¹ I am indebted to my colleague, Father Synan, E. A., for calling my attention to the following quotations, which suggest that Aquinas may even have anticipated the specifically Kantian conception of analyticity. Summa Contra Gentiles, 10:Google Scholar ‘… those propositions ought to be the most evident in which the same thing is predicated of itself, for example, man is man, or whose predicates are included in the definition of their subjects, for example, man is an animal' (Aquinas, St Thomas, On the Truth of the Catholic Faith, Summa Contra Gentiles, translated by Pegis, Anton C., Book 1: God. [Garden City, New York, 1955], p. 80).Google Scholar Commentary on Aristotle's, De Anima, II, 14 (at 418a26):Google Scholar ‘“Essentially” [‘per se’] is said in two ways. In one way, when the predicate of a proposition falls within the definition of the subject, e.g. “man is an animal”; for animal enters into the definition of man…’ (Aristotle's De Anima in the Version of William of Moerbeke and the Commentary of St Thomas Aquinas, translated by Foster, Kenelm and Humphries, Silvester [London, 1951], p. 263).Google Scholar

² Summa Theologica 1, Q 25, art. 3;Google Scholar the quoted words are to be found in Basic Writings of St Thomas Aquinas, edited by Pegis, Anton C. (whose Preface attributes the translation largely to Laurence Shapcote), vol. 1 (New York, 1945), p. 263;Google Scholar the very next article (art. 4) in Summa Theologica is devoted to the denial that God can make the past not to have been, inasmuch as ‘that the past should not have been implies a contradiction’ and ‘nothing that implies a contradiction falls under the scope of God's omnipotence’ (Ibid. p. 265). Aquinas' actual words in the last quoted sentence (as reproduced in his Opera Omnia, Vol. 1, Parma, 1852, p. 113)Google Scholar read, ‘sub omnipotentia Dei non cadit aliquid quod contradictionem implicat’ (‘anything that implies a contradiction does not fall under God's omnipotence’), and it is words like these which Lev Shestov is quoting in the Athens and Jerusalem passage cited below (see footnote 8 of this paper).

³ See, e.g. Wolter, Allan B. O.F.M., ‘Ockham and the Textbooks: On the Origin of Possibility’, Franziskanische Studien, XXXII (1950), 70–96.Google Scholar

⁴ Letter (to Denis Mesland) of 2 May 1644 (Descartes, , Philosophical Letters, translated by Kenny, Anthony, Oxford, 1970, pp. 150–1).Google Scholar It appears that even Descartes sometimes made what might well appear (though not perhaps to him) as exceptions to his absolute denial that the power of God could have any limits whatever, specifically admitting the impossibility of its ever being brought about that what has happened should not have happened, and insisting that it marks no deficiency of power in God that He does not do that. Or was he only arguing ad hominem when he appeared to concede as much to Henry More in his letter to him of 5 February 1649? In that letter of his to More, Descartes maintains that dividing atoms is definitely something perceived to be possible, unlike changing the past. ‘We do not take it’ as marking any impotence in someone to be unable to do a thing whose possibility we do not understand, Descartes says, but only things that we do distinctly perceive to be possible. However, Descartes argues, changing the past is something which we perceive to be altogether impossible, and therefore God is no less all-powerful for not doing that. But, in the letter to Mesland quoted in the text, Descartes made the point that our perceiving something to be impossible (and even its being impossible) did not mean that God could not have made it possible and even, indeed, actual. So that our perception that changing the past is impossible would not, perhaps, definitely establish for Descartes that even God could not do it. See Oeuvres de Descartes, edited by Adam, Charles and Tannery, Paul, Correspondance V (Paris, 1974), p. 273, lines 7–26.Google Scholar

⁵ Zenkovsky, V. V., A History of Russian Philosophy, Vol. II (translated by Kline, George L., New York and London, 1953, p. 785)Google Scholar gives reasons for the conclusion that Shestov was indeed a Jew who converted. However, Wernham, James C. S., Two Russian Thinkers, an Essay in Berdyaev and Shestov (Toronto, 1968, p. 102)Google Scholar, remains unconvinced.

