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by Paul Thagard
MIT Press, 2000
Review by Majid Amini on Nov 9th 2001

Coherence in Thought and ActionIf there was ever an attempt to construct a grand unified theory of human consciousness with its multifarious manifestations, Coherence in Thought and Action is certainly a competing, and capable, candidate. What essentially Paul Thagard does is to tender coherence as the holy grail of human inference and thinking. The thrust of the book is epitomized by Thagard's repeated observation that 'the foundational search for certainty was pointless, and that what mattered was the growth of knowledge, not its foundations.' (p. 90) Thagard thinks that the key to the growth of knowledge and to its very understanding is nothing other than coherence.

The book consists of nine chapters, but Chapter 2 contains the core of Thagard's conception of coherence with its technical details and finesses. In fact, it is this chapter that both friends and foes of coherence need to stick their critical teeth into. Chapter 1 offers a broad historical-cum-analytical overview of the role of coherence in philosophy and psychology and delineates Thagard's brand of cognitive naturalism as a symbiosis of philosophy and psychology built on that notion. Chapters 3 to 7 explore the relevance and application of coherence to a wide variety of topics ranging from the nature of knowledge and reality to the philosophical and psychological problems in ethics and politics, and finally to the nature of emotions and how emotional coherence underpin beauty in science and art. Chapter 8 attempts a defense of coherentism against the rival probabilistic approach to the issues of theory choice and belief revision in particular and to inference in general. The finale in Chapter 9 is a blueprint for a coherentist research project in cognitive science, in synchrony, of course, with the philosophical movement of cognitive naturalism.

However, in order to appreciate the significance of Thagard's contention to ensconce coherence at the center of philosophy, a brief background to the debate may not be amiss. Generally, coherence has been a recurrent theme in philosophy; indeed, it does not take long to find a philosopher commenting on certain competing accounts to commend the more coherent scientific or ethical theory, or the more coherent plan, or the more coherent theory of something else. Yet, there has not been much of an account of what exactly coherence itself was. The problem was not that of coming by synonymous, or near synonymous, words or phrases like one's beliefs cohere if they "hang together" or one's goals make up a coherent plan if they "fit well with one another." The problem was not even that of itemizing the ingredients of coherence such as appropriateness of means to ends, logical consistency, and so on. The problem was, however, the lack of any specification of how these ingredients were to be calculated and combined with respect to a set of propositions. That is, how one was supposed to work out the degree each item on the list would contribute to the overall coherence of a theory or strategy: 'no insight on how to achieve it.' (p. 6) Practically speaking, there was no decision procedure for determining comparative coherence.

Yet, without such an account, counseling to choose the most coherent cluster of thoughts or course of action would be no more than empty words. In fact, the received opinion was that an account of coherence sufficiently detailed and definite to be turned into a computer program was beyond reach. Coherence is not something for which we have an algorithm, but is something that we ultimately judge, in Hilary Putnam's "memorable" expression, by 'seat of the pants' feel. [Reason, Truth and History (Cambridge: Cambridge University Press, 1982) p. 133] It is, therefore, against this background that Thagard's attempt to characterize coherence 'as mathematically precise as the tools of deductive logic and probability theory' (p. 16) becomes interesting and challenging.

Formally, Thagard defines coherence in terms of the notion of a coherence problem as follows:

Let E be a finite set of elements {ei} and C be a set of constraints on E understood as a set {(ei, ej)} of pairs of elements of E. C divides into C+, the positive constraints on E, and C-, the negative constraints on E. With each constraint is associated a number w, which is the weight (strength) of the constraint. The problem is to partition E into two sets, A and R, in a way that maximizes compliance with the following two coherence conditions:

· If (ei, ej) is in C+, then ei is in A if and only if ej is in A.

· If (ei, ej) is in C-, then ei is in A if and only if ej is in R.

Let W be the weight of the partition, that is, the sum of the weights of the satisfied constraints. The coherence problem is then to partition E into A and R in a way that maximizes W. (p. 18)

What this means in "plain language" is that: given (1) a number of elements like propositions or objectives, (2) two sets of positive and negative constraints such that if a certain element is in, then another one should also be in, and if a certain element is in, another one should be out, and (3) weights for the constraints that specify how important satisfying a constraint is, then one needs to find a way of dividing up the set of elements into an accepted (A) and a rejected (R) set which satisfy as many constraints as possible. Thus, the higher the summed weights of the satisfied constraints, the more coherent the solution to the coherence problem would be in a particular case.

But, how can one compute this conception of coherence? That is, back to our earlier pragmatic problem of how to measure comparative coherence. Thagard moots the following five possible algorithms for calculating coherence:

· An exhaustive search algorithm that considers all possible solutions

· An incremental algorithm that considers elements in arbitrary order

· A connectionist algorithm that uses an artificial neural network to assess coherence

· A greedy algorithm that uses locally optimal choices to approximate a globally optimal solution

· A semidefinite programming (SDP) algorithm that is guaranteed to satisfy a high proportion of the maximum satisfiable constraints (p. 26; original emphasis)

In the process of essaying each one in turn, he dismisses the first two for being of limited use but argues that the other three provide effective means of computing coherence. Thagard's favorites, however, are connectionist algorithms as, he claims, there is a 'natural alignment between coherence problems and connectionist networks' and they provide the 'most psychologically appealing models of coherence optimization'. (pp. 33 & 40 respectively)

Having sketched the formal and implementational components of Thagard's account of coherence, I would like to raise three sets of point. The first point to note about the formal characterization of coherence is the use of the biconditional clause "if and only if" which is indicative of a larger issue about the insufficiency of coherence for constituting truth. The question is: how are we supposed to understand such clauses -- in a coherence way on pain circularity or in a non-coherence manner? My entry is patently parochial but symptomatic of the global issue about the nature of truth. The significance of the question lies in the twist of Thagard's tale where he parts company with conventional coherentists by not defending 'a coherence theory of truth, since there are good reasons for preferring a correspondence theory'. (p. 74) In fact, rather iconoclastically for a coherentist, he attempts to 'argue against a coherence theory of truth'. (p. 85; original emphasis) Nonetheless, in a spirit of conciliation, he says: 'truth is a matter also of correspondence, not coherence alone.' (p. 78) Thus, Thagard's eclectic approach allows him to parry perennial problems of coherentism such as isolation objection that a set of beliefs may be internally coherent but not true - the case of illusory but consistent theories. But, obviously, his eclecticism does not curry favor with hard-line and puritanical coherentists.

