• Raymond Aron is widely regarded as the most important figure in the history of twentieth-century French liberalism. Yet his status within the history of liberal thought has been more often proclaimed than explained. Though he is frequently lauded as the inheritor of France's liberal tradition, Aron's formative influences were mostly non-French and often radically anti-liberal thinkers. This book explains how, why, and with what consequences he belatedly defined and aligned himself with a French …Read more
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    The expressibility of fragments of Hybrid Graph Logic on finite digraphs
    with James Gate
    Journal of Applied Logic 11 (3): 272-288. 2013.
  • Taking as its starting point recent claims that Jean-Paul Sartre's Critique de la Raison Dialectique was written as an attempt to overcome the historical relativism of Raymond Aron's Introduction à la philosophie de l'histoire, the present article traces this covert dialogue back to a fundamental disagreement between the two men over the interpretation of Wilhelm Dilthey's anti-positivist theory of Verstehen or 'understanding'. In so doing it counters a longstanding tendency to emphasise the con…Read more
  •  6
    Context-sensitive transitive closure operators
    Annals of Pure and Applied Logic 66 (3): 277-301. 1994.
    We introduce a new logical operator CSTC and show that incorporating this operator into first-order logic enables as to capture the complexity class PSPACE. We also show that by varying how the operator is applied we can capture the complexity classes P, NP, the classes of the Polynomial Hierarchy PH, and PSPACE. As such, the operator CSTC can be regarded as a general purpose operator. We also give applications of these characterizations by showing that P and NP coincide with those problems acce…Read more
  •  3
    Monotonicity and the Expressibility of NP Operators
    Mathematical Logic Quarterly 40 (1): 132-140. 1994.
    We investigate why similar extensions of first-order logic using operators corresponding to NP-complete decision problems apparently differ in expressibility: the logics capture either NP or LNP. It had been conjectured that the complexity class captured is NP if and only if the operator is monotone. We show that this conjecture is false. However, we provide evidence supporting a revised conjecture involving finite variations of monotone problems
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    We investigate the definability in monadic ∑11 and monadic Π11 of the problems REGk, of whether there is a regular subgraph of degree k in some given graph, and XREGk, of whether, for a given rooted graph, there is a regular subgraph of degree k in which the root has degree k, and their restrictions to graphs in which every vertex has degree at most k, namely REGkk and XREGkk, respectively, for k ≥ 2 . Our motivation partly stems from the fact that REGkk and XREGkk are logspace equivalent to CON…Read more
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    The most extensive account ever, at least in English, of the constitutional doctrine of 'separation of powers', as well as one of the most extensive in English of the idea of 'the rule of law' and its European counterpart, the notion of a 'legal state (German, Rechtsstaat)'. It draws on sources in several languages and disciplines, and many legal systems both ancient and modern. It also proposes a novel basis for judicial independence - outside the tricky sphere of separation of powers.
  •  17
    Facing Walter's Dilemma
    Ratio Juris 10 (4): 397-402. 1997.
    Jörgen Jörgensen (1938) asks why there should not be a valid deduction even though the premises are imperatives (“Jörgensen’s Dilemma”). Robert Walter (1996; 9 Ratio Juris 168), following Hans Kelsen, thinks that there can be a valid deduction if the premises, although in prescriptive (including imperative) language, are actually descriptions of prescriptions. It is suggested that Walter then has his own dilemma: the more possible it is, for such descriptions to be valid, the less likely it …Read more
  • Kelsen and the Exegetical Tradition
    In Richard Tur & William L. Twining (eds.), Essays on Kelsen, Clarendon Press. pp. 123--46. 1986.
    Hans Kelsen’s Pure Theory of Law, presented as a form of legal positivism, is interpreted as establishing metaphysical bases of legal science, on analogy with Kant’s “metaphysical bases of natural science (Metaphysische Anfangsgründe der Naturwissenschaft)”. It is asked, in the light of the Pure Theory’s acknowledged difficulties, how far it succeeds in escaping from the exegetical tradition in Western legal theory.