-
2Flirting with Skepticism about Practical WisdomIn Maria Silvia Vaccarezza & Mario De Caro (eds.), Practical Wisdom: Philosophical and Psychological Perspectives, Routledge. 2021.This paper maps out various options for thinking about two issues: the structural relationship between practical wisdom and the moral virtues, and the various functions of practical wisdom. With the help of a case study of the virtue of honesty, three main concerns are raised for what I call the Standard Model of practical wisdom. Two other models, the Socratic Model and the Fragmentation Model, are also critically evaluated. I end by taking seriously an eliminativist approach according to which…Read more
-
32Expansions of o-minimal structures by fast sequencesJournal of Symbolic Logic 70 (2): 410-418. 2005.Let ℜ be an o-minimal expansion of (ℝ,
-
33Expansions of the real field by open sets: definability versus interpretabilityJournal of Symbolic Logic 75 (4): 1311-1325. 2010.An open U ⊆ ℝ is produced such that (ℝ, +, ·, U) defines a Borel isomorph of (ℝ, +, ·, ℕ) but does not define ℕ. It follows that (ℝ, +, ·, U) defines sets in every level of the projective hierarchy but does not define all projective sets. This result is elaborated in various ways that involve geometric measure theory and working over o-minimal expansions of (ℝ, +, ·). In particular, there is a Cantor set E ⊆ ℝ such that (ℝ, +, ·, E) defines a Borel isomorph of (ℝ, +, ·, ℕ) and, for every exponen…Read more
-
31Expansions of o-minimal structures by dense independent setsAnnals of Pure and Applied Logic 167 (8): 684-706. 2016.
-
23Extensions of ordered theories by generic predicatesJournal of Symbolic Logic 78 (2): 369-387. 2013.Given a theoryTextending that of dense linear orders without endpoints, in a language ℒ ⊇ {
-
53Expansions of o-Minimal Structures by Iteration SequencesNotre Dame Journal of Formal Logic 47 (1): 93-99. 2006.Let P be the ω-orbit of a point under a unary function definable in an o-minimal expansion ℜ of a densely ordered group. If P is monotonically cofinal in the group, and the compositional iterates of the function are cofinal at +\infty in the unary functions definable in ℜ, then the expansion (ℜ, P) has a number of good properties, in particular, every unary set definable in any elementarily equivalent structure is a disjoint union of open intervals and finitely many discrete sets
-
15Connectedness in Structures on the Real Numbers: O-Minimality and UndecidabilityJournal of Symbolic Logic 87 (3): 1243-1259. 2022.We initiate an investigation of structures on the set of real numbers having the property that path components of definable sets are definable. All o-minimal structures on $(\mathbb {R},
-
30Moscone Center West, San Francisco, CA January 15–16, 2010Bulletin of Symbolic Logic 16 (3). 2010.
-
60Pfaffian differential equations over exponential o-minimal structuresJournal of Symbolic Logic 67 (1): 438-448. 2002.In this paper, we continue investigations into the asymptotic behavior of solutions of differential equations over o-minimal structures.Let ℜ be an expansion of the real field (ℝ, +, ·).A differentiable mapF= (F1,…,F1): (a, b) → ℝiisℜ-Pfaffianif there existsG: ℝ1+l→ ℝldefinable in ℜ such thatF′(t) =G(t, F(t)) for allt∈ (a, b) and each component functionGi: ℝ1+l→ ℝ is independent of the lastl−ivariables (i= 1, …,l). If ℜ is o-minimal andF: (a, b) → ℝlis ℜ-Pfaffian, then (ℜ,F) is o-minimal (Propos…Read more
-
70Environmental Rights in a Welfare State? A Comment on DeMerieuxOxford Journal of Legal Studies 23 (1): 111-125. 2003.The derivation of a category of ‘environmental rights’ (as argued in this journal by Margaret DeMerieux) from certain cases heard in the European Court of Human Rights is examined. Opposing the majority judicial opinion of that court, there is emerging a dissenting view which is reluctant to extend a rights perspective to those nuisances which can, in theory, be avoided by relocation of the family home. This critique is then extended to Marcic v Thames Water Utilities in which the claimant used …Read more
-
2We say that E is R-sparse if f(Ek) has no interior, for each k 2 N and f : Rk ! R de nable in R. (Throughout, \de nable" means \de nable without parameters".) In this note, we consider the extent to which basic metric and topological properties of subsets of R de nable in (R;E)# are determined by the corresponding properties of subsets of R de nable in (R;E), when R is an o-minimal expansion of (R;
Areas of Interest
20th Century Philosophy |
Philosophy of Physical Science |