Convergence and submeasures in Boolean algebras

A Boolean algebra carries a strictly positive exhaustive submeasure if and only if it has a sequential topology that is uniformly Frechet.Comment: In memory of Bohuslav Balca

Measures on Boolean algebras

We present a necessary and sufficient condition for a Boolean algebra to carry a finitely additive measure

Algebraic characterizations of measure algebras

We present necessary and sufficient conditions for the existence of a countably additive measure on a complete Boolean algebra

What Has Athens to Do with Rome? Tocqueville and the New Republicanism

The recent debate over “republican” conceptions of freedom as non-domination has re- invigorated philosophical discussions of freedom. However, “neo-Roman” republicanism, which has been characterized as republicanism that respects equality, has largely ignored the work of Alexis de Tocqueville, although he too took his task to be crafting a republicanism suited to equality. I therefore provide a philosophical treatment of the heart of Tocqueville’s republicanism, including an analysis of his conception of freedom as freedom in combined action and a philosophical reconstruction of his primary argument for the importance of this kind of freedom. A comparison of Philip Pettit’s and Tocqueville’s republicanism exposes limitations in the neo-Roman conception of freedom as non-domination and its ideal of the free citizen and shows why neo-Roman republicanism, to live up to its motivating ideals, should accommodate elements of “neo- Athenian” republicanism and freedom in combined action

Tocqueville, Pascal, and the Transcendent Horizon

Most students of Tocqueville know of his remark, “There are three men with whom I live a little every day; they are Pascal, Montesquieu, and Rousseau.” In this paper I trace out the contours of Pascal’s influence upon Tocqueville’s understanding of the human condition and our appropriate response to it. Similar temperaments lead both Tocqueville and Pascal to emphasize human limitations and contingency, as Peter Lawler rightly emphasizes. Tocqueville and Pascal both emphasize mortality, ignorance of the most important subjects, the effects of historical contingency on what we take to be human nature, and both represent the complex internal dynamic of human nature in terms of the interplay of “angel” and “brute.” The most important difference between them concerns their relative estimates of human power and the significance of human action. Whereas the motif of human weakness is fundamental for Pascal, Tocqueville repeatedly affirms that, under the right conditions, human beings are “powerful and free.” Beginning from Pascalian premises, and endeavoring to be more faithful to some of those premises than Pascal himself was, Tocqueville aims to illuminate the possibility of an amelioration of the human condition through a “new political science” that redeems the political realm without divinizing it

Critical aspect ratio for tungsten fibers in copper-nickel matrix composites

Stress-rupture and tensile tests were conducted at 816 C (1500 F) to determine the effect of matrix composition on the minimum fiber length to diameter ratio (critical aspect ratio) below which fibers in a tungsten fiber/copper-nickel alloy matrix composite could not be stressed to their ultimate load carrying capability. This study was intended to simulate some of the conditions that might be encountered with materials combinations used in high-temperature composites. The critical aspect ratio for stress-rupture was found to be greater than for short-time tension, and it increased as the time to rupture increased. The increase was relatively slight, and calculated fiber lengths for long service appear to be well within practical size limits for effective reinforcement and ease of fabrication of potential gas turbine components

Tocqueville, Pascal, and the Transcendent Horizon

Most students of Tocqueville know of his remark, “There are three men with whom I live a little every day; they are Pascal, Montesquieu, and Rousseau.” In this paper I trace out the contours of Pascal’s influence upon Tocqueville’s understanding of the human condition and our appropriate response to it. Similar temperaments lead both Tocqueville and Pascal to emphasize human limitations and contingency, as Peter Lawler rightly emphasizes. Tocqueville and Pascal both emphasize mortality, ignorance of the most important subjects, the effects of historical contingency on what we take to be human nature, and both represent the complex internal dynamic of human nature in terms of the interplay of “angel” and “brute.” The most important difference between them concerns their relative estimates of human power and the significance of human action. Whereas the motif of human weakness is fundamental for Pascal, Tocqueville repeatedly affirms that, under the right conditions, human beings are “powerful and free.” Beginning from Pascalian premises, and endeavoring to be more faithful to some of those premises than Pascal himself was, Tocqueville aims to illuminate the possibility of an amelioration of the human condition through a “new political science” that redeems the political realm without divinizing it