John Corcoran. 1979 Review of Hintikka and Remes. The Method of Analysis (Reidel, 1974). Mathematical Reviews 58 3202 #21388. -/- The “method of analysis” is a technique used by ancient Greek mathematicians (and perhaps by Descartes, Newton, and others) in connection with discovery of proofs of difficult theorems and in connection with discovery of constructions of elusive geometric figures. Although this method was originally applied in geometry, its later application to number played an important role in the early development (...) of algebra [Jacob Klein, English translation, Greek mathematical thought and the origin of algebra, especially pp. 154–157, M.I.T. Press, Cambridge, Mass., 1968]. -/- It is universally agreed that the method of analysis begins by “assuming the thing sought after” (e.g., in geometry, the truth of the proposition to be proved or the existence of the geometric figure to be constructed). Aside from this, little else can be taken for granted. There is disagreement concerning the “direction of analysis”, i.e. whether one is to seek implications of the assumption or whether one is to seek implicants of it. There is also disagreement concerning what is to be “anatomized” (analyzed), i.e., whether one analyzes mathematical objects (figures), mathematical propositions (the axioms, known theorems, and analytic assumption) or an imagined proof (of the analytic assumption from axioms and known theorems). (shrink)

We are currently experiencing a planetary crisis that will lead, if worst comes to worst, to the end of the entire world as we know it. Several feminist scholars have suggested that if the Earth is to stay livable for humans and nonhumans alike, the ways in which many human beings – particularly in the wealthy parts of the world, infested with Eurocentrism, colonialism, neoliberalism, and capitalism – inhabit this planet requires radical, ethical, and political transformation. In this article, we (...) propose that feminist theory, particularly feminist posthumanities, and Black feminist and decolonial thought, together with creative practices such as writing, have much to contribute to transformative planetary activism that imagines different and other kinds of worlds and futures based on an ethical consideration of nonhuman others and collective caring for the planet. (shrink)