We take a fresh look at the logics of informational dependence and independence of Hintikka and Sandu and Väänänen, and their compositional semantics due to Hodges. We show how Hodges’ semantics can be seen as a special case of a general construction, which provides a context for a useful completeness theorem with respect to a wider class of models. We shed some new light on each aspect of the logic. We show that the natural propositional logic carried by the semantics (...) is the logic of Bunched Implications due to Pym and O’Hearn, which combines intuitionistic and multiplicative connectives. This introduces several new connectives not previously considered in logics of informational dependence, but which we show play a very natural rôle, most notably intuitionistic implication. As regards the quantifiers, we show that their interpretation in the Hodges semantics is forced, in that they are the image under the general construction of the usual Tarski semantics; this implies that they are adjoints to substitution, and hence uniquely determined. As for the dependence predicate, we show that this is definable from a simpler predicate, of constancy or dependence on nothing. This makes essential use of the intuitionistic implication. The Armstrong axioms for functional dependence are then recovered as a standard set of axioms for intuitionistic implication. We also prove a full abstraction result in the style of Hodges, in which the intuitionistic implication plays a very natural rôle. (shrink)

Although Kant envisaged a prominent role for logic in the argumentative structure of his Critique of pure reason, logicians and philosophers have generally judged Kant's logic negatively. What Kant called `general' or `formal' logic has been dismissed as a fairly arbitrary subsystem of first order logic, and what he called `transcendental logic' is considered to be not a logic at all: no syntax, no semantics, no definition of validity. Against this, we argue that Kant's `transcendental logic' is a logic in (...) the strict formal sense, albeit with a semantics and a definition of validity that are vastly more complex than that of first order logic. The main technical application of the formalism developed here is a formal proof that Kant's Table of Judgements in §9 of the Critique of pure reason, is indeed, as Kant claimed, complete for the kind of semantics he had in mind. This result implies that Kant's 'general' logic is after all a distinguished subsystem of first order logic, namely what is known as geometric logic. (shrink)

This paper offers a novel method for nominalizing metalogic without transcending first-order reasoning about physical tokens (inscriptions, etc.) of proofs. A kind of double-negation scheme is presented which helps construct, for any platonistic statement in metalogic, a nominalistic statement which has the same assertability condition as the former. For instance, to the platonistic statement there is a (platonistic) proof of A in deductive system D corresponds the nominalistic statement there is no (metalogical) proof token in (possibly informal) set theory for (...) the claim that there is no proof of A in D. And it is argued that the nominalist can use all the platonistic results by transforming them into such nominalistic correlates. (shrink)

Following its inception (Barwise and Perry, 1983), situation theory has quickly matured (Cooper et al., 1990; Devlin, 1991) and under the familiarname of situation semantics has been applied to a number of linguistic issues (Barwise, 1987; Barwise, 1989; Barwise and Etchemendy, 1987; Cooper, 1986; Cooper, 1991; Cooper et al., 1990; Fenstad et al., 1987), including quanti cation and anaphora (Gawron and Peters, 1990). In the past, the development of a `mathematical'situation theory has been held back by a lack of availability (...) of appropriate technical tools. But by now, the theory has assembled its mathematical foundations based on intuitions basically coming from set theory and logic (Aczel, 1988; Barwise, 1989; Cooper et al., 1990). With a remarkably original view of information (which is fully adapted by situation theory) (Dretske, 1981), a `logic,' based not on truth but on information, is being developed (Devlin, 1991). This logic will probably be an extension of rst-order logic (Barwise, 1977) rather than being an alternative to it. (shrink)

Over recent years, various semantics have been proposed for dealing with updates in the setting of logic programs. The availability of different semantics naturally raises the question of which are most adequate to model updates. A systematic approach to face this question is to identify general principles against which such semantics could be evaluated. In this paper we motivate and introduce a new such principle the refined extension principle. Such principle is complied with by the stable model semantics for (single) (...) logic programs. It turns out that none of the existing semantics for logic program updates, even though generalisations of the stable model semantics, comply with this principle. For this reason, we define a refinement of the dynamic stable model semantics for Dynamic Logic Programs that complies with the principle. (shrink)

