions, particularly if we want to make use of the machinery of Bayesian probability; for to do this, we must generate a probability distribution across all of the propositions in question. Fingerprints need not apply.


The relationship between evidence and probability is a particularly interesting one. The second feature of evidence we noted at the outset was that it comes in differing strengths. We have various options for representing evidential strength: positive (E is evidence for H), comparative (E1 is stronger evidence for H than E2), and numerical (the probability of H, given E, is .95, which would typically be written P(H|E) = .95). The numerical representation gives us some simple and intuitive ways of capturing the comparative assessment (P(H|E1) > P(H|E2)) and the positive assessment (P(H|E) > P(H)). These advantages come at a price, since the representation of our beliefs as a massive set of conjunctions, disjunctions and negations of simple propositions, and of our degrees of rational credibility as a probability distribution of infinitely precise numerical values across that set, cannot be perfectly squared either with introspection or with experimental evidence on human rationality (Kahneman, Tversky and Slovic, 1982). But there are various devices (e.g. probability intervals) that the devotee of probabilistic accounts of evidence can employ to lessen these difficulties; and just as in logic, some degree of idealization is to be expected in any normative formal reconstruction of our epistemic practices and concepts. (See Bayesian Epistemology)


It might seem that philosophers who take evidence to be propositional have just traded one problem for another. If a bloodstain cannot serve as evidence but the proposition this is a bloodstain can, then what serves as evidence for the belief about the bloodstain? If it must always be another proposition, we seem doomed to an infinite regress that never makes contact with experience. But if the bloodstain itself, or even the experience one would describe as one’s seeing the bloodstain, can serve to justify the proposition this is a bloodstain, then why be squeamish at the outset? Why not admit the stain, or the experience, as evidence in its own right?


One way of addressing this problem is to embrace a form of foundationalism in which certain beliefs, typically beliefs about one’s present experiential states, are justified in virtue of the manner in which they are connected with one’s experience. The idea of direct acquaintance plays a vital role here: on some current conceptions (BonJour 2002; Fumerton 2005; McGrew 1995, 1998), one’s foundational beliefs are justified because they express one’s acquaintance with aspects of one’s experience, and the acquaintance relation brings with it some high epistemic standing. The experience one has on the occasion of seeing the bloodstain provides a significant part of one’s justification for the belief that there is a bloodstain. In ordinary language we would go further and say that the experience was evidence. But given the theoretical payoff involved in treating evidence as propositional, it may be worth the small divergence from common usage. (See Foundationalism)


This form of foundationalism is highly controversial, both with respect to the standing of the foundations (do we have such beliefs? do they play the evidential role foundationalists say they do?) and with respect to the support they are supposed to give (can such foundations really give us justification for the wide range of our further beliefs?). It also raises several deep questions about the level of awareness required for something to count as one’s evidence, since awareness comes in degrees but the status of a belief as evidence, as opposed to the weight of that evidence, does not appear to be a matter of degree. It resolves the question of whether false propositions, or beliefs in false propositions, can count as evidence (on this conception they cannot); but since this resolution is somewhat controversial, it may be taken either as a merit or as a drawback to acquaintance foundationalism, though it is interesting to note that the requirement that knowledge not be crucially based on a false premise – clearly a related, though not an equivalent, notion – is one of the major ways of addressing the Gettier problem. In any event, these are serious questions that cannot be made to disappear by rejecting foundationalism: the question of the relationship between experience and experiential beliefs remains, for example, regardless of one’s stance on the propositional question or one’s preferred answer to the epistemic regress problem. And this form of foundationalism has the attraction of isolating and attempting to meet head-on questions about the structure of our knowledge and the justification for our epistemic starting points while preserving a role for experience.


