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A central problem in epistemology is when we are justified in holding a proposition to be true. This is a problem because it is not at all evident how epistemic justification should be understood, and classical accounts of that notion have turned out to be severely problematic. Descartes thought that a person is justified in holding something to be true just in case the proposition in question can be derived from impeccable first principles characterized by their presenting themselves as being self-evident to the subject in question.

But, as is often argued, little of what we take ourselves to justifiably believe satisfies these austere conditions: many of our apparently justified beliefs, it is commonly thought, are neither based on self-evident truths nor derivable in a strict logical sense from other things we believe in. Thus, the rationalist picture of justification faces severe skeptical challenges. Similar problems hound empiricist attempts to ground all our knowledge in the allegedly indubitable data of the senses.

Depending on how they are understood, sense data are either not indubitable or else not informative enough to justify a sufficient portion of our purported knowledge. The exact characterization of foundationalism is a somewhat contentious issue. There is another form of foundationalism according to which some beliefs have some non-doxastic source of epistemic support that requires no support of its own. This support can be defeasible and it can require supplementation to be strong enough for knowledge.

This sort of non-doxastic support would terminate the regress of justification. To do so it may not have to appeal to self-evidence, indubitability or certainty. Such foundationalist views vary on the source of the non-doxastic support, how strong the support is on its own, and what role in justification coherence plays, if any. Some critics of this position have questioned the intelligibility of the non-doxastic support relation.

Thus, Davidson (1986) complains that advocates have been unable to explain the relation between experience and belief that allows the first to justify the second. This is an on-going debate the detailed coverage of which is outside the scope of the present article. The difficulties pertaining to both rationalism and empiricism have led many epistemologists to think that there must be something fundamentally wrong with the way in which the debate has been framed, prompting their rejection of the foundationalist justificatory structure underlying rationalism and empiricism alike.

Rather than conceiving the structure of our knowledge on the model of Euclidean geometry, with its basic axioms and derived theorems, these epistemologists favor a holistic picture of justification which does not distinguish between basic or foundational and non-basic or derived beliefs, treating rather all our beliefs as equal members of a web of belief (Quine and Ullian, 1970). Our purported knowledge, on this view, is more like a raft, which may have to be rebuilt on the open sea, to use Neuraths famous metaphor, than like a pyramid standing on its apex (Neurath 1983/1932, Sosa 1980).

Of course the mere rejection of foundationalism is not itself an alternative theory because it leaves us with no positive account of justification. A more substantial contrasting proposal is that what justifies our beliefs is ultimately the way in which they hang together or dovetail so as to produce a coherent set. As Davidson puts it, [w]hat distinguishes a coherence theory is simply the claim that nothing can count as a reason for a belief except another belief (Davidson, 1986).

The fact that our beliefs cohere can establish their truth, even though each individual belief may lack justification entirely if considered in splendid isolation, or so it is thought. Following C. I. Lewis (1946), some proponents think of this situation as analogous to how agreeing testimonies in court can lead to a verdict although each testimony by itself would be insufficient for that purpose. There is an obvious objection that any coherence theory of justification or knowledge must immediately face.

It is called the isolation objection: how can the mere fact that a system is coherent, if the latter is understood as a purely system-internal matter, provide any guidance whatsoever to truth and reality? Since the theory does not assign any essential role to experience, there is little reason to think that a coherent system of belief will accurately reflect the external world. A variation on this theme is presented by the equally notorious alternative systems objection. For each coherent system of beliefs there exist, conceivably, other systems that are equally coherent yet incompatible with the first system.

If coherence is sufficient for justification, then all these incompatible systems will be justified. But this observation, of course, thoroughly undermines any claim suggesting that coherence is indicative of truth. As we shall see, most, if not all, influential coherence theorists try to avoid these traditional objections by assigning some beliefs that are close to experience a special role, whether they are called supposed facts asserted (Lewis, 1946), truth-candidates (Rescher, 1973), cognitively spontaneous beliefs (BonJour, 1985) or something else.

