Albert Casullo

There are four approaches to analyzing the concept of a priori knowledge. The primary target of the reductive approach is the concept of a priori justification. The primary target of the nonreductive approach is the concept of a priori knowledge. There are two approaches to analyzing each primary target. A theory-neutral approach provides an analysis that does not presuppose any general theory of knowledge or justification. A theory-laden approach provides an analysis that does presuppose some general theory of knowledge or justification (call it the background theory). Those who embrace a theory-laden analysis incur a special burden: they must separate the features of their analysis that are constitutive of the a priori from those that are constitutive of the background theory. My goal is to illustrate how the failure to separate these features leads to erroneous conclusions about the nature of a priori knowledge.

Kripke claims that there are necessary a posteriori truths and contingent a priori truths. These claims challenge the traditional Kantian view that (K)  All knowledge of necessary truths is a priori and all a priori knowledge is of necessary truths. Kripke’s claims continue to be resisted, which indicates that the Kantian view remains attractive. My goal is to identify the most plausible principles linking the epistemic and the modal. My strategy for identifying the principles is to investigate two related questions. Are there compelling general supporting arguments for (K)? Are there decisive counterexamples to (K)? My investigation uncovers two intuitively plausible principles that are not open to decisive counterexamples but which enjoy no compelling independent support.

Radical empiricism is the view that experience is the only source of knowledge. Hence, radical empiricism denies the existence of a priori knowledge. Its most famous proponents are John Stuart Mill and W. V. Quine. Although both reject a priori knowledge, they offer different empiricist accounts of the knowledge alleged by their opponents to be a priori. My primary concern in this paper is not with the cogency of their positive accounts. My focus is their arguments against a priori knowledge. My goal is to establish that although they offer very different arguments against the existence of a priori knowledge, each of their arguments suffers from a common defect. They both fail to appreciate the phenomenon of epistemic overdetermination and its role in the theory of knowledge.

Edward Erwin has recently argued against the thesis that the concepts a priori truth’ and ‘necessary truth’ are extensionally equivalent. This thesis consists of two logically independent claims: all a priori truths are necessary; and all necessary truths are a priori. Erwin leaves the first claim unchallenged and elects to devote his efforts exclusively to undermining the second. The brunt of his attack on the second claim rests on alleged unclarities in the concept of an a priori truth. He attempts to show that the E.E.H. cannot be defended upon any plausible interpretation of this concept. Although I agree that the E.E.H., as stated above, is open to Erwin's objections, I shall argue that a slightly revised version of it can be defended against these objections.

David Henderson and Terry Horgan offer a detailed account of the structure of conceptual analysis that is embedded within a more general account of a priori justification. Their account highlights an important feature of conceptual analysis that has been overlooked in the recent debate. Although it is generally recognized that conceptual analysis involves an inference from premises to the effect that some concept does (or does not) apply to a range of particular cases to a general conclusion about the nature of the concept itself, the details of that inference have not been fully articulated. Henderson and Horgan offer an articulation of the inferential connection which, taken in conjunction with their account of a priori justification, yields a startling conclusion about the epistemic status of the results of conceptual analysis. My view is that their account of a priori justification misses the mark and, as a consequence, they arrive at a conclusion about the epistemic status of the results of conceptual analysis that many will find implausible. Moreover, I fear that because many will find their overall conclusion implausible, they will either overlook or dismiss the important feature of the inferential connection that Henderson and Horgan correctly highlight. Hence, I have two goals. First, I want to track down the source of their mischaracterization of the a priori and to show why it is a mischaracterization. Second, I want to highlight the important feature of the inferential connection involved in conceptual analysis that they identify, articulate its bearing on the debate over the existence of a priori knowledge and assess its implications

This paper examines the view that ordinary particulars are complexes of universals. Russell's attempt to develop such a theory is articulated and defended against some common misinterpretations and unfounded criticisms in Section I. The next two sections address an argument which is standardly cited as the primary problem confronting the theory: (1) it is committed to the necessary truth of the principle of the identity of indiscernibles; (2) the principle is not necessarily true. It is argued in Section II that a proponent of the theory need not accept (1) and an argument against (2) is presented in Section III. The final section attempts to show that Russell's theory ultimately fails because of inadequacies in its treatment of space and time. The paper closes with a suggestion for remedying this difficulty

Empiricist theories of knowledge are attractive for they offer the prospect of a unitary theory of knowledge based on relatively well understood physiological and cognitive processes. Mathematical knowledge, however, has been a traditional stumbling block for such theories. There are three primary features of mathematical knowledge which have led epistemologists to the conclusion that it cannot be accommodated within an empiricist framework: 1) mathematical propositions appear to be immune from empirical disconfirmation; 2) mathematical propositions appear to be known with certainty; and 3) mathematical propositions are necessary. Epistemologists who believe that some nonmathematical propositions, such as logical or ethical propositions, cannot be known a posteriori also typically appeal to the three factors cited above in defending their position. The primary purpose of this paper is to examine whether any of these alleged features of mathematical propositions establishes that knowledge of such propositions cannot be a posteriori.

In recent years empiricism has come under attack. Some argue that the view is incoherent and conclude, on that basis, that some knowledge is a priori. Whatever the merits of such arguments against empiricism, they cannot be parlayed into an argument in support of the a priori unless the latter is not open to those arguments. My primary contention is that the a priori is open to the arguments offered against empiricism. Hence, they do not advance the case for the a priori. I go on to offer an alternative strategy. The leading idea is that, instead of arguing against empiricism, rationalists should marshal empirical support for their position.