LOGIC AND REALITY: ESSAYS ON THE LEGACY OF ARTHUR PRIOR.
Arthur Prior was a truly philosophical logician. Though he believed formal logic to be worthy of study in its own right, of course, the source of Prior's great passion for logic was his faith in its capacity for clarifying philosophical issues, untangling philosophical puzzles, and solving philosophical problems. Despite the fact that he has received far less attention than he deserves, Prior has had a profound influence on the development of philosophical and formal logic over the past forty years, a fact to which the present volume bears eloquent witness. The genesis of the volume was the 1989 Arthur Prior Memorial Conference, held appropriately enough at the University of Canterbury in Christchurch, New Zealand, where Prior had his first appointment in philosophy. However, this is not a volume of proceedings. Only eight of the twenty-two essays were actually presented at the conference. The rest (with the exception of three previously unpublished essays by Prior) were solicited by the editor specially for the volume. The subtitle--Essays on the Legacy of Arthur Prior--is an appropriate one. Few of the essays devote much space to Prior's work per se. Rather, most address issues that, if not first raised by Prior, were revisited by him and subjected to his typically keen and distinctively original analysis. The papers themselves divide pretty evenly into the technical and the less technical. In this short review I will focus on the latter.
The volume opens with Copeland's informative overview of Prior's all too brief life that sets the stage nicely for the essays to follow. Copeland focuses on Prior's contributions to modal and tense logic, and pays particular heed to the extent to which Prior anticipated the possible-worlds semantics associated most often with Kripke's name. Notably, in the paper "Interpretations of Different Modal Logics in the `Property Calculus'"--included in the volume--Prior and his collaborator Carew Meredith sketched all the basic elements of possible-worlds semantics. Importantly, though, the presentation of these results is proof theoretic in form: modal operators are simply defined in terms of the quantifiers, rather than being interpreted semantically as quantifiers.
The proof-theoretic character of the account is explained in part by its 1956 date, at which point developments in the semantics of modal logic were still rather inchoate. However, it is also plausible that the proof-theoretic approach reflects the fact that Prior would have been loathe to consider possible-worlds semantics a genuine semantics for modal discourse. As Lloyd Humberstone points out in his contribution, Prior took worlds to be world propositions, that is, propositions p such that [inverted]A q((p [right arrow] q) [equivalence] [diamond] (p [conjunction] q)). Propositions, in turn, Prior viewed as logical constructions to be analyzed ultimately in terms of primitive modal notions. Prior would thus have been strongly inclined toward the sort of homophonic semantics that Humberstone develops. In a homophonic modal semantics, modal operators are interpreted in terms of primitive notions of necessity and possibility in the metalanguage, rather than in terms of possible worlds. Humberstone proves soundness and completeness theorems for modal logic relative to such a model theory; the completeness theorem is particularly interesting, as he is forced to confront problems of construction that have no parallel in an extensional semantics.
This is not to say that all is well with Prior's analysis. In his piece on propositional quantification, Mark Richard argues convincingly that Prior's view that propositions are logical constructions is inadequate, as it provides no systematic account of the truth conditions of sentences that quantify into intentional contexts. Furthermore, Richard argues (again, convincingly) that substitutional quantification falters on much the same point. Richard concludes that quantification into intentional contexts must be objectual. However, wishing to remain faithful to Prior's rejection of intensions, Richard attempts to see how far he can push an extensional notion of proposition. The account is surprisingly robust, but faces a major hurdle. For Richard's account of the semantics of the modal operators appeals to possible worlds. Unwilling to take worlds as semantical primitives, Richard admits that, to avoid intensions, he also needs an extensional account of possible worlds. However, Humberstone's semantics suggests that perhaps Richard is giving up too much here--he needn't adopt possible world semantics if he is willing to live with intensional primitives.
Roger Teichmann offers clever, allegedly nominalist, analyses of statements of property identity and event identity. Insofar as it involves second-order quantifiers the account is very Priorean. But Richard's paper is relevant here, as his criticism of Prior's analysis of propositional quantification seems to generalize to Teichmann's use of general second-order quantifiers in his account. If Richard is correct, these quantifiers must be objectual. If so, it seems that Teichmann owes us a nonintensional, objectual semantics before his account can be counted as a nominalist success story.
