Hypatia's silence. Truth, justification, and entitlement.

Hartry Field distinguished two concepts of type-free truth: scientific truth and disquotational truth. We argue that scientific type-free truth cannot do justificatory work in the foundations of mathematics. We also present an argument, based on Crispin Wright's theory of cognitive projects and entitlement, that disquotational truth can do justificatory work in the foundations of mathematics. The price to pay for this is that the concept of disquotational truth requires non-classical logical treatment

Theories of vagueness and theories of law

It is common to think that what theory of linguistic vagueness is correct has implications for debates in philosophy of law. I disagree. I argue that the implications of particular theories of vagueness on substantive issues of legal theory and practice are less far-reaching than often thought. I focus on four putative implications discussed in the literature concerning (i) the value of vagueness in the law, (ii) the possibility and value of legal indeterminacy, (iii) the possibility of the rule of law, and (iv) strong discretion. I conclude with some methodological remarks. Delineating questions about conventional meaning, the metaphysics/metasemantics of (legal) content determination, and norms of legal interpretation and judicial practice can motivate clearer answers and a more refined understanding of the space of overall theories of vagueness, interpretation, and law

Lewis meets Brouwer: constructive strict implication

C. I. Lewis invented modern modal logic as a theory of "strict implication". Over the classical propositional calculus one can as well work with the unary box connective. Intuitionistically, however, the strict implication has greater expressive power than the box and allows to make distinctions invisible in the ordinary syntax. In particular, the logic determined by the most popular semantics of intuitionistic K becomes a proper extension of the minimal normal logic of the binary connective. Even an extension of this minimal logic with the "strength" axiom, classically near-trivial, preserves the distinction between the binary and the unary setting. In fact, this distinction and the strong constructive strict implication itself has been also discovered by the functional programming community in their study of "arrows" as contrasted with "idioms". Our particular focus is on arithmetical interpretations of the intuitionistic strict implication in terms of preservativity in extensions of Heyting's Arithmetic.Comment: Our invited contribution to the collection "L.E.J. Brouwer, 50 years later