I see the perspective of Tolerance as enshrining an attitude toward philosophical work that stresses its continuity with the procedures of conceptual clarification through mathematisation found in the sciences. What I have tried to show is that Carnap's understanding of the philosophical foundations of mathematics is inseparable from his understanding of the business of philosophy of empirical science.

The incompleteness of formal systems for arithmetic has been a recognized fact of mathematics. The term “incompleteness” suggests that the formal system in question fails to offer a deduction which it ought to. This chapter focuses on the status of a formal system, Peano Arithmetic, and explores a viewpoint on which Peano Arithmetic occupies an intrinsic, conceptually well-defined region of arithmetical truth. The idea is that it consists of those truths which can be perceived directly from the purely arithmetical content (...) of a categorical conceptual analysis of the notion of natural number. The chapter explores its conceptual stability in light of the apparently destabilizing effect, through extensibility, of the phenomenon of incompleteness. It also offers heuristic and conceptual support for the viewpoint that Peano Arithmetic is the strongest natural first-order system for arithmetic, and that there is a sense in which it is complete with respect to purely arithmetical truth. (shrink)

This paper examines C.L.R James’s interpretation of Athenian democracy in “Every Cook Can Govern” (1956). It seeks to explain why Athenian democracy remained indispensable to James’s political thought. I argue that James reinterprets Athens as a proto-workers’ state, and explore the resulting contradictions and complexities. Within “Every Cook Can Govern” James presents a radical interpretation of Athenian Democracy at three points: (1) James claims that slavery in Athens was humane and economically insignificant, (2) he supports the theory of the “Athenian (...) Miracle” found in Pericles’s Funeral Oration, and (3) he chooses to end his essay with a misleading interpretation of the anti-tyranny oath of Demophantos. James idealizes Athenian political realities, and ultimately invents his own version of Athens. But his idealization arose from principled skepticism regarding mainstream views of Athenian democracy and his political commitment to defending the capabilities of the ordinary person. (shrink)

The New Evil Demon problem has been hotly debated since the case was introduced in the early 1980’s (e.g. Lehrer and Cohen 1983; Cohen 1984), and there seems to be recent increased interest in the topic. In a forthcoming collection of papers on the New Evil Demon problem (Dutant and Dorsch, forthcoming), at least two of the papers, both by prominent epistemologists, attempt to resist the problem by appealing to the distinction between justification and excuses. My primary aim here is (...) to critically evaluate this new excuse maneuver as a response to the New Evil Demon problem. -/- Their response attempts to give us reason to reject the idea that victims of the New Evil Demon have justification for believing as they do. I shall argue that this approach is ultimately unsuccessful, however much of value can be learned from these attempts. In particular, progress in the debate can be made by following those who advance the excuse maneuver and make explicit the connection between epistemic justification and epistemic norms. By doing so, the questions being debated are clarified, as is the methodology being used to attempt to answer them. (shrink)

There are various equivalent formulations of the Church-Turing thesis. A common one is that every effective computation can be carried out by a Turing machine. The Church-Turing thesis is often misunderstood, particularly in recent writing in the philosophy of mind.