The Dative or Ablative of this ‘plurale tantum’ was used by one of the earlier Republican writers. It is quoted by Ps.-Placidus from a MS. which had the marginal note ‘capillis muliebribus ante, id est a fronte, pendentibus.’ These marginal notes were often direct traditions from the earliest glossographi, the ‘glossematum scriptores,’ who provided material also for Varro and Verrius Flaccus, either directly or through the writings of earlier grammatici.

The relation of the glossae breviores of Placidus, or rather Pseudo–Placidus, to Festus1 epitome of Verrius has been the subject of much discussion; but after Karl's detailed examination inDe Placidi Glossis , the view has generally prevailed that Ps.–Plac. is not dependent on Festus, and that any similarities between them are referable to the use of similar sources by Verrius and our compiler.

Reanimated for the contemporary literature in the writings of Quine, [16]) and Kuhn [7], the conventionalism of Duhem [2] and Poincaré [12] has emerged in the last few years as one of the genuinely interesting topics in the philosophy of science. The theory in question—let us follow Grünbaum [3] in calling it the D-thesis, after its founder, Pierre Duhem—claims three things: a single scientific hypothesis H is never disconfirmable in isolation from its fellow; every single hypothesis H of science presupposes, (...) explicitly or implicitly, the support of a conjunction A = A, • A2 • … • Am of auxiliary assumptions or hypotheses; the failure of an observational consequence of H in face of contradictory evidence disconfirms only the conjunction of H and A, not H alone—i.e. establishes only ∼. The logical picture is as follows. (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)

Is logic normative for reasoning? In the wake of work by Gilbert Harman and John MacFarlane, this question has been reduced to: are there any adequate bridge principles which link logical facts to normative constraints on reasoning? Hitherto, defenders of the normativity of logic have exclusively focussed on identifying adequate validity bridge principles: principles linking validity facts—facts of the form 'gamma entails phi'—to normative constraints on reasoning. This paper argues for two claims. First, for the time being at least, Harman’s (...) challenge cannot be surmounted by articulating validity bridge principles. Second, Harman’s challenge can be met by articulating invalidity bridge principles: principles linking invalidity facts of the form 'gamma does not entail phi' to normative constraints on reasoning. In doing so, I provide a novel defence of the normativity of logic. (shrink)