In this article I try to show the philosophical continuity of Russell's ideas from his paradox of classes to Principia mathematica. With this purpose, I display the main results (descriptions, substitutions and types) as moments of the same development, whose principal goal was (as in his The principles) to look for a set of primitive ideas and propositions giving an account of all mathematics in logical terms, but now avoiding paradoxes. The sole way to reconstruct this central period in Russell (...) is to resort to unpublished manuscripts, which show the publications of these years to be the extremities of one same iceberg. Thus the logical problems (doubts about propositions, matrices and functions) are parallel to the ontological (the searching for genuine logical subjects) and methodological ones (the status of eliminative reduction). Paradoxes were the cause that the kind of (constructive) definition already applied by Russell, as an inheritance of Moorean analysis, obtained a new trait: ontological elimination, which, beginning with a ?no classes theory? and the theory of descriptions, led to a new theory of judgment (already present in manuscripts from 1906), ?incomplete symbols, and logical constructions. (shrink)

Chess is sometimes referred to as a ‘mind-sport’. Yet, in obvious ways, chess is very unlike physical sports such as tennis and soccer; it doesn't require the levels of fitness and athleticism necessary for such sports. Nor does it involve the sensory-governed, skilled behaviour required in activities such as juggling or snooker. Nevertheless, I suggest, chess is closer than it may at first seem to some of these sporting activities. In particular, there are interesting connections between the way that we (...) use our perceptual imagination in sports, and also in chess. The same distinction between calculation and natural instinct applies in chess as it does in many physical sports. (shrink)