Topological Foundations of Cognitive Science

A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers: ** Topological Foundations of Cognitive Science, Barry Smith ** The Bounds of Axiomatisation, Graham White ** Rethinking Boundaries, Wojciech Zelaniec ** Sheaf Mereology and Space Cognition, Jean Petitot ** A Mereotopological Definition of 'Point', Carola Eschenbach ** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel ** Mass Reference and the Geometry of Solids, Almerindo E. Ojeda ** Defining a 'Doughnut' Made Difficult, N .M. Gotts ** A Theory of Spatial Regions with Indeterminate Boundaries, A.G. Cohn and N.M. Gotts ** Mereotopological Construction of Time from Events, Fabio Pianesi and Achille C. Varzi ** Computational Mereology: A Study of Part-of Relations for Multi-media Indexing, Wlodek Zadrozny and Michelle Ki

A study in empirical knowledge: The preconditions and structure of measurement

This is an epistemological study, in which measure ment is taken as a paradigm of perceptual recognition---a notion in which perception is joined with judgment as a factor in understanding. Hence it has proved necessary to give an analysis of such recognition in general, with metric contexts as a special case. This has been done in terms of a very weak fundamental form of 'theory', as a form of basic comprehension, in which language (as part of the theories analysed) is not essentially involved, but treated as a special development. One type of theory is given thorough formal analysis: those 'recognitive theories' whose elements are taken, in the theory itself, to be recognized directly from perception, or extrapolated as in principle recognizable. Another type consists of 'substantive theories', seen as constructed to provide deeper understanding of the reality underlying recognized structures, but essentially involving elements not taken to be recognizable: this type receivesonly informal treatment, in terms of its associations with the first (especially in measurement). Special consideration is (unusually) given to attention and neglect,not in psychological terms, but as theory-guided selection from total experience. Neglect is seen not merely as negation of attention, but often a positive strategy (in measurement, strictly determined). Part I introduces the basic concepts, distinguishing the general approach from other relevant traditionsfoundational studies in measurement (Suppes et al.); linguistic analysis; some epistemologies (e.g., Goodman); philosophy of science. Part II sets up the formal analysis. Part III applies this analysis to contexts of measurement, with examples (only distance is fully treated others only in synopsis). Probability assessment is analysed as distinct from measurement. Part IV examines consequences for wider philosophical questions: language-based problems of knowledge and meaning; Wittgenstein's 'private language': and theory-based considerations of ontology; identity; truth, falsity and error; and observation in science.<p

An Introduction to the Foundations of Chemical Information Theory. Tarski–Lesniewski Logical Structures and the Organization of Natural Sorts and Kinds

Organic mathematics is an applied mathematics of philosophical atomism. The order of the chemical elements in the table of elements is the source of order for the logical operations of addition and subtraction of atomic numbers. The inverse square laws of physics are the source of organization of subatomic structures of chemical atoms (atomic and molecular structures). These facts are foundational to the logic of the chemical sciences and are therefore the scientific basis for chemical information theory. The theories and facts of the chemical sciences are so perplex that several forms of symbolic representations are necessary to communicate the broad range of scientific concepts used to inquire into the nature of natural sorts and kinds. The logics proposed by Tarski, Lesniewski and Malatesta are applied to the construction of a numerical “spine” of perplex numbers representing atomic numbers as meta-symbols in meta-languages. The orbital angular momenta of certain collections of electrical particles (also known as “handedness”) are critical components in constructing the logical propositions of the perplex number “spine”. Biological communication channels can function if and only if the natural sorts and kinds are consistent with the matching patterns of the optical isomers. The terms spinners and twisters are introduced to express the electro-mechanical torques necessary for encoding chemical information. This hypothesis can be tested by several categories of experiments, including clinical pharmaco-dynamics and clinical toxico-dynamics of dissymmetric isomers of different sorts and kinds

