The paper attempts to analyze in some detail the main problems encountered in reasoning using diagrams, which may cause errors in reasoning, produce doubts concerning the reliability of diagrams, and impressions that diagrammatic reasoning lacks the rigour necessary for mathematical reasoning. The paper first argues that such impressions come from long neglect which led to a lack of well-developed, properly tested and reliable reasoning methods, as contrasted with the amount of work generations of mathematicians expended on refining the methods of (...) reasoning with formulae and predicate calculus. Next, two main groups of problems occurring in diagrammatic reasoning are introduced. The second group, called diagram imprecision, is then briefly summarized, its detailed analysis being postponed to another paper. The first group, called collectively the generalization problem, is analyzed in detail in the rest of the paper. The nature and causes of the problems from this group are explained, methods of detecting the potentially harmful occurrences of these problems are discussed, and remedies for possible errors they may cause are proposed. Some of the methods are adapted from similar methods used in reasoning with formulae, several other problems constitute new, specifically diagrammatic ways of reliable reasoning. (shrink)
A new book by Zenon Pylyshyn is always a cause for celebration among philosophers of psychology. While many hard-nosed experimental cognitive scientists are attentive to philosophers’ concerns, Pylyshyn stands alone in the extraordinary efforts he takes to understand, address, and struggle with the philosophical puzzles that the mind, and perception in particular, raises. Pylyshyn’s most recent work, Things and Places: How the Mind Connects with the World, does not disappoint. It is philosophically rich. Indeed, the approach to object perception (...) that Pylyshyn develops in this book takes inspiration from Evans’s (1982) and Perry’s (1979) work on demonstratives and indexicals, draws on Dretskean (1981, 1986, 1988) ideas about representation, and tangles with Strawson (1959), Quine (1992), and Clark (2000, 2004) over how to understand the role of concepts in perception. In short, it is just the kind of book philosophers of psychology should lavishly slather with clotted cream and joyously devour at their next tea party. The main focus of this review will be Pylyshyn’s theory of FINSTs (an acronym for Fingers of INSTantion, for reasons to be soon clarified). FINSTs are the primary subject of the first three chapters of Things and Places, after which they basically disappear for about eighty pages, to reappear in the final and lengthiest fifth chapter, where they are put to use in a speculative (and, to my mind, slightly incredible) explanation of data from mental imagery experiments. The fourth chapter is an engaging polemic against using subjective experience as a source of evidence about psychological processing and, in particular, the danger in assuming that because mental images appear to have spatial properties, they must be represented spatially. This chapter stands alone and would be of interest to followers of the imagery debate or, for that matter, to instructors looking for counter-examples when.. (shrink)
El objetivo de este trabajo es discutir la interpretación tradicional según la cual los razonamientos de Zenón de Elea en contra de la multiplicidad constituyen una defensa de la tesis monista. Intentaré demostrar que las objeciones zenonianas a la multiplicidad suponen una critica previa a la existencia de "lo uno". Por este motivo, Zenón no es monista ni pluralista, sino, más bien, un crítico de las perspectivas metafísicas que consideran al ser en términos numéricos, i. e. como uno o como (...) múltiple. Para ello me concentraré en el análisis de la interpretación que Aristóteles desarrolla sobre la filosofía de Zenón, considerando algunos pasajes de Física, Refutaciones sofísticas y, fundamentalmente, Metafísica, III. 4. 1001b7-13. También incluiré algunos testimonios del comentario a la Física de Simplicio, en los que se discuten las interpretaciones de Eudemo de Rodas y Alejandro de Afrodisia, que ratifican el punto de vista aristotélico sobre la filosofía de Zenón. The aim of this paper is to discuss the traditional interpretation according to which the arguments of Zeno of Elea against multiplicity constitute a defense of monism. I will try to prove that Zeno's objections on plurality suppose a previous critique to the existence of the one. Therefore Zeno is neither a monist nor a pluralist but a philosopher who criticizes metaphysical theories that consider being in numerical terms, i. e. as many or as one. I will focus on the analysis of the interpretation of Zeno's philosophy developed by Aristotle. I will consider some passages from Physics, Sophistical Refutations and mainly Metaphysics III. 4. 1001b7-13. I will also include some testimonies from Simplicius' commentary on Aristotle's Physics, where he discusses the interpretations of Eudemus of Rhodes and Alexander of Aphrodisias that support the Aristotelian point of view on Zeno's philosophy. (shrink)
The imagery debate re-enacts controversies persisting since Descartes. The controversy remains important less for what we can learn about visual imagery than about cognitive science itself. In the tradition of Arnauld, Reid, Bartlett, Austin and Ryle, Pylyshyn’s critique exposes notorious mistakes being unwittingly rehearsed not only regarding imagery but also in several independent domains of research in modern cognitive science.
En este breve comentario discuto algunos aspectos de la interpretación de la epistemología de Davidson que sugiere Willian Duica en su reciente libro. Luego de una presentación somera del libro me centro en tres asuntos centrales de la interpretación de Duica. En primer lugar, argumento que su lectura de la crítica de Davidson al dualismo esquema/contenido es muy restrictiva y deja abierta la posibilidad de un realismo directo empirista. En segundo lugar, argumento que en su lectura el propio Duica se (...) compromete inadvertidamente con un empirismo de este tipo y, de este modo, su interpretación entra en tensión con el coherentismo de Davidson. Finalmente, discuto algunos aspectos de la interpretación que hace Duica de la tesis davidsoniana de la triangulación. In this short comment I discuss some aspects of William Duica's interpretation of Davidson's epistemology in a recent book. After a brief review of the book, I focus on three central issues of Duica's interpretation. First, I argue that his reading of Davidson's criticism of the scheme/content dualism is too restrictive and leaves open the possibility of an empiricist direct realism. Second, I argue in his reading Duica inadvertently commits himself to an empiricism of this sort and, as a result, his interpretation is in tension with Davidson's own coherentism. Finally, I discuss some aspects of Duica's interpretation of Davidsonian triangulation. (shrink)