Given the traditional formulation of knowledge (see Justified True Belief), one of the key considerations is that of how beliefs can obtain justification (if at all). There are three major schools of thought on how justification is obtained, plus the sceptical school, which denies that justification is possible at all. The three non-sceptical schools are Infinitism, Foundationalism, and Coherentism. All three schools model beliefs as a network of one kind or another, and claim that justification arises only in appropriate network configurations. Their primary differences centre around the topography of that network, and also the nature of the network nodes themselves, to a lesser degree. In this essay I will deal primarily with Coherentism, but I'll give all three models a cursory introduction so that Coherentism may be compared and contrasted with its alternatives.

The Infinitist claims that a belief is justified by resting on an infinite regress of other beliefs. Thus, belief A is justified by belief B, and belief B is in turn justified by belief C, and so on ad infinitum. It's not a very popular school of thought. Foundationalism is more popular, and its key feature is that some beliefs (or "states", more generally) are considered justified without reference to other beliefs. Such beliefs are foundational, and other beliefs can obtain justification only by building upon them in an appropriate manner. Coherentism stands in contrast to these in that justification can emerge in an appropriate finite network of beliefs, without any of those beliefs being foundational or self-justifying; without justification being inherent in any of those beliefs. Strict Coherentism recognises no such thing as a self-justified belief.

The idea of justification "emerging" in a network of belief, as opposed to originating in some node and being propagated by appropriate relationships, is a rather slippery one, and warrants further explanation. If Foundationalism is analogous to a house, built upwards from its foundations in a structured manner, then Coherentism may be thought of as analogous to a ship, the hull of which is constructed of many metal panels, none of which float on their own, but which form a floating whole when appropriately connected. No particular panel on a ship can properly be considered foundational: the ship's ability to float arises spontaneously when a sufficient number of panels are appropriately connected.

As with the other models of justification, Coherentism must answer two important questions with regards to its model: what sorts of things are the nodes in its network, and what relationship do those nodes bear to each other? In the case of Coherentism, these questions can be phrased, "what is it that must cohere?" and, "what are the attributes of the coherence relationship?"

As a first approximation, the nodes in a Coherentist network are "beliefs". Most commonly, they are a set of beliefs held by a particular individual, although it's also possible for Coherentist models to range over broader sets than this, such as the beliefs of a group. Standard versions of Coherentism, however, take the subjective view of belief. There is also the question as to whether Coherentist networks can contain nodes representing things other than beliefs, such as experiential states. The most popular views of Coherentism shy away from this option. [Ref: The Stanford Encyclopedia of Philosophy (Winter 2003 Edition).]

The coherence relationship itself is rather harder to pin down, precisely. It may involve logical or probabilistic consistency, inferential connectedness, lack of anomalies, explanatory value, relevance, and so on. To plumb the depths of each of these candidates would take far too long, so suffice it to say that they are all problematic. Even a concept as well defined as "logical consistency" has its questionable cases, in which logically inconsistent propositions may be considered coherent. I'm inclined to dismiss acceptance of logically inconsistent propositions as sloppy thinking, but more reputable philosophers than I have argued the contrary.

A serious possible objection to Coherentism is the Isolation Objection. If we accept that the nodes in a coherent network are "beliefs", then it is entirely feasible to construct a beautifully consistent network of beliefs which nevertheless bears little or no relation to the world it purports to describe. The problematic isolation results from the fact that sense experience has not been granted any status in the model. The ancient Greek model of science seemed to suffer from this approach, since they were arguably more concerned with the purity of their relations of ideas than they were with giving them a reality check!

But this is not an objection to the essence of Coherentism; rather it is an objection to one of its forms. The Isolation Objection can be addressed by allowing elements of sense experience into the network, and this is the kind of coherence that Quine appears to embrace when he claims, "The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even of pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges." It seems to be a lingering concern of Coherentists that admitting "edges" to the network of belief (as per Quine) is tantamount to admitting foundations, and conceding defeat to Foundationalism. In closing, I'd like to address that concern in my own words.

I've been utilising the language of discrete mathematics in talking about nodes in a network, and I believe that treating the matter as a problem in discrete mathematics will prove illuminating. Foundationalism (in a strict form) follows the pattern of a "directed acyclic graph", meaning that justification finds its source only inside root nodes (foundations), and can only be passed from one node to another in one direction, and never in a circular manner. A slightly more relaxed version of Foundationalism may allow loops to enter the picture (a "directed graph", now), such that beliefs are supported not only by their foundations, but by each other as well (but never without foundations). Coherentism qualitatively changes this such that justification arises from the relationship between nodes, as opposed to within the nodes themselves, but remains a "directed graph" in form.

But justification via coherent inter-node relationships and self-justification are not inherently mutually exclusive: it's quite feasible to combine the two. The Isolation Objection only becomes a problem if we disallow the node-internal form of justification, and there's no compelling reason to do so, in my view. Reverting to analogy again, a Coherentist model which "impinges on experience only along the edges" (to use Quine's phrase) is like a spider's web: most of its integrity comes from a complex set of interlocking threads within the web itself, but it still finds crucial anchor points in the surrounding environment. No doubt this model has its flaws, but it combines the best strengths of both Foundationalism and Coherentism, in my view. It remains a Coherentist model, but a less radical one than the prevailing model.