Depue & Morrone-Strupinsky's (D&M-S's) implicit assumption appears to be that affiliative bonding is either strengthened or maintained with time; however, it is more realistic that it can also be weakened or destroyed by conflictive interpersonal interactions. Without specifying the mechanisms by which antagonistic stimuli deteriorate affiliative bonding, the model is incapable of accounting for the dynamics associated with this complex phenomenon.
Tyler Burge's theory of proper names is being revived with the help of Generative Grammar. The complex syntax of DPs appears to encourage the Burgean analysis of proper names which attributes complex semantic structures to the uses of proper names. I will argue, however, that the Millian view of proper names which hypothesizes simple semantics for names is also compatible with the complex syntactic structures. In order to defend this thesis, I will show that Paul Elbourne's implementation of Burge's insight (...) is no better than the Millian semantics of proper names. (shrink)
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)
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)
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)
Cellular pattern formations of some epithelia are believed to be governed by the direct lateral inhibition rule of cell differentiation. That is, initially equivalent cells are all competent to differentiate, but once a cell has differentiated, the cell inhibits its immediate neighbors from following this pathway. Such a differentiation repeats until all non-inhibited cells have differentiated. The cellular polygonal patterns can be characterized by the numbers of undifferentiated cells and differentiated ones. When the differentiated cells become large in size, the (...) polygonal pattern is deformed since more cells are needed to enclose the large cell. An actual example of such a cellular pattern was examined. The pupal wing epidermis of a butterfly Pieris rapae shows a transition of the equivalent-size cell pattern to the pattern involving large cells. The process of the transition was analyzed by using the method of weighted Voronoi tessellation that is useful for treatment of irregularly sized polygons. The analysis supported that the pattern transition of the early stage of the pupal wing epidermis is governed by the lateral inhibition rule. The differentiation takes place in order of largeness, but not smallness, of the apical polygonal area in the differentiating region of the pupal wing. (shrink)
In the psychology of teaching, teaching of knowledge is one of the central themes. The psychology of teaching itself is also knowledge, so that the psychology of teaching and the teaching of psychology mutually include each other. Here, I would like to consider a phenomenon in the art of questioning in teaching a literary work of art and would like to show its relevance to the psychology of teaching in general.
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)
A reduction rule is introduced as a transformation of proof figures in implicational classical logic. Proof figures are represented as typed terms in a -calculus with a new constant P (()). It is shown that all terms with the same type are equivalent with respect to -reduction augmented by this P-reduction rule. Hence all the proofs of the same implicational formula are equivalent. It is also shown that strong normalization fails for P-reduction. Weak normalization is shown for P-reduction with another (...) reduction rule which simplifies of (( ) ) into an atomic type. (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.
In the social world, multiple sensory channels are used concurrently to facilitate communication. Among human and nonhuman pri- mates, faces and voices are the primary means of transmitting social signals (Adolphs, 2003; Ghazanfar and Santos, 2004). Primates recognize the correspondence between species-specific facial and vocal expressions (Massaro, 1998; Ghazanfar and Logothetis, 2003; Izumi and Kojima, 2004), and these visual and auditory channels can be integrated into unified percepts to enhance detection and discrimination. Where and how such communication signals are (...) integrated at the neural level are poorly understood. In particular, it is unclear what role “unimodal” sensory areas, such as the auditory cortex, may play. We recorded local field potential activity, the signal that best correlates with human imaging and event-related potential signals, in both the core and lateral belt regions of the auditory cortex in awake behaving rhesus monkeys while they viewed vocalizing conspecifics. We demonstrate unequivocally that the primate auditory cortex integrates facial and vocal signals through enhancement and suppression of field potentials in both the core and lateral belt regions. The majority of these multisensory responses were specific to face/voice integration, and the lateral belt region shows a greater frequency of multisensory integration than the core region. These multisensory processes in the auditory cortex likely occur via recip- rocal interactions with the superior temporal sulcus. (shrink)
