Greek, Indian and Arabic Logic marks the initial appearance of the multi-volume Handbook of the History of Logic. Additional volumes will be published when ready, rather than in strict chronological order. Soon to appear are The Rise of Modern Logic: From Leibniz to Frege. Also in preparation are Logic From Russell to Gödel, The Emergence of Classical Logic, Logic and the Modalities in the Twentieth Century, and The Many-Valued and Non-Monotonic Turn in Logic. Further volumes will follow, including Mediaeval and (...) Renaissance Logic and Logic: A History of its Central. In designing the Handbook of the History of Logic, the Editors have taken the view that the history of logic holds more than an antiquarian interest, and that a knowledge of logic's rich and sophisticated development is, in various respects, relevant to the research programmes of the present day. Ancient logic is no exception. The present volume attests to the distant origins of some of modern logic's most important features, such as can be found in the claim by the authors of the chapter on Aristotle's early logic that, from its infancy, the theory of the syllogism is an example of an intuitionistic, non-monotonic, relevantly paraconsistent logic. Similarly, in addition to its comparative earliness, what is striking about the best of the Megarian and Stoic traditions is their sophistication and originality. Logic is an indispensably important pivot of the Western intellectual tradition. But, as the chapters on Indian and Arabic logic make clear, logic's parentage extends more widely than any direct line from the Greek city states. It is hardly surprising, therefore, that for centuries logic has been an unfetteredly international enterprise, whose research programmes reach to every corner of the learned world. Like its companion volumes, Greek, Indian and Arabic Logic is the result of a design that gives to its distinguished authors as much space as would be needed to produce highly authoritative chapters, rich in detail and interpretative reach. The aim of the Editors is to have placed before the relevant intellectual communities a research tool of indispensable value. Together with the other volumes, Greek, Indian and Arabic Logic, will be essential reading for everyone with a curiosity about logic's long development, especially researchers, graduate and senior undergraduate students in logic in all its forms, argumentation theory, AI and computer science, cognitive psychology and neuroscience, linguistics, forensics, philosophy and the history of philosophy, and the history of ideas. (shrink)
This article serves to present a large mathematical perspective and historical basis for the Axiom of Replacement as well as to affirm its importance as a central axiom of modern set theory.
Naturalistic teleological accounts of mental content rely on an etiological theory of function. Nanay has raised a new objection to an etiological theory, and proposed an alternative theory of function that attributes modal force to claims about function. The aim of this paper is both to defend and to cast a new light on an etiological theory of function. I argue against Nanay’s “trait type individuation objection,” suggesting that an etiological theory also attributes modal force to claims about function. An (...) etiological theory of function can be thought to analyze claims about function with modal force, not relying on any theory of counterfactuals. (shrink)
This paper replies to Nanay’s response to my recent paper. My suggestions are the following. First, “should” or “ought” does not need to be deontic. Second, etiological theories of function, like provability logic, do not need to attribute modal force to their explanans. Third, the explanans of the homological account of trait type individuation does not appeal to a trait’s etiological function, that is, what a trait should or ought to do. Finally, my reference to Cummins’s notion of function was (...) intended to note that the homological account is permitted to use this non-etiological notion of function. (shrink)
Evolutionary theory has recently been applied to language. The aim of this paper is to contribute to such an evolutionary approach to language. I argue that Kripke’s causal account of proper names, in terms of natural selection, captures the norm of uses of a proper name, which is to refer to the same object as past others’ uses in a linguistic community. My argument appeals to Millikan’s theory of direct proper functions, which captures the norms of various functional entities in (...) terms of natural selection. (shrink)
Evolutionary theory has recently been applied to language. The aim of this paper is to contribute to such an evolutionary approach to language. I argue that Kripke’s causal account of proper names, from an ecological point of view, captures the information carried by uses of a proper name, which is that a certain object is referred to. My argument appeals to Millikan’s concept of local information, which captures information about the environment useful for an organism.
