An implication is a proposition, a consequence is a relation between propositions, and an inference is act of passage from certain premise-judgements to another conclusion-judgement: a proposition is true, a consequence holds, whereas an inference is valid. The paper examines interrelations, differences, refinements and linguistic renderings of these notions, as well as their history. The truth of propositions, respectively the holding of consequences, are treated constructively in terms of verification-objects. The validity of an inference is elucidated in terms of the (...) existence of a chain of immediately evident steps linking premises and conclusion. (shrink)
The paper offers an interpretation of thesis 6.01. The treatment touches upon variables, identity, elementary propositions, internal relations. Klammerausdrücke, and operations. Wittenstein's notations are found not to cover the particular form of definition by induction that is used at 6 and 6.01. It is concluded that Wittgenstein's ability to design of a formal system of logic does not match his outstanding logico-philosophical insight.
This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice. This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively pursued (...) today is predicativistic constructivism based on Martin-Löf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics? (shrink)
The purpose of this paper is to show how a MacIntyre-inspired business school could contribute to developing practical wisdom in students through its curriculum, methods, faculty, student selection criteria, and governance. Despite MacIntyre's critiques, management can be presented, in MacIntyrean terms, as a second-order, domain-relative practice, with practical wisdom as corresponding virtue. Management education consists in developing practical wisdom. How? Primarily by initiating students and enabling them to participate in communal traditions of inquiry focused on, although not limited to, the (...) purposes and ends of business. The transmission of objective knowledge, analytical skills, and techniques is subordinated to the end goal. We consider traditions centered on shareholder value maximization, the balancing of stakeholder interests, and the fulfillment of the common good of firms. Each gives rise to a particular kind of business school. A MacIntyrean business school is one that seeks the common good of firms. (shrink)
In this article I focus on some of Joseph Margolis's contributions to medical ethics. I first discuss some of Margolis's normative and metaphysical views on death and abortion, particularly in his early work Negativities, as well as some of his metaphysical assumptions. Then these views and assumptions are related to his theory of persons and, by implication, his theory of culture, set forth in a number of later works. In the course of the discussion, I call attention to some controversial (...) issues of today, such as embryonic stem cell research and the creation of embryos for the sole purpose of research, and ask for Margolis's views on them, given his earlier contributions and assumptions. Finally, I comment on his relativism and his program for research in aesthetics and ethics. (shrink)