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  1. Gödel, Nagel, Minds, and Machines.Solomon Feferman - 2009 - Journal of Philosophy 106 (4):201-219.
    Ernest Nagel Lecture, Columbia University, Sept. 27, 2007.
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  • Computing, Modelling, and Scientific Practice: Foundational Analyses and Limitations.Philippos Papayannopoulos - 2018 - Dissertation,
    This dissertation examines aspects of the interplay between computing and scientific practice. The appropriate foundational framework for such an endeavour is rather real computability than the classical computability theory. This is so because physical sciences, engineering, and applied mathematics mostly employ functions defined in continuous domains. But, contrary to the case of computation over natural numbers, there is no universally accepted framework for real computation; rather, there are two incompatible approaches --computable analysis and BSS model--, both claiming to formalise algorithmic (...)
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  • A análise gödeliana do conceito de percepção.Sérgio Schultz - 2012 - Doispontos 9 (2).
    Normal 0 21 false false false PT-BR X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Tabela normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin-top:0cm; mso-para-margin-right:0cm; mso-para-margin-bottom:10.0pt; mso-para-margin-left:0cm; line-height:115%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;} No presente artigo expomos alguns aspectos das concepções gödelianas acerca da percepção. Procuramos mostrar aqui que a comparação realizada por Gödel entre percepção sensível e racional, bem como suas concepções sobre esta última, correspondem a (...)
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  • On Causality as the Fundamental Concept of Gödel’s Philosophy.Srećko Kovač - 2020 - Synthese 197 (4):1803-1838.
    This paper proposes a possible reconstruction and philosophical-logical clarification of Gödel's idea of causality as the philosophical fundamental concept. The results are based on Gödel's published and non-published texts (including Max Phil notebooks), and are established on the ground of interconnections of Gödel's dispersed remarks on causality, as well as on the ground of his general philosophical views. The paper is logically informal but is connected with already achieved results in the formalization of a causal account of Gödel's onto-theological theory. (...)
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  • Gödel's Cantorianism.Claudio Ternullo - 2015 - In Eva-Maria Engelen & Gabriella Crocco (eds.), Kurt Gödel: Philosopher-Scientist. Presses Universitaires de Provence. pp. 417-446.
    Gödel’s philosophical conceptions bear striking similarities to Cantor’s. Although there is no conclusive evidence that Gödel deliberately used or adhered to Cantor’s views, one can successfully reconstruct and see his “Cantorianism” at work in many parts of his thought. In this paper, I aim to describe the most prominent conceptual intersections between Cantor’s and Gödel’s thought, particularly on such matters as the nature and existence of mathematical entities (sets), concepts, Platonism, the Absolute Infinite, the progress and inexhaustibility of mathematics.
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  • Richard Tieszen. After Gödel. Platonism and Rationalism in Mathematics and Logic.Dagfinn Føllesdal - 2016 - Philosophia Mathematica 24 (3):405-421.
  • Use and Misuse of Godel's Theorem.Shingo Fujita - 2003 - Annals of the Japan Association for Philosophy of Science 12 (1):1-14.
  • Is Cantor's Continuum Problem Inherently Vague?Kai Hauser - 2002 - Philosophia Mathematica 10 (3):257-285.
    I examine various claims to the effect that Cantor's Continuum Hypothesis and other problems of higher set theory are ill-posed questions. The analysis takes into account the viability of the underlying philosophical views and recent mathematical developments.
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  • Existence and Identity in Free Logic: A Problem for Inferentialism?Neil Tennant - 2007 - Mind 116 (464):1055-1078.
    Peter Milne (2007) poses two challenges to the inferential theorist of meaning. This study responds to both. First, it argues that the method of natural deduction idealizes the essential details of correct informal deductive reasoning. Secondly, it explains how rules of inference in free logic can determine unique senses for the existential quantifier and the identity predicate. The final part of the investigation brings out an underlying order in a basic family of free logics.
