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Juliette Kennedy [45]Juliette Cara Kennedy [3]
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Juliette Kennedy
University of Helsinki
Juliette Cara Kennedy
University of Helsinki
  1. On the Philosophical Development of Kurt Gödel.Juliette Kennedy & Mark van Atten - 2015 - In Juliette Kennedy & Mark van Atten (eds.), Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer. Springer Verlag.
  2. On the Philosophical Development of Kurt Gödel.Mark Van Atten & Juliette Kennedy - 2003 - Bulletin of Symbolic Logic 9 (4):425-476.
    It is by now well known that Gödel first advocated the philosophy of Leibniz and then, since 1959, that of Husserl. This raises three questions:1.How is this turn to Husserl to be interpreted? Is it a dismissal of the Leibnizian philosophy, or a different way to achieve similar goals?2.Why did Gödel turn specifically to the later Husserl's transcendental idealism?3.Is there any detectable influence from Husserl on Gödel's writings?Regarding the first question, Wang [96, p.165] reports that Gödel ‘[saw] in Husserl's work (...)
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  3.  10
    Inner Models From Extended Logics: Part 1.Juliette Kennedy, Menachem Magidor & Jouko Väänänen - 2020 - Journal of Mathematical Logic 21 (2):2150012.
    If we replace first-order logic by second-order logic in the original definition of Gödel’s inner model L, we obtain the inner model of hereditarily ordinal definable sets [33]. In this paper...
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  4.  8
    Interpreting Gödel: Critical Essays.Juliette Kennedy (ed.) - 2014 - Cambridge: Cambridge University Press.
    The logician Kurt Gödel published a paper in 1931 formulating what have come to be known as his 'incompleteness theorems', which prove, among other things, that within any formal system with resources sufficient to code arithmetic, questions exist which are neither provable nor disprovable on the basis of the axioms which define the system. These are among the most celebrated results in logic today. In this volume, leading philosophers and mathematicians assess important aspects of Gödel's work on the foundations and (...)
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  5.  27
    On Formalism Freeness: Implementing Gödel's 1946 Princeton Bicentennial Lecture.Juliette Kennedy - 2013 - Bulletin of Symbolic Logic 19 (3):351-393.
    In this paper we isolate a notion that we call “formalism freeness” from Gödel's 1946 Princeton Bicentennial Lecture, which asks for a transfer of the Turing analysis of computability to the cases of definability and provability. We suggest an implementation of Gödel's idea in the case of definability, via versions of the constructible hierarchy based on fragments of second order logic. We also trace the notion of formalism freeness in the very wide context of developments in mathematical logic in the (...)
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  6.  40
    Gödel’s Modernism: On Set-Theoretic Incompleteness.Juliette Cara Kennedy & Mark van Atten - 2004 - Graduate Faculty Philosophy Journal 25 (2):289-349.
    On Friday, November 15, 1940, Kurt Gödel gave a talk on set theory at Brown University. The topic was his recent proof of the consistency of Cantor’s Continuum Hypothesis with the axiomatic system ZFC for set theory. His friend from their days in Vienna, Rudolf Carnap, was in the audience, and afterward wrote a note to himself in which he raised a number of questions on incompleteness.
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  7.  28
    On Formalism Freeness: Implementing Gödel's 1946 Princeton Bicentennial Lecture.Juliette Kennedy - 2013 - Association for Symbolic Logic: The Bulletin of Symbolic Logic 19 (3).
    In this paper we isolate a notion that we call "formalism freeness" from Gödel's 1946 Princeton Bicentennial Lecture, which asks for a transfer of the Turing analysis of computability to the cases of definability and provability We suggest an implementation of Gödel's idea in the case of definability, via versions of the constructible hierarchy based on fragments of second order logic. We also trace the notion of formalism freeness in the very wide context of developments in mathematical logic in the (...)
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  8. Gödel, Carnap and the Fregean Heritage.Gabriella Crocco - 2003 - Synthese 137 (1-2):21 - 41.
    Thorough a detailed analysis of version III of Gödel's Is mathematics syntax of language?, we propose a new interpretation of Gödel's criticism against the conventionalist point of view in mathematics. When one reads carefully Gödel's text, it brings out that, contrary to the opinion of some commentators, Gödel did not overlook the novelty of Carnap's solution, and did not criticise him from an old-fashioned conception of science. The general aim of our analysis is to restate the Carnap/Gödel debate in the (...)
