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 V_{1}
and V_{2}, 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.