Depending on how this special role is construed, these theories may be more fruitfully classified as versions of weak foundationalism than as pure coherence theories. An advocate of weak foundationalism typically holds that while coherence is incapable of justifying beliefs from scratch, it can provide justification for beliefs that already have some initial, perhaps miniscule, degree of warrant, e. g. , for observational beliefs. A fair number of distinguished contemporary philosophers have declared that they advocate a coherence theory of justification.

Apart from this superficial fact, these theories often address some rather diverse issues loosely united by the fact that they in one way or the other take a holistic approach to the justification of beliefs. Here are some of the problems and questions that have prompted coherentist inquiry (cf. Bender, 1989): The regress problem How can we gain knowledge given that our information sources (senses, testimony etc) are not reliable? How can we know anything at all given that we do not even know whether our own beliefs or memories are reliable?

Given a set of beliefs and a new piece of information (typically an observation), when is a person justified in accepting that information? What should a person believe if confronted with a possibly inconsistent set of data? The fact that these separate, though related, issues are sometimes discussed in one swoop presents a challenge to the reader of the relevant literature. To get a firmer grasp of the coherence theory and the way in which it is invoked, it is helpful to introduce it, following tradition, as a response to the regress problem.

This will also serve to illustrate some challenges that a coherence theory faces. We will then turn to the concept of coherence itself as that concept is traditionally conceived. Unfortunately, not all prominent authors associated with the coherence theory use the term coherence in this traditional sense, and the section that follows is devoted to such non-standard coherence theories. The arguably most systematic and prolific discussion of the coherence theory of justification has focused on the relationship between coherence and probability.

The rest of the article will be devoted to this development, which took off in the mid-1990s inspired by seminal work by C. I. Lewis (1946) and which has given us precise and sophisticated definitions of coherence as well as detailed studies of the relationship between coherence and truth (probability), culminating in some potentially disturbing impossibility results that shed doubt on the possibility of defining coherence in a way that makes it indicative of truth. What these results entail, more precisely, and how the worries they raise can be addressed will be the topic of our final discussion. 2.

The Regress Problem On the traditional justified true belief account of knowledge, a person cannot be said to know that a proposition p is true without having good reasons for believing that p is true. If Lucy knows that she will pass tomorrows exam, she must have good reasons for thinking that this is so. Consider now Lucys reasons. They will presumably consist of other beliefs she has, e. g. , beliefs about how well she did earlier, about how well she has prepared, and so on. For Lucy to know that she will pass the exam, these other beliefs, upon which the first belief rests, must also be things that Lucy knows.

Knowledge, after all, cannot be based on something less than knowledge, i. e. , on ignorance (cf. Rescher 1979, 76). Since the reasons are themselves things that Lucy knows, those reasons must in turn be based on reasons, and so on. Thus, any knowledge claim requires a never-ending chain, or regress, of reasons for reasons. This seems strange, or even impossible, because it involves reference to an infinite number of beliefs. But most of us think that knowledge is possible. What is the coherentists response to the regress?

The coherentist can be understood as proposing that nothing prevents the regress from proceeding in a circle. Thus, A can be a reason for B which is a reason for C which is a reason for A. If this is acceptable, then what we have is a chain of reasons that is never-ending but which does not involve an infinite number of beliefs. It is never-ending in the sense that for each belief in the chain there is a reason for that belief also in the chain. Yet there is an immediate problem with this response due to the fact that justificatory circles are usually thought to be vicious ones.

If someone claims C and is asked why she believes it, she may reply that her reason is B. If asked why she believes B, she may assert A. But if prompted to justify her belief in A, she is not allowed to refer back to C which in the present justificatory context is still in doubt. If she did justify A in terms of C nonetheless, her move would lack any justificatory force whatsoever. The coherentist may respond by denying that she ever intended to suggest that circular reasoning is a legitimate dialectical strategy.

What she objects to is rather the assumption that justification should at all proceed in a linear fashion whereby reasons are given for reasons, and so on. This assumption of linearity presupposes that what is, in a primary sense, justified are individual beliefs. This, says the coherentist, is simply wrong: it is not individual beliefs that are primarily justified, but entire belief systems. Particular beliefs can also be justified but only in a secondary or derived sense, if they form part of a justified belief system.

