A. N. Prior

Thank Goodness that's Over

In a pair of very important papers, namely “Space, Time and Individuals” (STI) in the Journal of Philosophy for October 1955 and “The Indestructibility and Immutability of Substances” (IIS) in Philosophical Studies for April 1956, Professor N. L. Wilson began something which badly needed beginning, namely the construction of a logically rigorous “substance-language” in which we talk about enduring and changing individuals as we do in common speech, as opposed to the “space-time” language favoured by very many mathematical logicians, perhaps most notably by Quine. This enterprise of Wilsons is one with which I could hardly sympathize more heartily than I do; and one wishes for this logically rigorous “substance-language” not only when one is reading Quine but also when one is reading many other people. How fantastic it is, for instance, that Kotarbinski1 should call his metaphysics “Reism” when the very last kind of entity it has room for is things —instead of them it just has the world-lines or life-histories of things; “fourdimensional worms”, as Wilson says. Wilson, moreover, has at least one point of superiority to another rebel against space-time talk, P. F. Strawson; namely he (Wilson) does seriously attempt to meet formalism with formalism—to show that logical rigour is not a monopoly of the other side. At another point, however, Strawson seems to me to see further than Wilson; he (Strawson) is aware that substance-talk cannot be carried on without tenses, whereas Wilson tries (vainly, as I hope to show) to do without them. Wilson, in short, has indeed brought us out of Egypt; but as yet has us still wandering about the Sinai Peninsula; the Promised Land is a little further on than he has taken us.

The Notion of the Present

Before directly discussing the notion of the present, I want to discuss the notion of the real. These two concepts are closely connected; indeed on my view they are one and the same concept, and the present simply is the real considered in relation to two particular species of unreality, namely the past and the future. So let’s begin with the real in general.

The Formalities of Omniscience

WHAT do we mean by saying that a being, God for example, is omniscient? One way of answering this question is to translate ‘God is omniscient’ into some slightly more formalised language than colloquial English, e.g. one with variables of a number of different types, including variables replaceable by statements, and quantifiers binding thes.

Calculi of Pure Strict Implication

In July 1956 the following problem was proposed by D. Meredith: To axiomatise a propositional calculus with strict implication as the sole undefined functor. Using ‘C1–5’ for those portions of Lewis’s S1–5 which are expressible in terms of strict implication alone, this problem was solved for C5 in August 1956 by C. A. Meredith, who proved the adequacy of the single axiom CCCCCttpqCrsCCspCuCrp, with substitution and detachment (Sections IX-XI below). A variety of connected results were obtained by the authors on the way to this one. In what follows, we shall generally indicate who is chiefly responsible for which results; but it may be noted now that results relating to systems weaker than C5 (which will be mentioned from time to time in different sections) and also references to other items in the literature, are mainly due to Lemmon.

Epimenides the Cretan

What I am offering here is a reconsideration, and in the end a solution, of the ancient paradox of the Epimenides. What has provoked this new assault on so old a stronghold is L. Jonathan Cohens [2], in which it is rightly pointed out that the Epimenidean as contrasted with the Eubulidean version of the Liar paradox is the one that threatens logicians who attempt to formalise the use of indirect rather than direct discourse. Among these he includes myself, referring to the system sketched on pp. 130–131 of my [4], and suggesting that I ought to have shown how a person interpreting this system in the obvious way can avoid semantic antinomies. Here too he is right, and my main purpose now is not to criticise his paper, but to fill in this lacuna in my own work to which he has drawn attention. I do want, however, to make one small criticism at the start, namely that Cohen fails to notice what it is that is really paradoxical about the Epimenides, and in consequence fails to perceive the same paradoxical character in a proposition which he is himself quite happy to accept as a ‘logical truth.’ The point about the Epimenides, as was noted by Church in [1], is not that when we examine the truth value of a Cretans assertion that nothing true is ever asserted by a Cretan we are led to contradictory conclusions, for we are not; the paradox is rather that such examination makes it seem possible to settle an empirical question on logical grounds. If we treat the Cretans assertion as true, and so assume that nothing true is ever asserted by a Cretan, it follows immediately that the Cretans assertion is false. If, however, we treat it as false, there is no way of deducing from this assumption that it is true. We can, therefore, consistently suppose it to be false, and this is all that we can consistently suppose. But to suppose it false (considering what the assertion actually is) is to suppose that something asserted by a Cretan is true; and this of course can only be some other assertion than the one mentioned. We thus reach the peculiar conclusion that if any Cretan does assert that nothing asserted by a Cretan is true, then this cannot possibly be the only assertion made by a Cretan — there must also be, beside this false Cretan assertion, some true one.