Acquaintance foundationalism is a form of epistemic internalism, and the notion of evidence generally plays a much more significant role in internalist epistemologies than it does in various forms of externalism. It would be overstatement to say that evidence plays no role in externalism, but the role is very different, in part because evidence itself is understood differently by externalists than by internalists. In Timothy Williamson’s form of “knowledge first” externalism, for example, one’s evidence is simply equated with the set of things one knows, where the concept of knowledge is taken to be primitive rather than analyzed into more fundamental concepts. (See Knowledge First Epistemology) In some forms of reliabilism, sensitivity to the evidence (not necessarily propositionally construed) is a means of being justified or warranted. The converse does not generally hold; on some externalist views, one may be justified or warranted without being (in any sense that an internalist would recognize) sensitive to evidence. (See Internalism and Externalism)


Evidentialism and the Objectivity Constraint


A position often espoused by those sympathetic to acquaintance foundationalism, though distinct from it, is known as evidentialism: it is the position that the epistemic status of a belief depends wholly on the evidence possessed by the believer. Just what this amounts to depends on the notion of evidence being employed, and accordingly evidentialism comes in both narrow and wide forms depending on whether evidence is taken to consist only of propositions or of a wider range of items. According to a recent version of wide evidentialism, evidence for a belief consists in the internal features of the believer exemplified at the time the belief is held. (Conee and Feldman 2004) But the internal features, in this version, are not restricted to beliefs.


One interesting feature of evidentialism, whether wide or narrow, is that it entails a strong objectivity constraint on rational belief, which at a first approximation runs like this:


Disagreements regarding the epistemic evaluation of any proposition are in principle traceable either to differences in the relevant evidence available to the disagreeing parties or to irrationality on the part of at least one of the disputants.


It might seem at first that this is overly stringent. In everyday life, and even in disciplines like science and history, reasonable and well-informed people often disagree. Here, however, we have an example of the distance between common and philosophical use of terms like “reasonable” and “well-informed.” A defender of the objectivity constraint will reply that someone may be reasonable in an everyday sense but fall far short of the ideal of rationality suggested by the constraint, just as someone may be a fine mathematician without being mathematically omniscient. Similarly, for two people to be “well-informed” is not the same thing as for them to possess precisely the same evidence. Yet in some cases of disagreement among experts we at least approximate this situation. It is interesting to note that in those cases, the experts themselves are often more than willing to accuse each other of irrationality, which suggests that they are at least tacitly invoking something like the objectivity constraint. (See Disagreement)


Another objection to the objectivity constraint arises from the suggestion that the facts about what it is rational to believe given one’s available evidence may not be perfectly sharp. Here we run into wider issues about the nature of epistemology. On a traditional view, the relationship between one’s high-level beliefs and one’s evidence is both necessary and a priori in a strong sense: roughly, the evidence logically determines a unique rational response, and that rational response is in principle discoverable by reflection alone. There are, of course, cases where the evidence does not specify a numerically precise rational stance. On the basis of the fact (true but somewhat vaguely stated) that more than half of all humans born live are male, and in the absence of any further information bearing on the matter, it would be unreasonable to assign any sharp probability to the gender of some particular child about to be born. But here one may well retain the objectivity constraint and argue that the proper rational response is simply to take a stance that goes no further than the evidence – to expect a male child more strongly than a female, but to remain uncommitted to any more precise position. The vagueness of the evidence will be reflected in the relative lack of detail in the commitment, but it does not follow that there is any vagueness in the connection between the evidence and that commitment.


One’s position on the objectivity constraint determines a great deal about one’s overall epistemology. But there is still room for philosophers who give lip service to the constraint to talk past one another if they are not in agreement regarding the concept of evidence being invoked. (See Objectivity)


The objectivity constraint leaves open the possibility that two people may possess nearly the same evidence, reason unimpeachably from it, and yet arrive at widely differing conclusions. One of the attractions of modeling evidence in probabilistic terms is that we can give models, in probability, of cases where this happens. Since the beliefs we take as unproblematic provide the background in terms of which we make judgments of relevance and independence, it is quite possible for there to be situations where Jack and Jill both learn that E, Jack’s probability for H goes up, and Jill’s goes down. Even more common is a case where one person does not see any significant relevance of E to H, while another, with a different base of evidence, takes E as highly relevant to H. Looking across the history of science, we see this quite often. The famous Michelson-Morley experiment revealed that, so far as optical experimentation is concerned, the motion of the earth in its revolution around the sun is undetectable.  Had the opponents of Galileo been informed of this, they would no doubt have taken it to be highly relevant to the question of the motion of the earth, since the result is exactly what would be predicted if the earth is motionless. By the time the experiment was actually performed in the late 19th century, however, a stationary earth was no longer a live option. The immediate impact of the evidence was on the dispute between two types of ether theory, and a few decades later it came to be seen as evidence for Einstein’s theory of special relativity. An even more striking case is that of Hanno the Navigator (c. 450 B.C.), who reported that in his travels to the south he reached a point where the sun seemed to rise and set to the north. Subsequent historians, situated comfortably in the northern hemisphere and generalizing their experience, dismissed his account as impossible. Today that very fact, so implausible that it was unlikely to be invented, is our best piece of evidence that Hanno’s report was truthful. But this is because we understand what happens when one crosses the equator.