This is a coherence approach because what makes a belief system justified, on this view, is precisely its coherence. A belief system is justified if it is coherent to a sufficiently high degree. This, in essence, is Laurence BonJours 1985 solution to the regress problem. This looks much more promising than the circularity theory. If epistemic justification is holistic in this sense, then a central assumption behind the regress is indeed false, and so the regress never gets started. Even so, this holistic approach raises many new questions to which the coherentist will need to respond.

First of all, we need to get clearer on what the concept of coherence involves as that concept is applied to a belief system. This is the topic of the next section. Second, the proposal that a singular belief is justified merely in virtue of being a member of a justified totality can be questioned because, plausibly, a belief can be a member of a sufficiently coherent system without in any way adding to the coherence of that system. Surely, a belief will have to contribute to the coherence of the system in order to become justified by that system.

A particular belief needs, in other words, to cohere with the system of which it is a member if that belief is to be considered justified. We will turn to this issue in section 4, in connection with Keith Lehrers epistemological work. Finally, we have seen that most coherence theories assign a special role to some beliefs that are close to experience in order to avoid the isolation and alternative systems objections. This fact raises the question of what status those special beliefs have. Do they have to have some credibility in themselves or can they be totally lacking therein?

A particularly clear debate on this topic is the Lewis-BonJour controversy over the possibility of justification by coherence from scratch, which we will examine more closely in section 5. 3. Traditional Accounts of Coherence By a traditional account of coherence we will mean one which construes coherence as a relation of mutual support, consistency or agreement among given data (propositions, beliefs, memories, testimonies etc. ). Early characterizations were given by, among others, Brand Blanshard (1939) and A. C. Ewing (1934).

According to Ewing, a coherent set is characterized partly by consistency and partly by the property that every belief in the set follows logically from the others taken together. Thus, a set such as {A1, A2, A1&A2}, if consistent, is highly coherent on this view because each element follows by logical deduction from the rest in concert. While Ewings definition is admirably precise, it defines coherence too narrowly. Few sets that occur naturally in everyday life satisfy the austere second part of his definition: the requirement that each element follow logically from the rest when combined.

Consider, for instance, the set consisting of propositions A, B and C, where A = John was at the crime scene at the time of the robbery B = John owns a gun of the type used by the robber C = John deposited a large sum of money in his bank account the next day This set is intuitively coherent, and yet it fails to satisfy Ewings second condition. The proposition A, for instance, does not follow logically from B and C taken together: that John owns a gun of the relevant type and deposited money in his bank the day after does not logically imply him being at the crime scene at the time of the crime.

Similarly, neither B nor C follows from the rests of the propositions in the set by logic alone. C. I. Lewiss definition of coherence, or congruence to use his term, can be seen as a refinement and improvement of Ewings basic idea. As Lewis defines the term, a set of supposed facts asserted is coherent (congruent) just in case every element in the set is supported by all the other elements taken together, whereby support is understood not in logical terms but in a weak probabilistic sense.

In other words, P supports Q if and only if the probability of Q is raised on the assumption that P is true. As is readily appreciated, Lewiss definition is less restrictive than Ewings: more sets will turn out to be coherent on the former than on the latter. (There are some uninteresting limiting cases for which this is not true. For instance, a set of tautologies will be coherent in Ewings but not in Lewiss sense. ) Let us return to the example with John.

The proposition A, while not logically entailed by B and C, is under normal circumstances nevertheless supported by those propositions taken together. If we assume that John owns the relevant type of gun and deposited a large sum the next day, then this should raise the probability that John did it and thereby also raise the probability that he was at the crime scene when the robbery took place. Similarly, one could hold that each of B and C is supported, in the weak probabilistic sense, by the other elements of the set.

If so, this set is not only coherent in an intuitive sense but also coherent according to Lewiss definition. Against Lewiss proposal one could hold that it seems arbitrary to focus merely on the support single elements of a set receive from the rest of the set (cf. Bovens and Olsson 2000). Why not consider the support any subset, not just singletons, receives from the rest? Another influential proposal concerning how to define coherence originates from Laurence BonJour (1985), whose account is considerably more complex than earlier suggestions.