Many philosophers, of course, have no qualms about ontological commitment to intensions. Despite his own desire to avoid them, Prior's views are highly relevant to discussions of the nature of intensional entities. Much of the character of Prior's work in quantified modal logic derives from his firm commitment to actualism--the view that only actually existing things exist in any sense--and his belief that there is no singular information about nonexistents; had Quine failed to exist, there would have been no information about him, not even that he fails to exist. (Crucial to this view is that Prior took names like `Quine' to be logically proper names whose meaning is their reference. In his contribution, Lambert argues that Prior fails to make clear sense of the notion of a logically proper name.) Translated into talk about intensions, Prior's view about singular information is an instance of the doctrine Alvin Plantinga has dubbed existentialism, namely, that singular propositions, properties, and relations are ontologically dependent upon the individuals they "involve," or are "about." Thus, for the existentialist, if Quine hadn't existed, neither would the proposition Quine is a philosopher have existed. Plantinga has argued that existentialism is false. In response, in his contribution, Peter Loptson proffers a modal semantics (similar to ones suggested by Fine, Adams, Almog, and Loptson himself in earlier work) that enables him to identify a subtle ambiguity in Plantinga's argument that renders it unsound.
Prior's research in tense logic is perhaps his deepest and most original work. Copeland provides a valuable service in his introduction by tracing the early history of this research. The book also benefits greatly from two short, previously unpublished pieces by Prior in which he elaborates his temporal realism about past, present, and future: time genuinely passes; formerly future events become present (assuming we endorse future events), and present events become irrevocably past. In McTaggart's terms (roughly), history is a dynamic "A-series" of past, present, and future. This contrasts sharply with the view that the world's history is a "timeless tapestry" of events complete from beginning to end "with everything laid out for good and all," devoid of passage, and with no absolute, objective present--roughly, McTaggart's "B-series."
The linguistic correlate of Prior's position is that tense, like modality, is irreducible. Just as Prior argued that talk about other possible worlds should be analyzed in terms of the primitive modal notions of possibility and necessity, so he argued that talk about times ("B-sentences") should be analyzed in terms of the primitive temporal notions of past, present, and future ("A-sentences"). For example, X is earlier than Y should be understood as: It either was, is, or will be the case that X was past and Y is present. (Prior would further analyze away the apparent reference to events here as well.) Richard Sylvan examines both Prior's arguments for this primacy of the A-sentences and an argument of McTaggart's, as reworked by D. H. Mellor, that the A, series is contradictory and hence that A-sentences must be reduced to B-sentences. Sylvan argues that Prior's position founders on its inability to represent certain B-sentences about time. He does not find any comparable problem for the view that B-sentences are primary, but points out instead simply that Mellor's argument against the coherence of the A-series is unsound.
Prior was not unaware of the sort of difficulty Sylvan points to, but maintained his temporal realism for both phenomenological and metaphysical reasons. These arguments are laid out clearly in the two essays on temporal realism. Phenomenologically, Prior points to our experience of time's passage (as manifested particularly in our experiences of relief, sadness, regret, etc. about certain affairs now being past) and argues that no sense can be made of this experience on the B-series view. Prior's metaphysical objection is that the B-series forces us to put all objects throughout history on an equal ontological footing, a view Prior finds intuitively repugnant. The A-series, by contrast, with its distinguished present, permits one to express the thesis of presentism, the temporal analog of actualism: the only things that exist are the things that exist now. Sylvan does not address Prior's phenomenological argument, but dismisses the philosophical argument as simply expressing a "metaphysical hang-up"--a charge that does not do justice to the power of actualist/presentist intuitions.