Two Additions to Positive Implication

Let LIC be the implicational fragment of Dummetts LC, axiomatised by Bull in [1] by adding the axiom (L) CCCpqrCCCqprr to positive implication. The system which Bull in [2] calls OIC, i.e. positive implication plus (0) CCCCpqqrCCCpqrr , is contained in LIC (it is thesis 34 in [1], p. 193); but it does not contain it, as the following matrix (due to Bull) verifies OIC but not (L) (CCC342CCC4322 = 2). Nor is (L) deducible in OIC supplemented by intuitionist axioms for negation, since the latter are all verified by the above matrix with Cp 5 for Np .

Faith, unbelief and evil: a fragment of a dialogue

The man who is isolated over against God is as such rejected by God. But to be this man can only be the choice of the Godless man himself. The witness of the Community of God to every individual man points in this direction: that this choice of the Godless is null and void, that he belongs to Jesus Christ from eternity and thus is not rejected, but rather chosen by God in Jesus Christ, that the reprobation which he deserves on the basis of his wrong choice is borne and removed by Jesus Christ; that on the basis of the true, the Divine choice he is chosen for eternal life with God. The promise of his election will determine him as a member of the Church to become himself a carrier of its witness to the whole world. And the revelation of his rejection can determine him only to believe in Jesus Christ as Him by whom it is borne and removed. (Fourth of Karl Barth’s “main theses” on God’s Election of Grace in his Dogmatic II/2)1

The logic of obligation and the obligations of the logician

Moral philosophers have sometimes claimed to deduce particular duties from the very nature of obligation. It would now be agreed by most that this cannot be done; and with this general view I have no serious quarrel. Yet there are1 forms of reasoning which in some sense owe their cogency to ‘the very nature of obligation’2. For example, if it is not possible to do A without doing B, we may infer that if it is permissible to do A, then it is permissible to do B. ‘Possible’ is a notoriously ambiguous word; so let it be understood that bare logical possibility is intended. It is impossible, for example, that John Jones should at once be drinking tea in the kitchen and not drinking tea; ergo, if it is permissible that he be drinking tea in the kitchen, it is permissible that he be drinking tea, i.e. it is not obligatory that he be not drinking it. No one, I think, would quarrel with this form of inference. And it holds because obligation (in terms of which permissiblity may be defined) is what it is. Replace ‘permissible’ by, for example, ‘not the case’, and the inference loses its cogency. (‘It is impossible to do A without

The fable of the four preachers

There was once a rather small town in Massachusetts that had four churches—far too many for the population, so that some sort of amalgamation was felt to be desirable. Repeated conferences succeeded in bringing about considerable agreement, but on one issue there was a deadlock, namely the nature of immortality. In what we may call Sect A, it was firmly believed that “death is not the end”, and that when this life is over we go to another place, where our happiness or misery depend on whether we have behaved well or ill down here. It was also insisted by Sect A, however, that in the other world we have no memories at all of the present one. In Sect B, which was perhaps themost “advanced” or “modernistic” of the four, it was just as firmly believed that death is the end, and that no one lives again. The adherents of Sect B, however, did not go so far as to say that there is no other world; on the contrary, they believed in its existence just as firmly as the adherents of Sect A. They believed, further, that as soon as anyone in our own world dies, another person—quite a different person—comes into being in the other world; and that Providence has so arranged it that the happiness or misery of this other person depends on whether the person who has just died has behaved well or ill during his life (his only life, of course). Sects C and D we shall consider a little later. With regard to Sects A and B, there were some low sceptics in the town who held that the difference between these two was merely a verbal one; they just could not see any real difference, they maintained, between saying that the persons in the other world have no memories of a life in this one, and saying that they had never lived in this one at all (their detailed experience, in the other world, being agreed to be exactly the same in either case). The adherents of

The paradox of the prisoner in logical form

The following is a simplified form of a paradox1 which has been circulating for a year or two2: On a certain Saturday a judge sentenced a man to be hanged on Sunday or Monday at noon, stipulating at the same time that the man would not know the day of his hanging until the morning of the day itself. The condemned man argued that if he were hanged on Monday, he would be aware of the fact by noon on Sunday, and this would contravene the judge’s stipulation. So the date of his hanging would have to be Sunday. Since, however, he had worked this out on Saturday, and so knew the date of his hanging the day before, the judge’s stipulation was again contravened. The date, therefore, could not be Sunday either. The prisoner concluded that he would not be hanged at all. However, he was—on Sunday or Monday (it does not matter which),