The first page of Frege’s classic “Uber Sinn und Bedeutung” sets for more than a hundred years now the agenda for much of semantics and the philosophy of mind. It presents a purported puzzle whose solution is said to call upon the “entities” of semantics (meanings) and psychological explanation (Psychological states, beliefs, concepts). The paper separates three separate alleged puzzles that can be read into Frege’s data. It then argues that none are genuine puzzles. In turn, much of the Frege-driven (...) theoretical development, motivated as an inevitable “solution”, is thrown into doubt. (shrink)

We investigate the philosophical significance of the existence of different semantic systems with respect to which a given deductive system is sound and complete. Our case study will be Corcoran’s deductive system D for Aristotelian syllogistic and some of the different semantic systems for syllogistic that have been proposed in the literature. We shall prove that they are not equivalent, in spite of D being sound and complete with respect to each of them. Beyond the specific case of syllogistic, the (...) goal is to offer a general discussion of the relations between informal notions—in this case, an informal notion of deductive validity—and logical apparatuses such as deductive systems and (model-theoretic or other) semantic systems that aim at offering technical, formal accounts of informal notions. Specifically, we will be interested in Kreisel’s famous ‘squeezing argument’; we shall ask ourselves what a plurality of semantic systems (understood as classes of mathematical structures) may entail for the cogency of specific applications of the squeezing argument. More generally, the analysis brings to the fore the need for criteria of adequacy for semantic systems based on mathematical structures. Without such criteria, the idea that the gap between informal and technical accounts of validity can be bridged is put under pressure. (shrink)

The purpose of this note is to acknowledge a gap in a previous paper — “The Complexity of Revision”, see [1] — and provide a corrected version of argument. The gap was originally pointed out by Francesco Orilia (personal communication and [4]), and the fix was developed in correspondence with Vann McGee.

This paper presents a bivalent extensional semantics for positive free logic without resorting to the philosophically questionable device of using models endowed with a separate domain of non-existing objects. The models here introduced have only one (possibly empty) domain, and a partial reference function for the singular terms (that might be undefined at some arguments). Such an approach provides a solution to an open problem put forward by Lambert, and can be viewed as supplying a version of parametrized truth non (...) unlike the notion of truth at world found in modal logic. A model theory is developed, establishing compactness, interpolation (implying a strong form of Beth definability), and completeness (with respect to a particular axiomatization). (shrink)

In this paper we apply the idea of Revision Rules, originally developed within the framework of the theory of truth and later extended to a general mode of definition, to the analysis of the arithmetical hierarchy. This is also intended as an example of how ideas and tools from philosophical logic can provide a different perspective on mathematically more “respectable” entities. Revision Rules were first introduced by A. Gupta and N. Belnap as tools in the theory of truth, and they (...) have been further developed to provide the foundations for a general theory of (possibly circular) definitions. Revision Rules are non-monotonic inductive operators that are iterated into the transfinite beginning with some given “bootstrapper” or “initial guess.” Since their iteration need not give rise to an increasing sequence, Revision Rules require a particular kind of operation of “passage to the limit,” which is a variation on the idea of the inferior limit of a sequence. We then define a sequence of sets of strictly increasing arithmetical complexity, and provide a representation of these sets by means of an operator G(x, φ) whose “revision” is carried out over ω2 beginning with any total function satisfying certain relatively simple conditions. Even this relatively simple constraint is later lifted, in a theorem whose proof is due to Anil Gupta. (shrink)

The method of analytic tableaux is employed in many introductory texts and has also been used quite extensively as a basis for automated theorem proving. In this paper, we discuss the complexity of the system as a method for refuting contradictory sets of clauses, and resolve several open questions. We discuss the three forms of analytic tableaux: clausal tableaux, generalized clausal tableaux, and binary tableaux. We resolve the relative complexity of these three forms of tableaux proofs and also resolve the (...) relative complexity of analytic tableaux versus resolution. We show that there is a quasi-polynomial simulation of tree resolution by analytic tableaux; this simulation is close to optimal, since we give a matching lower bound that is tight to within a polynomial. (shrink)

