Albert Casullo

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.

The distinction between a priori knowledge and a posteriori knowledge has come under attack in the recent literature by Philip Kitcher, John Hawthorne, C. S. Jenkins, and Timothy Williamson. Evaluating the attacks requires answering two questions. First, have they hit their target? Second, are they compelling? My goal is to argue that the attacks fail because they miss their target. Since the attacks are directed at a particular concept or distinction, they must accurately locate the target concept or distinction. Accurately locating the target concept or distinction requires correctly articulating that concept or distinction. The attacks miss their target because they fail to correctly articulate the target concept or distinction. I go on to present a different challenge to the a priori-a posteriori distinction. This challenge is not directed at the coherence or significance of the distinction. Its target is the traditional view that all knowledge (or justified belief) is either a priori or a posteriori.

The analytic/synthetic distinction has played a central role in discussions of a priori knowledge throughout the twentieth century. One of the primary reasons for the prominence of this distinction is the widespread influence of the tradition of logical empiricism which endorsed the following principles: All analytic propositions are knowable a prioriand All propositions knowable a priori are analytic.Hence, proponents of the a priori often argue in support of the contention that the propositions of a particular discipline, say mathematics or logic, are knowable a priori by arguing that it consists solely of analytic propositions. On the other hand, detractors of the a priori often reject such knowledge on the grounds that the analytic/synthetic distinction is not cogent. My primary goal in this paper is to challenge the prevalent acceptance of.

My purpose in this paper is to examine the role of intuition in conceptual analysis and to assess whether that role can be parlayed into a plausible defense of a priori knowledge. The focus of my investigation is George Bealer’s attempt to provide such a defense. I argue that Bealer’s account of intuition and its evidential status faces three problems. I go on to examine the two primary arguments that Bealer offers against empiricism: the Starting Points Argument and the Argument from Epistemic Norms. I argue that the Starting Points Argument fails because Bealer fails to show that intuitions are a priori evidence and that the Argument from Epistemic Norms fails because it is open to the Stalemate Problem. I conclude by offering an alternative approach to defending the a priori status of intuitions that avoids the Stalemate Problem. The alternative approach highlights the role of empirical investigation in defending the a priori.

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.