Common probabilistic fallacies and putative paradoxes are surveyed, including those arising from distribution repartitioning, from the reordering of expectation series, and from misconceptions regarding expected and almost certain gains in games of chance. Conditions are given for such games to be well-posed. By way of example, Bernoulli's “Petersburg Paradox” and Hacking's “Strange Expectations” are discussed and the latter are resolved. Feller's generalized “fair price, in the classical sense” is critically reviewed.

Reasoning that compares two objects or situations to draw conclusions about previously unknown properties of one of them has traditionally been taken to be ampliative and probabilistic. I propose that it is apodeictic reasoning from a premise about isomorphic structures that is often uncertain, but which we may have good reasons to believe. I characterize the structures and their isomorphism, describe patterns of reasoning appropriate to them, and discuss some complications not immediately obvious.

Recently, Michael Redhead has argued that the grouping of particles into multiplets by grand unified gauge theories (GUT's) does not, by itself, imply an ontological reduction in the number of elementary particles. While sympathetic to Redhead's argument, in this note I argue that under certain conditions involving Kaluza-Klein theories, GUT's would provide such an ontological reduction.

Discussion of Wittgenstein's philosophy has suffered from a scarcity of commentators who understand his work well enough to explain it in their own words. Apart from certain notable exceptions, all too many advocates and critics alike have tended merely to repeat slogans, with approval or ridicule as the case may be. The result has been an unusual degree of polarization and acrimony—some philosophers abandoning normal critical standards, falling under the spell and becoming fanatical supporters; and others taking an equally extreme opposite view, deriding the absence of analytic technique, and refusing to see anything of value in Wittgenstein's work.