In an earlier paper we have shown that a proposition can have a well-defined probability value, even if its justification consists of an infinite linear chain. In the present paper we demonstrate that the same holds if the justification takes the form of a closed loop. Moreover, in the limit that the size of the loop tends to infinity, the probability value of the justified proposition is always well-defined, whereas this is not always so for the infinite linear chain. This (...) suggests that infinitism sits more comfortably with a coherentist view of justification than with an approach in which justification is portrayed as a linear process. (shrink)

We have earlier shown by construction that a proposition can have a welldefined nonzero probability, even if it is justified by an infinite probabilistic regress. We thought this to be an adequate rebuttal of foundationalist claims that probabilistic regresses must lead either to an indeterminate, or to a determinate but zero probability. In a comment, Frederik Herzberg has argued that our counterexamples are of a special kind, being what he calls ‘solvable’. In the present reaction we investigate what Herzberg means (...) by solvability. We discuss the advantages and disadvantages of making solvability a sine qua non , and we ventilate our misgivings about Herzberg’s suggestion that the notion of solvability might help the foundationalist. (shrink)

This book expounds and defends a new conception of the relation between truth and meaning. Atlas argues that the sense of a sense-general sentence radically underdetermines (independently of indexicality) its truth-conditional content. He applies this linguistic analysis to illuminate old and new philosophical problems of meaning, truth, falsity, negation, existence, presupposition, and implicature. In particular, he demonstrates how the concept of ambiguity has been misused and confused with other concepts of meaning, and how the interface between semantics and pragmatics has (...) been misunderstood. The problems he tackles are common to philosophy, linguistics, cognitive psychology, and artificial intelligence, and his conclusions will be of interest to all those working in these fields. (shrink)

In order to handle inconsistent knowledge bases in a reasonable way, one needs a logic which allows nontrivial inconsistent theories. Logics of this sort are called paraconsistent. One of the oldest and best known approaches to the problem of designing useful paraconsistent logics is da Costa’s approach, which seeks to allow the use of classical logic whenever it is safe to do so, but behaves completely differently when contradictions are involved. Da Costa’s approach has led to the family of logics (...) of formal (in)consistency (LFIs). In this paper we provide in a modular way simple non-deterministic semantics for 64 of the most important logics from this family. Our semantics is 3-valued for some of the systems, and infinite-valued for the others. We prove that these results cannot be improved: neither of the systems with a three-valued non-deterministic semantics has either a finite characteristic ordinary matrix or a two-valued characteristic non-deterministic matrix, and neither of the other systems we investigate has a finite characteristic non-deterministic matrix. Still, our semantics provides decision procedures for all the systems investigated, as well as easy proofs of important proof-theoretical properties of them. (shrink)

One of the most important paraconsistent logics is the logic mCi, which is one of the two basic logics of formal inconsistency. In this paper we present a 5-valued characteristic nondeterministic matrix for mCi. This provides a quite non-trivial example for the utility and effectiveness of the use of non-deterministic many-valued semantics.

This papers aims to analyse sentences of a self-referential language containing a truth-predicate by means of a Smullyan-style tableau system. Our analysis covers three variants of Kripke's partial-model semantics (strong and weak Kleene's and supervaluational) and three variants of the revision theory of truth (Belnap's, Gupta's and Herzberger's).

The aim of this paper is to show that it’s not a good idea to have a theory of truth that is consistent but ω -inconsistent. In order to bring out this point, it is useful to consider a particular case: Yablo’s Paradox. In theories of truth without standard models, the introduction of the truth-predicate to a first order theory does not maintain the standard ontology. Firstly, I exhibit some conceptual problems that follow from so introducing it. Secondly, I show (...) that in second order theories with standard semantics the same procedure yields a theory that doesn’t have models. So, while having an ω - inconsistent theory is a bad thing, having an unsatisfiable theory of truth is actually worse. This casts doubts on whether the predicate in question is, after all, a truthpredicate for that language. Finally, I present some alternatives to prove an inconsistency adding plausible principles to certain theories of truth. (shrink)

Book Information Algebraic Methods in Philosophical Logic. By J. Michael Dunn and Gary Hardegree. Clarendon Press. Oxford. 2001. Pp. xv + 470. 60.50.

