"Truth entails coherence, not vice versa."
Does this refute coherence theories of truth?

It very much depends on what you think the statement means.

A Non-Coherentist (say, for example, a Correspondence Theorist) would maintain that the stated entailment should be interpreted as "A entails B."   This interpretation would be based on the premise that A is not the same as B - truth is not the same as coherence - and therefore coherence results from truth, not vice versa.   So a Correspondence Theorist would maintain that the title quote does refute the Coherence Theory.  

But a Coherence Theorist would deny that this is the proper interpretation.   Instead, the Coherentist would maintain that "Truth is coherence" and would therefore understand the stated entailment as "A entails A," and would not simply disagree with, but would not even understand, the "not vice versa" business.   A Coherence Theorist would agree with the Correspondence Theorist that "Truth entails coherence."   But the Coherence Theorist would deny that this is because "Truth results in coherence" and would argue instead that this is because "Truth is coherence".   The Coherence Theorist would therefore understand the "not vice versa" phrase as meaning "not(A entails A)" - in other words as denying an obvious identity - and obviously nonsense.   So a Coherence Theorist would maintain that the title quote does not refute the Coherence Theory.

Only if one understands the "not vice versa" phrase as meaning "not(coherence entails truth)" can the titled quote be seen as a refutation of the coherence theory of truth.   But this is an understanding that the Correspondence Theorist would agree is obvious, while the Coherence Theorist would refuse to accept as not logically possible.

So how one understands what the words mean will result from how one thinks about truth, not vice versa.   The statement cannot therefore really be used as a refutation of coherence theories of truth.   Although it is often employed by critics of the Coherence Theory of truth.

Coherence?

A "Coherence Theory of Truth" maintains that the truth of any (true) proposition consists in its coherence with some specified set of propositions.   To best appreciate the coherence thesis, it is easiest to contrast it with its main competitor - the Correspondence Theory of Truth.   Advocates of the correspondence theory believe that a belief is (generally) ontologically distinct from the objective conditions which make the belief true.   Coherentists do not believe that there is an ontological distinction between beliefs and what makes beliefs true.   From the Coherentist's perspective, reality is something like a collection of beliefs.   Consequently, a belief cannot be true because it corresponds to something which is not a belief.   Instead, the truth of a belief can only consist in its coherence with other beliefs.   A coherence theory of truth sometimes leads to the view that truth comes in degrees.   A belief is true to the degree that it coheres with other beliefs.

Coherence theories thus differ from the Correspondence Theory in two essential respects.   The competing theories give conflicting accounts of the relation between propositions and their truth conditions.   According to one, the relation is coherence, according to the other, it is correspondence. The competing theories also give conflicting accounts of truth conditionals.   According to coherence theories, the truth conditionals of propositions consist in other propositions.   The correspondence theory, in contrast, states that the truth conditionals of propositions are not (in general) propositions, but rather objective features of the world. (Even the correspondence theorist holds that propositions about propositions have propositions as their truth conditionals.)

Coherence theorists (at least those who do not believe that the "Specified set" is the set of propositions believed by an omniscient intellect) are committed to the rejection of both the law of the excluded middle (that either P or 星 is true) and the principle of transcendence (no matter what the evidence in support of P, it is possible that 星).   Since the Coherentist is dealing with propositions believed and not the set of all possible propositions, it is not necessary that for every proposition either P or 星 will cohere with the given specified set of beliefs.   And since any proposition that coheres with a set of beliefs is known to cohere with the set, it is not possible for P to be true and not known to be true.  

(A Coherentist does accept the principle of bivalence, since any proposition P will either cohere or not cohere with the given specified set.   And a Coherentist who maintains that the "Specified set" is the set of propositions believed by an omniscient intellect is effectively agreeing with the Correspondence Theorist, just using different words to describe what the truth corresponds with.   The Correspondence Theorist maintains that true propositions correspond to the world - facts, states of affairs, or what-have-you.   The omniscient-intellect Coherentist maintains that true propositions cohere with the set of all possible true propositions.   Given that both would agree that the totality of reality (whether of a realist or an anti-realist variety) is fully described by the set of all possible true propositions, these two positions are effectively the same.)

There are several different versions of the coherence theory of truth.   Versions of the coherence theory differ on two major issues - (i) they provide different accounts of what constitutes the coherence relation; and (ii) they provide different accounts of the set (or sets) of propositions with which true propositions cohere (the "Specified set").

According to one common version of the coherence theory, the coherence relation is simply consistency.   To say that a proposition "coheres" with a specified set of propositions is to say that the proposition is logically consistent with the set - i.e. does not contradict any member (or group of members) of the set.   The "Truth entails coherence" criticism attacks this account of coherence as unsatisfactory for the following reason.   Consider two propositions (say "P" and "星") which do not yet belong to a specified set.   The critic argues that it is logically possible that both of these propositions could each be suitably consistent with some particular specified set and yet be inconsistent with each other.   If coherence is consistency, and truth is coherence, the Coherence Theorist would have to claim that both propositions are true.   But this is intuitively difficult to accept and challenges the theory's notion of coherence as consistency.   (The argument can be suitably reworked to address the various other ways that the Coherentist chooses to understand "coherence".)   The critic then offers the argument that (at most) only one of these two propositions is true (independently of coherence), and that truth entails coherence, and not vice versa.

