On the Interpreted Sense Calculus \( SC_\alpha ^v \)

  • Aldo Bressan


A. Bressan’s communication at the congress, to which the present paper is related, concerned a memoir, written by Bonotto and Bressan (1984), and Bressan’s forthcoming work “A transfinite sense theory for iterated belief sentences,” [TST], which, in various respects, is strongly based on that memoir and generalizes it. The principal aim of the present paper is to give a brief but complete account of the basic semantics of [TST], with short explanations and without proofs. Thus a part of said memoir is embodied as a special case. The remaining part of the memoir and the present paper are briefly described in subsections (A) and (B) respectively of this introduction. Its subsection (C) is devoted to motivations for these works.


Designation Rule Probability Calculus Basic Semantic Logical Symbol Classical Particle Mechanic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Anderson, C. A., 1980, Some New Axioms for the Logic of Sense and Denotation: Alternative (0), Nous, 14:217–234.CrossRefGoogle Scholar
  2. Bacon, J., 1980, Substance and First Order Quantification over Individual Concepts, J.S.L., 45:193–203.Google Scholar
  3. Bealer, G., 1982, “Quality and Concept,” Clarendon Press, Oxford.CrossRefGoogle Scholar
  4. Bigelow, J. C., 1978a, Believing in Semantics, Linguistic and Philosophy, 2:101–144.CrossRefGoogle Scholar
  5. Bigelow, J. C., 1978b, Semantics of Thinking, Speaking and Translation, in: “Meaning and Translation: Philosophical and Linguistic Approaches, M. Guenthner-Reutter and M. Guenthner, eds., Duckworth, London.Google Scholar
  6. Bonotto, C., 1981/82, Synonymy for Bressan’s Modal Calculus MCv, Part 1: A Synonymy Relation for MCv, Part 2: A Sufficient Criterium for Nonsynonymy, Atti 1st. Veneto di Scienze, Lettere ed Arti, 140:11–24, 85-99.Google Scholar
  7. Bonotto, C. and Bressan, A., 1983/84, On a Synonymy Relation for Extensional First Order Theories, Part 1: A Notion of Synonymy, Part 2: A Sufficient Criterion for Non-Synonymy. Applications, Part 3: A Necessary and Sufficient Condition for Synonymy, Rend. Sem. Mat. Univ. Padova, 69:63–76, 70:13-19, 71:1-13.Google Scholar
  8. Bonotto, C. and Bressan, A., 1984, On Generalized Synonymy Notions and Corresponding Quasi Senses, memoir in Atti Accad. Naz. dei Lincei (VIII), 17, sect.1:163–208.Google Scholar
  9. Bressan, A., 1962, Metodo di Assiomatizzazione in Senso Stretto della Meccanica Classica..., Rend. Sem. Mat. Univ. Padova, 32:55–212.Google Scholar
  10. Bressan, A., 1972a, “A General Interpreted Modal Calculus,” Yale University Press, New Haven.Google Scholar
  11. Bressan, A., 1972b, On the Usefulness of Modal Logic in Axiomatization of Physics, in: “Proceedings of the Biennal Meeting of the Phil. of Sci. Association, 1972,” K. F. Schaffner and R. S. Cohen, eds., 1974, pp.285-303 (see also pp.315-321 and 331-334).Google Scholar
  12. Bressan, A., 1973/74, The Interpreted Type Free Modal Calculus MC Involving Individuals, Part 1: The Interpreted Language ML on which MC is based, Part 2: Foundations of MC, Part 3: Ordinals and Cardinals in MC, Rend. Sem. Mat. Univ. Padova, 49:157–194, 50:19-57, 51:1-25.Google Scholar
  13. Bressan, A., 1978, “Relativistic Theories of Materials,” Springer, Berlin.CrossRefGoogle Scholar
  14. Bressan, A., 1978/79, On Wave Functions in Quantum Mechanics, Part 1: On a Fundamental Property of Wave Functions. Its Deduction from Postulates with a Good Operative Character and Experimental Support, Part 2: On Fundamental Observables and Quantistic States, Part 3: A Theory of Quantum Mechanics in Which Wave Functions are Defined by Surely Fundamental Observables, Rend. Sem. Mat. Univ. Padova, 60:77–98, 61:221-228, 62:365-392.Google Scholar
  15. Bressan, A., 1980, On Equilibrium in Rational Mechanics, Determinism, and Physical Completeness, Scienza e Cultura, 2:32–41.Google Scholar
  16. Bressan, A., 1981a, Extensions of the Modal Calculi MCv and MC. Comparison of them with Similar Calculi Endowed with Different Semantics. Applications to Probability Theory, in: “Aspects of Philosophical Logic,” U. Moennich, ed., Reidel, Dordrecht.Google Scholar
  17. Bressan, A., 1981b, On Physical Possibility, in: “Italian Studies in the Philosophy of Science,” M. L. Dalla Chiara, ed., Reidel, Dordrecht.Google Scholar
  18. Bressan, A., 1984, Substantial Uses of Physical Possibility in Principles and Definitions belonging to Well Known Classical Theories of Continuous Media, memoir in Atti Accad. Naz. Lincei (VIII), 17:137–162.Google Scholar
