I perform an economic and ethical analysis on wealth and income inequality. Economists have performed many statistical studies that reveal a number of, often contradictory, findings in connection with the distribution of wealth and income. Hence, the statistical findings leave us with no better knowledge of the effects that inequality has on economic progress. At the same time, the existing theoretical results have not provided us with a definitive answer concerning the effects of inequality on progress. By gaining knowledge of (...) the nature of inequality, and bringing basic economic principles to bear on the subject, we can come to an understanding of what the causal relationship is between inequality and economic progress. Furthermore, I apply a new theory of ethics – rational egoism – to assess economic inequality. I show that, in the right context, economic inequality is both economically and morally desirable. (shrink)
Machine generated contents note: Part I. General: 1. The Gödel editorial project: a synopsis Solomon Feferman; 2. Future tasks for Gödel scholars John W. Dawson, Jr., and Cheryl A. Dawson; Part II. Proof Theory: 3. Kurt Gödel and the metamathematical tradition Jeremy Avigad; 4. Only two letters: the correspondence between Herbrand and Gödel Wilfried Sieg; 5. Gödel's reformulation of Gentzen's first consistency proof for arithmetic: the no-counter-example interpretation W. W. Tait; 6. Gödel on intuition and on Hilbert's finitism W. W. (...) Tait; 7. The Gödel hierarchy and reverse mathematics Stephen G. Simpson; 8. On the outside looking in: a caution about conservativeness John P. Burgess; Part III. Set Theory: 9. Gödel and set theory Akihiro Kanamori; 10. Generalizations of Gödel's universe of constructible sets Sy-David Friedman; 11. On the question of absolute undecidability Peter Koellner; Part IV. Philosophy of Mathematics: 12. What did Gödel believe and when did he believe it? Martin Davis; 13. On Gödel's way in: the influence of Rudolf Carnap Warren Goldfarb; 14. Gödel and Carnap Steve Awodey and A. W. Carus; 15. On the philosophical development of Kurt Gödel Mark van Atten and Juliette Kennedy; 16. Platonism and mathematical intuition in Kurt Gödel's thought Charles Parsons; 17. Gödel's conceptual realism Donald A. Martin. (shrink)
Pope John Paul II's opposition to the Iraq War was not that it failed to meet the conditions of Just War Theory. Indeed, we cannot tell from what he publicly said whether he thought it met those conditions or not, for he would have opposed it in any case. His thinking was rather that even just and necessary wars always come, as it were, too late, and are never able to solve the problems that made wars just and necessary. He (...) was not trying therefore to enter into the details of Just War Theory. He wanted to subsume the principles of war into the principles of peace and to do so, not by denying justice, but by transcending it with charity. This article shows how this thinking is to be understood and the many means the Pope devised for putting this thinking into practice. (shrink)
We initiate the reverse mathematics of general topology. We show that a certain metrization theorem is equivalent to Π2 1 comprehension. An MF space is defined to be a topological space of the form MF(P) with the topology generated by $\lbrace N_p \mid p \in P \rbrace$ . Here P is a poset, MF(P) is the set of maximal filters on P, and $N_p = \lbrace F \in MF(P) \mid p \in F \rbrace$ . If the poset P is countable, (...) the space MF(P) is said to be countably based. The class of countably based MF spaces can be defined and discussed within the subsystem ACA0 of second order arithmetic. One can prove within ACA0 that every complete separable metric space is homeomorphic to a countably based MF space which is regular. We show that the converse statement, "every countably based MF space which is regular is homeomorphic to a complete separable metric space," is equivalent to Π2 1-CA0. The equivalence is proved in the weaker system Π1 1-CA0. This is the first example of a theorem of core mathematics which is provable in second order arithmetic and implies Π2 1 comprehension. (shrink)
A mass problem is a set of Turing oracles. If P and Q are mass problems, we say that P is weakly reducible to Q if every member of Q Turing computes a member of P. We say that P is strongly reducible to Q if every member of Q Turing computes a member of P via a fixed Turing functional. The weak degrees and strong degrees are the equivalence classes of mass problems under weak and strong reducibility, respectively. We (...) focus on the countable distributive lattices P w and P s of weak and strong degrees of mass problems given by nonempty Π 1 0 subsets of 2 ω . Using an abstract Gödel/Rosser incompleteness property, we characterize the Π 1 0 subsets of 2 ω whose associated mass problems are of top degree in P w and P s , respectively. Let R be the set of Turing oracles which are random in the sense of Martin-Löf, and let r be the weak degree of R. We show that r is a natural intermediate degree within P w . Namely, we characterize r as the unique largest weak degree of a Π 1 0 subset of 2 ω of positive measure. Within P w we show that r is meet irreducible, does not join to 1, and is incomparable with all weak degrees of nonempty thin perfect Π 1 0 subsets of 2 ω . In addition, we present other natural examples of intermediate degrees in P w . We relate these examples to reverse mathematics, computational complexity, and Gentzen-style proof theory. (shrink)
What's the world made of? Donuts! and Beer! -- Protagoras, Gorgias, Captain Kirk, and Denny Crane -- Socrates : The Sergeant Schultz of Ancient Greece -- Plato is the new American Idol -- Aristotle loves Lucy -- Charlie Harper's Non-Epicurean lifestyle -- St. Augustine's Highway to Heaven -- Scully shaves Mulder with Ockham's Razor -- Larry Hagman dreams of Descartes -- Locke versus Hobbes, or The Brady Bunch takes on Survivor -- Can or can't Kant like vampires? -- Reading Hegel (...) in Outer Space -- John Stuart Mill and the Utilitarian Heroism of Dexter Morgan -- Karl Marx and Adam Smith, meet Alex P. Keaton -- Dr. Gregory House and the Nietzschean Superman -- Don Draper, George Costanza and the non-meaning of life -- Jersey Shore's 'The Situation': The Randian Ideal man with a tan? -- Earl Hickey meets Karma in My name is Earl -- Lost but not least. (shrink)
Clark, R. L. Facts, fact-correlates, and fact-surrogates.--Heintz, J. The real subject-predicate asymmetry.--Stenius, E. All men are mortal.--Wilson, N. L. Notes on the form of certain elementary facts.--Binkley, R. The ultimate justification of moral rules.--Castañeda, H. Goodness, intentions, and propositions.--Patterson, R. L. An analysis of faith.--Simpson, E. Discrimination as an example of moral irrationality.--Welsh, P. Osborne on the art of appreciation.--Lachs, J. The omnicolored sky: Baylis on perception.--Strawson, P. F. Causation in perception.--Reid, C. L. Charles A. Baylis: a bibliography.
