In this 1992 book, Professor Koslow advances an account of the basic concepts of logic. A central feature of the theory is that it does not require the elements of logic to be based on a formal language. Rather, it uses a general notion of implication as a way of organizing the formal results of various systems of logic in a simple, but insightful way. The study has four parts. In the first two parts the various sources of the general (...) concept of an implication structure and its forms are illustrated and explained. Part 3 defines the various logical operations and systematically explores their properties. A generalized account of extensionality and dual implication is given, and the extensionality of each of the operators, as well as the relation of negation and its dual, are given substantial treatment because of the novel results they yield. Part 4 considers modal operators and studies their interaction with logical operators. By obtaining the usual results without the usual assumptions this new approach allows one to give a very simple account of modal logic minus the excess baggage of possible world semantics. (shrink)

In his article 'Rejection' (1996), Timothy Smiley had shown how a logical system allowing rules of rejection could provide a categorical axiomatization of the classical propositional calculus. This paper shows how rules of rejection, when placed in a multiple conclusion setting, can also provide categorical axiomatizations of a range of non-classical calculi which permit truth-value gaps, among them the calculus in Smiley's own 'Sense without denotation' (1960).

This book offers a unique synthesis of past and current work on the structure, meaning, and use of negation and negative expressions, a topic that has engaged thinkers from Aristotle and the Buddha to Freud and Chomsky. Horn's masterful study melds a review of scholarship in philosophy, psychology, and linguistics with original research, providing a full picture of negation in natural language and thought; this new edition adds a comprehensive preface and bibliography, surveying research since the book's original publication.

But Findlay's remark, like so much that has been written on the subject of time in the present century, was provoked in the first place by McTaggart's ...

This highly acclaimed book is a major contribution to the philosophy of language as well as a systematic interpretation of Frege, indisputably the father of ...

The logical properties of the 'if-then' connective of ordinary English differ markedly from the logical properties of the material conditional of classical, two-valued logic. This becomes apparent upon examination of arguments in conversational English which involve (noncounterfactual) usages of if-then'. A nonclassical system of propositional logic is presented, whose conditional connective has logical properties approximating those of 'if-then'. This proposed system reduces, in a sense, to the classical logic. Moreover, because it is equivalent to a certain nonstandard three-valued logic, its (...) decision procedure is almost as efficient as that of the classical logic. It therefore provides a rational and convenient system in which to formalize English arguments. (shrink)

Part I The Imperative Mood 'Virtue, then, is a disposition governing our choices '. ARISTOTLE, Eth. Nic. 36 Prescriptive Language. ...

Multiple -conclusion logic extends formal logic by allowing arguments to have a set of conclusions instead of a single one, the truth lying somewhere among the conclusions if all the premises are true. The extension opens up interesting possibilities based on the symmetry between premises and conclusions, and can also be used to throw fresh light on the conventional logic and its limitations. This is a sustained study of the subject and is certain to stimulate further research. Part I reworks (...) the fundamental ideas of logic to take account of multiple conclusions, and investigates the connections between multiple - and single - conclusion calculi. Part II draws on graph theory to discuss the form and validity of arguments independently of particular logical systems. Part III contrasts the multiple - and the single - conclusion treatment of one and the same subject, using many-valued logic as the example; and Part IV shows how the methods of 'natural deduction' can be matched by direct proofs using multiple conclusions. (shrink)

Such a conception, says Dummett, will form "a base camp for an assault on the metaphysical peaks: I have no greater ambition in this book than to set up a base ...

Many areas of philosophy employ a distinction between factual and non-factual (descriptive/non-descriptive, cognitive/non-cognitive, etc) uses of language. This book examines the various ways in which this distinction is normally drawn, argues that all are unsatisfactory, and suggests that the search for a sharp distinction is misconceived. The book develops an alternative approach, based on a novel theory of the function and origins of the concept of truth. The central hypothesis is that the main role of the normative notion of truth (...) is to encourage speakers to argue, with long-run behavioural advantages. This offers a fresh perspective on many debates about realism in contemporary philosophy. [A new, greatly extended edition of this book is forthcoming from OUP in 2025 – a draft of the new edition is also available on PhilPapers.]. (shrink)

W. Labov's & T. Labov's findings concerning their child grammar acquisition ("Learning the Syntax of Questions" in Recent Advances in the Psychology of Language, Campbell, R. & Smith, P. Eds, New York: Plenum Press, 1978) are interpreted in terms of different semantics of why & other wh-questions. Z. Dubiel.

The appropriateness of S5 as a logic of knowledge has been attacked at some length in the philosophical literature. Here one particular attack based on the interplay between knowledge and belief is considered: Suppose that knowledge satisfies S5, belief satisfies KD45, and both the entailment property (knowledge implies belief) and positive certainty (if the agent believes something, she believes she knows it) hold. Then it can be shown that belief reduces to knowledge: it is impossible to have false beliefs. While (...) the entailment property has typically been viewed as perhaps the least controversial of these assumptions, an argument is presented that it can plausibly be viewed as the culprit. More precisely, it is shown that this attack fails if we weaken the entailment property so that it applies only to objective (nonmodal) formulas, rather than to arbitrary formulas. Since the standard arguments in favor of the entailment property are typically given only for objective formulas, this observation suggests that care must be taken in applying intuitions that seem reasonable in the case of objective formulas to arbitrary formulas. (shrink)

McCawley supplements his earlier book—which covers such topics as presuppositional logic, the logic of mass terms and nonstandard quantifiers, and fuzzy ...

