Works by Carl J. Posy
24 found
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| Carl J. Posy [24] | Carl Jeffrey Posy [1] |
- Mathematical Intuitionism.Carl J. Posy -2020 - Cambridge University Press.L. E. J. Brouwer, the founder of mathematical intuitionism, believed that mathematics and its objects must be humanly graspable. He initiated a program rebuilding modern mathematics according to that principle. This book introduces the reader to the mathematical core of intuitionism – from elementary number theory through to Brouwer's uniform continuity theorem – and to the two central topics of 'formalized intuitionism': formal intuitionistic logic, and formal systems for intuitionistic analysis. Building on that, the book proposes a systematic, philosophical foundation (...) for intuitionism that weaves together doctrines about human grasp, mathematical objects and mathematical truth. (shrink)
- Kant’s Mathematical Realism.Carl J. Posy -1984 -The Monist 67 (1):115-134.Though my title speaks of Kant’s mathematical realism, I want in this essay to explore Kant’s relation to a famous mathematical anti-realist. Specifically, I want to discuss Kant’s influence on L. E. J. Brouwer, the 20th-century Dutch mathematician who built a contemporary philosophy of mathematics on constructivist themes which were quite explicitly Kantian. Brouwer’s theory is perhaps most notable for its belief that constructivism requires us to abandon the traditional logic of mathematical reasoning in favor of different canon of reasoning, (...) called intuitionistic logic. Brouwer thought that classical logic is intrinsically bound up with a nonconstructive view of mathematics. This means that, according to Brouwer, when we do mathematics we must give up bivalence, we must no longer use such familiar logical laws as excluded middle, and we must sometimes forebear from the classic method of reductio ad absurdum. All of these are intuitionistically invalid classical principles. (shrink)
- Varieties of indeterminacy in the theory of general choice sequences.Carl J. Posy -1976 -Journal of Philosophical Logic 5 (1):91 - 132.
- Brouwer's constructivism.Carl J. Posy -1974 -Synthese 27 (1-2):125 - 159.
- Kant’s Philosophy of Mathematics: Modern Essays.Carl J. Posy -1992 - Springer.Kant's views about mathematics were controversial in his own time, and they have inspired or infuriated thinkers ever since. Though specific Kantian doctrines fell into disrepute earlier in this century, the past twenty-five years have seen a surge of interest in and respect for Kant's philosophy of mathematics among both Kant scholars and philosophers of mathematics. The present volume includes the classic papers from the 1960s and 1970s which spared this renaissance of interest, together with updated postscripts by their authors. (...) It also includes the most important recent work on Kant's philosophy of mathematics. The essays bring to bear a wealth of detailed Kantian scholarship, together with powerful new interpretative tools drawn from modern mathematics, logic and philosophy. The cumulative effect of this collection upon the reader will be a deeper understanding of the centrality of mathematics in all aspects of Kant's thought and a renewed respect for the power of Kant's thinking about mathematics. The essays contained in this volume will set the agenda for further work on Kant's philosophy of mathematics for some time to come. (shrink)
- A free IPC is a natural logic: Strong completeness for some intuitionistic free logics.Carl J. Posy -1982 -Topoi 1 (1-2):30-43.IPC, the intuitionistic predicate calculus, has the property(i) Vc(A c /x) xA.Furthermore, for certain important , IPC has the converse property (ii) xA Vc(A c /x). (i) may be given up in various ways, corresponding to different philosophic intuitions and yielding different systems of intuitionistic free logic. The present paper proves the strong completeness of several of these with respect to Kripke style semantics. It also shows that giving up (i) need not force us to abandon the analogue of (ii).
- The language of appearances and things in themselves.Carl J. Posy -1981 -Synthese 47 (2):313 - 352.
- Kant and conceptual semantics.Carl J. Posy -1991 -Topoi 10 (1):67-78.
- Where have all the objects gone?Carl J. Posy -1986 -Southern Journal of Philosophy 25 (S1):17-36.
- Between Leibniz and Mill: Kant's Logic and the Rhetoric of Psychologism.Carl J. Posy -1997 -Philosophy and Rhetoric 30 (3):243 - 270.
- Epistemology, ontology and the continuum.Carl J. Posy -2000 - In Emily Grosholz & Herbert Breger,The growth of mathematical knowledge. Boston: Kluwer Academic Publishers. pp. 199--219.No categories
- On brouwer's definition of unextendable order.Carl J. Posy -1980 -History and Philosophy of Logic 1 (1-2):139-149.It is argued that the tensed theory of the creative subject provides a natural formulation of the logic underlying Brouwer's notion of unextendable order and explains the link between that notion and virtual order. The tensed theory of the creative subject is also shown to be a useful tool for interpreting recent evidence about the stages of Brouwer's thinking concerning these two notions of order.
- Transcendental Idealism and Causality: An Interpretation of Kant's Argument in the Second Analogy.Carl J. Posy -1984 - In William Leonard Harper & Ralf Meerbote,Kant on Causality, Freedom, and Objectivity. Univ of Minnesota Press. pp. 20-41.
