J. Philosophical Logic. Bibliography 145. BIRKHOFF, G., 1966: Lattice Theory. Providence, R. I.: American Mathematical

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1 Bibliography ADDISON, J. W., HENKIN, L., and T ARSKI, A., eds., 1965: The Theory of Models. Amsterdam: North-Holland. ALSTON, W. P., 1958: Ontological Commitments. In: BENACERRAF and PUTNAM, 1964, pp ARNAULD, A., and NICOLE, P., 1662: La logique ou l'art de penser. Stuttgart: Fromann, BENACERRAF, P., 1965: What Numbers Could Not Be. Philosophical Rev. 74, and PUTNAM, H., eds., 1964: Philosophy of Mathematics. Englewood Cliffs, N. J.: Prentice-Hall. BERNAYs, P., 1935: On Platonism in Mathematics. In: BENACERRAF and PUTNAM, 1964, pp : Quelques points de vue concernant Ie probleme de l'evidence. Synthese 5, : Mathematische Existenz und Widerspruchsfreiheit. In: Etudes de Philo sophie des sciences en hommage a F. GONSETH, pp NeucMtel: Griffon. 1967: What Do Some Recent Results in Set Theory Suggest? In: LAKATOS, 1967, pp : Die schematische Korrespondenz und die idealisierten Strukturen. Dialectica 24, BETH, E. W., 1956: L'existence en mathematiques. Paris: Gauthier-Villars. 1962: Extension and Intension. In: Logic and Language, pp Dordrecht, Holland: D. Reidel. 1966: The Foundations of Mathematics. New York: Harper and Row. and Piaget,]., 1961: Epistemologie mathematique et psychologie. Paris: Presses Universitaires de France. English translation by W. MAYs, Mathematical Psychology and Epistemology. New York: Gordon and Breach, 1966.

2 Bibliography 145 BIRKHOFF, G., 1966: Lattice Theory. Providence, R. I.: American Mathematical Society. Boo LOS, G., 1971: The Iterative Conception of Set. J. Philosophy 68, BOURBAKI, N., 1962: L'architecture des mathematiques. In: F. LE LIONNAIS, ed., Les grands courants de la pensee mathematique, 2nd ed., pp Paris: Blanchard. BUNGE, M., 1967: Scientific Research. New York: Springer-Verlag : A Program for the Semantics of Science. To appear in: J. Philosophical Logic. CANTOR, G., 1883: Grundlagen einer allgemeinen Mannigfaltigkeitslehre. In: E. ZERMELO, ed., Georg Cantor Gesammelte Abhandlungen, pp Hildesheim, West Germany: G. alms. CARNAP, R., 1937: The Logical Syntax of Language. New York: Harcourt Brace. 1939: Foundations of Logic and Mathematics. Chicago: University of Chicago Press. 1950: Empiricism, Semantics, and Ontology. In: BENACERRAF and PUTNAM, 1964, pp : Meaning and Synonymy in Natural Languages. In: CARNAP, 1956, pp : Meaning and Necessity, 2nd edition. Chicago: University of Chicago Press. CASTONGUAY, c., 1972: Naturalism in Mathematics. To appear in: J. Philosophical Logic. CHENG, C. Y., 1969: Referentiality and Its Conditions. Abstract in: J. Philosophy 66, 783. CHURCH, A., 1944: Review of Lewis (1944). J. Symbolic Logic 9, COHEN, P. J., 1966: Set Theory and the Continuum Hypothesis. New York: Benjamin : Comments on the Foundations of Set Theory. In: SCOTT, 1971, pp CURRY, H. B., and FEYs, R., 1958: Combinatory Logic. Amsterdam: North-Holland. DAVIDSON, D., 1967: Truth and Meaning. Synthese 17, EDWARDS, P., ed., 1967: The Encyclopedia of Philosophy, 6 vols. New York: MacMillan and Free Press. FEFERMAN, S., 1969: Set-theoretical Foundations of Category Theory. In: S. MAc LANE, ed., Reports of the Midwest Category Seminar III, pp Berlin-New York: Springer-Verlag. 10 LEP 9

