The Context of Inference

References

• van Atten, M. 2009. ‘The development of intuitionistic logic’, in E. Zalta, Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/entries/intuitionistic-logic-development/
   Google Scholar
• Brouwer, L. E. J. 1928. ‘Mathematics, science, and language’, in W. Ewald, From Kant to Hilbert: A Sourcebook in the Foundations of Mathematics, New York: Oxford University Press, 1175–85.
   Google Scholar
• Chagrov, A. V. 1992. ‘Decidable modal logic with undecidable admissibility problem’, Algebra and Logic, 31, 53–61. doi: 10.1007/BF02259858
   Google Scholar
• Citkin, A. I. 1977. ‘On admissible rules of intuitionistic propositional logic’, Mathematics of the USSR-Sbornik, 31, 279–88. doi: 10.1070/SM1977v031n02ABEH002303
   Web of Science ®Google Scholar
• Currie, G. 1987. ‘Remarks on Frege's conception of inference’, Notre Dame Journal of Formal Logic, 28 (1), 55–68. doi: 10.1305/ndjfl/1093636846
   Google Scholar
• van Dalen, D. 2005. Mystic, Geometer, and Intuitionist: The Life of L. E. J. Brouwer, vol. II. Hope and Disillusion, New York: Oxford University Press.
   Google Scholar
• Dawson, J. W. 1993. ‘The compactness of first-order logic: from Gödel to Lindström’, History and Philosophy of Logic, 14 (1), 15–37. doi: 10.1080/01445349308837208
   Web of Science ®Google Scholar
• Franks, C. 2010. ‘Cut as consequence’, History and Philosophy of Logic, 31 (4), 349–79. doi: 10.1080/01445340.2010.522365
   Web of Science ®Google Scholar
• Franks, C. 2017. ‘Glivenko's theorem’, http://www.nd.edu/∼cfranks/writing/glivenko.pdf.
   Google Scholar
• Frege, G. 1879. Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle: L. Nebert. Translated by T. W. Bynum as Conceptual Notation: A Formula Language of Pure Thought Modeled upon the Formula Language of Arithmetic, in T. W. Bynum, Conceptual Notation and Related Articles, New York: Oxford University Press, 101–208.
   Google Scholar
• Frege, G. 1882. ‘Über die wissenschaftliche Berechtigung einer Begriffsschrift’, Zeitschrift für Philosophie und philosophische Kritik, 81, 48–56. Translated by T. W. Bynum as ‘On the scientific justification of a conceptual notation’, in T. W. Bynum, Conceptual Notation and Related Articles, New York: Oxford University Press, 83–89.
   Google Scholar
• Frege, G. 1883. ‘Über den Zweck der Begriffsschrift’, Sitzungsberichte der Jenaischen Gesellschaft für Medizin und Naturwissenschaft für das Jahr 1882, 16, 1–10. Translated by T. W. Bynum as ‘On the aim of the ‘Conceptual Notation”, in T. W. Bynum, Conceptual Notation and Related Articles, New York: Oxford University Press, 90–100.
   Google Scholar
• Frege, G. 1906. ‘Foundations of geometry: second series’, translated and reprinted in G. Frege, Collected Papers, B. F. McGuiness (ed.). Oxford: Blackwell, 293–340.
   Google Scholar
• Frege, G. 1910. ‘Letter to Jourdain’, translated and reprinted in G. Frege, Philosophical and Mathematical Correspondence, G. Gabriel, et al. (eds.). Chicago: University of Chicago Press.
   Google Scholar
• Frege, G. 1917. ‘Letter to Dingler’, translated and reprinted in G. Frege, Philosophical and Mathematical Correspondence, G. Gabriel, et al. (eds.). Chicago: University of Chicago Press.
   Google Scholar
• Frege, G. 1918. ‘Negation’, translated and reprinted in G. Frege, Collected Papers, B. F. McGuiness (ed.). Oxford: Blackwell.
