Can intergenerational equity be operationalized?

A long Utilitarian tradition has the ideal of equal regard for all individuals, both those now living and those yet to be born. The literature formalizes this ideal as asking for a preference relation on the space of infinite utility streams that is complete, transitive, invariant to finite permutations, and respects the Pareto ordering; an ethical preference relation, for short. This paper argues that operationalizing this ideal is problematic. Most simply, every ethical preference relation has the property that almost all (in the sense of outer measure) pairs of utility streams are indifferent. Even if we abandon completeness and respect for the Pareto ordering, every irreflexive preference relation that is invariant to finite permutations has the property that almost all pairs of utility streams are incomparable (not strictly ranked). Moreover, no ethical preference relation can be measurable. As a consequence, the existence of an ethical preference relation is independent of the axioms used in almost all of formal economics and all of classical analysis. Finally, even if an ethical preference relation exists, it cannot be "explicitly described." These results have implications for game theory, for macroeconomics, and for economic development.Intergenerational equity, infinite utility streams, long run averages, overtaking criterion, Utilitarianism

On the Axiom of Canonicity

The axiom of canonicity was introduced by the famous Polish logician Roman Suszko in 1951 as an explication of Skolem's Paradox (without reference to the L\"{o}wenheim-Skolem theorem) and a precise representation of the axiom of restriction in set theory proposed much earlier by Abraham Fraenkel. We discuss the main features of Suszko's contribution and hint at its possible further applications

Semantics out of context: nominal absolute denotations for first-order logic and computation

Call a semantics for a language with variables absolute when variables map to fixed entities in the denotation. That is, a semantics is absolute when the denotation of a variable a is a copy of itself in the denotation. We give a trio of lattice-based, sets-based, and algebraic absolute semantics to first-order logic. Possibly open predicates are directly interpreted as lattice elements / sets / algebra elements, subject to suitable interpretations of the connectives and quantifiers. In particular, universal quantification "forall a.phi" is interpreted using a new notion of "fresh-finite" limit and using a novel dual to substitution. The interest of this semantics is partly in the non-trivial and beautiful technical details, which also offer certain advantages over existing semantics---but also the fact that such semantics exist at all suggests a new way of looking at variables and the foundations of logic and computation, which may be well-suited to the demands of modern computer science

ISABELLE - THE NEXT 700 THEOREM PROVERS

Isabelle is a generic theorem prover, designed for interactive reasoning in a variety of formal theories. At present it provides useful proof procedures for Constructive Type Theory, various first-order logics, Zermelo-Fraenkel set theory, and higher-order logic. This survey of Isabelle serves as an introduction to the literature. It explains why generic theorem proving is beneficial. It gives a thorough history of Isabelle, beginning with its origins in the LCF system. It presents an account of how logics are represented, illustrated using classical logic. The approach is compared with the Edinburgh Logical Framework. Several of the Isabelle object-logics are presented