  19. Bressan, A. and Montanaro, A., 1980/83, Contributions to Foundations of Probability Calculus on the Basis of the Modal Logical Calculus MCv or MCv*, Part 1: Basic Theorems of a Recent Modal Version of the Probability Calculus Based on MCv or MCv*, Part 2: On a Known Existence Rule of the Probability Calculus, Part 3: An Analysis of the Notion of Random Variable, Rend. Sem. Mat. Univ. Padova, 64:163–182, 65:263-270, 70:1-11.Google Scholar
  20. Bressan, A. and Montanaro, A., 1982, Axiomatic Foundations of the Kinematics Common to Classical Physics and Special Relativity, Rend. Sem. Mat. Univ. Padova, 68:7–26.Google Scholar
  21. Bressan, A. and Zanardo, A., 1981, General Operators Binding Variables in the Interpreted Calculus MCv, Atti Accad. Naz. Lincei (VIII), 70:191–197.Google Scholar
  22. Carnap, R., 1947, “Meaning and Necessity,” Chicago University Press, Chicago.Google Scholar
  23. Carnap, R., 1955, Meaning and Synonymy in Natural Languages, Phil. Studies, 6.Google Scholar
  24. Carnap, R., 1958, “Introduction to Symbolic Logic and its Applications,” Dover Publ., New York.Google Scholar
  25. Church, A., 1951, A formulation of the logic of sense and denotation, (a) (Abstract) J.S.L., 12:21.Google Scholar
  26. (b).
    Church, A., 1951, (full article) in: “Structure, Method, and Meaning. Essays in honor of H. Sheffer,” Liberal Art Press, New York.Google Scholar
  27. (c).
    Church, A., 1951, Outline of a revised formulation of..., Nous 7:24–33, 8:135-156.CrossRefGoogle Scholar
  28. Cresswell, M. J., 1973, “Logics and Languages,” Methuen, London.Google Scholar
  29. Cresswell, M. J., 1975, Hyperintensional Logic, Studia Logica, 34:25–38.CrossRefGoogle Scholar
  30. Cresswell, M. J., 1980, Quotational Theories of Propositional Attitude, J. Phil. Logic, 9:17–40.CrossRefGoogle Scholar
  31. Hermes, H., 1959, Modal Operators in Axiomatization of Mechanics, in: “Proceedings of the Colloque International sur la Methode Axiomatique Classique et Moderne,” Paris.Google Scholar
  32. Gupta, A., 1980, The Common Logic of Common Nouns, Yale Univ. Press, New Haven.Google Scholar
  33. Kaplan, D., 1975, How to Russell a Frege-Church, The J, of Philosophy, 72:716–729.CrossRefGoogle Scholar
  34. Lewis, D. K., 1970, General Semantics, Synthese, 22:18–67.CrossRefGoogle Scholar
  35. Mendelson, E., 1964, “Introduction to Mathematical Logic,” Van Nostrand-Reinhold Co., New York.Google Scholar
  36. Monk, J. D., 1969, “Introduction to Set Theory,” McGraw Hill, New York.Google Scholar
  37. Omodeo, E., 1977, The Elimination of Descriptions from A. Bressan’s Modal Language MLv on which the Logical Calculus MCv is Based, Rend. Sem. Mat. Univ. Padova, 56:269–292.Google Scholar
  38. Omodeo, E., 1980, Three Existence Principles in a Modal Calculus Without Descriptions Contained in A. Bressan’s MCv, Notre Dame J. of Formal Logic, 21:711–727.CrossRefGoogle Scholar
  39. Painlevé, P., 1922, “Les Axiomes de la Méchanique,” Gauthier, Villars, eds., Paris.Google Scholar
  40. Parks, Z., 1976, Investigations into Quantified Modal Logic I, Studia Logica, 35:109–125.CrossRefGoogle Scholar
  41. Parsons, T., 1982, Intensional Logic in Extensional Language, J.S.L., 47:289–328.Google Scholar
  42. Parsons, T., 1981, Frege’s Hierarchies of Indirect Senses and the Paradox of Analysis, in.: “Midwest Studies in Philosophy VI: The Foundations of Analytic Philosophy,” Univ. of Minnesota Press, Minneapolis.Google Scholar
  43. Partee, B. H., 1973, The Semantics of Belief Sentences, in: “Approaches to Natural Languages,” J. Hintikka, J. Moravcsik and P. Suppes, eds., Reidel, Dordrecht.Google Scholar
  44. Pitteri, M., 1984, On the Axiomatic Foundations of Temperature, appendix in the revised edition of Truesdell’s book “Rational Thermodynamics,” Springer, Berlin.Google Scholar
  45. Stegmüller, W., 1976, “The Structure and Dynamics of Theories,” Springer, Berlin.CrossRefGoogle Scholar
  46. Zampieri, G., 1982, Diffeomorphisms Constructively Associated with Mutually Diverging Spacetimes, which Allow a Natural Identification of Event Points in General Relativity, Atti Ace. Naz. Lincei (VIII), 73:132–137, 221-225.Google Scholar
  47. Zampieri, G., 1982/83, A Choice of Global 4-Velocity Field in General Relativity, Atti Ist. Veneto Sci. Lettere e Arti, 141:201–216.Google Scholar
  48. Zanardo, A., 1981, A Completeness Theorem for the General Interpreted Modal Calculus MCv of A. Bressan, Rend. Sem. Mat. Univ. Padova, 64:39–57.Google Scholar
  49. Zanardo, A., 1983, On the Equivalence Between the Calculi MCv and ECv+1 of A. Bressan, Notre Dame J. of Formal Logic, 34:367–388.CrossRefGoogle Scholar
  50. Zanardo, A., 1984, Individual Concepts as Propositional Variables, being printed in Notre Dame J. of Formal Logic.Google Scholar

Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • Aldo Bressan
    • 1
  1. 1.Istituto di Analisi e MeccanicaUniversità di PadovaPadovaItaly

Personalised recommendations