3 146 Bibliography FEYERABEND, P., 1962: Explanation, Reduction, and Empiricism. In: H. FEIGL and W. SELLARS, eds., Minnesota Studies in the Philosophy of Science, Vol. 3, pp Minneapolis, Minn.: University of Minnesota Press. FRAASSEN, B. VAN, 1967: Meaning Relations among Predicates. NOlls 1, FREYD, P., 1965: The Theories of Functors and Models. In: ADDISON, HENKIN, and TARSKI, 1965, pp FREYTAG-LoRINGHOFF, B. VON, 1951: Philosophical Problems of Mathematics. New York: Philosophical Library. FRISCH, J. c., 1969: Extension and Comprehension in Logic. New York: Philosophical Library. GLYMOUR, c., 1970: On Some Patterns of Reduction. Philosophy of Science 37, GOBLE, L. F., 1967: Abstract of A Coherence Theory of Meaning. Doctoral dissertation, University of Pittsburgh. Dissertation Abstracts 28, 5104-A. GODEL, K., 1944: RUSSELL'S Mathematical Logic. In: BENACERRAF and PUTNAM, 1964, pp : What is Cantor's Continuum Problem? In: BENACERRAF and PUTNAM, 1964, pp GOGUEN, J. A., 1969: The Logic of Inexact Concepts. Synthese 19, : Mathematical Representation of Hierarchically Organized Systems. In: Global Systems Dynamics. New York: S. Karger. GONSETH, F., 1936: La logique en tant que physique de l'objet quelconque. In: Actes du Congres international de Philosophie scientifique, pp Paris: Hermann. 1948: Les conceptions mathematiques et Ie reel. Archives de l'institut international des Sciences theoriques, serie A, n.2, : Mon itineraire philosophique. Revue internationale de philosophie, nos , fasc.3-4. GOODMAN, N., 1956: A World of Individuals. In: BENACERRAF and PUT NAM, 1964, pp GOODSTEIN, R. L., 1968: Existence in Mathematics. Compositio Mathematica 20, : Empiricism in Mathematics. Dialectica 23, GRANGER, G.-G., 1968: Essai d'une philosophie du style. Paris: A. Colin. GRASSMANN, H. G., 1844: Die lineare Ausdehnungslehre, ein neuer Zweig der Mathematik: In: Gunther Grassmann Gesammelte Werke. Leipzig: Teubner, 1894.

4 Bibliography 147 HANF, W., 1965: Model-theoretic Methods in the Study of Elementary Logic. In: ADDISON, HENKIN, and TARSKI, 1965, pp HART, W. D., 1970: Skolem's Promises and Paradoxes. J. Philosophy 67, HATCHER, W. S., 1968: Foundations of Mathematics. Philadelphia: Saunders. HEIJENOORT, J. VAN, 1967: G6del's Theorem. In: EDWARDS, HEMPEL, c., 1948: Problems and Changes in the Empiricist Criterion of Meaning. In: LINSKY, 1952, pp : Review of Lewis (1946). J. Symbolic Logic 13, HENKIN, L., 1950: Completeness in the Theory of Types. In: HINTIKKA, 1969, pp : The Representation Theorem for Cylindrical Algebras. In: Mathematical Interpretation of Formal Systems, pp Amsterdam: North-Holland. -, MONK, D., and TARSKI, A., 1971: Cylindric Algebras. Amsterdam: N orth-holland. HINTIKKA, J., 1968: Logic and Philosophy. In: KLIBANSKY, 1968, pp : The Philosophy of Mathematics. London: Oxford University Press. JUBIEN, M., 1969: Two Kinds of Reduction. J. Philosophy 66, KALMAR, L., 1967: Foundations of Mathematics - Whither Now? In: LAKATOS, 1967, pp KAUPPI, R., 1967: Einfiihrung in die Theorie der Begriffsysteme. Tampere: Tampereen Yliopisto. KEYNES, J. N., 1887: Formal Logic, 2nd edition. London: MacMillan. KLEENE, S. c., 1952: Introduction to Metamathematics. Princeton, N. J.: Van Nostrand. KLIBANSKY, R., ed., 1968: Contemporary Philosophy, Vol. 1. Firenze: Nuova Italia Editrice. KNEALE, W., and KNEALE, M., 1962: The Development of Logic. London: Oxford University Press. KORNER, S., 1960: The Philosophy of Mathematics. New York: Harper and Row : Reply to Mr. Kumar. British J. Philosophy of Science 18, KREISEL, G., 1953: A Variant to Hilbert's Theory of the Foundations of Mathematics. British J. Philosophy of Science 4, : Models, Translations, and Interpretations. In: Mathematical Interpretation of Formal Systems, pp Amsterdam: North Holland. 10*