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  9.  23
    Gödel's Logic.Mark van Atten & Juliette Kennedy - 2009 - In Dov Gabbay (ed.), The Handbook of the History of Logic. Elsevier. pp. 449-509.
  10.  35
    Regular Ultrafilters and Finite Square Principles.Juliette Kennedy, Saharon Shelah & Jouko Väänänen - 2008 - Journal of Symbolic Logic 73 (3):817-823.
    We show that many singular cardinals λ above a strongly compact cardinal have regular ultrafilters D that violate the finite square principle $\square _{\lambda ,D}^{\mathit{fin}}$ introduced in [3]. For such ultrafilters D and cardinals λ there are models of size λ for which Mλ / D is not λ⁺⁺-universal and elementarily equivalent models M and N of size λ for which Mλ / D and Nλ / D are non-isomorphic. The question of the existence of such ultrafilters and models was (...)
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  11.  24
    On Regular Reduced Products.Juliette Kennedy & Saharon Shelah - 2002 - Journal of Symbolic Logic 67 (3):1169-1177.
    Assume $\langle \aleph_0, \aleph_1 \rangle \rightarrow \langle \lambda, \lambda^+ \rangle$ . Assume M is a model of a first order theory T of cardinality at most λ+ in a language L(T) of cardinality $\leq \lambda$ . Let N be a model with the same language. Let Δ be a set of first order formulas in L(T) and let D be a regular filter on λ. Then M is $\Delta-embeddable$ into the reduced power $N^\lambda/D$ , provided that every $\Delta-existential$ formula true (...)
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  12.  5
    Critical Studies/Book Reviews.Juliette Kennedy - forthcoming - Philosophia Mathematica.
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  13.  26
    More on Regular Reduced Products.Juliette Cara Kennedy & Saharon Shelah - 2004 - Journal of Symbolic Logic 69 (4):1261 - 1266.
    The authors show. by means of a finitary version $\square_{\lambda D}^{fin}$ of the combinatorial principle $\square_\lambda^{h*}$ of [7]. the consistency of the failure, relative to the consistency of supercompact cardinals, of the following: for all regular filters D on a cardinal A. if Mi and Ni are elementarily equivalent models of a language of size $\leq \lambda$ , then the second player has a winning strategy in the Ehrenfeucht- $Fra\uml{i}ss\acute{e}$ game of length $\lambda^{+}$ on $\pi_{i} M_{i}/D$ and $\pi_{i} N_{i}/D$ . (...)
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  14.  31
    Aesthetics and the Dream of Objectivity: Notes From Set Theory.Juliette Kennedy & Jouko Väänänen - 2015 - Inquiry: An Interdisciplinary Journal of Philosophy 58 (1):83-98.
    In this paper, we consider various ways in which aesthetic value bears on, if not serves as evidence for, the truth of independent statements in set theory.... the aesthetic issue, which in practice will also for me be the decisive factor—John von Neumann, letter to Carnap, 1931For me, it is the aesthetics which may very well be the final arbiter—P. J. Cohen, 2002.
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  15.  3
    Review of Floyd and Mühlhölzer on Wittgenstein's Annotations to Hardy. [REVIEW]Juliette Kennedy - forthcoming - Philosophia Mathematica.
  16. Kant, Co-Production, Actuality and Pedestrian Space: On the Philosophical Writings of Fred Sandback.Juliette Kennedy - forthcoming - In Roman Kossak & Philip Ording (eds.), Simplicity: Ideals of Practice in Mathematics and the Arts. Springer.
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  17.  3
    Logicality and Model Classes.Juliette Kennedy & Jouko Väänänen - 2021 - Bulletin of Symbolic Logic 27 (4):385-414.
    We ask, when is a property of a model a logical property? According to the so-called Tarski–Sher criterion this is the case when the property is preserved by isomorphisms. We relate this to model-theoretic characteristics of abstract logics in which the model class is definable. This results in a graded concept of logicality in the terminology of Sagi [46]. We investigate which characteristics of logics, such as variants of the Löwenheim–Skolem theorem, Completeness theorem, and absoluteness, are relevant from the logicality (...)
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  18.  81
    Introduction.Juliette Kennedy & Gabriel Sandu - 2003 - Synthese 137 (1):1-1.
    The present volume collects presented at a symposium on The History of Logic held in Helsinki in June 11–13, 2000 hosted by the University of Helsinki, Finland. They bear on issues in the history of logic and foundations of mathematics and are contributions by some of the most renown scholars in the field.
