There is no single coherence theory of truth, but rather an assortment of perspectives that are commonly collected under this title. In general, coherence theory sees truth as coherence with some specified set of sentences, propositions or beliefs. A pervasive tenet is the idea that truth is primarily a property of whole systems of propositions and can be ascribed to individual propositions only derivatively according to their coherence with the whole. Where theorists differ is mainly on the question of whether coherence entails many possible true systems of thought or only a single absolute system. In general, then, truth requires a proper fit of elements within the whole system. Very often, though, coherence is taken to imply something more than simple logical consistency. For example, the completeness and comprehensiveness of the underlying set of concepts is considered to be critical factor in judging its utility and validity.
According to another version of coherence theory, championed especially by H.H. Joachim, truth is a systematic coherence that involves more than logical consistency. In this view, a proposition is true to the extent that it is a necessary constituent of a systematically coherent whole. Others of this school of thought, for example, Brand Blanshard, hold that this whole must be so interdependent that every element in it necessitates, and even entails, every other element. Exponents of this view infer that the most complete truth is a property solely of a unique coherent system, called the absolute, and that humanly knowable propositions and systems have a degree of truth that is proportionate to how fully they approximate this ideal. (Baylis 1962).
Some versions of coherence theory have been claimed to characterize the essential and intrinsic properties of formal systems in logic and mathematics. A claim like this needs to be qualified by the observation that formal reasoners are content to contemplate axiomatically independent but mutually contradictory systems side by side, for example, the various alternative geometries. On the whole, coherence theories have been criticized as lacking justification in their application to other areas of truth, especially with respect to assertions about the natural world, empirical data in general, assertions about practical matters of psychology and society, especially when used without support from the other major theories of truth.
Coherence theories distinguish the thought of continental rationalist philosophers, especially Spinoza, Leibniz, and G.W.F. Hegel, along with the British philosopher F.H. Bradley. They have found a resurgence also among several proponents of logical positivism, notably Otto Neurath and Carl Hempel.
Perhaps the best-known objection to a coherence theory of truth is Bertrand Russell's. Russell maintained that since both a belief and its negation will, individually, cohere with at least one set of beliefs, this means that contradictory beliefs can be shown to be true according to coherence theory, and therefore that the theory cannot work. However, what most coherence theorists are concerned with is not all possible beliefs, but the set of beliefs that people actually hold. The main problem for a coherence theory of truth, then, is how to specify just this particular set, given that the truth of which beliefs are actually held can only be determined by means of coherence.