⁶ Shestov, Leon, ‘In Memory of a Great Philosopher: Edmund Husserl’, translated by Kline, Geroge L., Philosophy and Phenomenological Research, XXII (1962), p. 461.Google Scholar

⁷ Ibid. p. 468.

⁸ Shestov, Lev, Athens and Jerusalem, translated by Martin, Bernard (Athens, Ohio, 1966), p. 309.Google Scholar (The first row of dots in the passage here is found in the text quoted.)

⁹ In our own day Professor Michael Dummett questions the supposition that to pray for something to have taken place is to pray for something which is logically excluded in every case. Apart from the psychological intelligibility of such a prayer, the point which Dummett is making is a verificationist one, in the spirit of Ayer's, A. J.Language, Truth and Logic.Google Scholar The move contemplated is the audacious step of equating an event's having occurred in the past with the existence now (or hereafter) of sufficient empirical evidence for that occurrence. On this basis, Dummett suggests we could conclude that the past is often indeterminate, as in the absence of sufficient evidence it would be neither true now that a particular event has actually occurred nor be true now that it had not occurred. Bold as this position is, it manifestly falls short of the Shestovian claim that up to a certain time a particular past event has really and determinately taken place previously and after that time it has really and determinately not taken place previously. (Dummett explains himself in two papers of his, ‘Bringing About the Past’ and ‘The Reality of the Past’, reproduced in his collection, Truth and Other Enigmas [Cambridge, Massachusetts, 1978], pp. 333–50 and 358–74 respectively.Google Scholar Ayer had originally proposed the reduction of facts about the past to verifying experiences in the (present and) future, in the first edition of Language, Truth and Logic, London, 1936, pp. 146–8.Google Scholar In the second edition [London, 1946, Introduction, pp. 18–19, and Chapter V, p. 102 n. I], he says or implies that that was not really what he meant there. Then in Philosophical Essays [London, 1954], p. 184Google Scholar, he again opposes the reductionist view of the past, while admitting that he did himself once advocate it.)

¹⁰ In Shestov's own case we are implicitly invited to connect the preoccupation with divine intervention to change the past in miraculous response to the prayers of suffering humanity, with the biographical fact that ‘something most terrible happened to him’ once, according to Lazarev, A. M., his ‘intimate friend for forty years’.Google Scholar (See Lazareff, Adolphe, Vie et connaissance, essais traduits du russe par B. de Schloezer, [Paries, 1948].Google Scholar The quoted remark about Shestov's biography occurs on p. 11; the characterization of Lazarev as having been his intimate friend is made on p. 5, in the Preface contributed by N. A. Berdyayev.)

¹¹ ‘A deductive argument is valid when its premisses, if true, do provide conclusive grounds for its conclusion, that is, when premisses and conclusion are so related that it is absolutely impossible for the premisses to be true unless the conclusion is true also’ (Copi, Irving M., Introduction to Logic, 5 edn [New York, 1978], p. 32).Google Scholar

¹² Traciatus Logico-Philosophicus, 2.2–2.05, 4.46–4.46; cf. Philosophical Investigations I, 513.Google Scholar

¹³ Goldstick, D., ‘Why We Might Still Have a Choice’, Australasian journal of Philosophy, LVII (1979), 305.CrossRefGoogle Scholar

¹⁴ See Leibniz's Theodicy, Essays on the Justice of God and the Freedom of Man in the Origin of Evil, Part Three, paragraphs 282, 367, 369, and Summary of the Controversy, Reduced to Formal Arguments, Objection III, Answer, and Objection VIII, Answer (Theodicy, by Leibniz, G. W., translated by Huggard, E. M. [London, 1952], pp. 298–300, 345, 346–7, 380–2, 386–8).Google Scholar However, Leibniz did specifically deny divine power to make a contradiction true. (After all, only if God were powerless to make a contradiction true would this world being the best of all logically possible worlds excuse Him from acting omnipotently to correct the manifest evils in it.)