The distinguished present of the A-series seems to entail a sort of absolutism about the present. In his article, Harre defends this view, arguing that an absolute present is essential to physics, in particular to the possibility of co-locating events. Harre deals with obvious objections from special relativity by arguing that the mathematics of special relativity is "auxiliary" rather than "representational," and that only the latter carries with it any ontological force. This position would seem to comport well with the A-series treatment of time, but Harre concludes that both A-series and B-series treatments are "alternative discourse forms for telling the history of the universe." It seems to the reviewer that this conclusion stems from Harre's dubious understanding of the A-series view as being essentially tied to consciousness.
As Prior notes, a major motivation for his preference for the A-series is his "belief in real freedom," his belief that there are, at each moment, genuine alternative possible futures that are actualized or not depending on which actions agents freely choose to perform. The open-ended character of the future, and its dependence on the choices of free agents, is captured with great formal rigor and precision in Belnap's contribution, in which he develops a lovely model theory of branching time with agents and choices. Although not formally difficult, Belnap's model theory is somewhat baroque. However, each piece of the apparatus is introduced with generous philosophical and technical motivation.
Graham Oddie's contribution complements Belnap's piece nicely. Oddie carefully attempts to reconstruct an argument of Prior's that the idea of the set of total consequences of an action (in both deterministic and libertarian settings) cannot be well defined, and hence that consequentialist moral theories depending on such an idea are bound to fail. After numerous unsuccessful (but instructive) attempts, Oddie finds a formulation of Prior's argument that appears to be immune to serious objection. He then skirts this argument by arguing for a conception of consequentialism that does not depend upon the coherence of the idea of the set of total consequences of an action.
The volume closes with articles by Priest and Resnik that expand upon arguments of Prior. Priest argues persuasively that Prior's reconstruction of an argument of Berkeley's for idealism is not faithful to the good Bishop, and offers a much more cogent reconstruction--one that Priest himself thinks is sound. The reviewer did not believe the conclusion, but has to admit that it is not obvious exactly where the false premise lies.
Resnik picks up on Prior's conviction that the bounds of logic cannot be determined a priori. In an interesting juxtaposition, Resnik then argues for a Rawlsian methodology for fixing the bounds of logic, as well as for a noncognitivist position that holds that there are no facts of logicality. But while there are no logical facts, on pragmatic grounds, Resnik argues that there ought to be only one logic.
The remaining essays concern Prior's formal legacy, with articles on applications of temporal logic in computer science, particularly database theory, and articles on modal proof theory and modal semantics. The authors are an impressive lot: Gabbay and Hodkinson, Rodriguez and Auger, van Benthem, Fine and Schurz, Segerberg, Bull, Bunder, and Tennant. Van Benthem's article is a particularly interesting presence in the volume. Postmodernists find traditional philosophical problems at best misguided, at worst pernicious. Van Benthem's essay thus might be described as "post-Priorean." Van Benthem seems to dismiss out of hand the cluster of traditional philosophical issues surrounding the interpretation of the semantics of modal logic as merely a quaint, "popular ideology concerning a conceptual framework which itself admits of many possible uses." This ideology, he continues, has now been supplanted by a more mature understanding of modal logic, one that sees its semantics as a powerful basis for a general theory of information and information flow. On this understanding, in the simplest case, the indices of a model are understood as "information states" rather than possible worlds, and the binary relation on indices is understood, not as accessibility across worlds, but as a relation indicating the "possible growth" of one information state to another. As befits a postmodern critique, van Benthem doesn't offer much in the way of argument. As far as I could see, nowhere does he provide any reason to think that the philosophical issues surrounding the "popular ideology" of possible-worlds semantics (e.g., actualism, esssentialism, etc.) are any less cogent now than ever. Indeed, the robust character of the distinctively "modernist" articles in this volume--articles that still clearly count as viable the large cluster of philosophical issues in modal and temporal logic that Prior addressed--seem to belie van Benthem's critique. That said, from his chosen perspective, van Benthem provides a typically elegant and worthwhile contribution that, like the rest of the articles in this fine volume, generously rewards careful study.
Texas A & M University
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|Publication:||The Philosophical Review|
|Article Type:||Book Review|
|Date:||Apr 1, 2000|
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