The second point to note is that Thagard's characterization of coherence is reminiscent of a familiar problem in graph theory known as MAX CUT. Formally, Michael Garey and David Johnson express the problem thus:

INSTANCE: Graph G = (V, E), "weigh" w(e) Î Z+ for each e Î E, positive integer K.

QUESTION: Can V be partitioned into two disjoint sets V1 and V2, such that the sum of the weights of the edges from E that have one endpoint in each set is at least K? [Computers and Intractability: A Guide to the Theory of NP-Completeness (New York: Freeman, 1979), p. 87]

Again, in "plain language", the question is whether one can find a way of cutting a network into two parts such that the total capacity of the links crossing the cut is maximized. Now, the intriguing point here is that Thagard's characterization of coherence is indeed a variation on MAX CUT, but MAX CUT is NP (Nondeterministic Polynomial)-complete. A problem is NP-complete when it is hard in principle: that is, no matter how large or fast a computer is, there are reasonably sized inputs for which there are no efficient (polynomial-time) procedures for solving the problem. In other words, like MAX CUT, Thagard's coherence is NP-complete and as such is computationally intractable.

However, Thagard himself is cognizant of these concerns and seems happy to settle for an approximation of optimal coherence: computing 'coherence is a matter of maximizing constraint satisfaction' which 'can be accomplished approximately'. (p. 40) That is, if the algorithms cannot be used to lasso the set of elements with the maximum summed weights of coherence, one should perhaps opt for a set that comes close. But the problem with such approximations is that not only they fail to form the most coherent set but also fail to ensure that the chosen set is not dramatically different from the most coherent one. In other words, there is no guarantee that the next most coherent set is not drastically divergent from the most coherent one.

Nevertheless, for Thagard, there are still ways of shoring up coherence with varying degrees of vigor. Minimally, by taking the cue from the title of the book, one could concentrate on the action part, rather than thought, and emphasize the centrality of coherence in conative contexts. In planning tasks where the problem is not so much about truth or falsity but devising the most efficient way of reconciling various practical goals and objectives, approximations of most coherent plans are as good as the most coherent ones. Thus, from a practical perspective, coherence as a criterion of adequacy does play a principal part in our reasoning deliberations.

Maximally, however, one may extend the debate to the level of thought. Thagard could pose the same problem of approximation to non-coherentist alternatives. For example, Bayesian probabilistic reasoning is similarly beset with computational intractability and as such it relies on approximations for computing posterior probabilities. Also probabilistic information updating leads to a combinatorial explosion, 'since we need to know the probabilities of a set of conjunctions whose size grow exponentially with the number of propositions.' (p. 250) Generally, and more importantly, it seems that any procedure sufficiently rich to be able to model everyday theory choices, whether scientific or otherwise, involves some measure of approximation.

The third point to note is the predilection that Thagard shows for connectionist algorithms in the implementation of coherence. Although Thagard is conscious of the computational limitations of connectionist algorithms, he capitalizes on the encouraging empirical results from a number of such neural network models of coherence to propose them for their psychological appeal. As a matter of fact, Thagard says that his 'characterization of coherence was abstracted' from connectionist methods in the first place. (p. 15) Unfortunately, however, he does not engage with the criticisms of connectionism pressed by the classical computational theorists of mind and advocates of domain-specificity and modularity of brain, especially in point of the psychological plausibility of connectionist models of mind, which plainly leaves lacunas in his coherentist lattice of cognition.

Overall, through his eclecticism and approximation algorithms, Thagard is able to tout a viable notion of coherence, while curtailing its traditional excessive claims by conceding, for example, that 'the formation of elements such as propositions and concepts and the construction of constraint relations between elements depend on processes to which coherence is only indirectly relevant.' (p. 24) More significantly, he prides himself for being able to vaccinate coherentism against the virus of isolation, i.e., there is no guarantee that the most coherent theory is also true. Nonetheless, the susceptibility still remains the Achilles' heel of coherentism: approximating maximum coherence is not yet the same thing as approximating truth. Indeed, Thagard himself admits that for the coherentist project to succeed one needs 'to see a much fuller account of the conditions under which progressively coherent theories can be said to approximate the truth.' (p. 280)

In conclusion, it is something of a cliché in reviewing to remark that little of the richness of the work in question can be captured in a review of this length. Nonetheless, this is particularly applicable to the present book. Here I have focused on the main philosophical constituents of Thagard's coherentist conception, but the real richness of the book is in the variety and depth of the examples with which this conception is illustrated. In all of those examples, there is ample space for debate on each of the controversial topics that Thagard touches.

© 2001 Majid Amini

Majid Amini, Department of History and Philosophy, University of the West Indies, Barbados

Personal Information: I did my undergraduate and postgraduate philosophy degrees at the University of London. I started teaching philosophy in 1991 and have taught at the Universities of London and Manchester in Britain. Since 1999, I have been the Co-ordinator of Philosophy at the University of the West Indies, Cave Hill Campus, Barbados.