The example of look-alikes from A Tale of Two Cities raises an additional question for the objectivity constraint: does the sudden realization of a heretofore unrecognized possibility count as evidence? No new fact need be introduced for a possibility to be recalled; even Sydney Carton’s dramatic gesture merely draws the attention of the court to the fact that sometimes different people resemble each other strikingly, which surely no one would deny. (It is not seriously entertained that the witness might have seen Carton rather than Darnay, though that suggestion is the means by which the witness’s testimony is undermined.) In the history of science it has often happened that the realization of a new possibility radically alters our estimate of the weight of evidence for and against various theories. But the very language we use here – that it alters our estimate of the weight of evidence – suggests that we are pre-reflectively inclined to count the realization of a mere possibility not as evidence but rather as something that influences our evaluation of the evidence. In that case, however, we may need to interpret the objectivity constraint in such a way that “irrationality” may include the failure to recognize alternative possibilities.


Evidence and Interpretation


The prevalence of disagreement among experts suggests that a great deal depends not simply on one’s evidence but on one’s interpretation of that evidence. In most circumstances it is fairly clear what counts as evidence and what counts as interpretation, though this distinction, like everything else in philosophy, has been challenged. Questions of interpretation of the evidence are closely linked to questions of inference, and these are among the most difficult and interesting problems in all of philosophy. If one adopts an internalist, foundationalist position, then one is bound to admit that a great deal of interpretation and/or inference goes on below the level of explicit consciousness. This involves some extension of the ordinary meanings of these terms, since interpretation and inference are in the first instance self-conscious processes.


In the case of scientific evidence, it is important to remember that inference is almost always accompanied by a certain amount of interpretation. The case of Boyle’s Law illustrates this well. By pouring measured amounts of mercury into a J shaped tube, Boyle was able to obtain data on the compression of the air trapped in the short end. From his data, he concluded that the pressure and the volume vary inversely, that is to say, that P and 1/V are in a linear relationship. But Boyle’s data points, if plotted with P and 1/V for axes, do not fall on this line: a dot-to-dot connection of the points looks a bit like the Mississippi River. Boyle was aware of this and dismissed the variations between his measurements and the theoretical values as the product of error. Today, using regression analysis, we can vindicate his judgment (within bounds – when the pressure is great enough to liquefy the air, the relationship between P and 1/V ceases to be even approximately linear); but the fact remains that the data do not quite speak for themselves. This point tells against a naive form of falsificationism according to which even the slightest mismatch between theory and evidence suffices to overturn a theory. But it is a grave exaggeration to claim, as some social constructivists have done, that the existence of an interpretive dimension to scientific inference undermines the objectivity of science. (Bloor and Edge 1998)


One popular and plausible way to characterize a wide range of inferential practices is that we are attempting to infer the best explanation of the evidence. (Lipton 2004) Some philosophers have gone so far as to suggest that inference to the best explanation is the only primitive rational form of non-deductive inference. (Harman 1973; Foster 1985, p. 227) Sir Arthur Conan Doyle’s Sherlock Holmes stories are full of ingenious applications of such reasoning, and they are the more interesting since they were explicitly modeled on the real life abilities of Dr. Joseph Bell, an Edinburgh physician who pioneered forensic pathology and played a critical role in the trial and conviction of the notorious wife-murderer Eugene Chantrell in 1878. (Liebow 1982)


Even granting that subconscious interpretation and inference take place, there is a significant problem of characterizing these activities. Philosophers, who cannot agree even on the outlines of a solution to the problem of induction, are nowhere close to a consensus on more complex and less easily codified forms of thought like explanatory inference and analogical reasoning. Yet these forms of reasoning are pervasive; and it would help a great deal to clarify, and perhaps sometimes to resolve, our disputes if we could at least begin to analyze them in terms of more general forms of non-demonstrative reasoning. Most of the current work in this direction makes use of the probability calculus. (Hellman 1997; McGrew 2003, 2005) But the project is relatively new, and there is a great deal more to be done.