5 148 Bibliography KREISEL, G., 1958: Wittgenstein's Remarks on the Foundations of Mathematics. British J. Philosophy of Science 9, : Hilbert's Programme. In: BENACERRAF and PUTMAN, 1964, pp : Model-Theoretic Invariants: Applications to Recursive and Hyperarithmetic Operations. In: ADDISON, HENKIN, and TARSKI, 1965, pp a: Informal Rigour and Completeness Proofs. In: LAKATOS, 1967, pp b: Mathematical Logic: What Has It Done for the Philosophy of Mathematics? In: R. SCHOENMAN, ed., Bertrand Russell: Philosopher of the Century, pp London: George Allen and Unwin. 1969: Two Notes on the Foundations of Set-Theory. Dialectica 23, : The Formalist-Positivist Doctrine of Mathematical Precision in the Light of Experience. L'Age de la science 3, : Observations on Popular Discussions of Foundations. In: SCOTT, 1971, pp KRIPKE, S., 1965: Semantical Analysis of Intuitionistic Logic I. In: V. N. CROSSLEY and M. A. E. DUMMETT, eds., Formal Systems and Recursive Functions, pp Amsterdam: North-Holland. KUMAR, D., 1967: Logic and Inexact Predicates. British J. Philosophy of Science 18, LADRIERE, J., 1957: Les limitations internes des formalismes. Paris: Gauthier-Villars. LAKATOS, I., 1962: Infinite Regress and the Foundations of Mathematics. Aristotelian Society Supplementary Vol. 36, : Proofs and Refutations (I)-(IV). British J. Philosophy of Science 14, 1-25, , , , ed., 1967: Problems in the Philosophy of Mathematics. Amsterdam: North-Holland. LAWVERE, F. W., 1966: The Category of Categories as a Foundation of Mathematics. In: Proceedings of the Conference on Categorical Algebra, La Jolla, 1965, pp New York: Springer-Verlag. 1969: Adjointness in Foundations. Dialectica 23, LEWIS, C. I., 1944: The Modes of Meaning. In: LINSKY, 1952, pp : An Analysis of Knowledge and Valuation. La Salle, Ill.: Open Court. 1951: Notes on the Logic of Intension. In: P. HENLE et ai., eds., Structure, Method, and Meaning: Essays in Honour of H. M. Sheffer, pp New York: Liberal Arts Press.