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  • Note on Absolute Provability and Cantorian Comprehension.Holger A. Leuz - manuscript
    We will explicate Cantor’s principle of set existence using the Gödelian intensional notion of absolute provability and John Burgess’ plural logical concept of set formation. From this Cantorian Comprehension principle we will derive a conditional result about the question whether there are any absolutely unprovable mathematical truths. Finally, we will discuss the philosophical significance of the conditional result.
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  • Kurt Gödel.Juliette Kennedy - 2008 - Stanford Encyclopedia of Philosophy.
  • The Search for New Axioms in the Hyperuniverse Programme.Claudio Ternullo & Sy-David Friedman - 2016 - In Andrea Sereni & Francesca Boccuni (eds.), Objectivity, Realism, and Proof. FilMat Studies in the Philosophy of Mathematics. Berlin: Springer. pp. 165-188.
    The Hyperuniverse Programme, introduced in Arrigoni and Friedman (2013), fosters the search for new set-theoretic axioms. In this paper, we present the procedure envisaged by the programme to find new axioms and the conceptual framework behind it. The procedure comes in several steps. Intrinsically motivated axioms are those statements which are suggested by the standard concept of set, i.e. the `maximal iterative concept', and the programme identi fies higher-order statements motivated by the maximal iterative concept. The satisfaction of these statements (...)
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  • Abstract Objects.Gideon Rosen - 2008 - Stanford Encyclopedia of Philosophy.
  • Books Received. [REVIEW] Anon - 1998 - British Journal for the Philosophy of Science 49 (1):195-198.
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  • Ipotesi del Continuo.Claudio Ternullo - 2017 - Aphex 16.
    L’Ipotesi del Continuo, formulata da Cantor nel 1878, è una delle congetture più note della teoria degli insiemi. Il Problema del Continuo, che ad essa è collegato, fu collocato da Hilbert, nel 1900, fra i principali problemi insoluti della matematica. A seguito della dimostrazione di indipendenza dell’Ipotesi del Continuo dagli assiomi della teoria degli insiemi, lo status attuale del problema è controverso. In anni più recenti, la ricerca di una soluzione del Problema del Continuo è stata anche una delle ragioni (...)
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  • The Development of Mathematical Logic From Russell to Tarski, 1900-1935.Paolo Mancosu, Richard Zach & Calixto Badesa - 2009 - In Leila Haaparanta (ed.), The Development of Modern Logic. Oxford University Press.
    The period from 1900 to 1935 was particularly fruitful and important for the development of logic and logical metatheory. This survey is organized along eight "itineraries" concentrating on historically and conceptually linked strands in this development. Itinerary I deals with the evolution of conceptions of axiomatics. Itinerary II centers on the logical work of Bertrand Russell. Itinerary III presents the development of set theory from Zermelo onward. Itinerary IV discusses the contributions of the algebra of logic tradition, in particular, Löwenheim (...)
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  • Non‐Classical Knowledge.Ethan Jerzak - 2019 - Philosophy and Phenomenological Research 98 (1):190-220.
    The Knower paradox purports to place surprising a priori limitations on what we can know. According to orthodoxy, it shows that we need to abandon one of three plausible and widely-held ideas: that knowledge is factive, that we can know that knowledge is factive, and that we can use logical/mathematical reasoning to extend our knowledge via very weak single-premise closure principles. I argue that classical logic, not any of these epistemic principles, is the culprit. I develop a consistent theory validating (...)
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  • Enciclopédia de Termos Lógico-Filosóficos.João Branquinho, Desidério Murcho & Nelson Gonçalves Gomes (eds.) - 2006 - São Paulo, SP, Brasil: Martins Fontes.
    Esta enciclopédia abrange, de uma forma introdutória mas desejavelmente rigorosa, uma diversidade de conceitos, temas, problemas, argumentos e teorias localizados numa área relativamente recente de estudos, os quais tem sido habitual qualificar como «estudos lógico-filosóficos». De uma forma apropriadamente genérica, e apesar de o território teórico abrangido ser extenso e de contornos por vezes difusos, podemos dizer que na área se investiga um conjunto de questões fundamentais acerca da natureza da linguagem, da mente, da cognição e do raciocínio humanos, bem (...)