On the other hand, the Coherentist can reply that the concern is with propositions believed, and not just any arbitrary propositions.   So it is irrelevant that "P" and "星" contradict each other, or are each logically consistent with some particular set of other propositions.   What is relevant is that given some previously delimited "Specified set" of beliefs, one or the other will cohere - not both.   In other words, the Coherentist would deny that the scenario proposed by the critic is logically possible.

Coherence theories generally agree that the "Specified set" consists of propositions believed or held to be true.   They differ on the question of who believes the propositions and when.   At one extreme, a coherence theorist can hold that the specified set of propositions is the largest consistent set of propositions currently believed by some group of actual people.   A moderate position has the specified set consisting of those propositions which will be believed when people like us (with finite cognitive capacities) have reached some limit of inquiry.   At the other extreme, a coherence theorist can maintain that the specified set contains the propositions which would be believed by an omniscient intellect, or by us at the ideal limit of investigation.

The "Truth entails coherence" criticism attacks any specification of a "Specified set" using an argument very similar to the one described above.   Consider two mutually contradictory propositions (say "P" and "星" again) which do not yet belong to the initially given "Specified set".   The critic argues that it is logically possible that each of these propositions could be properly coherent (however the Coherentist chooses to understand "coherence") with a different subset (which by stipulation are to be considered equal across any measure of significance) of the given "Specified set".   Then the resulting two "Specified sub-sets" will also be mutually contradictory.   The argument is that there is no basis from which to choose which of the two "Specified sub-sets" is to be regarded as true.   In other words, there is no basis from which to judge which of the two initial mutually contradictory propositions is true and which is false.   Like before, this is intuitively difficult to accept and challenges the theory's notion of truth as coherence.   The specification objection notes that, having somehow established an appropriate "maximally coherent set of propositions", the Coherentist is forced to make one extra claim - that this maximally coherent set is to be preferred to some alternative maximally coherent set.   In other words, that this coherent set is "True" whereas that one is false.   The critic offers the argument that (at most) only one of these two sets is true (independently of coherence), and that truth entails coherence, and not vice versa.

On the other hand, Coherentists do not believe that the truth of a proposition consists in coherence with any arbitrarily chosen set of propositions.   Rather, they hold that truth consists in coherence with a set of beliefs, or with a set of propositions held to be true. Since it can be assumed that no one actually believes a set of propositions within which a sub-set can be found that each of those two mutually contradictory propositions coheres, coherence theorists can conclude that one is false without contradicting themselves.   In other words, the Coherentist would again deny that while the scenario proposed by the critic is logically possible, it is not practically possible given the beliefs that people actually do have.

The most telling criticism implied by the title quote is the argument that a coherence theory of truth has no means of answering questions like: (i) what is it about a specified set of coherent propositions that makes them coherent?   (ii)   why do some sets of propositions cohere, and not others?   (iii)   is there any way of distinguishing between two internally coherent sets of propositions that are mutually contradictory?   Correspondence Theorists would maintain that it is the nature of the underlying reality that makes the difference.   In the words of the title quote: (i) it is the evidence transcendent fact of truth that results in the coherence of true beliefs;   (ii) true beliefs cohere because reality itself is coherent; and (iii) what distinguishes between two internally coherent sets of propositions that are mutually contradictory is that one corresponds to reality and the other does not.   In other words, the Correspondence Theorist maintains that it is truth that explains coherence, and not coherence that defines truth.

On the other hand, the Coherentist can reply that the questions asked commit something of a "frame error".   We cannot "get outside" our set of beliefs and compare propositions to objective facts.   We can only know that a proposition coheres with a set of beliefs.   We can never know that a proposition corresponds to reality.   The coherence of a proposition with a set of beliefs is considered a good indication that the proposition corresponds to "reality" (however understood) and that we can thereby have a justified belief that a proposition corresponds with reality.   But we can never get beyond that justification.   So if there is anything that can be called the "cause" of the coherence of our set of coherent beliefs, it cannot be anything other than another belief.   So the critics' talk of a thing called "Truth" that is the cause of the coherence is nothing but another belief that coheres in the usual way.   Trying to talk of something that is not a belief is to talk of something that we have no access to.

The end result of all of this give and take between the Coherentist and the Critic is that whether or not the title quote is seen as a refutation of the coherence theory of truth or simply a tautology abutted to a bit of nonsense, will intimately depend on one's theory of truth.   It is a refutation of the coherence theories of truth only for those who do not need such a refutation.   And it is not a refutation of the coherence theories of truth for those who hold such a theory.

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