We introduce a framework for a graph-theoretic analysis of the semantic paradoxes. Similar frameworks have been recently developed for infinitary propositional languages by Cook and Rabern, Rabern, and Macauley. Our focus, however, will be on the language of first-order arithmetic augmented with a primitive truth predicate. Using Leitgeb’s notion of semantic dependence, we assign reference graphs (rfgs) to the sentences of this language and define a notion of paradoxicality in terms of acceptable decorations of rfgs with truth values. It is (...) shown that this notion of paradoxicality coincides with that of Kripke. In order to track down the structural components of an rfg that are responsible for paradoxicality, we show that any decoration can be obtained in a three-stage process: first, the rfg is unfolded into a tree, second, the tree is decorated with truth values (yielding a dependence tree in the sense of Yablo), and third, the decorated tree is re-collapsed onto the rfg. We show that paradoxicality enters the picture only at stage three. Due to this we can isolate two basic patterns necessary for paradoxicality. Moreover, we conjecture a solution to the characterization problem for dangerous rfgs that amounts to the claim that basically the Liar- and the Yablo graph are the only paradoxical rfgs. Furthermore, we develop signed rfgs that allow us to distinguish between ‘positive’ and ‘negative’ reference and obtain more fine-grained versions of our results for unsigned rfgs. (shrink)
This paper deals with a major problem of the early days of the science of palaeontology, the nature and origin of fossils. In 1725, the German physician and academician, Dr Johann Beringer, was deceived into believing that fraudulent, carved stones were true fossils. Despite an extensive analysis, Beringer was not able to fit his ‘fossils’ to any contemporary concept of how fossils originate. The reason for Beringer's inability to classify his stones is explored here. It is argued (...) that the carvings embodied a sixteenth-century, Neoplatonic, concept of fossils, a concept that was outdated in Beringer's time. Beringer chose not to explain his stones rather than to accept the meaning they implied. (shrink)
J.S. Mill's plural voting proposal in Considerations on Representative Government presents political theorists with a puzzle: the elitist proposal that some individuals deserve a greater voice than others seems at odds with Mill's repeated arguments for the value of full participation in government. This essay looks at Mill's arguments for plural voting, arguing that, far from being motivated solely by elitism, Mill's account is actually driven by a commitment to both competence and participation. It goes on to argue that, for (...) Mill, much of the value of political participation lies in its unique ability to educate the participants. That ability to educate is not, however, a product of participation alone; rather, for Mill, the true educative benefits of participation obtain only when competence and participation work together in the political sphere. Plural voting, then, is a mechanism for allowing Mill to take advantage of the educative benefits that arise from the intersection of competence and participation. (shrink)