Where Ewing and Lewis proposed to define coherence in terms of one single concept”logical consequence and probability, respectively”BonJour thinks that coherence is a concept with a multitude of different aspects corresponding to the following coherence criteria (9799): A system of beliefs is coherent only if it is logically consistent. A system of beliefs is coherent in proportion to its degree of probabilistic consistency. The coherence of a system of beliefs is increased by the presence of inferential connections between its component beliefs and increased in proportion to the number and strength of such connections.

The coherence of a system of beliefs is diminished to the extent to which it is divided into subsystems of beliefs which are relatively unconnected to each other by inferential connections. The coherence of a system of beliefs is decreased in proportion to the presence of unexplained anomalies in the believed content of the system. A difficulty pertaining to theories of coherence that construe coherence as a multidimensional concept is to specify how the different dimensions are to be amalgamated so as to produce an overall coherence judgment.

It could well happen that one system S is more coherent than another system T in one respect, whereas T is more coherent than S in another. Perhaps S contains more inferential connections than T, but T is less anomalous than S. If so, which system is more coherent in an overall sense? Bonjours theory is largely silent on this point. BonJours account also raises another general issue. The third criterion stipulates that the degree of coherence increases with the number of inferential connections between different parts of the system.

Now as a system grows larger the probability that there will be relatively many inferentially connected beliefs is increased simply because there are more possible connections to be made. Hence, one could expect there to be a positive correlation between the size of a system and the number of inferential connection between the beliefs contained in the system. BonJours third criterion, taken at face value, entails therefore that a bigger system will generally have a higher degree of coherence due to its sheer size. But this is at least not obviously correct.

A possible modified coherence criterion could state that what is correlated with higher coherence is not the number of inferential connections but rather the inferential density of the system, where the latter is obtained by dividing the number of inferential connections by the number of beliefs in the system. 4. Other Accounts of Coherence We will return, in section 6, to the problem of defining the traditional concept of coherence while addressing some of the concerns that we have raised, e. g. , concerning the relationship between coherence and system size.

The point of departure for the present discussion, however, is the observation that several prominent self-proclaimed coherentists construe the central concept, and to some extent also its role in philosophical inquiry, in ways that depart somewhat from the traditional view. Among them we find Nicolas Rescher, Keith Lehrer and Paul Thagard. Central in Reschers account, as laid out in Rescher (1973), his most influential book on the subject, is the notion of a truth-candidate. A proposition is a truth-candidate if it is potentially true, so that there is something that speaks in its favor.

Reschers truth-candidates are obviously related to Lewiss supposed facts asserted. In both cases, the propositions of interest are prima facie rather than bona fide truths. Although Reschers 1973 book is entitled A Coherence Theory of Truth, the purpose of Reschers investigation is not to investigate the possibility of defining truth in terms of coherence but to find a truth criterion, which he understands to be a systematic procedure for selecting from a set of conflicting and even contradictory truth-candidates those elements which it is rational to accept as bona fide truths.

His solution amounts to first identifying the maximal consistent subsets of the original set, i. e. , the subsets that are consistent but would become inconsistent if extended by further elements of the original set, and then choosing the most plausible among these subsets. Plausibility is spelled out in a way that reveals no obvious relation to the traditional concept of coherence. While the traditional concept of coherence plays a role in the philosophical underpinning of Reschers theory, it does not figure essentially in the final product.

In a later book, Rescher develops a more traditional system-theoretic view on coherence (Rescher 1979). Keith Lehrer employs the concept of coherence in his definition of justification, which in turn is a chief ingredient in his complex post-Gettier definition of knowledge. According to Lehrer, a person is justified in accepting a proposition just in case that proposition coheres with the relevant part of her cognitive system. This is the relational concept of coherence alluded to earlier.

In Lehrer (1990), the relevant part is the acceptance system of the person, consisting of reports to the effect that the subject accepts this and that. Thus, S accepts that A would initially be in Ss acceptance system, but not A itself. In later works, Lehrer has emphasized the importance of coherence with a more complex cognitive entity which he calls the evaluation system (e. g. , Lehrer 2000 and 2003). The starting point of Lehrers account of coherence is the fact that we can think of all sorts of objections an imaginative critic may raise to what a person accepts.

