William Ewald

Intuitionistic tense and modal logic

Construction des analogues intuitionnistes des principaux systemes de la logique temporelle classique

Comparative Jurisprudence (I): What Was it Like to Try a Rat?

38 8 The trend towards systematization and abstraction continued under the influence of the natural-law philosophers of the Enlightenment8 9 and as a major component of the movement towards codification.9 0 Savigny, as we have seen, accepted this ideal, 91 and indeed insisted that it should be possible to calculate with legal concepts, almost as though one were doing a bit of

Temporal verification of carrier-sense local area network protocols

We examine local area network protocols and verify the correctness of two representative algorithms using temporal logic. We introduce an interval temporal logic that allows us to make assertions of the form “in the next k units, X holds.” This logic encodes intuitive arguments about contention protocols quite directly. We present two proofs of an Ethernet-like contention protocol, one using the interval temporal logic and one using classical temporal logic. We also verify a contention-free protocol using an invariant that seems to have wide applicability for such protocols.

The jurisprudential approach to comparative law: a field guide to "rats"

What, precisely, is the relevance of legal philosophy to comparative law? On the face of things, the two subjects appear to have a great deal to say to each other. Comparative law the study of all the worlds legal systems, in all ages and all places should, by exhibiting the empirical, observed variability in human law, be both a spur to philosophical reflection and testing-ground for philosophical theories. Legal philosophy, on the other hand, should help both to lay the methodological foundations for comparative law to say how, in general, a foreign legal system ought to be studied and, more concretely, to suggest specific topics of inquiry: How are the institutions of punishment, or contract, or tort thought of in other legal cultures than our own?

David Hilbert's Lectures on the Foundations of Arithmetic and Logic 1917-1933

Introduction.- Hilberts Lectures on Principles of Mathematics from 1917-18.- Hilberts Lectures on the Logical Calculus from 1920.- Chapter 3: Hilberts Lectures on Problems of Mathematical Logic from 1920.- Hilberts Lectures on Foundations of Mathematics from 1921-22.- Hilberts Lectures on Logical Foundations of Mathematics from 1922-23.- Hilberts Lectures on the Infinite from 1924-25.- Hilberts Typescript on the Foundations of Thought from c. 1925.- Hilberts Lecture on Infinity from 1933.- Miscellanea.- Appendix A: Bernayss Habilitation Thesis from 1918.- Appendix B: First Edition of Hilbert and Ackermann, 1928.

Unger's Philosophy: A Critical Legal Study

Of all the scholars associated with the Critical Legal Studies movement, none has garnered greater attention or higher praise than Roberto Unger of Harvard Law School. In this Article, William Ewald argues that Professor Ungers reputation as a brilliant philosopher of law is undeserved. Despite the seeming erudition of his books, Professor Ungers work displays little familiarity with the basic philosophical literature, and the philosophical, legal, and political analysis in those works-in particular, the celebrated critique of liberalism in Knowledge and Politics-is so riddled with logical and historical errors as to be unworthy of serious scholarly attention.

Lectures on Proof Theory

The lectures in the Summer Semester of 1920 ended with consistency proofs for extremely weak fragments of arithmetic. The question, made explicit in the Introduction to Chapter 2 (see p. 296) was then this: Can these consistency proofs somehow be extended to establish the consistency of increasingly stronger and thus mathematically more interesting systems? The lectures of 1921/22 and 1922/23 give a resoundingly positive answer. However, the ‘extensions’ require a remarkable mathematical/logical and methodological breakthrough that leads to Hilbert’s proof theory and his finitist consistency programme.

Lectures on the Infinite

The following set of lectures from the Winter Semester of 1924/25 (Hilbert 1924/25* ) has a different character from the other lecture notes published in this Volume. Hilbert’s logic lectures from the fall of 1917 to the spring of 1924, addressed to advanced students of mathematics, are a remarkable technical achievement.

Lectures on the Principles of Mathematics

The following lectures, delivered during the Winter Semester 1917/18, are a pivotal event in the development of mathematical logic and mark the start of Hilbert1#x2019;s long and fruitful collaboration with Paul Bernays. Towards the end of his lectures on set theory in the preceding Summer Semester, Hilbert had stated (p. 146), 1#x2018;I hope to be able to explore a foundation for logic more deeply next semester1#x2019;.1 Those earlier lectures had been concerned with the mathematical articulation of set theory and with the prospects for a settheoretic reduction of mathematics. For Chapter IV of the set theory course, Hilbert had announced an enticing and enigmatic title: 1#x2018;Applications of Set Theory to Mathematical Logic1#x2019;. The lectures, however, did not reach the topic of logic proper, and give no hint of the approach Hilbert began exploring a few months later.

Lectures on Logic

During the two years following the 1917/18 lectures which form Chapter 1 of this Volume, Hilbert appears to have devoted little time to foundations, at least in public. A letter from Bernays to Russell on 8 April 1920 remarks, ‘As you may know, Professor Hilbert I am honoured to be his assistant has been working intensively for a number of years on the problems of mathematical logic’. But Bernays gives no details about Hilbert’s activities.