1. “The representation of logic as conceived with a characteristic of sentences, truth, rather than of transitions from sentences to sentences, had deleterious effects both in logic and philosophy.“ Michael Dummett, Frege: Philosophy of Language, Duckworth, London, 1973, pp. 432–433. Dummett’s remark is quoted with approval by Ian Hacking, for whom ”logic is the science of deduction“ in accordance with ”rules of inference“ like Gentzen’s introduction and elimination rules. See Ian Hacking, ‘What Is Logic?’ Journal of Philosophy
76, 285–319, quoting from pp. 292–293; and Gerhard Gentzen, ‘Investigations into Logical Deduction’, a translation of a 1935 paper by M. E. Szabo in The Collected Papers of Gerhard Gentzen, North Holland, Amsterdam, 1969, pp. 68–131. See also W. C. Kneale, `The Province of Logic’, in H. D. Lewis, Contemporary British Philosophy, Third Series, Allen and Unwin, London, 1956.
2. For an example, see my “Reasoning and Evidence One Does Not Possess’, Midwest Studies in Philosophy
5 1980, 163–182, esp. p. 172.
3. Gottlob Frege, Grundgesetze (1893), partial translation by M. Furth, The Basic Laws of Arithmetic, University of California Press, Berkeley, 1967, pp. 12–13.
4. W. V. Quine, Methods of Logic, Holt, Rinehart, and Winston, New York, 1972, pp. 1–5.
5. Quine, Methods of Logic,p. 39, and ‘Truth by Convention’, in The Ways of Paradox,Random House, New York, 1966, pp. 70–99. I will say more about this article in the text below.