These objections might be directly incompatible with what that person accepts or they might threaten to undermine her reliability in making assessments of the kind in question. For instance, a critic might object to her claim that she sees a tree by suggesting that she is merely hallucinating. That would be an example of the first sort of objection. An example of the second sort would be a case in which the critic replies that the person cannot tell whether she is hallucinating or not. Coherence, and (personal) justification, results when all objections have been met.

Lehrers concept of coherence does not seem to have much in common with the traditional concept of mutual support. If one takes it as essential that such a theory make use of a concept of systematic or global coherence, then Lehrers theory is not a coherence theory in the traditional sense because, in Lehrers view, [c]oherence ¦ is not a global feature of the system (1997, 31), nor does it depend on global features of the system (31). A critic may wonder what reasons there are for calling the relation of meeting objections to a given claim relative to an evaluation system a relation of coherence.

Lehrers answer seems to be that it is a relation of fitting together with, rather than, say, a relation of being inferable from: [i]f it is more reasonable for me to accept one of [several] conflicting claims than the other on the basis of my acceptance system, then that claim fits better or coheres better with my acceptance system (116), and so [a] belief may be completely justified for a person because of some relation of the belief to a system to which it belongs, the way it coheres with the system, just as a nose may be beautiful because of some relation of the nose to a face, the way it fits with the face (88).

Olsson (1999) has objected to this view by pointing out that it is difficult to understand what it means for a belief to fit into a system unless the former does so in virtue of adding to the global coherence of the latter. Paul Thagards theory is clearly influenced by the traditional concept of coherence but the specific way in which the theory is developed gives it a somewhat non-traditional flavor, in particular considering its strong emphasis on explanatory relations between beliefs.

Like Rescher, Thagard takes the fundamental problem to be which elements of a given set of typically conflicting claims that have the status of prima facie truths to single out as acceptable. However, where Rescher proposes to base the choice of acceptable truths on considerations of plausibility, Thagard suggests the use of explanatory coherence for that purpose. According to Thagard, prima facie truths can cohere (fit together) or incohere (resist fitting together).

The first type of relation includes relations of explanation and deduction, whereas the second type includes various types of incompatibility, such as logical inconsistency. If two propositions cohere, this gives rise to a positive constraint. If they incohere, the result is a negative constraint. A positive constraint between two propositions can be satisfied either by accepting both or by rejecting both. By contrast, satisfying a negative constraint means accepting one proposition while rejecting the other.

A coherence problem, as Thagard sees it, is one of dividing the initial set of propositions into those that are accepted and those that are rejected in such a way that most constraints are satisfied. Thagard presents several different computational models for solving coherence problems, including a model based on neural networks. How acceptability depends on coherence, more precisely, is codified in Thagards principles of explanatory coherence (Thagard, 2000): Principle E1 (Symmetry)

Explanatory coherence is a symmetric relation, unlike, say, conditional probability. That is, two propositions A and B cohere with each other equally. Principle E2 (Explanation) A hypothesis coheres with what it explains, which can either be evidence or another hypothesis. Hypotheses that together explain some other proposition cohere with each other. The more hypotheses it takes to explain something, the lower the degree of coherence. Principle E3 (Analogy) Similar hypotheses that explain similar pieces of evidence cohere. Principle E4 (Data Priority)

Propositions that describe the results of observation have a degree of acceptability on their own. Principle E5 (Contradiction) Contradictory propositions are incoherent with each other. Principle E6 (Competition) If A and B both explain a proposition, and if A and B are not explanatorily connected, then A and B are incoherent with each other (A and B are explanatorily connected if one explains the other or if together they explain something). Principle E7 (Acceptance) The acceptability of a proposition in a system of propositions depends on its coherence with them.

