Bryson Brown

Nicholas Rescher has argued we must tolerate inconsistency because of our cognitive limitations. He has also produced, together with R. Brandom, a serious attempt at exploring the logic of inconsistency. Inconsistency tolerance calls for a systematic rewriting of our logical doctrines: it requires a paraconsistent logic. However, having given up all aggregation of premises, Rescher's proposal for a paraconsistenl logic fails to account for the reductive reasoning Rescher appeals to in his account of inconsistency tolerance. A non-adjunctive logic developed by P.K. Schotch and RE. Jennings provides just what Rescher's logic is lacking: It allows a tolerant attitude toward inconsistency while giving an account of reductive reasoning

In this paper we introduce a paraconsistent reasoning strategy, Chunk and Permeate. In this, information is broken up into chunks, and a limited amount of information is allowed to flow between chunks. We start by giving an abstract characterisation of the strategy. It is then applied to model the reasoning employed in the original infinitesimal calculus. The paper next establishes some results concerning the legitimacy of reasoning of this kind - specifically concerning the preservation of the consistency of each chunk and concludes with some other possible applications and technical questions

An argument for skepticism about the past exploits a circularity in the arguments connecting present observations to claims about past events. Arguments supporting claims about the past depend on current observations together with processes linking current observations to those claims. But knowledge of processes requires knowledge of the past: Knowledge of the present alone cannot provide evidence for claims about the past. A practical, coherentist response to this challenge rejects the assumption that we come to the problem with no information about the past. Beginning with partial and imperfect information about the past, a coherentist tests ideas about processes against the particular evidence of traces left by past processes, and particular claims about the past against ideas about the processes linking those events to present traces. However, this common-sense response is inadequate when faced with a radical skeptic prepared to insist on the problem of the criterion. An answer to this radicalskeptic can be drawn from Wilfrid Sellars ‘bootstrap’ argument in “Empiricism and the Philosophy of Mind.” The result is a better response to the problem of the criterion than Chisholm’s ‘particularism’.

Just what forms do (or should) our cognitive attitudes towards scientific theories take? The nature of cognitive commitment becomes particularly puzzling when scientists' commitments are) inconsistent. And inconsistencies have often infected our best efforts in science and mathematics. Since there are no models of inconsistent sets of sentences, straightforward semantic accounts fail. And syntactic accounts based on classical logic also collapse, since the closure of any inconsistent set under classical logic includes every sentence. In this essay I present some evidence that there really was a substantial cognitive commitment to OQT, and that some of its characteristics have a simple and straightforward explanation in terms of a model based on a form of paraconsistent logic.