The calculators on the insolubles: Bradwardine, Kilvington, Heytesbury, Swyneshed and Dumbleton

The most exciting and innovative period in the discussion of the insolubles (i.e., logical paradoxes) before the twentieth century occurred in the second quarter of the fourteenth in Oxford, and at its heart were many of the Calculators. It was prompted by Thomas Bradwardine's iconoclastic ideas about the insolubles in the early 1320s. Framed largely within the context of the theory of (logical) obligations, it was continued by Richard Kilvington, Roger Swyneshed, William Heytesbury and John Dumbleton, each responding in different ways to Bradwardine's analysis, particularly his idea that propositions had additional hidden and implicit meanings. Kilvington identified an equivocation in what was said; Swyneshed preferred to modify the account of truth rather than signification; Heytesbury exploited the respondent's role in obligational dialogues to avoid Bradwardine's tendentious closure postulate on signification; and Dumbleton relied on other constraints on signification to give new life to two long-standing accounts of insolubles that Bradwardine had summarily dismissed. The present paper focusses on the central thesis of each thinker's response to the insolubles and their interaction.