Comprehensive account of constructive theory of first-order predicate calculus. Covers formal methods including algorithms and epi-theory, brief treatment of Markov’s approach to algorithms, elementary facts about lattices and similar algebraic systems, more. Philosophical and reflective as well as mathematical. Graduate-level course. 1963 ed. Exercises.

Speech act theory is one of the more lasting products of the linguistic movement in philosophy of the mid−Twentieth century. Within philosophy itself the movement's products did not in general prove so durable. Particularly striking in this respect is the perceived fate of what was one of the most characteristic applications of the linguistic turn in philosophy, namely the view that many traditional philosophical problems are such as to yield to an understanding of the distinctive function of a particular part (...) of language. Most typically, the crucial insight was held to be that despite appearances, the function of the part of language in question is not assertoric, or descriptive, and that the traditional problems arose at least in part from a failure to appreciate this point. Thus problems in moral philosophy were thought to yield to an appreciation that moral discourse is expressive rather than descriptive, problems in the philosophy of mind to an understanding of distinctive r×le of psychological ascriptions, and so on. The philosophical journals of the 1950s are rich with views like these. (No general term for this approach seems to have become widely accepted at the time. I shall call it "non−factualism", for what it denies, most characteristically, is the fact−stating r×le of language of a certain kind.). (shrink)

This paper is about Truth Minimalism, Norm Expressivism, and the relation between them. In particular, it is about whether Truth Minimalism can help to solve a problem thought to plague Norm Expressivism. To start with, let me explain what I mean by 'Truth Minimalism' and 'Norm Expressivism.'.

From the point of view of non-classical logics, Heyting's implication is the smallest implication for which the deduction theorem holds. This book studies properties of logical systems having some of the classical connectives and implication in the neighbourhood of Heyt ing's implication. I have not included anything on entailment, al though it belongs to this neighbourhood, mainly because of the appearance of the Anderson-Belnap book on entailment. In the later chapters of this book, I have included material that might be (...) of interest to the intuitionist mathematician. Originally, I intended to include more material in that spirit but I decided against it. There is no coherent body of material to include that builds naturally on the present book. There are some serious results on topological models, second order Beth and Kripke models, theories of types, etc., but it would require further research to be able to present a general theory, possibly using sheaves. That would have postponed pUblication for too long. I would like to dedicate this book to my colleagues, Professors G. Kreisel, M.O. Rabin and D. Scott. I have benefited greatly from Professor Kreisel's criticism and suggestions. Professor Rabin's fun damental results on decidability and undecidability provided the powerful tools used in obtaining the majority of the results reported in this book. Professor Scott's approach to non-classical logics and especially his analysis of the Scott consequence relation makes it possible to present Heyting's logic as a beautiful, integral part of non-classical logics. (shrink)

This completely self-contained study, widely considered the best book in the field, is intended to serve both as an introduction to quantification theory and as ...

This brief paperback is designed for symbolic/formal logic courses. It features the tree method proof system developed by Jeffrey. The new edition contains many more examples and exercises and is reorganized for greater accessibility.

A bivalent valuation is snt iff sound (standard PC inference rules take truths only into truths) and non-trivial (not all wffs are assigned the same truth value). Such a valuation is normal iff classically correct for each connective. Carnap knew that there were non-normal snt valuations of PC, and that the gap they revealed between syntax and semantics could be "jumped" as follows. Let $VAL_{snt}$ be the set of snt valuations, and $VAL_{nrm}$ be the set of normal ones. The bottom (...) row in the table for the wedge 'v' is not semantically determined by $VAL_{snt}$ , but if one deletes from $VAL_{snt}$ all those valuations that are not classically correct at the aforementioned row, one jumps straights to $VAL_{nrm}$ and thus to classical semantics. The conjecture we call semantic holism claims that the same thing happens for any semantic indeterminacy in any row in the table of any connective of PC, i.e., to remove it is to jump straight to classical semantics. We show (i) why semantic holism is plausible and (ii) why it is nevertheless false. And (iii) we pose a series of questions concerning the number of possible steps or jumps between the indeterminate semantics given by $VAL_{snt}$ and classical semantics given by $VAL_{nrm}$. (shrink)

If a certain semantic relation (which we call 'local consequence') is allowed to guide expectations about which rules are derivable from other rules, these expectations will not always be fulfilled, as we illustrate. An alternative semantic criterion (based on a relation we call 'global consequence'), suggested by work of J.W. Garson, turns out to provide a much better - indeed a perfectly accurate - guide to derivability.