Abstract
First, language and axioms of Church's paper 'Comparison of Russell's Resolution of the Semantical Antinomies with that of Tarski' are slightly modified and a version of the Liar paradox tentatively reconstructed. An obvious natural solution of the paradox leads to a hierarchy of truth predicates which is of a different kind from the one defined by Church: it depends on the enlargement of the semantical vocabulary and its levels do not differ in the ramified-type-theoretical sense. Second, two attempts are made in order to justify the Russellian, and perhaps Churchian, idea that language should not be fragmented beyond what is required by type distinctions. After all, because of reducibility, which seems to allow a semantics without propositions, this comes out to be possible only at the cost of resorting to two disputable theses.
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REFERENCES
Anderson, C. A.: 1989, 'Russellian Intensional Logic', in J. Almog, J. Perry and H. Wettstein (eds.), Themes from Kaplan, Oxford University Press, Oxford, pp. 67-107.
Church, A.: 1976, 'Comparison of Russell's Resolution of the Semantical Antinomies with that of Tarski', The Journal of Symbolic Logic 41, 747-760.
Church, A.: 1984, 'Russell's Theory of Identity of Propositions', Philosophia Naturalis 21, 513-522.
Cocchiarella, N.: 1980, 'The Development of the Theory of Logical Types and the Notion of Logical Subject in Russell's Early Philosophy', Synthese 45, 71-115.
Cocchiarella, N.: 1986, 'Frege, Russell, and Logicism: A Logical Reconstruction', in L. Haaparanta and J. Hintikka (eds.), Frege Synthesized, Reidel, Dordrecht, pp. 197-252.
Goldfarb, W. D.: 1989, 'Russell's Reasons for Ramification', in C. W. Savage and C. A. Anderson (eds.), Rereading Russell: Essays in Russell's Metaphysics and Epistemology, University of Minnesota Press, Minneapolis, pp. 22-40.
Hylton, P.: 1990, 'Logic in Russell's Logicism', in D. Bell and N. Cooper (eds.), The Analytic Tradition, Basil Blackwell, Oxford, pp. 137-172.
Hylton, P.: 1993, 'Functions and Propositional Functions in Principia Mathematica', in A. D. Irvine and C. A. Wedeking (eds.), Russell and Analitic Philosophy, University of Toronto Press, Toronto, pp. 342-360.
Landini, G.: 1993, 'Reconciling PM's Ramified Type Theory with the Doctrine of the Unrestricted Variable of the Principles', in A. D. Irvine and C. A. Wedeking (eds.), Russell and Analitic Philosophy, University of Toronto Press, Toronto, pp. 361-394.
Martino, E.: forthcoming, 'Russellian Type Theory and Semantical Paradoxes, to appear in C. A. Anderson and M. Zeleny (eds), Logic, Meaning and Computation: Essays in Memory of Alonzo Church, Kluwer Academic Publishers, Dordrecht.
Myhill, J.: 1979, 'A Refutation of an Unjustified Attack on the Axiom of Reducibility', in G. W. Roberts (ed.), Bertrand Russell Memorial Volume, Allen and Unwin, London, pp. 81-90.
Pears, D.: 1983, 'Russell's 1913 Theory of Knowledge Manuscript', in C. W. Savage and C. A. Anderson (eds.), Rereading Russell: Essays in Russell's Metaphysics and Epistemology, University of Minnesota Press, Minneapolis, pp. 169-182
Russell, B.: 1903, The Principles of Mathematics, Cambridge University Press, Cambridge.
Russell, B.: 1908, 'Mathematical Logic as Based on the Theory of Types', American Journal of Mathematics, 30, reprinted in R. C. Marsh (ed.), Logic and Knowledge, Allen and Unwin, London 1956, pp. 59–102.
Russell, B.: 1910, Principia Mathematica, Cambridge University Press, Cambridge.
Russell, B.: 1910–11, 'Knowledge by Acquaintance and Knowledge by Description', Proceedings of the Aristotelian Society, 11, 108-28, reprinted in B. Russell, Mysticism and Logic, Routledge and Kegan Paul, London 1963.
Russell, B.: 1912, The Problems of Philosophy, London, Oxford University Press, reprinted by Hackett Pub. Co., Indianapolis 1991.
Russell, B.: 1913, 'Theory of Knowledge: The 1913 Manuscript', in E. R. Eames and K. Blackwell, K. (eds.), The collected Papers of Bertrand Russell, vol. 7, Allen and Unwin, London 1984.
Russell, B.: 1914, Our Knowledge of the External World, Allen and Unwin, 2nd ed., London 1926.
Russell, B.: 1918–19, 'The Philosophy of Logical Atomism', The Monist 28, 495-527; 29, 32–63, 190–222, 345–80, reprinted in R. C. Marsh (ed.), Logic and Knowledge, Allen and Unwin, London 1956, pp. 177–281.
Sainsbury, R. M.: 1979, Russell, Routledge and Kegan, London.
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Giaretta, P. Liar, Reducibility and Language. Synthese 117, 355–374 (1998). https://doi.org/10.1023/A:1005076008996
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DOI: https://doi.org/10.1023/A:1005076008996