A note on the consistency operator

It is a well known empirical observation that natural axiomatic theories are pre-well-ordered by consistency strength. For any natural theory $T$, the next strongest natural theory is $T+\mathsf{Con}_T$. We formulate and prove a statement to the effect that the consistency operator is the weakest natural way to uniformly extend axiomatic theories

MENCIUS\u27 JUN-ZI, ARISTOTLE\u27S MEGALOPSUCHOS, & MORAL DEMANDS TO HELP THE GLOBAL POOR

It is commonly believed that impartial utilitarian moral theories have significant demands that we help the global poor, and that the partial virtue ethics of Mencius and Aristotle do not. This ethical partiality found in these virtue ethicists has been criticized, and some have suggested that the partialistic virtue ethics of Mencius and Aristotle are parochial (i.e., overly narrow in their scope of concern). I believe, however, that the ethics of Mencius and Aristotle are both more cosmopolitan than many presume and also are very demanding. In this paper, I argue that the ethical requirements to help the poor and starving are very demanding for the quintessentially virtuous person in Mencius and Aristotle. The ethical demands to help even the global poor are demanding for Mencius jun-zi (君子chön-tzu / junzi) and Aristotle\u27s megalopsuchos. I argue that both the jun-zi and megalopsuchos have a wide scope of concern for the suffering of poor people. I argue that the relevant virtues of the jun-zi and megalopsuchos are also achievable for many people. The moral views of Mencius and Aristotle come with strong demands for many of us to work harder to alleviate global poverty

The Strength of Abstraction with Predicative Comprehension

Frege's theorem says that second-order Peano arithmetic is interpretable in Hume's Principle and full impredicative comprehension. Hume's Principle is one example of an abstraction principle, while another paradigmatic example is Basic Law V from Frege's Grundgesetze. In this paper we study the strength of abstraction principles in the presence of predicative restrictions on the comprehension schema, and in particular we study a predicative Fregean theory which contains all the abstraction principles whose underlying equivalence relations can be proven to be equivalence relations in a weak background second-order logic. We show that this predicative Fregean theory interprets second-order Peano arithmetic.Comment: Forthcoming in Bulletin of Symbolic Logic. Slight change in title from previous version, at request of referee

What Is Wisdom? Cross-Cultural and Cross-Disciplinary Syntheses

This article explores the nature of wisdom using an integrative cross-cultural and cross-disciplinary approach by drawing on contemporary research as well as the philosophical and contemplative disciplines of both East and West. To do this the article first analyzes definitional issues. These issues include difficulties of definition in general, and of wisdom in particular, the common elements and limitations of current definitions, as well as possible varieties or subtypes of wisdom. It then uses integrative definitions of wisdom and its major subtypes as a framework to investigate the characteristics, capacities, and components of wisdom; the varieties of self-knowledge that foster and constitute it; the perceptual, cognitive, and developmental processes essential to it; and the existential issues—for example, meaning, mystery, suffering, and death—that wisdom ponders and responds to. The article then examines wisdom's intimate link with other virtues, especially ethics and benevolence, and questions the claim that emotional regulation is an inherent element of wisdom, arguing instead that emotional regulation and wisdom are distinct, yet mutually facilitating virtues. Finally, the article provides evidence for the “self-demanding” nature of wisdom which implies that to understand it fully we may need to cultivate it ourselves