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  19.  14
    Gödel and the Integrated Self, Or: On the Philosopher's Second Sailing.Juliette Kennedy - 2021 - Theoria 87 (4):874-884.
    Theoria, Volume 87, Issue 4, Page 874-884, August 2021.
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  20. The Philosophy of Penelope Maddy.Sophia Arbeiter & Juliette Kennedy (eds.) - forthcoming - Springer.
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  21. Mapping Traces: Editorial Introduction.María Clara Cortés, Juliette Kennedy & Andrés Villaveces - 2021 - Theoria 87 (4):870-873.
    Theoria, Volume 87, Issue 4, Page 870-873, August 2021.
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  22. Can the Continuum Hypothesis Be Solved?Juliette Kennedy - 2011 - The Institute Letter.
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  23.  6
    Gödel's Incompleteness Theorems.Juliette Kennedy - 2022 - Cambridge University Press.
    This Element takes a deep dive into Gödel's 1931 paper giving the first presentation of the Incompleteness Theorems, opening up completely passages in it that might possibly puzzle the student, such as the mysterious footnote 48a. It considers the main ingredients of Gödel's proof: arithmetization, strong representability, and the Fixed Point Theorem in a layered fashion, returning to their various aspects: semantic, syntactic, computational, philosophical and mathematical, as the topic arises. It samples some of the most important proofs of the (...)
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  24. Gödel's Modernism: On Set Theoretic Incompleteness, Revisited.Juliette Kennedy - 2009 - In Sten Lindström, Erik Palmgren, Krister Segerberg & Viggo Stoltenberg-Hansen (eds.), Logicism, Intuitionism and Formalism: What has become of them? Springer.
  25.  2
    Gödel, Tarski and the Lure of Natural Language: Logical Entanglement, Formalism Freeness.Juliette Kennedy - 2020 - Cambridge: Cambridge University Press.
    Is mathematics 'entangled' with its various formalisations? Or are the central concepts of mathematics largely insensitive to formalisation, or 'formalism free'? What is the semantic point of view and how is it implemented in foundational practice? Does a given semantic framework always have an implicit syntax? Inspired by what she calls the 'natural language moves' of Gödel and Tarski, Juliette Kennedy considers what roles the concepts of 'entanglement' and 'formalism freeness' play in a range of logical settings, from computability and (...)
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  26. On Applications of Transfer Principles in Model Theory.Juliette Kennedy & Jouko Vaananen - 2007 - In Alessandro Andretta (ed.), On Applications of Transfer Principles in Model Theory. Quaderni di Matematica.
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  27. On Embedding Models of Arithmetic of Cardinality Aleph_1 Into Reduced Powers.Juliette Kennedy & Saharon Shelah - 2003 - Fundamenta Mathematicae 176 (1).
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  28. On Gödel's Logic.Juliette Kennedy & Mark van Atten - 2009 - In Dov Gabbay (ed.), The Handbook of the History of Logic. Elsevier.
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  29. Review of “Kurt Gödel: Das Album”,.Juliette Kennedy - 2007 - The Mathematical Intelligencer 29 (3): 73-75,.
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  30. Review of The Autonomy of Mathematical Knowledge.Juliette Kennedy - 2011 - Bulletin of Symbolic Logic 17 (1):119-122.
  31.  58
    Set Theory, Arithmetic, and Foundations of Mathematics: Theorems, Philosophies.Juliette Kennedy & Roman Kossak (eds.) - 2011 - Cambridge University Press.
    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. (...)
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  32. Turing, Gödel and the “Bright Abyss”.Juliette Kennedy - 2017 - In Alisa Bokulich & Juliet Floyd (eds.), Philosophical Explorations of the Legacy of Alan Turing. Springer Verlag.
    I hold up my hand and I count five fingers. I take it on faith that the mapping from fingers onto numbers is recursive in the sense of the mathematician’s definition of the informal concept, “human calculability following a fixed routine.” I cannot prove the mapping is recursive—there is nothing to prove! Of course, mathematicians can prove many theorems about recursiveness, moving forward, so to speak, once the definition of the concept “recursive” has been isolated. Moving backwards is more difficult (...)
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  33. Gödel's Philosophical Developments.Mark Van Atten & Juliette Kennedy - 2003 - Bulletin of Symbolic Logic 9:470-92.