Let A and B be subsets of the reals. Say that A κ ≥ B, if there is a real a such that the relation "x ∈ B" is uniformly Δ 1 (a, A) in L[ ω x,a,A 1 , x,a,A]. This reducibility induces an equivalence relation $\equiv_\kappa$ on the sets of reals; the $\equiv_\kappa$ -equivalence class of a set is called its Kleene degree. Let K be the structure that consists of the Kleene degrees and the induced partial order (...) K ≥. A substructure of K that is of interest is P, the Kleene degrees of the Π 1 1 sets of reals. If sharps exist, then there is not much to P, as Steel [9] has shown that the existence of sharps implies that P has only two elements: the degree of the empty set and the degree of the complete Π 1 1 set. Legrand [4] used the hypothesis that there is a real whose sharp does not exist to show that there are incomparable elements in P; in the context of V = L, Hrbacek has shown that P is dense and has no minimal pairs. The Hrbacek results led Simpson [6] to make the following conjecture: if V = L, then p forms a universal homogeneous upper semilattice with 0 and 1. Simpson's conjecture is shown to be false by showing that if V = L, then Godel's maximal thin Π 1 1 set is the infimum of two strictly larger elements of P. The second main result deals with the notion of jump in K. Let A' be the complete Kleene enumerable set relative to A. Say that A is low-n if A (n) has the same degree as $\varnothing^{(n)}$ , and A is high-n if A (n) has the same degree as $\varnothing^{(n + 1)}$ . Simpson and Weitkamp [7] have shown that there is a high (high-1) incomplete Π 1 1 set in L. They have also shown that various other Π 1 1 sets are neither high nor low in L. Legrand [5] extended their results by showing that, if there is a real x such that x # does not exist, then there is an element of P that, for all n, is neither low-n nor high-n. In § 2, ZFC is used to show that, for all n, if A is Π 1 1 and low-n then A is Borel. The proof uses a strengthened version of Jensen's theorem on sequences of admissible ordinals that appears in [7, Simpson-Weitkamp]. (shrink)
The Sociosexual Orientation Inventory (SOI; Simpson & Gangestad 1991) is a self-report measure of individual differences in human mating strategies. Low SOI scores signify that a person is sociosexually restricted, or follows a more monogamous mating strategy. High SOI scores indicate that an individual is unrestricted, or has a more promiscuous mating strategy. As part of the International Sexuality Description Project (ISDP), the SOI was translated from English into 25 additional languages and administered to a total sample of 14,059 (...) people across 48 nations. Responses to the SOI were used to address four main issues. First, the psychometric properties of the SOI were examined in cross-cultural perspective. The SOI possessed adequate reliability and validity both within and across a diverse range of modern cultures. Second, theories concerning the systematic distribution of sociosexuality across cultures were evaluated. Both operational sex ratios and reproductively demanding environments related in evolutionary-predicted ways to national levels of sociosexuality. Third, sex differences in sociosexuality were generally large and demonstrated cross-cultural universality across the 48 nations of the ISDP, confirming several evolutionary theories of human mating. Fourth, sex differences in sociosexuality were significantly larger when reproductive environments were demanding but were reduced to more moderate levels in cultures with more political and economic gender equality. Implications for evolutionary and social role theories of human sexuality are discussed. Key Words: culture; gender; mating; reproduction; sex differences; sex roles; sexual strategies; sociosexuality. (shrink)
We are not convinced by Gangestad & Simpson that differential mating strategies within each sex would be greater than such strategies between sexes. The target article does not provide actual evidence of human males who do not desire mating with multiple females, or evidence that the benefits for females of short-term matings with multiple males have ever outweighed the associated costs.
