This is the Editor's Introduction to "Well-Founded Belief: New Essays on the Epistemic Basing Relation" (Routledge, 2020).

In Lehrer’s case of the superstitious lawyer, a lawyer possesses conclusive evidence for his client’s innocence, and he appreciates that the evidence is conclusive, but the evidence is causally inert with respect to his belief in his client’s innocence. This case has divided epistemologists ever since Lehrer originally proposed it in his argument against causal analyses of knowledge. Some have taken the claim that the lawyer bases his belief on the evidence as a data point for our theories to accommodate, (...) while others have denied that the lawyer has knowledge, or that he bases his belief on the evidence. In this paper, we move the dialectic forward by way of arguing that the superstitious lawyer genuinely infers his client’s innocence from the evidence. To show that the lawyer’s inference is genuine, we argue in defense of a version of a doxastic construal of the ‘taking’ condition on inference. We also provide a pared-down superstitious lawyer-style case, which displays the key features of the original case without including its complicated and distracting features. But interestingly, although we argue that the lawyer’s belief is based on his good evidence, and is also plausibly doxastically justified, we do not argue that the lawyer knows that his client is innocent. (shrink)

Although the theory of definability had many important antecedents—such as the descriptive set theory initiated by the French semi-intuitionists in the early 1900s—the main ideas were first laid out in precise mathematical terms by Alfred Tarski beginning in 1929. We review here the basic notions of languages, explicit definability, and grammatical complexity, and emphasize common themes in the theories of definability for four important languages underlying, respectively, descriptive set theory, recursive function theory, classical pure logic, and finite-universe logic. We review (...) the history of previous studies of the similarities and differences in the theories of definability of the first three of these four languages. A seminal role leading toward unification of the theories has been played by the separation principles introduced by Nikolai Luzin in 1927. Emphasizing analogies and driving toward further unification embracing finite-universe logic we concentrate on a simple example—the first and second separation principles for existential-universal first-order sentences . Using this as a test case for the fundamental problem of how to “finitize” arguments in classical pure logic to the finite-universe case, we are led to the analogous negative solution by using the theory of certain special graphs: a graph is - special for any positive integers m , n , p , q iff it is bipartite with m red points and n blue points and for every p -tuple of red points there is a blue point to which they are all connected . As an aside we introduce for further study a natural “Ramseyesque” increasing sequence A of positive integers, where A is the least positive integer n for which an -special graph exists. (shrink)

The articles collected in this volume are concerned with the transmission and development of the Greek achievement among Syriac scholars of the Fertile Crescent during the four centuries after 500CE, particularly in the fields of rhetoric and philosophy. Cumulatively they show how many aspects of Greek culture were received and elaborated in Syriac, and contribute to understanding the ways in which that culture exercised a powerful influence on the medieval Near East and the burgeoning Islamic civilisation.