Tartu Ülikooli toimetised. Tööd semiootika alalt. 1964-1992. 0259-4668

http://www.ester.ee/record=b1331700*es

Putnam's internal realism: from metaphysical to natural realism

El objetivo central de la tesis es de hacer una analisis del realismo interno de Hilary Putnam y compararlo con las doctrinas del realismo metafisico y el realismo natural. La razon por la que tal comparacion se hace es porque Putnam mantuvo cada uno de estas tres doctrinas en algun periodo en su larga carrera filosofica. En el primer capitulo se hace un analisis del realismo metafisico tal como Putnam lo comprendio. En este capitulo se muestran las paradojas y los problemas que llevaron a Putnam a eventualmente abandonar dicha doctrina. El segundo capitulo se ocupa de exponer los primeros desarrollos de la doctrina del realismo interno, como los son el argumento de los modelos, el verificacionismo semantico y el celebre argumento del cerebro en la cubeta. Lo que se busca en este capitulo es mostrar los problemas que trae la teoria realista de la referencia y cómo el realismo interno se presenta como una alternativa a tal enfoque. En el tercer capitulo presento una de las ideas centrales del realismo interno, la idea de la verdad como asertabilidad garantizada. A diferencia de la idea realista de la verdad como correspondencia, el enfoque internista mantiene la idea que la verdad no puede estar desligada de la justificacion, de manera que la justificacion siempre debe estar disponible para la verdad. El cuarto capítulo se ocupa de analizar la relación y el lugar de los esquemas conceptuales en el realismo interno. En éste capítulo defiendo la idea (propuesta por Jennifer Case, 2001) que los esquemas conceptuales deben ser entendidos como lenguajes opcionales. La idea de la relatividad conceptual es muy importante en la filosofia de Putnam pues combate la idea de la dicotomia entre hechos y convenciones. De otro lado, en este capitulo defiendo la idea que la relatividad conceptual es una constante en la filosofia de Putnam, contradiciendo asi los criticos que insisten que la filofofia de Putnam esta en constante cambio. El quinto capítulo es una confrontación entre el realismo interno y el realismo natural, inspirado por William James, Wittgenstein y Austin. En este capitulo muestro que, luego del análisis de ambos enfoques, la idea de una semejanza entre éstos no es del todo obsoleta. Sin embargo, en este ultimo capitulo enfatizo que Putnam es ambivalente en cuanto a los sense-data, pues en su periodo internista los acepta para luego (en su 1999) abandonarlos y finalmente (en su 2012) volver a aceptarlos de uuna cierta forma. En este ultimo capitulo tambien me ocupo del funcionalismo, el cual el mismo Putnam culpo de ser una doctrina solipsista. Argumento que una caracteristica del funcionalismo, a saber, la plasticidad composicional, es una evidencia del caracter abierto y liberal del realismo interno. Termino concluyendo que el realismmo interno es efectivamente una alternativa relevante frente a las doctrinas del realismo metafisico y natural. Sin embargo tal enfoque no esta libre de criticas, especialmente la ambiguedad en cuanto a los sense data. Concluyo tambien que las criticas que hiciera Putnam de su propio enfoque no son del todo justificadas.The main objective of this thesis is to asses Putnam’s internal realism and see how the doctrine fares when compared with the doctrines of metaphysical realism and natural realism. The reason for comparing these three doctrines is because Putnam embraced each of them during some points in his long philosophical career. In the thesis I hope to argue that internal realism is an attractive philosophical approach which satisfactorily answers the paradoxes of metaphysical realism. In the first chapter I present the doctrine of metaphysical realism as Putnam understood it criticized it. Putnam’s version of metaphysical realism is based on three theses: reality consists of a determined quantity of objects, there is only one correct way to describe such reality, and truth is a relation of correspondence between language and reality. These three theses are not necessarily accepted by most metaphysical realists (especially the correspondence theory of truth), but they represent a coherent doctrine which internal realism sets to counter. It is important to signal that metaphysical realism is an ontological and not an epistemological thesis, in the sense that what matters for it is the postulation of a stance and not its verification or way of knowing it. In the second chapter I discuss the early development of the doctrine of internal realism. I consider the model-theoretic argument, the idea behind verificationist semantics (inspired by Dummett) and the famous argument of Brains in a Vat. The main thrust of this chapter is to counter the metaphysical idea that there exist one definite reference relation between word and object. The aforementioned arguments show that such metaphysical relation is only an illusion and that there are many possible interpretations for the referents of words. In the third chapter I analyze one of the main tenets of internal realism, namely, the idea that truth is identified with warranted assertability. As opposed to the metaphysical realist, the internal realist holds the idea that truth cannot be independent from justification. However, there are certain occasions where truth is justification-transcendent. The important lesson to learn from internal realism is that in such occasions justification must be available in principle. This idea is a very strong counter to the metaphysical idea that truth always transcends justification and that it is to be understood as a correspondence between words and objects. The fourth chapter is a defense of the doctrine of conceptual relativity. In this chapter I defend the idea that such doctrine is the most important part of internal realism because it undermines the metaphysical idea that there exists a defined totality of objects. Internal realism is the idea that there doesn’t exist a dichotomy between facts and values, and therefore our definition of object depends on our interests and theories. The fifth, and final, chapter is an analysis of the doctrine of natural realism and its comparison to internal realism. I argue that there are more similitudes between the two doctrines than there are differences. Both doctrines embrace the ideas of conceptual relativity and common-sense, therefore, Putnam’s criticisms against internal realism are not necessarily justified

Edmund Husserl between Platonism and Aristotelianism

The volume contains the first collection of essays delaying with the relations between, on the one hand, Husserl's philosophy, and, on the other, the traditions of Platonism and Aristotelianism

The Significance of Evidence-based Reasoning for Mathematics, Mathematics Education, Philosophy and the Natural Sciences