   Google Scholar
• Frege, G. 1923. ‘Compound thoughts’, translated and reprinted in G. Frege, Collected Papers, B. F. McGuiness (ed.). Oxford: Blackwell.
   Google Scholar
• Frege, G. 1980. Philosophical and Mathematical Correspondence, G. Gabriel, et al. (eds.). Chicago: University of Chicago Press.
   Google Scholar
• Gentzen, G. 1932. ‘Über die Existenz unabhängiger Axiomensysteme zu unendlichen Satzsystemen’, Mathematische Annalen, 107, 329–50. Translated as ‘On the existence of independent axiomsystems for infinite sentence systems’, in M. E. Szabo, The Collected Papers of Gerhard Gentzen, London: North Holland, 29–52. doi: 10.1007/BF01448897
   Google Scholar
• Gentzen, G. 1934–35. ‘Untersuchungen über das logische Schliessen’. Gentzen's doctoral thesis at the University of Göttingen, translated as ‘Investigations into logical deduction’, in M. E. Szabo, The Collected Papers of Gerhard Gentzen, London: North Holland, 68–131.
   Google Scholar
• Glivenko, V. 1929. ‘Sur quelques points de la logique de M. Brouwer’, Bulletin Academie des Sciences de Belgique, 15 (5), 183–88.
   Google Scholar
• Gödel, K. 1930. ‘Die Vollständigkeit der Axiome des logischen Functionenkalküls’, Monatshefte für Mathematik und Physik, 37, 349–60. Translated by S. Bauer-Mengelberg as ‘The completeness of the axioms of the functional calculus of logic’, reprinted in Feferman et al., Kurt Gödel, Collected Works, Vol I: Publications 1929–1936, New York: Oxford University Press, 102–123. doi: 10.1007/BF01696781
   Google Scholar
• Gödel, K. 1932. ‘Zum intuitionistischen Aussagenkalkül’, Anzeiger der Akademie der Wissenschaftischen in Wien, 69, 65–66. Translated by J. Dawson as ‘On the intuitionistic propositional calculus’, in Feferman et al., Kurt Gödel, Collected Works, Vol I: Publications 1929–1936, New York: Oxford University Press, 223–225.
   Google Scholar
• Gurevich, Y. 1984. ‘Toward logic tailored for computational complexity’, in M. Richter, et al., Computation and Proof Theory, Springer Lecture Notes in Mathematics, Vol. 1104, 175–216.
   Google Scholar
• Hakli, R., and Negri, S. 2012. ‘Does the deduction theorem fail for modal logic?’, Synthese, 187 (3), 849–67. doi: 10.1007/s11229-011-9905-9
   Web of Science ®Google Scholar
• Harrop, R. 1956. ‘On disjunctions and existential statements in intuitionistic systems of logic’, Mathematische Annalen, 132, 347–61. doi: 10.1007/BF01360048
   Web of Science ®Google Scholar
• Heyting, A. 1956. Intuitionism: An Introduction, Amsterdam: North Holland.
   Google Scholar
• Iemhoff, R. 2001. Provability Logic and Admissible Rules, Ph.D. thesis, Institute for Logic, Language, and Computation, Universiteit van Amsterdam.
   Google Scholar
• Iemhoff, R. 2016. ‘Consequence relations and admissible rules’, Journal of Philosophical Logic, 45 (3), 327–48. doi: 10.1007/s10992-015-9380-8
   Web of Science ®Google Scholar
• Johansson, I. 1937. ‘Der Minimalkalkül, ein reduzierter intuitionistischer Formalismus’, Compositio Mathematica, 4, 119–36.
   Google Scholar
• de Jongh, D. H. J. 1968. Investigations on the Intuitionistic Propositional Calculus, Ph.D. thesis, University of Wisconsin, Madison.
   Google Scholar
• Kleene, S. C. 1945. ‘On the interpretation of intuitionistic number theory’, Journal of Symbolic Logic, 10, 109–24. doi: 10.2307/2269016
   Google Scholar
• Kolmogorov, A. 1925. ‘О принципе tertium non datur’, Sbornik: Mathematics, 32 (4), 646–67. Translated as ‘On the principle of the excluded middle’ by J. van Heijenoort, in van Heijenoort, From Frege to Gödel: A Source Book in Mathematical Logic: 1879–1931, Cambridge: Harvard University Press, 416–437.
