Online research in philosophy

There has been a significant shift in the discussion of a priori knowledge. The shift is due largely to the influence of Quine. The traditional debate focused on the epistemic status of mathematics and logic. Kant, for example, maintained that arithmetic and geometry provide clear examples of synthetic a priori knowledge and that principles of logic, such as the principle of contradiction, provide the basis for analytic a priori knowledge. Quine’s rejection of the analytic-synthetic distinction and his holistic empiricist account of mathematic and logical knowledge undercut the traditional defenses of the a priori in two ways. First, one could no longer defend the view that mathematical and logical knowledge is a priori solely by rejecting Mill’s inductive empiricism. Moreover, holistic empiricism proved to be a more challenging position to refute than inductive empiricism. Second, the rejection of the analytic-synthetic distinction blocked an alternative defense of the a priori status of mathematics and logic that appealed to their alleged analyticity.

a priori. Since I ended up defending an unpopular answer to this question—"No"—it’s hardly surprising that people have scrutinized the account, or that many have concluded that I stacked the deck in the first place. Of course, this was not my view of the matter. My own judgment was that I’d uncovered the tacit commitments of mathematical apriorists and that the widespread acceptance of mathematical apriorism rested on failure to ask what was needed for knowledge to be a priori . Nevertheless, my critics have raised important challenges, and have offered rival conceptions that are less demanding. I want to examine their objections to my explication of a priori knowledge, and to explore whether the weaker alternatives succeed in preserving traditional philosophical claims. What follows is a mixture of penitence and intransigence.

The distinction between a priori and a posteriori knowledge has been the subject of an enormous amount of discussion, but the literature is biased against recognizing the intimate relationship between these forms of knowledge. For instance, it seems to be almost impossible to find a sample of pure a priori or a posteriori knowledge. In this paper, it will be suggested that distinguishing between a priori and a posteriori is more problematic than is often suggested, and that a priori and a posteriori resources are in fact used in parallel. We will define this relationship between a priori and a posteriori knowledge as the bootstrapping relationship. As we will see, this relationship gives us reasons to seek for an altogether novel definition of a priori and a posteriori knowledge. Specifically, we will have to analyse the relationship between a priori knowledge and a priori reasoning , and it will be suggested that the latter serves as a more promising starting point for the analysis of aprioricity. We will also analyse a number of examples from the natural sciences and consider the role of a priori reasoning in these examples. The focus of this paper is the analysis of the concepts of a priori and a posteriori knowledge rather than the epistemic domain of a posteriori and a priori justification.

In this paper I will offer a novel understanding of a priori knowledge. My claim is that the sharp distinction that is usually made between a priori and a posteriori knowledge is groundless. It will be argued that a plausible understanding of a priori and a posteriori knowledge has to acknowledge that they are in a constant bootstrapping relationship. It is also crucial that we distinguish between a priori propositions that hold in the actual world and merely possible, non-actual a priori propositions, as we will see when considering cases like Euclidean geometry. Furthermore, contrary to what Kripke seems to suggest, a priori knowledge is intimately connected with metaphysical modality, indeed, grounded in it. The task of a priori reasoning, according to this account, is to delimit the space of metaphysically possible worlds in order for us to be able to determine what is actual.

Suppose that it is necessary that if one believes that the F is F if any unique thing is, one believes of the F, if there is one, that it is F if any unique thing is. I argue that it follows (in all but a few cases) that it is also necessary that if one knows a priori that the F is F if any unique thing is, one knows a priori of the F, if there is one, that it is F if any unique thing is. I claim that because of this, a priori knowledge of de re propositions, including contingent de re propositions, is a relatively common phenomenon. However, because attributions of belief and knowledge are context-sensitive, the question whether it possible to know a priori of a given object that it is F if anything is will typically have different answers in different contexts.

I argue that you can have a priori knowledge of propositions that neither are nor appear necessarily true. You can know a priori contingent propositions that you recognize as such. This overturns a standard view in contemporary epistemology and the traditional view of the a priori, which restrict a priori knowledge to necessary truths, or at least to truths that appear necessary.

The book sets out to analyse the notion of a priori justification and of a priori knowledge.

A thumbnail sketch of the philosophical thinking about the a priori would surely include that it has been dominated by two major approaches: the Kantian absolute conception of it and the Millian-Quinean absolute rejection of it (section 2). Yet, one can find in the literature claims about the existence of a ›functional a priori‹, a ›relative a priori‹, a ›relativised a priori‹ and suchlike. They are all meant to carve a space between the two extremes. An important thought behind the search for a middle ground is that the supposed coincidence between the constitutive and the unrevisable is wrong. The entitlement to accept a principle as being constitutive of experience prior to any empirical justification of it is compatible with an entitlement to revise or abandon such a principle on empirical grounds. If a priori principles are meant to be independent of experience, how should this claim of independence be understood so that room is left for the possibility that a principle is both independent of experience and revisable on empirical grounds (section 3)? A straightforward and natural way to approach this issue is to think of constitutive principles along the lines of Poincaréan conventions, which can be seen as delineating a new sense of the a priori – the conventional a priori principles. These are substantive principles that are constitutive of theoretical frameworks – in the sense that they define (or constitute) the object of knowledge – without being either synthetic a priori or empirical generalisations. Still, their negation is conceivable and they are revisable on empirical grounds (section 4).

Recent defenses of a priori knowledge can be applied to the idea of conventions in science in order to indicate one important sense in which conventionalism is correct-some elements of physical theory have a unique epistemological status as a constitutive part of our physical theory. I will argue that the former a priori should be treated as empirical in a very abstract sense, but still conventional. Though actually coming closer to the Quinean position than the standard treatments of conventionalism, the picture of knowledge developed here is very different from that developed in Quinean holism in that categories of knowledge can be differentiated.