In this multi-disciplinary investigation we show how an evidence-based perspective of quantification---in terms of algorithmic verifiability and algorithmic computability---admits evidence-based definitions of well-definedness and effective computability, which yield two unarguably constructive interpretations of the first-order Peano Arithmetic PA---over the structure N of the natural numbers---that are complementary, not contradictory. The first yields the weak, standard, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically verifiable Tarskian truth values to the formulas of PA under the interpretation. The second yields a strong, finitary, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically computable Tarskian truth values to the formulas of PA under the interpretation. We situate our investigation within a broad analysis of quantification vis a vis: * Hilbert's epsilon-calculus * Goedel's omega-consistency * The Law of the Excluded Middle * Hilbert's omega-Rule * An Algorithmic omega-Rule * Gentzen's Rule of Infinite Induction * Rosser's Rule C * Markov's Principle * The Church-Turing Thesis * Aristotle's particularisation * Wittgenstein's perspective of constructive mathematics * An evidence-based perspective of quantification. By showing how these are formally inter-related, we highlight the fragility of both the persisting, theistic, classical/Platonic interpretation of quantification grounded in Hilbert's epsilon-calculus; and the persisting, atheistic, constructive/Intuitionistic interpretation of quantification rooted in Brouwer's belief that the Law of the Excluded Middle is non-finitary. We then consider some consequences for mathematics, mathematics education, philosophy, and the natural sciences, of an agnostic, evidence-based, finitary interpretation of quantification that challenges classical paradigms in all these disciplines

The Significance of Evidence-based Reasoning in Mathematics, Mathematics Education, Philosophy, and the Natural Sciences

In this multi-disciplinary investigation we show how an evidence-based perspective of quantification---in terms of algorithmic verifiability and algorithmic computability---admits evidence-based definitions of well-definedness and effective computability, which yield two unarguably constructive interpretations of the first-order Peano Arithmetic PA---over the structure N of the natural numbers---that are complementary, not contradictory. The first yields the weak, standard, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically verifiable Tarskian truth values to the formulas of PA under the interpretation. The second yields a strong, finitary, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically computable Tarskian truth values to the formulas of PA under the interpretation. We situate our investigation within a broad analysis of quantification vis a vis: * Hilbert's epsilon-calculus * Goedel's omega-consistency * The Law of the Excluded Middle * Hilbert's omega-Rule * An Algorithmic omega-Rule * Gentzen's Rule of Infinite Induction * Rosser's Rule C * Markov's Principle * The Church-Turing Thesis * Aristotle's particularisation * Wittgenstein's perspective of constructive mathematics * An evidence-based perspective of quantification. By showing how these are formally inter-related, we highlight the fragility of both the persisting, theistic, classical/Platonic interpretation of quantification grounded in Hilbert's epsilon-calculus; and the persisting, atheistic, constructive/Intuitionistic interpretation of quantification rooted in Brouwer's belief that the Law of the Excluded Middle is non-finitary. We then consider some consequences for mathematics, mathematics education, philosophy, and the natural sciences, of an agnostic, evidence-based, finitary interpretation of quantification that challenges classical paradigms in all these disciplines

À quoi bon la métaphysique?

La présente thèse a pour objet l'examen de la légitimité de l'entreprise métaphysique, dans ses rapports avec le réalisme métaphysique scientifique. La tâche de fournir une description véridique de la nature, de la structure et de la composition ultimes du monde tel qu'il est en réalité semble désormais (depuis l'avènement de la modernité, en fait) l'apanage de la science plutôt que de la métaphysique. Le problème est donc le suivant : quelle place pour la métaphysique? La métaphysique n'est plus depuis belle lurette la « reine de toutes les sciences ». Doit-elle être « éliminée » comme le recommandait Carnap? Ma thèse sera guidée par trois grandes questions. Premièrement, étant donné que l'aspiration de connaître le « monde tel qu'il est » présuppose l'adoption du réalisme, la question se posera de la définition et de la défense d'une telle conception. Nous verrons dans le premier chapitre qu'un réalisme robuste requiert un engagement ontologique ferme envers une métaphysique réaliste comprenant à la fois les objets du sens commun et les entités théoriques postulées par la science. Je me demanderai en deuxième lieu s'il est nécessaire, ou du moins, s'il vaut la peine d'admettre, en sus de ces entités physiques, des entités proprement « métaphysiques », comme les universaux ou les tropes, postulées par la métaphysique. Et même si la réponse à cette deuxième question m'apparaît devoir être assez négative, je me demanderai en troisième lieu s'il pourrait y avoir néanmoins un avantage ou une utilité, sur le plan explicatif, heuristique, ou même seulement à titre illustratif, à postuler de telles entités et à tenir un tel discours.\ud ______________________________________________________________________________ \ud MOTS-CLÉS DE L’AUTEUR : métaphysique, réalisme, métamétaphysique, philosophie analytique, philosophie des sciences, philosophie de la connaissance, tropes, universaux