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  • Logical Constants.John MacFarlane - 2008 - Mind.
    Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...)
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  • Gödel's Path From the Incompleteness Theorems (1931) to Phenomenology (1961).Richard Tieszen - 1998 - Bulletin of Symbolic Logic 4 (2):181-203.
  • Summum Bonum.Nelson Gomes - 2006 - Analytica 10 (2).
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  • Truth Vs. Provability – Philosophical and Historical Remarks.Roman Murawski - 2002 - Logic and Logical Philosophy 10:93.
  • The Paradox of Gödel’s Numbering and the Philosophy of Modern Metamathematics.Djidjian Robert - 2017 - Wisdom 9 (2):18-28.
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  • Logical Foundations and Kant's Principles of Formal Logic.Srećko Kovač - 2019 - History and Philosophy of Logic 41 (1):48-70.
    The abstract status of Kant's account of his ‘general logic’ is explained in comparison with Gödel's general definition of a formal logical system and reflections on ‘abstract’ concepts. Thereafter, an informal reconstruction of Kant's general logic is given from the aspect of the principles of contradiction, of sufficient reason, and of excluded middle. It is shown that Kant's composition of logic consists in a gradual strengthening of logical principles, starting from a weak principle of contradiction that tolerates a sort of (...)
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  • Naturalising Badiou: Mathematical Ontology and Structural Realism.Fabio Gironi - unknown
    This thesis offers a naturalist revision of Alain Badiou’s philosophy. This goal is pursued through an encounter of Badiou’s mathematical ontology and theory of truth with contemporary trends in philosophy of mathematics and philosophy of science. I take issue with Badiou’s inability to elucidate the link between the empirical and the ontological, and his residual reliance on a Heideggerian project of fundamental ontology, which undermines his own immanentist principles. I will argue for both a bottom-up naturalisation of Badiou’s philosophical approach (...)
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  • On the Mathematical Nature of Logic, Featuring P. Bernays and K. Gödel.Oran Magal - unknown
    The paper examines the interrelationship between mathematics and logic, arguing that a central characteristic of each has an essential role within the other. The first part is a reconstruction of and elaboration on Paul Bernays’ argument, that mathematics and logic are based on different directions of abstraction from content, and that mathematics, at its core it is a study of formal structures. The notion of a study of structure is clarified by the examples of Hilbert’s work on the axiomatization of (...)
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  • A Common Ground and Some Surprising Connections.Edward N. Zalta - 2002 - Southern Journal of Philosophy 40 (S1):1-25.
    This paper serves as a kind of field guide to certain passages in the literature which bear upon the foundational theory of abstract objects. The foundational theory assimilates ideas from key philosophers in both the analytical and phenomenological traditions. I explain how my foundational theory of objects serves as a common ground where analytic and phenomenological concerns meet. I try to establish how the theory offers a logic that systematizes a well-known phenomenological kind of entity, and I try to show (...)
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  • Richness and Reflection.Neil Barton - 2016 - Philosophia Mathematica 24 (3):330-359.
    A pervasive thought in contemporary philosophy of mathematics is that in order to justify reflection principles, one must hold universism: the view that there is a single universe of pure sets. I challenge this kind of reasoning by contrasting universism with a Zermelian form of multiversism. I argue that if extant justifications of reflection principles using notions of richness are acceptable for the universist, then the Zermelian can use similar justifications. However, I note that for some forms of richness argument, (...)
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  • Arithmetic, Mathematical Intuition, and Evidence.Richard Tieszen - 2015 - Inquiry: An Interdisciplinary Journal of Philosophy 58 (1):28-56.
