OTTER Experiments in a System of Combinatory Logic

This paper describes some experiments involving the automated theorem-proving program OTTER in the system TRC of illative combinatory logic. We show how OTTER can be steered to find a contradiction in an inconsistent variant of TRC, and present some experimentally discovered identities in TRC

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

Measures on Boolean algebras

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

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

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