6 Bibliography 149 LINSKY, 1., ed., 1952: Semantics and the Philosophy of Language. Urbana, Ill.: University of Illinois Press. LYNDON, R., 1966: Notes on Logic. Princeton, N. J.: Van Nostrand. MAc LANE, S., 1968: Category Theory. In: KLIBANSKY, 1968, pp : Categorical Algebra and Set-theoretic Foundations. In: SCOTI, 1971, pp and BIRKHOFF, G., 1967: Algebra. New York: MacMillan. MARCUS, R. BARCAN, 1962: Interpreting Quantification. Inquiry 5, MARTIN, R. M., 1964: On Connotation and Attribute. J. Philosophy 61, MATES, B., 1970: Review of White (1967). J. Symbolic Logic 35, 303. MEHLBERG, H., 1960: The Present Situation in the Philosophy of Mathematics. Synthese 12, MONTAGUE, R., 1968: Pragmatics. In: KLIBANSKY, 1968, pp MOODY, E. W., 1953: Truth and Consequence in Mediaeval Logic. Amsterdam: North-Holland. Moss, J. M. B., 1971: Kreisel's Work on the Philosophy of Mathematics I. Realism. In: R. GANDY and C. YATES, eds., Logic Colloquium '69, pp Amsterdam: North-Holland. MOSTOWSKI, A., 1967: Recent Results of Set Theory. In: LAKATOS, 1967, pp MYHILL, J., 1951: On the Ontological Significance of the Lowenheim Skolem Theorem. In: I. M. COPI and J. A. GOULD, eds., Contemporary Readings in Logical Theory, pp New York: MacMillan. NAGEL, E., 1944: Logic Without Ontology. In: BENACERRAF and PUTNAM, 1964, pp : The Structure of Science. New York: Harcourt, Brace and World. PARSONS, c., 1971a: A Plea for Substitutional Quantification. J. Philosophy 68, b: Ontology and Mathematics. Philosophical Rev. 80, PIAGET, J., 1970a: L'epistemologie genetique. Paris: Presses Universitaires de France. 1970b: Genetic Epistemology. New York: Columbia University Press. and INHELDER, B., 1969: The Gaps in Empiricism. In: A. KOESTLER and J. R. SMYTHIES, eds., Beyond Reductionism, pp London: Hutchinson. POLYA, G., 1962: Mathematical Discovery. New York: Wiley.

7 150 Bibliography POSZGAY, 1., 1971: Liberal Intuitionism as a Basis for Set Theory. In: Scon, 1971, pp PRIOR, A. N., 1971: Objects of Thought. London: Oxford University Press. PUTNAM, H., 1968: Foundations of Set Theory. In: KLIBANSKY, 1968, pp QUINE, W. V., 1951: On Carnap's Views on Ontology. In: QUINE, 1966a, pp : From a Logical Point of View. New York: Harper and Row. 1958: Speaking of Objects. In: QUINE, 1969a, pp : Word and Object. Cambridge, Mass.: M. I. T. Press. 1966a: The Ways of Paradox. New York: Random House. 1966b: Ontological Reduction. In: QUINE, 1966a, pp a: Ontological Relativity and Other Essays. New York: Columbia University Press. 1969b: Ontological Relativity. In: QUINE, 1969a, pp c: Existence and Quantification. In: QUINE, 1969a, pp RESCHER, N., 1969: The Concept of Nonexistent Possibles. In: RESCHER, N., Essays in Philosophical Analysis. Pittsburgh: University of Pittsburgh Press. ROBINSON, A., 1966a: Non-standard Analysis. Amsterdam: North-Holland b: Formalism 64. In: Y. BAR-HILLEL, ed., Logic, Methodology and Philosophy of Science, pp Amsterdam: North-Holland. RUSSELL, B., 1919: Introduction to Mathematical Philosophy. London: Allen and Unwin. - and WHITEHEAD, A. N., 1927: Principia Mathematica to *56. Cambridge: Cambridge University Press, SCHEFFLER, I., 1967: Science and Subjectivity. Indianapolis, Ind.: Bobbs Merrill. Scon, D., ed., 1971: Axiomatic Set Theory. Providence, R. I.: American Mathematical Society. SUSZKO, R., 1967: An Essay in the Formal Theory of Extension and Intension. Studia Logika 20, SVENONIUS,1., 1972: Translation and Reduction. To appear in J. Philosophical Logic. T AKEUTI, G., 1969: The Universe of Set Theory. In: Foundations of Mathematics, Symposium Papers Commemorating the Sixtieth Birthday of Kurt Godel, pp New York: Springer-Verlag. TARSKI, A., 1956: Logic, Semantics, Metamathematics. London: Oxford University Press. -, MOSTOWSKI, A., and ROBINSON, R. M., 1953: Undecidable Theories. Amsterdam: North-Holland.

