This chapter contains sections titled: The Project of Formalism The Nature of Justification The Structures of Justification The Ground of Justification The Immanent Intelligibility of Law Conclusion References.

Remarks on the Foundations of Mathematics, Wittgenstein, despite his official 'mathematical nonrevisionism', slips into attempting to refute Gödel's theorem. Actually, Wittgenstein could have used Gödel's theorem to good effect, to support his view that proof, and even truth, are 'family resemblance' concepts. The reason that Wittgenstein did not see all this is that Gödel's theorem had become an icon of mathematical realism, and he was blinded by his own ideology. The essay is a reply to Juliet Floyd's work on Gödel: (...) what she says Wittgenstein said, I say he should have said, but didn't (couldn't). (shrink)

Wittgenstein's distinction between understanding and interpretation is fundamental to the account of meaning in _Philosophical Investigations. In his discussion of rule-following, Wittgenstein explicitly rejects the idea that understanding or grasping a rule is a matter of interpretation. Wittgenstein explains meaning and rule-following in terms of action, rejecting both realist and Cartesian accounts of the mental. I argue that in his effort to employ Wittgenstein's views on meaning and rule-following, Professor Morawetz embraces the position Wittgenstein rejects. In the course of making (...) his case for law as a "deliberative practice", Professor Morawetz embraces interpretation as a fundamental element of human practices, thereby taking up precisely the view Wittgenstein rejects. (shrink)

Ludwig Wittgenstein's work on rules has been put to a variety of uses by legal theorists. One wave of theorists employs Wittgenstein in an effort to show that law is radically indeterminate. They base their arguments on Saul Kripke's influential reading of Wittgenstein's Philosophical Investigations. This essay begins with a consideration of Kripke's view and its implications for law. Like many before, I conclude that Kripke's view is defective, and as such teaches us little about law. But it is important (...) to explore the view in detail nonetheless, because only by doing so can we understand the mistakes of the second wave of theorists who employ Wittgenstein's remarks on rules in jurisprudential argument. The second wave includes Brian Bix and Andrei Marmor, who turn to Wittgenstein's remarks on rules to explain how it is that law can be determinate and also to show that law can often be understood without interpretation. I argue that both Bix and Marmor fail, and more importantly, that Wittgenstein's remarks on rules have little to offer legal theory. Nothing much can be learned about legal rules or legal interpretation by attending to Wittgenstein's remarks, because they were aimed at wholly different phenomena. (shrink)

A survey of current evidence available concerning Wittgenstein's attitude toward, and knowledge of, Gödel's first incompleteness theorem, including his discussions with Turing, Watson and others in 1937–1939, and later testimony of Goodstein and Kreisel; 2) Discussion of the philosophical and historical importance of Wittgenstein's attitude toward Gödel's and other theorems in mathematical logic, contrasting this attitude with that of, e.g., Penrose; 3) Replies to an instructive criticism of my 1995 paper by Mark Steiner which assesses the importance of Tarski's semantical (...) work, both for our understanding of Wittgenstein's remarks on Gödel, and our understanding of Gödel's theorem itself. (shrink)

This chapter contains section titled: History and Context Clarifications Alternative Legal Positivisms The Rule of Recognition and the Basic Norm The Divisions Within Contemporary Legal Positivism Debates and Distinctive Views Critiques of Legal Positivism Two Critics: Ronald Dworkin and John Finnis Methodological Questions and the Way Forward Conclusion Note References Further Reading.

odel’s theorem than he has often been credited with. Substantively, they find in Wittgenstein’s remarks “a philosophical claim of great interest,” and they argue that, when this claim is properly assessed, it helps to vindicate some of Wittgenstein’s broader views on G¨.

What is new here is the detailed discussion of several important results in the classical foundations of mathematics and of the relation of logic to mathematics. As regards logical questions, the central thesis of Wittgenstein's later philosophy is well known, both from the earlier posthumous volume and from the writings of his many disciples. In the Investigations the thesis is applied to the "logic of our expressions" in everyday contexts; here he discusses in the same spirit the more specialized language (...) used in talking about the foundations of mathematics. (shrink)

A general introduction to the celebrated foundational crisis, discussing how the characteristic traits of modern mathematics (acceptance of the notion of an “arbitrary” function proposed by Dirichlet; wholehearted acceptance of infinite sets and the higher infinite; a preference “to put thoughts in the place of calculations” and to concentrate on “structures” characterized axiomatically; a reliance on “purely existential” methods of proof) provoked extensive polemics and alternative approaches. Going beyond exclusive concentration on the paradoxes, it also discusses the role of the (...) axiom of Choice, issues of predicativity, and goes on to present the ideas of intuitionism and Hilbert's program. The essay closes with Gödel's contributions and the aftermath. (shrink)

According to several commentators, Kurt Godel's incompleteness discoveries were assimilated promptly and almost without objection by his contemporaries - - a circumstance remarkable enough to call for explanation. Careful examination reveals, however, that there were doubters and critics, as well as defenders and rival claimants to priority. In particular, the reactions of Carnap, Bernays, Zermelo, Post, Finsler, and Russell, among others, are considered in detail. Documentary sources include unpublished correspondence from Godel's Nachlass.

This essay investigates the indeterminacy thesis - roughly the claim that the content of authoritative legal materials (such as the texts of constitutions, statutes, cases, rules, and regulations) does not determine the outcome of particular legal disputes. The indeterminacy thesis can be formulated as either "strong" or weak." The strong version of the indeterminacy thesis is demonstrably false, but several weak versions of the thesis are true but lack the radical implications of strong indeterminacy.The strong indeterminacy thesis is the claim (...) that all cases are "hard" cases - or that in any case any conceivable result can be derived from existing legal doctrine. Strong indeterminacy does not hold if there are easy cases - cases in which some outcomes cannot be legally correct. For example, if it were the case that the first paragraph of this abstract did not slander Gore Vidal, then there would be at least one easy case, and strong indeterminacy would be false.Weak versions of the indeterminacy thesis include the claim that important cases are indeterminate, that the law does not necessarily determine outcomes, or that every case could become indeterminate if political conditions supported indeterminacy. These weaker claims may be true, but they lack the critical bite associated with strong indeterminacy.The essay also distinguishes between "determinacy," "indeterminacy," and "underdeterminacy." The law is "determinate" with respect ot a given case if and only if the set of results that can be squared with the legal materials contains only one member. The law is "indeterminate" with respect to a given case if and only if the set of results that can be squared with the legal materials is identical with the set of all imaginable results. The law is "underdeterminate" with respect to a given case if and only if the set of results that can be squared with the legal materials is a nonidentical subset of the set of all imaginable results.This article was first published in 1987, and some of the author's views have been revised in interim. (shrink)