Restricting attention to the class of extensive games defined by von Neumann and Morgenstern with the added assumption of perfect recall, we specify the information of each player at each node of the game-tree in a way which is coherent with the original information structure of the extensive form. We show that this approach provides a framework for a formal and rigorous treatment of questions of knowledge and common knowledge at every node of the tree. We construct a particular information (...) partition for each player and show that it captures the notion of maximum information in the sense that it is the finest within the class of information partitions that satisfy four natural properties. Using this notion of “maximum information” we are able to provide an alternative characterization of the meet of the information partitions. (shrink)

In a number of influential papers, Hartry Fieldhas advanced an account of truth and referencethat we might dub quasi-disquotationalism. According to quasi-disquotationalism, truth and reference are to be explained in terms of disquotationand facts about what constitute a goodtranslation into our language. Field suggeststhat we might view quasi-disquotationalism aseither (a) an analysis of our ordinarytruth-theoretic concepts of reference andtruth, or (b) an account of certain otherconcepts that improve upon our ordinaryconcepts. In this paper, I argue that (i) ifthe view is (...) understood along the lines of (a)it fails, and (ii) if it is construed along thelines of (b) it is, at best, under-motivated. (shrink)

Although a very recent topic in contemporary logic, the subject of combinations of logics has already shown its deep possibilities. Besides the pure philosophical interest offered by the possibility of defining mixed logic systems in which distinct operators obey logics of different nature, there are also several pragmatical and methodological reasons for considering combined logics. We survey methods for combining logics (integration of several logic systems into a homogeneous environment) as well as methods for decomposing logics, showing their interesting properties (...) and applications. (shrink)

We investigate the properties of Yablo sentences and formulas in theories of truth. Questions concerning provability of Yablo sentences in various truth systems, their provable equivalence, and their equivalence to the statements of their own untruth are discussed and answered.

We investigate the properties of Yablo sentences and for- mulas in theories of truth. Questions concerning provability of Yablo sentences in various truth systems, their provable equivalence, and their equivalence to the statements of their own untruth are discussed and answered.

Answering a question formulated by Halbach (2009), I show that a disquotational truth theory, which takes as axioms all positive substitutions of the sentential T-schema, together with all instances of induction in the language with the truth predicate, is conservative over its syntactical base.

By a classical result of Kotlarski, Krajewski and Lachlan, pathological satisfaction classes can be constructed for countable, recursively saturated models of Peano arithmetic. In this paper we consider the question of whether the pathology can be eliminated; we ask in effect what generalities involving the notion of truth can be obtained in a deflationary truth theory (a theory of truth which is conservative over its base). It is shown that the answer depends on the notion of pathology we adopt. It (...) turns out in particular that a certain natural closure condition imposed on a satisfaction class—namely, closure of truth under sentential proofs—generates a nonconservative extension of a syntactic base theory (Peano arithmetic). (shrink)

Conservativeness has been proposed as an important requirement for deflationary truth theories. This in turn gave rise to the so-called ‘conservativeness argument’ against deflationism: a theory of truth which is conservative over its base theory S cannot be adequate, because it cannot prove that all theorems of S are true. In this paper we show that the problems confronting the deflationist are in fact more basic: even the observation that logic is true is beyond his reach. This seems to conflict (...) with the deflationary characterization of the role of the truth predicate in proving generalizations. However, in the final section we propose a way out for the deflationist — a solution that permits him to accept a strong theory, having important truth-theoretical generalizations as its theorems. (shrink)

We discuss two desirable properties of deflationary truth theories: conservativeness and maximality. Joining them together, we obtain a notion of a maximal conservative truth theory – a theory which is conservative over its base, but can’t be enlarged any further without losing its conservative character. There are indeed such theories; we show however that none of them is axiomatizable, and moreover, that there will be in fact continuum many theories of this sort. It turns out in effect that the deflationist (...) still needs some additional principles, which would permit him to construct his preferred theory of truth. (shrink)

Types now play an essential role in computer science; their ascent originates from Principia Mathematica. Type checking and type inference algorithms are used to prevent semantic errors in programs, and type theories are the native language of several major interactive theorem provers. Some of these trace key features back to Principia.