   Google Scholar
• Koslow, A. 1992. A Structuralist Theory of Logic, Cambridge: Cambridge University Press.
   Google Scholar
• Kreisel, G., and Putnam, H. 1957. ‘Eine Unableitbarkeitsbeweism ethode für den Intuitionistischen Aussagenkalkül’, Zeitschrift für Mathematische Logik and Grundlagen der Mathematik, 3, 74–78.
   Google Scholar
• Lawvere, F. W. 1964. ‘An elementary theory of the category of sets’, Proceedings of the National Academy of Sciences, 52 (6), 1506–11. doi: 10.1073/pnas.52.6.1506
   PubMed Web of Science ®Google Scholar
• Lorenzen, P. 1955. Einführung in die operative Logik und Mathematik, Berlin: Springer.
   Google Scholar
• Łukasiewicz, J. 1952. ‘On the intuitionistic theory of deduction’, Koninklijke Nederlandse Akademie van Wetenschappen, Proceedings, series A, 55, 202–12.
   Google Scholar
• van der Molen, T. 2016. ‘The Johansson/Heyting Letters and the Birth of Minimal Logic’, Institute for Logic, Language, and Computation, Amsterdam.
   Google Scholar
• Plato. ‘Crito’, translated by G. M. A. Grube 1997, in J. M. Cooper, Plato: Complete Works, Indianapolis: Hackett.
   Google Scholar
• Quine, W. V. O. 1970. Philosophy of Logic, Minneapolis, MN: Prentice-Hall.
   Google Scholar
• Robinson, A. 1951. On the Metamathematics of Algebra, Amsterdam: North Holland.
   Google Scholar
• Rose, G. F. 1953. ‘Propositional calculus and realizability’, Transactions of the American Mathematical Society, 75, 1–19. doi: 10.1090/S0002-9947-1953-0055952-4
   Web of Science ®Google Scholar
• Rybakov, V. V. 1992. ‘Rules of inference with parameters for intuitionistic logic’, The Journal of Symbolic Logic, 57 (3), 912–23. doi: 10.2307/2275439
   Web of Science ®Google Scholar
• Rybakov, V. 1997. Admissibility of Logical Inference Rules, Amsterdam: Elsevier.
   Google Scholar
• Schroeder-Heister, P. 2008. ‘Lorenzen's operative justification of intuitionistic logic’, in M. van Atten, P. Boldini, M. Bourdeau, G. Heinzmann, One Hundred Years of Intuitionism (1907–2007), Basel: Birkhäuser.
   Google Scholar
• Skolem, T. 1957. ‘Review: Paul Lorenzen, Einfuhrung in die Operative Logik und Mathematik’, The Journal of Symbolic Logic, 22 (3), 289–90. doi: 10.2307/2963596
   Google Scholar
• Smith, N. J. J. 2009. ‘Frege's judgement stroke and the conception of logic as the study of inference not consequence’, Philosophy Compass, 4 (4), 639–65. doi: 10.1111/j.1747-9991.2009.00219.x
   Google Scholar
• Solovay, R. M. 1976. ‘Provability interpretations of modal logic’, Israel Journal of Mathematics, 25, 287–304. doi: 10.1007/BF02757006
   Web of Science ®Google Scholar
• Stoothoff, R. H. 1963. ‘Note on a doctrine of Frege’, Mind, 72 (287), 406–8. doi: 10.1093/mind/LXXII.287.406
   Web of Science ®Google Scholar
• Terwijn, S. A. 2004. ‘Intuitionistic logic and computation’, Vriendenboek ofwel Liber Amicorum ter gelegenheid van het afscheid van Dick de Jongh, Institute for Logic, Language, and Computation, Amsterdam.
   Google Scholar