A.N. Prior and ‘The Nature of Logic’

Logical realism, by Arthur Norman Prior understood as the view that logic is not about language but about reality, is a consistent and strong tenet in all of Prior's philosophical work. Recent discoveries in letters from Prior to his wife, Mary Prior, and to his cousin, Hugh Teague, serve to highlight the influence of J.N. Findlay with regard to Prior's logical realism. Through the letters, we come to learn, that the title of Prior's M.A. thesis from 1937 was ‘The Nature of Logic’, that he didn't consider it good and finally, that he attributed much of the work to Findlay. It is argued here that Findlay's criticism of philosophical idealism, evident in his early writings and documented by Prior's letters, moderated Prior's views on Marxism and Karl Barth's theology, and indeed constitute the foundation of Prior's temporal realism. We are thus able to improve our knowledge on all of these aspects. Regarding Marxism, we can extend backwards the time when Prior was aware of the logical problems with Marx's dialectics from the time given by Mary in her 2003 interview with Hasle. Regarding Barth, we can see how Prior's work on ridding Barthian theology of philosophical idealism led him to investigate the importance of the ontological argument with regard to the philosophical foundation of Barthian theology. Finally, the analysis of Findlay's influence helps us better understand the nature of Prior's logical realism and appreciate (i) why Prior said that he directly and indirectly owed all he knew of logic and ethics to Findlay and (ii) why Prior called Findlay the founding father of tense-logic.     

Reasonable Doubt: A Note on ‘Neutral’ Illatives and Arguments

George Bowles and Thomas Gilbert claim that illatives such as so, therefore, and hence convey the meaning that the premise confers upon the conclusion a probability greater than 1/2. This claim is false, for there are straightforward uses of these illatives that do not convey the meaning that the probability is greater than 1/2. In addition, because Bowles' and Gilbert's claim is false, a revision of their definition of argument is required.     

‘Now’ and ‘Then’ in Tense Logic

According to Hans Kamp and Frank Vlach, the two-dimensional tense operators “now” and “then” are ineliminable in quantified tense logic. This is often adduced as an argument against tense logic, and in favor of an extensional account that makes use of explicit quantification over times. The aim of this paper is to defend tense logic against this attack. It shows that “now” and “then” are eliminable in quantified tense logic, provided we endow it with enough quantificational structure. The operators might not be redundant in some other systems of tense logic, but this merely indicates a lack of quantificational resources and does not show any deep-seated inability of tense logic to express claims about time. The paper closes with a brief discussion of the modal analogue of this issue, which concerns the role of the actuality operator in quantified modal logic.     

Reiteration: The ‘Imperative of the Word’ and Echoing the ‘Significative Terms’

Abstract

The act of reiteration is viewed as a therapeutic reply that is especially responsive in the face of what Lacan (1977) and Heidegger (1927/1962) respectively refer to as “empty speech” and “idle talk.” By hearing and selecting those key signifiers and phrasings that bear the client's story of distress, the act of reiteration allows us to focus and address the “subject who speaks” rather than the commonsense storyline itself. As an active and continuing punctuation of the client's direct discourse at the level of the word, the act of reiteration is only the first moment of a more complete narrative reply. But in keeping the therapist ever grounded in the client's direct expressions, it is this first moment of reiteration that leaves the therapist positioned to be responsive to the client's discourse of “rhetorical displacements,” of intimation and allusion, as these “echo” from “elsewhere.”     

Defining ‘Dead’ in Terms of ‘Lives’ and ‘Dies’

What is it for a thing to be dead? Fred Feldman holds, correctly in my view, that a definition of ‘dead’ should leave open both (1) the possibility of things that go directly from being dead to being alive, and (2) the possibility of things that go directly from being alive to being neither alive nor dead, but merely in suspended animation. But if this is right, then surely such a definition should also leave open the possibility of things that go directly from being dead to being neither alive nor dead, but merely in suspended animation. I show that Feldman’s own definition of ‘dead’ (in terms of ‘lives’ and ‘dies’) does not leave this possibility open. I propose a new definition that does.     

A note on ‘scepticism and absurdity’

In ‘Scepticism and Absurdity’ (Inquiry, Vol. 7, No. 2) Ingemund Gullvag concludes that recent attempts to counter scepticism have failed. It is suggested that where the attempts Gullvåg investigates are complex theories of a sociological and linguistic‐psychological nature, we need only refer to a simple and inspectable fact of language to counter scepticism.     

Predicate Metric Tense Logic for ‘Now’ and ‘Then’

In a number of publications A.N. Prior considered the use of what he called ‘metric tense logic’. This is a tense logic in which the past and future operators P and F have an index representing a temporal distance, so that Pnα means that α was true n-much ago, and Fnα means that α will be true n-much hence. The paper investigates the use of metric predicate tense logic in formalising phenomena ormally treated by such devices as multiple indexing or quantification over times.     

