Coherence of Knowledge

When beliefs are justified, what is the structure of their justification? According to foundationalism, all justification rests in the end on basic beliefs that do not require further justification; they are supposed to be "self-justifiying". All other justified beliefs inherit their status from those basic beliefs. However, the beliefs that we might be prepared to treat as self-justifying are unlikely to form sufficient foundations for our knowledge. Foundationalism - at least in its stronger forms - seems to adhere to the myth of the given, and the attacks on this myth from various sides have been successful. Thus foundationalism does not provide a correct account of the structure of justification.

Coherentism is understood as the array of non-foundationalist approaches to the theory of justification. According to coherentism, a belief is justfied if it "coheres" with a system of beliefs. Several coherentist accounts of the justification of empirical beliefs have been put forward and studied by epistemologists. Coherentism faces several challenges. It needs to provide a picture of how empirical input is possible at all. Moreover, some accounts of coherence put epistemic justification out of reach by putting coherence itself out of reach - coherence, on these accounts, cannot be grasped by beings with our computational abilities. We intend to show, however, that the restriction imposed by metamathematical results are less severe than some epistemologists have claimed.

Among philosophers of mathematics, "antifoundationalism" has recently received considerable attention. Although mathematics has provided the model for foundationalism, mathematical justification itself seems to be locally foundationalist at best. The basic "beliefs" in mathematics, the mathematical axioms, are no more self-justifying than ordinary empirical beliefs. The results in Reverse Mathematics suggest the picture of a web of mathematical beliefs that support each other. Axioms turn out to be equivalent to other mathematical principles and theorems, and the "axiom" inherits its plausibility from (at least some of) its consequences just as much as the consequences inherit their epistemic status from the allegedly self-justifying axiom.

In this project, we are especially interested in a holistic approach. We seek a uniform notion of justification that will suit both empirical and mathematical beliefs. We combine recent anti-foundationalist approaches from two areas: epistemology and the philosophy of science. In particular, we explore the relation of anti-foundationalist structuralism in philosophy of mathematics, as put forward by Stewart Shapiro and others, with coherentism in epistemology.