8 Bibliography 151 THARP, L., 1971: Ontological Reduction. J. Philosophy 68, THOM, R., 1970: Les mathematiques "modernes": une erreur pedagogique et philosophique? L'Age de la science 3, THOMASON, J. F., 1971: Ontological Relativity and the Inscrutability of Reference. Philosophical Studies 22, ULLIAN, J. S., 1969: Is Any Set Theory True? Philosophy of Science 36, WANG, H., 1963: A Survey of Mathematical Logic. Amsterdam: North Holland. 1966: Process and Existence in Mathematics. In: Y. BAR-HILLEL et ai., eds., Essays in the Foundations of Mathematics, pp Jerusalem: Hebrew University Press. WHITE, A. R., 1967: Coherence Theory of Truth. In: EDWARDS, 1967.

9 Index of Names Addison, J. W. 43 d'alembert, J. Ie Rond 93 Alston, W. P. 92 Aristotle 9, 13, 74 Arnauld, A. 10 Benacerraf, P. 105, 124, 128 Bernays, P. 6, 22, 50, 81-85, 94, 99, 101, 109, 114 Beth, E. W. 39, 78, 87, 92, 93, ' Birkhoff, G. 14, 105, 108 Boolos, G. 99 Bourbaki, N. 129 Bunge, M. 33, Buridan, J. 64 Cantor, G. 50, 74, 76, 77, 90 Carnap, R. 3, 20, 35, 53, 60, 64, Cheng, C. Y. 136 Church, A. 60, 131 Cohen, P. 43, 66, 79, 93 Curry, H. B. 16 Davidson, D. 44, 68 Dedekind, R. 138, 139 Descartes, R. 11, 127 Feferman, S. 94, 101 Fermat, P. 127 Feyerabend, P. 111 Feys, R. 16 Fraassen, B. van 59 Fraenkel, A. 94, 101 Frege, G. 19, 121, 138, 139, 142 Freud, S. 88 Freyd, P. 104 Freytag-L6ringhoff, B. van 74, 75,77 Frisch, J. c. 9, 11 Glymour, C. 111, 129 Goble, L. F. 45 G6del, K , 43, 45, 50, 64, 67, 77, 90, 93, 94, 101, 109, 112, 113, 114, 127, 131, 133, 136 Goguen, J. A. 36, 37, 73, 110 Gonseth, F , 89, 110 Goodman, N. 66 Goodstein, R. L. 65, 66, 79 Granger, G.-G. 7, 95-97, 105 Grassman, H. G. 105 Hanf, W. 124, 129 Hart, W. D. 43 Hatcher, W. S. 19, 44, 101, 105, 112, 121 Heijenoort, J. van 67

10 154 Hempel, C. 45, 46, 58, 59, 60, 62 Henkin, 1. 19, 20, 24, 29, 43, 56, 77 Herbrand, J. 115, 125, 128 Hilbert, D. 50, 115, 124 Hintikka, J. 43, 44 Inhelder, B. 89 Jones, T. 73 Jubien, M. 136, 141 Kalmar,1. 65, 66 Kant, I. 108 Kauppi, R. 11 Keynes, J. N. 12, 15, 33, 34 Kleene, S. C. 55, 63, 112 Klein, F. 105 Kneale, M. 10 Kneale, W. 10 Korner, S. 37, 38 Kreisel, G. 6, 7, 50, 66, 83-86, 88, 93, 94, 96, 98, 108, 109, , 124, 125, 129, 130, 131, 136, 142, 143 Kripke, S. 24 Kumar, D. 37 Ladriere, J. 50 Lakatos, I. 52, 65, 66, 68, 86, 90,93 Lawvere, F. W. 100, 103, 105, Leibniz, G. W. 11 Lewis, C. I. 6, 41, 46, 58-63, 68-71, 73, 97 Lowenheim,1. 43, 55, 114, 129, 137, 140 Lyndon, R. 44, 50 MacLane, S. 95, 100, 103, 105 Marcus, R. Barcan 80, 133 Index of Names Martin, R. M. 39 Mates, B. 64 Mehlberg, H. 50 Mill, J. S. 33, 34 Mobius, A. F. 105 Monk, D. 29 Montague, R. 39, 68, Moody, E. W. 10, 64 Morris, C. 3, 20 Moss, J. M. B. 84, 94 Mostowski, A. 94, 114 Myhill, J. 50, 67, 86 Nagel, E. 74, 75, 79, 111, 112, 116, 129 Neumann, J. von 22, 120, 138, 142 Nicole, P. 10 Parsons, C. 133, 134 Peano, G. 42, 105 Peirce, C. S. 41, 42, 46 Piaget, J. 7, 78, 86-90, 92, 94, 95, 97, 99, 109, 110, 134 Poincare, H. 74, 75 Polya, G. 65 Porphyry 9 Poszgay, Prior, A. N. 135 Putnam, H. 85, 86, 128 Quine, W. V. 8, 45, 57, 70, 80, 92, Rescher, N , 136 Robinson, A. 79, 92, 109, 126 Robinson, R. M. 114 Russell, B. 19, 20, 67 Scheffler, I. 90 Scott, D. 66 Sheffer, H. M. 61