    This paper provides examples in arithmetic of the account of rational intuition and evidence developed in my book After Gödel: Platonism and Rationalism in Mathematics and Logic . The paper supplements the book but can be read independently of it. It starts with some simple examples of problem-solving in arithmetic practice and proceeds to general phenomenological conditions that make such problem-solving possible. In proceeding from elementary ‘authentic’ parts of arithmetic to axiomatic formal arithmetic, the paper exhibits some elements of the (...)
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  • Gödel and 'the Objective Existence' of Mathematical Objects.Pierre Cassou-Noguès - 2005 - History and Philosophy of Logic 26 (3):211-228.
    This paper is a discussion of Gödel's arguments for a Platonistic conception of mathematical objects. I review the arguments that Gödel offers in different papers, and compare them to unpublished material (from Gödel's Nachlass). My claim is that Gödel's later arguments simply intend to establish that mathematical knowledge cannot be accounted for by a reflexive analysis of our mental acts. In other words, there is at the basis of mathematics some data whose constitution cannot be explained by introspective analysis. This (...)
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  • Gödel, Kant, and the Path of a Science.Srećko Kovač - 2008 - Inquiry: Journal of Philosophy 51 (2):147-169.
    Gödel's philosophical views were to a significant extent influenced by the study not only of Leibniz or Husserl, but also of Kant. Both Gödel and Kant aimed at the secure foundation of philosophy, the certainty of knowledge and the solvability of all meaningful problems in philosophy. In this paper, parallelisms between the foundational crisis of metaphysics in Kant's view and the foundational crisis of mathematics in Gödel's view are elaborated, especially regarding the problem of finding the “secure path of a (...)
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  • Gödel's Introduction to Logic in 1939.P. Cassou-Nogues - 2009 - History and Philosophy of Logic 30 (1):69-90.
    This article presents three extracts from the introductory course in mathematical logic that Gödel gave at the University of Notre Dame in 1939. The lectures include a few digressions, which give insight into Gödel's views on logic prior to his philosophical papers of the 1940s. The first extract is Gödel's first lecture. It gives the flavour of Gödel's leisurely style in this course. It also includes a curious definition of logic and a discussion of implication in logic and natural language. (...)
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  • Naturalism and Abstract Entities.Feng Ye - 2010 - International Studies in the Philosophy of Science 24 (2):129-146.
    I argue that the most popular versions of naturalism imply nominalism in philosophy of mathematics. In particular, there is a conflict in Quine's philosophy between naturalism and realism in mathematics. The argument starts from a consequence of naturalism on the nature of human cognitive subjects, physicalism about cognitive subjects, and concludes that this implies a version of nominalism, which I will carefully characterize. The indispensability of classical mathematics for the sciences and semantic/confirmation holism does not affect the argument. The disquotational (...)
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  • Gödel’s Philosophical Program and Husserl’s Phenomenology.Xiaoli Liu - 2010 - Synthese 175 (1):33 - 45.
    Gödel’s philosophical rationalism includes a program for “developing philosophy as an exact science.” Gödel believes that Husserl’s phenomenology is essential for the realization of this program. In this article, by analyzing Gödel’s philosophy of idealism, conceptual realism, and his concept of “abstract intuition,” based on clues from Gödel’s manuscripts, I try to investigate the reasons why Gödel is strongly interested in Husserl’s phenomenology and why his program for an exact philosophy is unfinished. One of the topics that has attracted much (...)
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  • Gödel’s Philosophical Program and Husserl’s Phenomenology.Xiaoli Liu - 2010 - Synthese 175 (1):33-45.
    Gödel’s philosophical rationalism includes a program for “developing philosophy as an exact science.” Gödel believes that Husserl’s phenomenology is essential for the realization of this program. In this article, by analyzing Gödel’s philosophy of idealism, conceptual realism, and his concept of “abstract intuition,” based on clues from Gödel’s manuscripts, I try to investigate the reasons why Gödel is strongly interested in Husserl’s phenomenology and why his program for an exact philosophy is unfinished. One of the topics that has attracted much (...)