On the basis of elementary thinkingabout language functioning,a solution of truth paradoxes isgiven and a correspondingsemantics of a truth predicateis founded. It is shown that it is precisely thetwo-valued description of the maximal intrinsic fixedpoint of the strong Kleene three-valuedsemantics.

The mathematical concept of pragmatic truth, first introduced in Mikenberg, da Costa and Chuaqui (1986), has received in the last few years several applications in logic and the philosophy of science. In this paper, we study the logic of pragmatic truth, and show that there are important connections between this logic, modal logic and, in particular, Jaskowski's discussive logic. In order to do so, two systems are put forward so that the notions of pragmatic validity and pragmatic truth can be (...) accommodated. One of the main results of this paper is that the logic of pragmatic truth is paraconsistent. The philosophical import of this result, which justifies the application of pragmatic truth to inconsistent settings, is also discussed. (shrink)

The classical theory of semantic information ( ESI ), as formulated by Bar-Hillel and Carnap in 1952, does not give a satisfactory account of the problem of what information, if any, analytically and/or logically true sentences have to offer. According to ESI , analytically true sentences lack informational content, and any two analytically equivalent sentences convey the same piece of information. This problem is connected with Cohen and Nagel’s paradox of inference: Since the conclusion of a valid argument is contained (...) in the premises, it fails to provide any novel information. Again, ESI does not give a satisfactory account of the paradox. In this paper I propose a solution based on the distinction between empirical information and <span class='Hi'>analytic</span> information . Declarative sentences are informative due to their meanings. I construe meanings as structured hyperintensions , modelled in Transparent Intensional Logic as so-called constructions . These are abstract, algorithmically structured procedures whose constituents are sub-procedures. My main thesis is that constructions are the vehicles of information. Hence, although analytically true sentences provide no empirical information about the state of the world, they convey <span class='Hi'>analytic</span> information , in the shape of constructions prescribing how to arrive at the truths in question. Moreover, even though analytically equivalent sentences have equal empirical content, their <span class='Hi'>analytic</span> content may be different. Finally, though the empirical content of the conclusion of a valid argument is contained in the premises, its <span class='Hi'>analytic</span> content may be different from the <span class='Hi'>analytic</span> content of the premises and thus convey a new piece of information. (shrink)

This title introduces students to non-classical logic, syllogistic, to quantificational and modal logic. The book includes exercises throughout and a glossary of terms and symbols. Taking students beyond classical mathematical logic, "Philosophical Logic" is a wide-ranging introduction to more advanced topics in the study of philosophical logic. Starting by contrasting familiar classical logic with constructivist or intuitionist logic, the book goes on to offer concise but easy-to-read introductions to such subjects as quantificational and syllogistic logic, modal logic and set theory. (...) Chapters of this title include: Sentential Logic; Quantificational Logic; Sentential Modal Logic; Quantification and Modality; Set Theory; Incompleteness; An Introduction to Term Logic; and, Modal Term Logic. In addition, the book includes a list of symbols and a glossary of terms for ease of reference and exercises throughout help students master the topics covered in the book. (shrink)

The paradox of knowability and the debate about it are shortly presented. Some assumptions which appear more or less tacitly involved in its discussion are made explicit. They are embedded and integrated in a Russellian framework, where a formal paradox, very similar to the Russell-Myhill paradox, is derived. Its solution is provided within a Russellian formal logic introduced by A. Church. It follows that knowledge should be typed. Some relevant aspects of the typing of knowledge are pointed out.