11 Index of Names Skolem, Th. 43, 50, 55, 114, 129, 137, 140 Solovay, R. M. 43 Stone, M. H. 126 Suszko, R. 28, 39 Svenonius, L. 123 Takeuti, G. 67, 93 Tarski, A. 17, 29, 31, 32, 42, 43, 44, 57, 109, 114 Tharp, L. 139, 142 Thorn, R. 86, 87, 89, 108, 109, 121, 130 Thomason, J. F. 142 Ullian, J. S. 67 Wang, H. 112, 113, 114, 118, 119, 141 Weierstrass, K. 92 Whitehead, A. N. 20 Zermelo, E. 94, 101,

12 Subject Index adequate translation 115 analyticity 58, 88 Aristotelian view of existence 74 background theory 33, 49, 51, 52, 56, 112, 113, 117, 134, 142 category theory 88, 95, coherence view of meaning 41, 45, 66,88 coherence view of truth 64-68, 93, 128 co-intension 47 comprehension 12, 22, 27, 55, 59 connotation 12, 34, 58 consequence, theory of 10, 39 consistency 53, 74-77, 78, 90, 107, 117, 121 construct 12 constructivism, in mathematics 78, 87-91, 94-98, 102, 105, 109, 133 core intension 33, 47, 48, 62, 63 correct translation 123 correspondence view of meaning 41-45, 66, 88 correspondence view of truth 44, 64-68, 93, 128 cross-fertilization of mathematical theories 102, 110, 127, 131, 141, 142 cylindric algebra 29 denotation 58 dual homomorphism 14, 28, 29, 32, 107 dualistic view of meaning 46, 47, 55-57, 66, 68, 70, 122 entailment, relation of 12, 16, 21, 49-54, 56, 58, 61, 66, 71, 83, 92,97, 107, 108, 113, , 126, 128 entailment relation induced by reference 16, 22, 61, 73 evidence, mathematical 81,84-86, 88, 93, 106 existence, mathematical 74-84, 88-94, 99, 44, 66, 101, 102, 130, 136, 140, 141 explanation 50, 86, 111, 122, , 139 extension 9-40, 47, 54, 58, 107, 122 extension of a set of constructs 30 extensional component of meaning 54, 143 extensional vagueness 34-38, 63