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  • Monads and Mathematics: Gödel and Husserl.Richard Tieszen - 2012 - Axiomathes 22 (1):31-52.
    In 1928 Edmund Husserl wrote that “The ideal of the future is essentially that of phenomenologically based (“philosophical”) sciences, in unitary relation to an absolute theory of monads” (“Phenomenology”, Encyclopedia Britannica draft) There are references to phenomenological monadology in various writings of Husserl. Kurt Gödel began to study Husserl’s work in 1959. On the basis of his later discussions with Gödel, Hao Wang tells us that “Gödel’s own main aim in philosophy was to develop metaphysics—specifically, something like the monadology of (...)
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  • Deflating skolem.F. A. Muller - 2005 - Synthese 143 (3):223-253.
    . Remarkably, despite the tremendous success of axiomatic set-theory in mathematics, logic and meta-mathematics, e.g., model-theory, two philosophical worries about axiomatic set-theory as the adequate catch of the set-concept keep haunting it. Having dealt with one worry in a previous paper in this journal, we now fulfil a promise made there, namely to deal with the second worry. The second worry is the Skolem Paradox and its ensuing Skolemite skepticism. We present a comparatively novel and simple analysis of the argument (...)
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  • Chateaubriand’s Realist Conception of Logic.Frank Thomas Sautter - 2010 - Axiomathes 20 (2-3):357-364.
    I present the realist conception of logic supported by Oswaldo Chateaubriand which integrates ontological and epistemological aspects, opposing it to mathematical and linguistic conceptions. I give special attention to the peculiarities of his hierarchy of types in which some properties accumulate and others have a multiple degree. I explain such deviations of the traditional conception, showing the underlying purpose in each of these peculiarities. I compare the ideas of Chateaubriand to the similar ideas of Frege, Tarski and Gödel. I suggest (...)
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  • Some Weakened Gödelian Ontological Systems.Srećko Kovač - 2003 - Journal of Philosophical Logic 32 (6):565-588.
    We describe a K B Gödelian ontological system, and some other weak systems, in a fully formal way using theory of types and natural deduction, and present a completeness proof in its main and specific parts. We technically and philosophically analyze and comment on the systems (mainly with respect to the relativism of values) and include a sketch of some connected aspects of Gidel's relation to Kant.
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  • Gödel on Concepts.Gabriella Crocco - 2006 - History and Philosophy of Logic 27 (2):171-191.
    This article is an attempt to present Gödel's discussion on concepts, from 1944 to the late 1970s, in particular relation to the thought of Frege and Russell. The discussion takes its point of departure from Gödel's claim in notes on Bernay's review of ?Russell's mathematical logic?. It then retraces the historical background of the notion of intension which both Russell and Gödel use, and offers some grounds for claiming that Gödel consistently considered logic as a free-type theory of concepts, called (...)
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  • Mentalismo, mecanicismo : el nuevo argumento de Penrose. [REVIEW]Enrique Alonso - 2001 - Revista de Filosofía (Madrid) 26 (1):139-164.
    Este ensayo ofrece un análisis crítico del último argumento que el matemático y filósofo Roger Penrose ofrece a favor de la tesis según la cual hay habilidades de la mente humana que nunca podrán ser igualadas por ingenio mecánico alguno. Al mismo tiempo se ofrece una descripción general de los últimos episodios del eterno enfrentamiento entre mentalismo y mecanicismo y se concluye con una sugerencia acerca de los puntos en los que cabe esperar nuevas situaciones de tensión entre estos dos (...)
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  • Intuition and Its Object.Kai Hauser - 2015 - Axiomathes 25 (3):253-281.
    The view that mathematics deals with ideal objects to which we have epistemic access by a kind of perception has troubled many thinkers. Using ideas from Husserl’s phenomenology, I will take a different look at these matters. The upshot of this approach is that there are non-material objects and that they can be recognized in a process very closely related to sense perception. In fact, the perception of physical objects may be regarded as a special case of this more universal (...)
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