It is a curious fact that in other disciplines we manage to get along at least tolerably well without paying terribly close attention to various formulations that the philosophers have proposed. In law, for example, there are established canons of evidence, such as the ancient rule that conviction in a criminal case should be made only on the evidence of at least two independent witnesses; in history, a canon often observed (but perhaps just as often flouted) is that in the absence of direct evidence to the contrary, a historical document deserves the benefit of the doubt with respect to matters of fact it affirms that cannot be independently verified. The two witness rule is sometimes justified by the observation that the testimony of one witness and that of the defendant cancel each other out (Franklin 2001), though by itself this leaves it unclear how many additional witnesses should be required and whether they should all have equal credit. A substantial body of legal theory is devoted to the question of the admissibility and credibility of testimony and documentary evidence. No absolutely rigorous argument is available for such canons, but they are often reasonable rules of thumb, representing a distillation of much experience and providing a hedge against abuses that might otherwise have dire consequences. One need only recall the case of the chemist Antoine Lavoisier, who was executed during the reign of terror upon his denunciation by an academic rival, to realize that there are both prudential and epistemic reasons to require more than the word of one accuser.


Absence of Evidence and Arguments from Silence


Some slogans regarding evidence are not restricted to particular disciplines but crop up in conversation and sometimes in written discussions on a wide variety of issues. One of these comes in two incompatible forms: Absence of evidence is not evidence of absence (a statement made popular by Carl Sagan) and Absence of evidence is evidence of absence. The first (negative) form is more common, and it is sometimes used in criticism of an argument from ignorance to the effect that one should believe a proposition because its denial has not been proved. It is doubtful whether anyone capable of being swayed by this crude argument could be helped by the slogan. But it is an interesting exercise to determine when the slogan is applicable. The answer appears to be that each version, positive and negative, applies under certain conditions. At a first approximation, we can take the absence of evidence to be evidence of absence – or more broadly and less memorably, we can take the lack of positive evidence for some hypothesis to be evidence against the hypothesis – just in case we have good reason to believe that if the hypothesis were true, we would have positive evidence. In one of Sir Arthur Conan Doyle’s stories, Sherlock Holmes finds the key to a mysterious theft in the fact that a dog did nothing in the night, from which he infers that the thief cannot have been a stranger; for if he had been a stranger, the dog would have been expected to bark during the intrusion. On the other hand, in some cases we would not expect to have positive evidence regardless of whether the hypothesis is true or false. Spontaneous proton decay, if it takes place at all, is an event so rare that our expectation of catching it happening is nearly zero. Consequently, our failure thus far to detect it does not give us much in the way of a reason to reject the theoretical possibility. One advantage of looking at the slogan in probabilistic terms is that the first approximation can be sharpened: ~E is evidence for ~H just in case P(E|H)/P(E|~H) > 1; and the stronger the inequality, the better the evidence. This formulation has the merit of drawing attention to the fact that E may be strong evidence for H even when both P(E|H) and P(E|~H) are quite small in absolute terms, provided that their ratio is very large.


Related questions about absence of evidence crop up in law and in history. In legal contexts, the question has to do with the weight of negative evidence – testimony from a witness that he did not notice something, by contrast with the positive evidence of a witness who testifies to what he did see or hear. In history, the question has to do with the weight of the argument from silence, particularly when a writer fails to mention a putative event or fact that should have been known to him. Such arguments from silence are as a rule quite weak; there are many examples where reasoning from silence would lead us astray. Marco Polo, who traveled across China and kept an extensive journal of his travels, never mentions the Great Wall of China. Pliny the Younger, who in two of his letters gives a detailed account of the eruption of Vesuvius in A. D. 79, does not mention that the eruption destroyed the populous towns of Pompeii and Herculaneum. In light of such examples, we should not be too quick to assume that we know what an ancient author would have mentioned had he been aware of it.