Principle E4 (Data Priority) reveals that Thagards theory is not a pure coherence theory, as it gives some epistemic priority to observational beliefs, making it rather a form of weak foundationalism. Moreover, Thagards theory is based on binary coherence/incoherence relations, i. e. , relations holding between two propositions. His basic theory does not handle incompatibilities that involve, in an essential way, more than two propositions. But incompatibilities of that sort may very well arise, as exemplified by the three propositions Jane is taller than Martha, Martha is taller than Karen and Karen is taller than Jane.

Nevertheless, Thagard reports the existence of computational methods for converting constraint satisfaction problems whose constraints involve more than two elements into problems that involve only binary constraints, concluding that his characterization of coherence suffices in principle for dealing with more complex coherence problems with nonbinary constraints (Thagard 2000, 19). Several other authors have defended coherence theories that emphasize the importance of explanatory relations, e. g. , William Lycan. See Lycan (1988) and, for a recent statement, Lycan (2012).

5. Justification by Coherence from Scratch The arguably most significant development of the coherence theory in recent years has been the revival of C. I. Lewiss work and the research program he inspired by translating parts of the coherence theory into the language of probability. This translation has made it possible to define concepts and prove results with mathematical precision. It has also led to increased transferability of concepts and results across fields, e. g. , between coherence theory and confirmation theory as it is studied in philosophy of science.

As an effect, the study of coherence, from being a fairly isolated and somewhat obscure part of epistemology, has developed into an interdisciplinary research program with connections to philosophy of science, cognitive psychology, artificial intelligence and philosophy of law. The rest of this article will be devoted to this recent transformation of the subject. To introduce Lewiss view on the role of coherence, consider the following famous passage on relatively unreliable witnesses who independently tell the same story from his 1946 book:

For any one of these reports, taken singly, the extent to which it confirms what is reported may be slight. And antecedently, the probability of what is reported may also be small. But congruence of the reports establishes a high probability of what they agree upon, by principles of probability determination which are familiar: on any other hypothesis than that of truth-telling, this agreement is highly unlikely; the story any one false witness might tell being one out of so very large a number of equally possible choices.

(It is comparable to the improbability that successive drawings of one marble out of a very large number will each result in the one white marble in the lot. ) And the one hypothesis which itself is congruent with this agreement becomes thereby commensurably well established. (246) While Lewis allows that individual reports need not be very credible considered in isolation for coherence to have a positive effect, he is firmly committed to the view that their credibility must not be nil.

He writes, in his discussion of reports from memory, that [i]f ¦ there were no initial presumption attaching to the mnemically presented ¦ then no extent of congruity with other such items would give rise to any eventual credibility (357). In other words, if a belief system is completely isolated from the world, then no justification will ensue from observing the coherence of its elements. Thus, Lewis is advocating weak foundationalism rather than a pure coherence theory.

In apparent agreement with Lewis, Laurence BonJour (1985, 148) writes: [a]s long as we are confident that the reports of the various witnesses are genuinely independent of each other, a high enough degree of coherence among them will eventually dictate the hypothesis of truth telling as the only available explanation of their agreement. However, BonJour proceeds to reject Lewiss point about the need for positive antecedent credibility: [w]hat Lewis does not see, however, is that his own [witness] example shows quite convincingly that no antecedent degree of warrant or credibility is required (148).

BonJour is here apparently denouncing Lewiss claim that coherence will not have any confidence boosting power unless the sources are initially somewhat credible. BonJour is proposing that coherence can play this role even if there is no antecedent degree of warrant, so long as the witnesses are delivering their reports independently. Several authors have objected to this claim of BonJours, arguing that coherence does not have any effect on the probability of the report contents if the independent reports lack individual credibility. The first argument to that effect was given by Michael Huemer (1997).

A more general proof in the same vein is presented in Olsson (2002). What follows is a sketch of the latter argument for the special case of two testimonies, couched essentially in the terminology of Huemer (2011). In the following, all probabilities are assumed to lie strictly between 0 and 1. Let E1 be the proposition that the first witness reports that A, and let E2 be the proposition that the second witness reports that A. Consider the following conditions: Conditional Independence P(E2 | E1,? A) = P(E2 | A) P(E2 | E1,¬A) = P(E2 | ¬A) Nonfoundationalism P(A | E1) = P(A) P(A | E2) = P(A).

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