On Jan Łukasiewicz's ‘The Principle of Contradiction and Symbolic Logic’

This is a companion article to the translation of ‘Zasada sprzeczno?ci a logika symboliczna’, the appendix on symbolic logic of Jan ?ukasiewicz's 1910 book O zasadzie sprzeczno?ci u Arytotelesa (On the Principle of Contradiction in Aristotle). While the appendix closely follows Couturat's 1905 book L'algebra de la logique (The Algebra of Logic), footnotes show that ?ukasiewicz was aware of the work of Peirce, Huntington and Russell (before Principia Mathematica). This appendix was influential in the development of the Polish school of logic, directly inspiring Stanis?aw Le?niewski and Leon Chwistek and more widely by serving as a text of the new symbolic logic. This appendix was an important source of the dominant algebraic logic in Poland, but also indicates that ?ukasiewicz appreciated Russell's axiomatic approach to logic.     

Franco Montagna’s Work on Provability Logic and Many-valued Logic

Franco Montagna, a prominent logician and one of the leaders of the Italian school on Mathematical Logic, passed away on February 18, 2015. We survey some of his results and ideas in the two disciplines he greatly contributed along his career: provability logic and many-valued logic.     

‘My Future Son is Possibly Alive’. Existential Presupposition and Empty Terms in Abelard's Modal Logic

The aim of this paper is to investigate the problem of existential import in Abelard's modal logic, and to ask whether the system of logical relationships that he proposes for modal propositions maintains its validity when some of the terms included in these propositions are empty. In the following, I first argue that, just as in the case of non-modal propositions, Abelard interprets modal propositions as having existential import, so that it is a necessary condition for the truth of propositions like ‘It is possible for my son to be alive’ or ‘it is necessary that all men are animals’ that their subjects’ referents exist. Then, I present the schemata of inferences that Abelard proposes to describe the logical behaviour of de rebus modal propositions. I argue that these systems of relations are valid only as long as all the terms contained in the formulas have an existing referent. I also claim that Abelard was aware of this difficulty (at least in the Logica Ingredientibus), and, accordingly, he explicitly decided to restrict the validity of his modal system to propositions that do not contain empty terms.     

The logic of obligation, ‘better’ and ‘worse’

Research for this paper was supported by a grant from the National Endowment for the Humanities, FT-33794. I am grateful to an anonymous referee of this journal for remarks on an earlier version of this paper.     

Heidegger on Plato,truth, and unconcealment: The 1931–32 lecture on The Essence of Truth

This paper discusses Heidegger's 1931–32 lecture course on The Essence of Truth. It argues that Heidegger read Platonic ideas, not only as stage‐setting for the western philosophical tradition's privileging of conceptualization over practice, and its correlative treatment of truth as correctness, but also as an early attempt to work through truth as the fundamental experience of unhiddenness. Wrathall shows how several of Heidegger's more‐famous claims about truth, e.g. that propositional truth is grounded in truth as world‐disclosure, and including Heidegger's critique of the self‐evidence of truth as correspondence, are first revealed in a powerful (if iconoclastic) reading of Plato.     

‘Diverse Epistemologies’, Truth and Archaeology: In Defence of Realism

In a recent journal article, as well as in a recent book chapter, in which she critiques my position on ‘indigenous knowledge’, Lesley Green of the Department of Social Anthropology at the University of Cape Town argues that ‘diverse epistemologies ought to be evaluated not on their capacity to express a strict realism but on their ability to advance understanding’. In order to examine the implications of Green’s arguments, and of Nelson Goodman and Catherine Elgin’s work in this regard, I apply them to a well-known controversy between Native American (or First Nations) creationism and archaeology. I argue that issues in social justice should be distinguished from issues in epistemology. Moreover, in tightening in this paper the link between knowledge and truth, I attempt to defend science as a ‘privileged way of seeing the world’. The analysis of truth, and of related concepts like reality and ‘the way the world is’, will assume a central role here. I contend that, ultimately, the only coherent and consistent position is a realist view of the pertinent issues and ideas.     

A Note on Bosbach’s Cone Algebras

In 2002, Dvure?enskij extended Mundici’s equivalence between unital abelian l-groups and MV-algebras to the non-commutative case. We analyse the relationship to Bosbach’s cone algebras and clarify the rôle of the corresponding pair of L-algebras. As a consequence, it follows that one of the two L-algebra axioms can be dropped.     

Sibley on ‘Beautiful’ and ‘Ugly’

Abstract

Frank Sibley's ideas have been particularly influential among contemporary philosophers interested in aesthetics. Most studies, however, have focused only on his earlier works. In this essay, I explore Sibley's account of the adjectives ‘beautiful’ and ‘ugly’, paying particular attention to three papers that have only recently been published and that have not yet received adequate attention. In particular, I discuss his account of the adjective ‘beautiful’, which relies on the controversial notion of an aesthetic ideal. In addition, I discuss an account of how aesthetic judgements may change in relation to our coming to know the kind of object being judged and whether, as Sibley maintains, ‘beautiful’ and ‘ugly’ are asymmetric in the sense specified by the author.