Extraordinary Claims and Extraordinary Evidence


Another common slogan, also popularized by Sagan, is that Extraordinary claims require extraordinary evidence. Much depends, of course, on what counts as extraordinary, both in a claim and in evidence. It cannot be simply that a claim is unprecedented. At a certain level of detail, almost any claim is unprecedented; but this does not necessarily mean that it requires evidence out of the ordinary to establish it. Consider this claim: “Aunt Matilda won a game of Scrabble Thursday night with a score of 438 while sipping a cup of mint tea.” Each successive modifying phrase renders the claim less likely to have occurred before; yet there is nothing particularly unbelievable about the claim, and the evidence of a single credible eyewitness might well persuade us that it is true.


The case is more difficult with respect to types of events that are deemed to be improbable or rare in principle, such as miracles. It is generally agreed in such discussions that such events cannot be common and that it requires more evidence to render them credible than is required in ordinary cases. (Sherlock 1769) David Hume famously advanced the maxim that No testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavours to establish (Beauchamp 2000, p. 87), which may have been the original inspiration for the slogan about extraordinary evidence. The proper interpretation of Hume’s maxim has been a source of some debate among Hume scholars, but one plausible formulation in probabilistic terms is that


P(M|T) > P(~M|T) only if P(M) > P(T|~M),


where M is the proposition that a miracle has occurred and T is the proposition describing testimonial evidence that it has occurred. This conditional statement is not a consequence of Bayes’s Theorem, but the terms of the latter inequality are good approximations for the terms of the exact inequality


P(M) P(T|M) > P(~M) P(T|~M)


when both P(~M) and P(T|M) are close to 1. There is, then, a plausible Bayesian rationale for Hume’s maxim so long as we understand it to be an approximation.


It does not follow that the maxim will do the work that Hume (arguably) and many of his followers (unquestionably) have hoped it would. Hume appears to have thought that his maxim would place certain antecedently very improbable events beyond the reach of evidence. But as John Earman has argued (Earman 2000), an event that is antecedently extremely improbable, and in this sense extraordinary, may be rendered probable under the right evidential circumstances, since it is possible in principle that


P(T|M)/P(T|~M) > P(~M)/P(M),


a condition sufficient to satisfy the rigorous condition underlying Hume’s maxim and the slogan about extraordinary events. The maxim is therefore less useful as a dialectical weapon than is often supposed. It may help to focus disagreements over extraordinary events, but it cannot resolve them.


Testimonial Evidence and Independence


Discussions of Hume often segue into discussions of the evidential status of testimony. A repeated theme in the voluminous literature is the value of independent testimony, which is indeed remarkable. The testimony of a number of independent witnesses, none of them particularly reliable, who give substantially the same account of some event may provide a very strong argument in its favor. Independence is, however, often difficult to establish: it is not sufficient (though it is generally necessary) that the witnesses not have conspired to give the same account. Minor discrepancies of detail are often, and reasonably, taken to establish that witnesses are not simply retailing agreed-upon talking points. Of course, the wider the discrepancies, the less we are able to credit all of the witnesses. But if they agree on the main points, those may be taken to be well established notwithstanding their differences on subsidiary points. (Starkie 1876, p. 831)


There is also a substantial philosophical debate on the question of whether testimony provides an independent source of evidence or whether its value should be analyzed in terms of some other form of evidence, such as the perceived correspondence between the testifier’s previous statements and the facts. Hume’s position is reductive: he insists that the credibility of a testifier is a matter of proportion of truths to total testimonies. It may well be doubted whether this could provide a sufficient ground for the reasonable confidence we repose in testimony. The reductive view is more plausible when the set of possible forms of argument to justify reliance on testimony is widened to include explanatory inferences. Whether this suffices to save the reductive approach to testimonial evidence is still a matter of debate. (See Testimony)





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_____ “A Defense of Strong Foundationalism,” in Pojman (1998)


_____ “Confirmation, Heuristics, and Explanatory Reasoning,” British Journal for the Philosophy of Science 54 (2003): 553-67


_____ “Toward a Rational Reconstruction of Design Reasoning,” Philosophia Christi 7 (2005): 253-98


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