I'm currently working on a paper on a priori knowledge, and I thought it might be helpful to start out with an overview of available positions, characterized in terms of the answers their defenders would give to a set of questions. I'd be really interested to hear whether people think anything important is missing from my overview, whether the description is helpful, etc..
Before I start, it's useful to have an umbrella term for all forms of the view that some appeal to conceptual truth or something in that area is what does (most of) the interesting epistemological work in helping us understand (at least some of ) our a priori knowledge. I'll refer to all such views as versions of the conceptual approach.
First, then, there is the question of whether or not a priori knowledge is a distinctive epistemological phenomenon at all. Those who deny this include Mill and Quine, both of whom argue, in their different ways, that what appear to be cases of a priori knowledge are in fact cases of ordinary empirical knowledge.
If it is agreed that a priori knowledge is a distinctive phenomenon, there is the question of whether or not to adopt any version of the conceptual approach. If the answer is no, then we can ask whether or not any form of factualism is correct for claims of a priori knowledge or justification: that is, whether there are facts corresponding to acceptable claims of this kind, or whether the acceptability of such claims has some other basis. Field defends a form of non-factualism, at least for basic a priori knowledge, arguing that claims of justification for basic a priori principles are merely expressions of pro-attitude towards these principles. Factualist positions available to non-defenders of the conceptual approach include innatism, certain forms of conventionalism which are not wedded to the conceptual approach, and some forms of rationalism (for instance, some of the thoughts of Gödel could be developed in this way: we could posit a priori knowledge of set theory, for instance, via a rational faculty which is 'something like a perception' of its objects, without our account appealing to conceptual truth).
For those who favour the conceptual approach, we now ask whether or not mind-independence realism is true for any of the a priori knowable subject matters that are covered by the account. Those who answer 'no' here I take to include Ayer, Carnap, Kant, defenders of implicit definition views such as Wright and Hale, and perhaps Boghossian.
Those who do want to be realists then have to decide whether to be rationalists: that is, whether to accept that some propositions can be known solely through the exercise of faculties other than the senses. (I take empiricism to be the denial of rationalism). Those who answer 'yes' to this question I take to include BonJour, Peacocke and Bealer.
There is one node left on my imagined diagram: that is the node which I want to occupy. This node represents the view that a priori knowledge is a distinctive epistemological phenomenon to be explained via some sort of conceptual approach, that we should be realists about at least some of the subject matters to be covered by the account, and that rationalism is not true.
(The fun part is fitting all those things together …)