- In the palmy days of Gladstone and Keble an Oxford double first meant a first obtained simultaneously in Classics and Mathematics. Twentieth-Century Oxonians are more feeble, and 'a double first' nowadays is usually a description of someone placed in the first class in both the First and the Second Public Examination in what is more or less the same subject. Amongst my own contemporaries John Lucas was remarkable for having been placed in the first class in 1948 by the Mathematical Moderators and again in the first class in 1951 by the Examiners in Literae Humaniores. It is not surprising therefore that this book he has written requires expertise in both fields if it is to be fully understood – which means, I fear, that few will fully understand it.
- In Louvain in the Fifteenth Century there was a fierce dispute between Peter de Rivo and Ferdinand of Cordova. Both were attempting a refutation of the determinist argument which Aristotle had set out in his famous Sea-Battle chapter. If someone yesterday had said that in two days' time there would be a sea-battle, given that what she said was true then, nothing that anyone can do now can prevent tomorrow's sea-battle, since what is past is fixed. Peter de Rivo avoided this result by denying that the statement made yesterday was capable then of being true or false, Ferdinand of Cordova by denying that someone who asserts the proposition 'The remark made yesterday was true' makes a statement about the past. Lucas comes down on the side of Peter de Rivo. He will be relieved to know that the Pope came down on the side of Ferdinand of Cordova. Those who accept a 'prosentential' theory of truth will find it easy to accept the papal decision: if Dinah yesterday said that in two days' time there would be a sea-battle, the proposition that what Dinah said was true is tantamount to this: Dinah said yesterday that in two days' time there would be a sea-battle and tomorrow there will be a sea-battle. This proposition is at least partly about the future, so there is no reason to suppose that it is about something that is now unpreventable.
- Believing that what will be true tomorrow was not necessarily true yesterday, Lucas introduces a system of 'temporal viewpoints': this allows for nonvacuous iteration of operators of the form 'It is the case at time t1 that'. 'It is the case at time t1 that it is the case at time t2 that p' may well differ in truth value from 'It is the case at time t1 that p'. This is thought of as a development of Reichenbach's doctrine of reference points, which he used to explain the difference between the aorist and the perfect tenses. Strangely, Lucas has other more plausible explanations of this difference (sentences containing verbs in the aorist are elliptical), and Reichenbach's obscure theory is little more than a red herring.
- Much of the middle of the book is given over to a development of this 'logic of temporal viewpoints', which is given a syntax and a semantics. The semantics is based on an array of 'trees', models of branching futures. Lucas recognizes that there is a different way of using these trees: the branches can be considered as different possibilities for the future; the trunk the area where earlier possibilities have been actualized, where no further alterations are open to us. This way of looking at things gives us a tensed modal logic1, in which the Law of Bivalence is restored. Arguably, the supposed logic of temporal viewpoints is nothing other than this tensed modal logic2, seen through distorting lenses.
- Lucas is above all an antideterminist. His views about truth are his means of avoiding the conclusion of the sea-battle argument. His theological views are also determined by these antideterminist concerns. God too moves through time in a world of foreclosing opportunities. He is better at predicting than you or I, but you and I, in virtue of our freedom, have the power to falsify even God's predictions. Time can do much: it can delay the coming of age of a proposition (when it receives a truth-value), it can render God mistaken. Lucas has written a book full of such controversial theses. The science with which he nearly blinds us is not in the end impossible even for the theologian. The theology is quarantined in the third and the last chapters, so it need not deter the scientist. The book is provocative, but the provocation is thoroughly enjoyable.
Review of "Lucas (J.R.) - The Future - An Essay on God, Temporality and Truth".
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