Michael Dummett has long argued that Frege is committed to recognizing a distinction between two sorts of analysis of propositional contents: 'analysis', which reveals the entities that one must grasp in order to apprehend a given propositional content; and 'decomposition', which is used in recognizing the validity of certain inferences. Whereas any propositional content admits of a unique ultimate 'analysis' into simple constituents, it also admits of distinct 'decompositions', no one of which is ultimately privileged over the others. I argue (...) that although Russell accepts this distinction between analysis and decomposition, Frege does not. In particular, I consider claims which Dummett makes regarding how 'analysis' and 'decomposition' are related to two different models Frege at least suggests in discussing the composition of thoughts, the part/whole model and the function/argument model; and I argue that in each case, while Russell accepts views which Dummett attributes to Frege, Frege does not. (shrink)

What is at stake philosophically for Russell in espousing logicism? I argue that Russell's aims are chiefly epistemological and mathematical in nature. Russell develops logicism in order to give an account of the nature of mathematics and of mathematical knowledge that is compatible with what he takes to be the uncontroversial status of this science as true, certain and exact. I argue for this view against the view of Peter Hylton, according to which Russell uses logicism to defend the unconditional (...) truth of mathematics against various Idealist positions that treat mathematics as true only partially or only relative to a particular point of view. (shrink)

Several interesting themes emerge from G. E. Moore’s previously unpub­lished review of _The Principles of Mathematics_. These include a worry concerning whether mathematical notions are identical to purely logical ones, even if coextensive logical ones exist. Another involves a conception of infinity based on endless series neglected in the Principles but arguably involved in Zeno’s paradox of Achilles and the Tortoise. Moore also questions the scope of Russell’s notion of material implication, and other aspects of Russell’s claim that mathematics reduces (...) to logic. (shrink)

Review of Russell’s Philosophy of Logical Atomism 1897–1905, by Jolen Galaugher (Palgrave Macmillan 2013).

I argue that in Bertrand Russell’s An Essay on the Foundations of Geometry (1897), his forms of externality serve the same fundamental role in grounding the possibility of geometry that Immanuel Kant’s forms of intuition serve in grounding geometry in his critical philosophy. Specifically, both provide knowledge of bare numerical difference, where we have no concept of this difference. Because geometry deals with such conceptually homogeneous magnitudes and their composition on both accounts, forms of intuition or externality (respectively) are at (...) its foundation. (shrink)