Abstract
The mainstream of the development of modern logic since the pioneering days from Boole to Frege has moved very decidedly in the direction of mathematical interests and applications. And, in fact, mathematics continues to the present day to occupy a central position on the logical stage. This may be illustrated — among many other ways — by the current prominence of what might be characterized as ‘the arithmetical sector’ of logic, including algorithmic theory, recursive functions, the calculi of lambda conversion, the logical theory of computability and of effective processes generally, among other components of lesser renown. The computer, and the whole host of technical issues that revolve about it, have had an enormous and reciprocally stimulative impact on recent work in logic. Results of great importance and interest continue to be obtained in this mathematical sector of logic, witness Paul J. Cohen’s remarkable proof of the independence of the continuum hypothesis.
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References
G. H. von Wright, An Essay in Modal Logic (Amsterdam, 1951). A.N. Prior, Formal Logic (Oxford, 1955 ).
S.A. Kripke, ‘A Completeness Theorem in Modal Logic’, The Journal of Symbolic Logic 24 (1959) 1–14.
S.A. Kripke, ‘Semantical Considerations on Modal Logic’, Acta PhilosophicaFennica,fasc. 16(1963)83–94. (Cf. also J. Hintikka, ibid.,65–81).
R. Feys, Modal Logics (ed. J. Dopp), (Louvain and Paris, 1965). J. B. Rosser and A.R. Turquette, Many-Valued Logics (Amsterdam, 1952 ).
A. N. Prior, Formal Logic (Oxford, 1955 ).
R. Ackermann, An Introduction to Many-Valued Logics (London, 1967 ).
A.A. Zinov’ev, Philosophical Problems of Many-Valued Logic (Dordrecht, 1963 ).
See also pp. 116–125.
Wilhelm Ackermann, ‘Begründung einer strengen Implikation’, The Journal of Symbolic Logic 21 (1956) 113–128.
A. R. Anderson, ‘Completeness Theorems for the System E of Entailment and the System EQ of Entailment with Quantification’, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 6 (1960) 201–216.
A.R. Anderson and N.D. Belnap, Jr., ‘The Pure Calculus of Entailment’, The Journal of Symbolic Logic 27 (1962) 19–52.
P. T. Geach, Reference and Generality (Ithaca, 1962). (B 1) Logical Syntax
R. Carnap Logical Syntax of Language (London, 1937).
R. Carnap, Introduction to Semantics, ( Cambridge, Mass., 1946 ).
R. Carnap Meaning and Necessity (Chicago, 1958).
W.V. Quine Word and Object (New York, 1959).
A. Tarski, Logic, Semantics, Metamathematics (Oxford, 1960 ).
H.P. Grice, ‘Meaning’, ThePhilosophicalReview 66(1957)377–388.
S. Toulmin The Uses of Argument (Cambridge, 1958).
R. M. Martin, Towards a Systematic Pragmatics (Amsterdam, 1959 ).
C. Perelman Traité de l’argumentation (Paris, 1958).
C. Perelman, The Idea of Justice and the Problem of Argument, tr. J. Petrie (New York, 1963 ).
J. Lyons Structural Semantics (London, 1963).
N. Chomsky, Aspects of the Theory of Syntax ( Cambridge, Mass., 1965 ).
J. J. Katz, The Philosophy of Language (New York, 1966 ).
G. H. von Wright Norm and Action (London, 1963).
N. Rescher (ed.), The Logic of Decision and Action (Pittsburgh, 1967 ).
G.H. von Wright, An Essay in Modal Logic (Amsterdam, 1951).
A.R. Anderson, The Formal Analysis of Normative Systems (New Haven 1956); reprinted in N. Rescher (ed.) The Logic of Decision and Action (Pittsburgh, 1967 ).
L. Bergstrom, Imperatives and Ethics (Stockholm, 1962).
N. Rescher, The Logic of Commands (London, 1966 ).
S. Hal1dén, On the Logic of ‘Better’ (Uppsala, 1957; Library of Theoria, no. 2).
G. H. von Wright, The Logic of Preference (Edinburgh, 1964 ).
R. C. Jeffrey, The Logic of Decision (New York, 1965). See also pp. 318–320.
Dana Scott, ‘Existence and Description in Formal Logic’ in R. Schoenman (ed.), Philosopher of the Century, Essays in Honor of Bertrand Russell (London, 1967 ).
B. van Fraassen, ‘The Completeness of Free Logic’, Zeitschrift für Mathematische Logik and Grundlagen der Mathematik 12 (1966) 219–234.
A.N. Prior, Time and Modality (Oxford, 1957 ).
G. H. von Wright, ‘And Next’, Acta Philosophica Fennica, fasc. 18 (1965) 293–304.
A. N. Prior, Past, Present, and Future (Oxford, 1967). See also pp. 221–223.
A. Tarski, ‘Appendix E’ to J. H. Woodger, Axiomatic Method in Biology (London, 1937 ).
N. Goodman and H. S. Leonard, ‘The Calculus of Individuals’, The Journal of Symbolic Logic 5 (1940) 45–55.
E. C. Luschei, The Logical Systems of Lesniewski (Amsterdam, 1962 ).
N. Goodman, The Structure of Appearance ( Cambridge, Mass., 1951 ).
W.V. Quine, ‘On What There is’, The Review of Metaphysics 2 (1948); reprinted in idem, From a Logical Point of View ( Cambridge, Mass., 1953 ).
A. Church, ‘The Need for Abstract Entities in Semantic Analysis’, Proceedings of the American Academy of Arts and Sciences 80 (1951) 100–112.
N. Goodman The Structure of Appearance (Cambridge, Mass., 1951).
D. Harrah Communication: A Logical Model (Cambridge, Mass., 1963).
N.D. Belnap, Jr. An Analysis of Questions: Preliminary Report (Santa Monica, 1963).
L. Aqvist A New Approach to the Logical Theory of InterrogativesPt. 1 (Uppsala, 1965).
J. Los. See the review of his Polish paper by H. Hiz in The Journal of Symbolic Logic 16 (1951) 58–59.
J. Hintikka, Knowledge and Belief (Cornell, 1962 ).
See also pp. 280–281.
S. Ja§kowski, ‘On the Rules of Suppositions in Formal Logic’ Studia Logicano. 1 (Warsaw, 1934).
N. Rescher, Hypothetical Reasoning (Amsterdam, 1964). David Harrah Communication: A Logical Model (Cambridge, Mass., 1963).
Y. Bar-Hillel, Language and Information (Jerusalem, 1964 ).
R. Carnap Logical Foundations of Probability (Chicago, 1950; 2nd ed., 1960).
H. E. Kyburg, Jr., ‘Recent Work in Inductive Logic’ American Philosophical Quarterly 1 (1964) 249–287.
R. Carnap Logical Foundations of Probability (Chicago, 1950, 2nd ed., 1960).
R. Carnap, The Continuum of Inductive Methods (Chicago, 1952). J. G. Kemeny. Carnap, The Continuum of Inductive Methods (Chicago, 1952). J. G. Kemeny, ‘A Logical Measure Function’, The Journal of Symbolic Logic 18 (1953) 289–308.
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Rescher, N. (1968). Recent Developments in Philosophical Logic. In: Topics in Philosophical Logic. Synthese Library, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3546-9_1
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