- Platonism and the Proto-ontology of Mathematics: Learning from the Axiom of Choice.Carl J. Posy -2023 - In Carl Posy & Yemima Ben-Menahem,Mathematical Knowledge, Objects and Applications: Essays in Memory of Mark Steiner. Springer. pp. 99-134.Benacerraf’s Problem about mathematical truth displays a tension, indeed a seemingly unbridgeable gap, between Platonist foundations for mathematics on the one hand and Hilbert’s ‘finitary standpoint’ on the other. While that standpoint evinces an admirable philosophical unity, it is ultimately an effete rival to Platonism: It leaves mathematical practice untouched, even the highly non-constructive axiom of choice. Brouwer’s intuitionism is a more potent finitist rival, for it engenders significant deviation from standard (classical) mathematics. The essay illustrates three sorts of intuitionistic (...) deviations (weakening, refinement and outright contradiction), and goes on to sketch the technical tools and arguments that engender those clashes with classical mathematics and the philosophical principles underlying those arguments. Those philosophical principles coalesce into a “standpoint” no less unified and no less finitary that Hilbert’s. This intuitionistic standpoint is sufficiently detailed that it itself provides a benchmark for comparing all the rival positions; and it is sufficiently robust that it dissolves the Benacerrafian dichotomy. However, the intuitionistic refutation of the axiom of choice reveals two distinct sub-streams within that intuitionistic standpoint. Distinguishing these streams suggests perhaps that in spite of that robustness, intuitionism has an internal dichotomy parallel to the Benacerrafian split. The Benacerrafian split is a crack in the foundations of mathematics. But I shall argue that this internal intuitionistic dichotomy is not at all a foundational gap; it is rather a special insight about the nature of mathematical thought. (shrink)
- The theory of empirical sequences.Carl J. Posy -1977 -Journal of Philosophical Logic 6 (1):47 - 81.
- Essay review.Carl J. Posy -1983 -History and Philosophy of Logic 4 (1-2):83-90.MICHAEL DUMMETT, Elements of intuitionism. With the assistance of Robert Minio. Oxford: Oxford University Press, 1977. xii + 466 pp. No price stated.
- Authenticity or Autonomy? Leibniz and Kant on Practical Rationality.Carl J. Posy -2008 - In Marcelo Dascal,Leibniz: What Kind of Rationalist? Springer. pp. 293--313.
- Editors' introduction.Carl J. Posy &Michael T. Ferejohn -1993 -Synthese 96 (3):333-334.No categories
- Introduction.Carl J. Posy -1984 -Topoi 3 (2):97-98.
- Kant's philosophy of mathematics.Carl J. Posy &Ofra Rechter (eds.) -2019 - New York, NY: Cambridge University Press.
- Mathematics as a transcendental science.Carl J. Posy -1991 - In Thomas M. Seebohm, Dagfinn Føllesdal, J. N. Mohanty & Jitendra Nath Mohanty,Phenomenology and the Formal Sciences. Dordrecht, Netherland: Springer. pp. 107–131.
- Strong Completeness for Some Intuitionistic Free Logics.Carl J. Posy -1991 - In Karel Lambert,Philosophical applications of free logic. New York: Oxford University Press. pp. 49.Export citation
Bookmark - Desmond Paul Henry. The truncation of truth-functional calculation. Notre Dame journal of formal logic, vol. 2 , pp. 193–205. [REVIEW]Gerald J. Massey &Carl J. Posy -1974 -Journal of Symbolic Logic 39 (1):174.
- van Dalen Dirk. Intuitionistic logic. Handbook of philosophical logic, Volume III, Alternatives to classical logic, edited by Gabbay D. and Guenthner F., Synthese library, vol. 166, D. Reidel Publishing Company, Dordrecht etc. 1986, pp. 225–339. Felscher Walter. Dialogues as a foundation for intuitionistic logic. Handbook of philosophical logic, Volume III, Alternatives to classical logic, edited by Gabbay D. and Guenthner F., Synthese library, vol. 166, D. Reidel Publishing Company, Dordrecht etc. 1986 .. [REVIEW]Carl J. Posy -1992 -Journal of Symbolic Logic 57 (2):754-756.
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David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Area Editors:
David Bourget
Gwen Bradford
Berit Brogaard
Margaret Cameron
David Chalmers
James Chase
Rafael De Clercq
Ezio Di Nucci
Esa Diaz-Leon
Barry Hallen
Hans Halvorson
Jonathan Ichikawa
Monte Johnson
Michelle Kosch
Øystein Linnebo
Paul Livingston
Brandon Look
Manolo Martínez
Matthew McGrath
Michiru Nagatsu
Susana Nuccetelli
Giuseppe Primiero
Jack Alan Reynolds
Darrell P. Rowbottom
Aleksandra Samonek
Constantine Sandis
Howard Sankey
Jonathan Schaffer
Thomas Senor
Daniel Star
Jussi Suikkanen
Aness Kim Webster
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