¹⁵ See his paper, ‘On the Concept of Logical Consequence’, reproduced in the collection of his papers, Logic, Semantics, Metamathematics, by Tarski, Alfred, translated by Woodger, J. H. (Oxford, 1956), pp. 409–20.Google Scholar

¹⁶ Tractatus Logico-Philosophicus, 2.221–2.225.

¹⁷ ‘Even the statement of the syllogism itself in its most guarded form: “If ‘a’ is ‘b’ and if ‘c’ is ‘a’, then ‘c’ is ‘b’” does no more, at least as far as my own analysis can find, than sum up in compact form this general description of my past experience: namely, “whenever I have encountered an ‘a’ which was a ‘b’, and a ‘c’ which was an ‘a’, then always I have noticed that ‘c’ was also ‘b”’ (Bridgman, P. W., The Intelligent Individual and Society [New York, 1938], pp. 65–6).Google Scholar No doubt, if Bridgman had been somewhat more careful, he would rather have written here: ‘“whenever I have encountered some a's which were all b's and a c which was one of those a's, …”’

¹⁸ See his famous essay, ‘Two Dogmas of Empiricism’, reprinted in his collection, From a Logical Point of View, by Orman Quine, Willard Van (Cambridge, Massachusetts, 1953), pp. 20–46Google Scholar, and Word and Object, by Orman Quine, Willard Van (Cambridge, Massachusetts, 1960), Chapters I and II (pp. 1–79).Google Scholar In Goldstick, D., ‘Cognitive Synonymy’, Dialectica, XXXIV (1980), 183–203CrossRefGoogle Scholar, I propose an interpretation and rebuttal of Quine's arguments.

¹⁹ Op. cit. 1st edn, p. 92.Google Scholar Ayer continues, ‘Or else we must accept the Kantian explanation which, apart from the epistemological difficulties which we have already touched on, only pushes the mystery a stage further back.’

²⁰ Such a line of thought as this is, at any rate, frequently attributed to Wittgenstein. See his Philosophical Investigations I, 251.Google Scholar

²¹ Strawson, P. F., Introduction to Logical Theory (London, 1952).Google Scholar

²² 'Wouldn't this imply that we can't learn anything new about an object in mathematics, since, if we do, it is a new object?

'This boils down to saying: If I hear a proposition of, say, number theory, but don't know how to prove it, then I don't understand the proposition either. This sounds extremely paradoxical… when I learn the proof, I learn something completely new, and not just the way leading to a goal with which I'm already familiar.

'But in that case it's unintelligible that I should admit, when I've got the proof, that it's a proof of precisely this proposition….

‘…There can't be two independent proofs of one mathematical proposition’ (Wittgenstein, Ludwig, Philosophical Remarks, edited by Rhees, Rush, and translated from the German by Raymond Hargreaves and Roger White [Oxford, 1975], pp. 183–4).Google Scholar

The fact that Wittgenstein was himself concerned about this objection to his philosophy is certainly to his credit; but in no way does it make the objection less fatal.

²³ But can a validly arguing deductive reasoner really know more at the end of his reasoning, and thanks to it, than what he knew at the beginning in knowing the premises of the argument if, as is in fact the case, every step in (what goes on psychologically in a mind performing) a fully articulated valid deduction involves merely (at the most) a selective reorganization of what the reasoner already knows? Even such a mental process of reorganization should be seen as capable of effecting a genuine increase in a reasoner's knowledge, I have argued (‘Cognitive Synonymy’, op. cit. pp. 200–3).Google Scholar

²⁴ A task which I have attempted to carry out in Goldstick, D., ‘The Truth-Conditions of Counter-factual Conditional Sentences’, by Mind, LXXXVII, 345 (1978), I–21.CrossRefGoogle Scholar

²⁵ Ibid. p. 14.