     
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  34.  14
    Janet L. Beery; Sarah J. Greenwald; Jacqueline A. Jensen-Vallin; Maura B. Mast . Women in Mathematics: Celebrating the Centennial of the Mathematical Association of America. Xii + 405 Pp., Bibl., Index. Cham: Springer, 2017. $139 . ISBN 9783319666938. [REVIEW]Juliette Kennedy - 2019 - Isis 110 (2):427-428.
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  35.  14
    Curtis Franks. The Autonomy of Mathematical Knowledge: Hilbert's Program Revisited. Cambridge University Press, Cambridge, 2009, 213 Pp. [REVIEW]Juliette Kennedy - 2011 - Bulletin of Symbolic Logic 17 (1):119-122.
  36.  7
    The Princeton Companion to Mathematics, Edited by Timothy Gowers , Princeton University Press, 2008, 1008 Pp. [REVIEW]Juliette Kennedy - 2009 - Bulletin of Symbolic Logic 15 (4):431-436.
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  37. Incompleteness - A Book Review.Juliette Kennedy - 2006 - Notices of the American Mathematical Society.
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  38. History of Logic.Juliette Kennedy & Gabriel Sandu - 2003 - Synthese 137:459-460.
     
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  39.  10
    Penelope Maddy, Defending the Axioms: On the Philosophical Foundations of Set Theory, Oxford University Press, Oxford, UK, 2011, 150pp. [REVIEW]Juliette Kennedy - 2014 - Bulletin of Symbolic Logic 20 (1):91-93.
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  40.  18
    Gödel's Thesis--An Appreciation.Juliette Kennedy - 2011 - In Baaz Mathias, Christos Papadimitriou, Hilary Putnam, Dana Scott & Charles Harper (eds.), Horizons of Truth. Cambridge University Press. pp. 95.
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  41.  10
    24th Workshop on Logic, Language, Information and Computation.Juliette Kennedy - forthcoming - Logic Journal of the IGPL.
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  42.  16
    Regular Ultrapowers at Regular Cardinals.Juliette Kennedy, Saharon Shelah & Jouko Väänänen - 2015 - Notre Dame Journal of Formal Logic 56 (3):417-428.
    In earlier work by the first and second authors, the equivalence of a finite square principle $\square^{\mathrm{fin}}_{\lambda,D}$ with various model-theoretic properties of structures of size $\lambda $ and regular ultrafilters was established. In this paper we investigate the principle $\square^{\mathrm{fin}}_{\lambda,D}$—and thereby the above model-theoretic properties—at a regular cardinal. By Chang’s two-cardinal theorem, $\square^{\mathrm{fin}}_{\lambda,D}$ holds at regular cardinals for all regular filters $D$ if we assume the generalized continuum hypothesis. In this paper we prove in ZFC that, for certain regular filters (...)
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  43.  13
    Preface.Juliette Kennedy & Jaap van Oosten - 2012 - Annals of Pure and Applied Logic 163 (10):1359.
  44. On Embedding Models of Arithmetic Into Reduced Powers.Juliette Kennedy - 2003 - Matematica Contemporanea 24 (1):91--115.
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  45.  19
    Kurt Gödel.Juliette Kennedy - 2008 - Stanford Encyclopedia of Philosophy.
  46.  11
    On the “Logic Without Borders” Point of View: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics.Juliette Kennedy - 2015 - In Andrés Villaveces, Roman Kossak, Juha Kontinen & Åsa Hirvonen (eds.), Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics. De Gruyter. pp. 1-14.
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  47.  3
    24th Workshop on Logic, Language, Information and Computation—WoLLIC 2017.Juliette Kennedy & Ruy de Queiroz - 2021 - Archive for Mathematical Logic 60 (5):525-527.
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  48.  5
    More on Regular Reduced Products.Juliette Cara Kennedy & Saharon Shelah - 2004 - Journal of Symbolic Logic 69 (4):1261-1266.
    The authors show, by means of a finitary version □finλ, D of the combinatorial principle □b*λ of [7], the consistency of the failure, relative to the consistency of supercompact cardinals, of the following: for all regular filters D on a cardinal λ, if Mi and Ni are elementarily equivalent models of a language of size ≤ λ, then the second player has a winning strategy in the Ehrenfeucht-Fraïssé game of length λ+ on ∏i Mi/D and ∏i Ni/D. If in addition (...)
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