The “units of selection” debate in philosophy of biology addresses which entity benefits from natural selection. Nanay has tried to explain why we are obsessed with the question about the meaning of life, using the notion of group selection, although he is skeptical about answering the question from a biological point of view. The aim of this paper is to give a biological explanation to the meaning of life. I argue that the meaning of life is survival and reproduction, appealing (...) to the teleological notion of function in philosophy of biology. (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)
This paper discusses the reception of Darwinian evolutionary theory and sociobiology in Japan. Darwinism was introduced into Japan in the late 19th century and Japanese people readily accepted the concept of evolution because, lacking Christianity, there was no religious opposition. However, the theory of evolution was treated as a kind of social scientific tool, i.e., social Spencerism and eugenics. Although evolutionary biology was developed during the late 19th and the early 20th century, orthodox Darwinian theory was neglected for a long (...) time. In the mid 1980s, sociobiology was introduced but it was ignored and criticized by a large part of the ecologist-evolutionist community in Japan. This hostile attitude was due to the absence of Darwinism among these scientists. Compared with the reception of sociobiology in English-speaking countries, there were both similarities and differences in Japan. (shrink)
Machine generated contents note: 1. Introduction Juliette Kennedy and Roman Kossak; 2. Historical remarks on Suslin's problem Akihiro Kanamori; 3. The continuum hypothesis, the generic-multiverse of sets, and the [OMEGA] conjecture W. Hugh Woodin; 4. [omega]-Models of finite set theory Ali Enayat, James H. Schmerl and Albert Visser; 5. Tennenbaum's theorem for models of arithmetic Richard Kaye; 6. Hierarchies of subsystems of weak arithmetic Shahram Mohsenipour; 7. Diophantine correct open induction Sidney Raffer; 8. Tennenbaum's theorem and recursive reducts James (...) H. Schmerl; 9. History of constructivism in the 20th century A. S. Troelstra; 10. A very short history of ultrafinitism Rose M. Cherubin and Mirco A. Mannucci; 11. Sue Toledo's notes of her conversations with Gödel in 1972-1975 Sue Toledo; 12. Stanley Tennenbaum's Socrates Curtis Franks; 13. Tennenbaum's proof of the irrationality of [the square root of] 2́. (shrink)
Gödel, Tarski, Church, and the Liar , by György Serény, pages 3–25. From foundations to ludics , by Jean-Yves Girard, pages 131 -- 168. Symmetry and interactivity in programming , by P.-L. Curien, pages 169 -- 180. Two spaces looking for a geometer , by Giorgio Parisi, pages 181 -- 196. Model theory: Geometrical and set-theoretic aspects and prospects , by Angus Macintyre, pages 197 -- 212. Foundations and applications: axiomatization and education , by F. William Lawvere, pages 213 -- (...) 224. Differential calculus and nilpotent real numbers , by Anders Kock, pages 225 -- 230. The empty set, the singleton, and the ordered pair , by Akihiro Kanamori, pages 273 -- 298. Computable and continuous partial homomorphisms on metric partial algebras , by Viggo Stoltenberg-Hansen and John V. Tucker, pages 299 -- 334. Survey of the Steinhaus tiling problem , by Steve Jackson and R. Daniel Mauldin, pages 335 -- 361. A universal approach to self-referential paradoxes, incompleteness and fixed points , by Noson S. Yanofsky, pages 362 -- 386. On the philosophical development of Kurt Gödel , by Mark van Atten and Juliette Kennedy, pages 425 — 476. Identity of proofs based on normalization and generality , by Kosta Došen, pages 477 — 503. (shrink)
In this paper I investigate the possibility of a dictatorship in the context of Harsanyi's Social Aggregation Theorem. Preliminarily, some propositions about Harsanyi's Theorem are presented using an alternative principle that I name Quasi-strong Pareto, which is the latter part of Strong Pareto. Then I define dictatorship as a requirement that social preference agrees with a dictator's preference or those of members of dictatorial group even if their preferences strictly contradict those of all other people in the society. Conclusively, although (...) in each version of Harsanyi's Theorem with Pareto Indifference, Weak Preference Pareto or Weak Pareto the social utility function may have a form of dictatorship, however if individuals' vNM utility functions are all 'individualistic' and Quasi-strong Pareto is satisfied, then the dictatorship is excluded. (shrink)
Background: Previous studies have found that the decision-making process for stored unused frozen embryos involves much emotional burden influenced by socio-cultural factors. This study aims to ascertain how Japanese patients make a decision on the fate of their frozen embryos: whether to continue storage discard or donate to research. Methods: Ten Japanese women who continued storage, 5 who discarded and 16 who donated to research were recruited from our infertility clinic. Tape-recorded interviews were transcribed and analyzed for emergent themes. Results: (...) A model of patients’ decision-making processes for the fate of frozen embryos was developed, with a common emergent theme, “coming to terms with infertility” resulting in either acceptance or postponing acceptance of their infertility. The model consisted of 5 steps: 1) the embryo-transfer moratorium was sustained, 2) the “Mottainai”- embryo and having another child were considered; 3) cost reasonability was taken into account; 4) partner’s opinion was confirmed to finally decide whether to continue or discontinue storage. Those discontinuing, then contemplated 5): the effect of donation. Great emotional conflict was expressed in the theme, steps 2, 4, and 5. Conclusions: Patients’ 5 step decision-making process for the fate of frozen embryos was profoundly affected by various Japanese cultural values and moral standards. At the end of their decision, patients used culturally inherent values and standards to come to terms with their infertility. While there is much philosophical discussion on the moral status of the embryo worldwide, this study, with actual views of patients who own them, will make a significant contribution to empirical ethics from the practical viewpoint. (shrink)
Answering a question of A. Kanamori, we prove that there is no Jónsson filter over the least Jonsson cardinal. We also notice that, assuming □ κ , the successor κ + cannot be Jonsson.
