Theorem

In this article, I develop the so-called ‘problem of linguistic creativity’ for two object-languages, one finite, the other infinite. I then employ an approach first outlined by Ludwig Wittgenstein’s collaborator Friedrich Waismann, to ‘dissolve’ that problem, in a sense made precise by working through the example. This is to unsettle the computational picture of linguistic understanding as turning on the generation of semantic information about sentences on the basis of semantic information about their constituent parts, and to provide a reasonably clear conception of to what such ‘philosophical dissolution’ of a problem amounts.

Рассматривается понятие математического доказательства в связи с применением компьютеров в математике. Исследуются особенности этого понятия, а также связанных эпистемологических проблем. Особое внимание уделяется проблеме обо- зримости на примере доказательства теоремы о четырех красках. Настоящая ра-бота представляет собой вторую статью в серии о понятии теоретико-типового доказательства.

Finding Equilibrium explores the post–World War II transformation of economics by constructing a history of the proof of its central dogma—that a competitive market economy may possess a set of equilibrium prices. The model economy for which the theorem could be proved was mapped out in 1954 by Kenneth Arrow and Gerard Debreu collaboratively, and by Lionel McKenzie separately, and would become widely known as the “Arrow-Debreu Model.” While Arrow and Debreu would later go on to win separate Nobel prizes in economics, McKenzie would never receive it. Till Duppe and E. Roy Weintraub explore the lives and work of these economists and the issues of scientific credit against the extraordinary backdrop of overlapping research communities and an economics discipline that was shifting dramatically to mathematical modes of expression. Based on recently opened archives, Finding Equilibrium shows the complex interplay between each man’s personal life and work, and examines compelling ideas about scientific credit, publication, regard for different research institutions, and the awarding of Nobel prizes. Instead of asking whether recognition was rightly or wrongly given, and who were the heroes or villains, the book considers attitudes toward intellectual credit and strategies to gain it vis-a-vis the communities that grant it. Telling the story behind the proof of the central theorem in economics, Finding Equilibrium sheds light on the changing nature of the scientific community and the critical connections between the personal and public rewards of scientific work.

L'etude de l'histoire de la composition des moments montre le lien entre le mot vecteur choisit par Hamilton et le rayon vecteur de la loi des aires de Kepler et explique pourquoi ce lien a ete oublie. En effet, l'introduction du produit vectoriel renvoit la loi de composition des aires au rebut. Elle appartient aux theoremes devenus inutiles tout comme le moment maximal contre lequel se battait Poinsot au cours de la querelle sur la theorie des couples presentee ici.

Lakatos's seminal work Proofs and Refutations introduced the meth- ods of proofs and refutations by discussing the history and methodological de- velopment of Euler's formula V − E + F = 2 for three dimensional polyhedra. Lakatos considered the history of polyhedra ...

This paper develops a property rights-based view of strategy (the “PRV”). A property right (or economic right) is an individual's net valuation, in expected terms, of the ability to directly consume the services of an asset (including, eg, a monopoly position) or consume it indirectly through exchange. Resources expended on exchanging, protecting and capturing such rights are transaction costs, so that we directly link property rights, transaction costs, and economic value. We assume that all relevant exchange is costly and that all agents ...