13 Subject Index factual theories 40, 45, 79, 136, 142 faithful translation 53, 116, 119, 123 formalism 55, 64, 85, 86 formalization, as process 49-54, 66, 86, 88, 90, 121, 122, 125, 126 formalization of a theory 49, 54, 121 formalized theory 16, 36 fruitfulness 78, 79, 93, 94, 100, 106, 110, 127, 140, 142 functor 104 heuristic component of a theory 38, 57, 63, 66, 85, 92, 95, 97, 100, 103, 118, 125, 128, 129, 133, 141 heuristics, mathematical 52, 55, 64, 67, 78, 87, 91-95, 97, 98, 101, 106, 110, , 138, 142, 143 informal rigour 83-86, 90, 93, 94, 96, 125, 127 intended model 56, 123 intension 9-40, 47, 53, 54, 58, 59, 107, intension of a set of constructs 30 intensional component of meaning 50, 52, 55, 57, 92, 116, 120, 121, 124, 143 intensional vagueness 35 intensionally related formulas 119 intuitionist mathematics 51, 55, 78, 79, 88, 102 inverse ratio, law of 9, 13, 107 L-comprehension 59 Lindenbaum algebra 26 linguistic component of meaning 40, 47, 50, 66, 68, 120, meaning 41-48, 55, 58, 61-63, 97, 101, 143 meaning, mathematical 43,49-57, 95-97, 101, 109, 115, 117, 118, , 143 meaning-preserving correspondences 51-54,102, 104, ,129, 139 model 17 model theory 17-23, 40, 42, 55-57, 117, 123, 137 morphism 103 natural mathematical theory 49,51, 55, 66, 116, 121, 122, 126 naturalness 99, 100, 101, 104 bis 106, 127, 139. non-existent possibles 59, 60, non-standard model 25, 57, 92, 109 objectivity, mathematical 50, 54, 63, 82-93, 99, 100, 106, 118, 120, 124, 126, 134 objects, mathematical 38, 43, 50, 55, 66, 74-84, 87-91, 95 bis 99, , 109, 118, 124, 126, 130, , 141 ontological commitment 130, ontological reduction ontology, for mathematics 37, 43, 57,80, 102, 103, 118, , 140, 142 Platonism, in mathematics 42-44, 50, 66, 74-77, 84, 87, 88, 90-94, 98, 107 Platonist view of existence 74 possible world 61, 68, proof theory 21, 40, 55, 115 proof-theoretic content of a theory , 124, 142, 143

14 158 proper explication of intension 15, 21 quasi-translation 51, 57, 67, 80, 118, 125 rank of a formula 21 reduction 42, 100, 103, , 124, 129, 135, 139, 140, 142 reference, relation of 12, 16, 18, 55-58, 60, 62, 69, 70, 83, 107, 108, 132, , 143 referential component of meaning 40, 47, 48, 50, 54, 55-57, 68, 83, 91, 97, 100, 103 referential explication of intension 15, 22, 24, 40, 60, 61 referential view of meaning 42-45, 56, 68, 99 reflective abstraction 87-90, 92, 94, 97, 99, 100, 110, 126 regular formula 26 relative existence 81-83, 89 rigour, mathematical 86, 90 semantical interpretation 53, 57, 114, 118, 140 semantically adequate theory 23, 59,69 Subject Index semantics of a formalized theory 23-25, 54-57, 143 set-theoretic semantics 25, 42-44, 56, 57, 70, 73, 77, 94, 99, 123, 130, 133, 135, 137, 143 signification 55, 58, 61-63, 84, 96, 97, 100, 129, 130 standard model 56, 123 structure, mathematical 82-84, 87-89, 94-96, 99, 102, 109, 118, 120, , 130, 131, 138 style , 127 substitutional interpretation of 3 80, 133, 136 suggestiveness 100, 105, 127 supposition, theory of 10, 39 syntactical interpretation 53, 96, 112, 113, 115, 118 syntax of a formalized theory 17,77 Tarskian explication of extension 20 translation 112, 119, 132 truth, mathematical 44, 64-68, 85,93 truth set 19, 20

15 Partial List of Symbols d 14 ExtM d k 27 ExtM (F) ,22 c 13 Ext.lt (F) 22 OM 18 C 12 Ext.lt (T) 31 OAt 22 Cn(G) 32 F 17 cp 18 Com (c) 15 F 30 'Jtk 29 Com (F) 28 Fk 26 g; 26 Con(c) 34 " 28 f-t ( F ~ 21 G ) ~ 27,28 "k 26 e 12 v 27,28 Int 27 em 18 D 33 Int(c) 13 e.lt 22 Dic(c) 34 Int(F) 21 Rp 18 r! 14 IntM (F) 22 T 17 tffk 27 Int.lt (F) 22 T Int(T) 31 e 26 'YJ 12 L 'YJM 22 M 17,:., 27,28 'YJ.It 22 vit 22 U 17 Ext (c) 13