I begin by drawing a parallel between the intuitionistic understanding of quantification over all natural numbers and the generality relativist understanding of quantification over absolutely everything. I then argue that adoption of an intuitionistic reading of relativism not only provides an immediate reply to the absolutist's charge of incoherence but it also throws a new light on the debates surrounding absolute generality.

Central to any form of Deflationism concerning truth (hereafter ‘DT’) is the claim that truth has no substantial theoretical role to play. For this reason, DT faces the following immediate challenge: if truth can play no substantial theoretical role then how can we model various prevalent kinds of indeterminacy—such as the indeterminacy exhibited by vague predicates, future contingents, liar sentences, truth-teller sentences, incomplete stipulations, cases of presupposition failure, and such-like? It is too hasty to assume that these phenomena are all (...) to be modelled via some epistemic conception of indeterminacy whereby indeterminacy is just some special species of ignorance which arises because of our limited powers of discrimination. Some non-epistemic model is called for—at least for certain species of indeterminacy. On what is perhaps the most enduring and popular non-epistemic model, indeterminacy gives rise to truth-value gaps. But is DT compatible with the possibility of truth-value gaps? Compatibilism says Yes; Incompatibilism says No. The broad goal of this paper is to defend a form of Incompatibilism. If DT is to make sense of various kinds of indeterminacy then truth-value gaps cannot be invoked to do so. The particular goals of this paper are: (i) To set forth a new form of Compatibilism which can address an argument against truth-value gaps given by Williamson (1994, pp. 187-192). (ii) To offer a new argument against truth-value gaps using principles entailed by DT, thereby undermining Compatibilism. (shrink)

In this book, a Grice/Strawson account of analyticity is explained and formalized, and a corresponding account of logic is offered. The implications of these views for science/substantive inquiry are explored and a neo-Carnapian/verificationist meta-theory is presented.

Several accounts of logical truth are compared and shown to define distinct concepts. Nevertheless, conditions are given under which they happen to declare exactly the same sentences logically true. These conditions involve the variety of objects in the domain, the richness of the language, and the logical resources available. It is argued that the class of sentences declared logically true by each of the accounts depends on particularities of the actual world.

The traditional view that all logical truths are metaphysically necessary has come under attack in recent years. The contrary claim is prominent in David Kaplan’s work on demonstratives, and Edward Zalta has argued that logical truths that are not necessary appear in modal languages supplemented only with some device for making reference to the actual world (and thus independently of whether demonstratives like ‘I’, ‘here’, and ‘now’ are present). If this latter claim can be sustained, it strikes close to the (...) heart of the traditional view. I begin this paper by discussing and refuting Zalta’s argument in the context of a language for propositional modal logic with an actuality connective (section 1). This involves showing that his argument in favor of real world validity his preferred explication of logical truth, is fallacious. Next (section 2) I argue for an alternative explication of logical truth called general validity. Since the rule of necessitation preserves general validity, the argument of section 2 provides a reason for affirming the traditional view. Finally (section 3) I show that the intuitive idea behind the discredited notion of real world validity finds legitimate expression in an object language connective for deep necessity. (shrink)

Although the use of possible worlds in semantics has been very fruitful and is now widely accepted, there is a puzzle about the standard definition of validity in possible-worlds semantics that has received little notice and virtually no comment. A sentence of an intensional language is typically said to be valid just in case it is true at every world under every model on every model structure of the language. Each model structure contains a set of possible worlds, and models (...) are defined relative to model structures, assigning truth-values to sentences at each world countenanced by the model structure. The puzzle is why more than one model structure is used in the definition of validity. There is presumably just one class of all possible worlds and just one model structure defined on this class that does correctly the things that model structures are supposed to do. (These include, but need not be limited to, specifying the set of individuals in each world as well as various accessibility relations between worlds.) Why not define validity simply as truth at every world under every model on this one model structure? What is the point of bringing in more model structures than just this one?

We investigate these questions in some detail and conclude that for many intensional languages the puzzle points to a genuine difficulty: the standard definition of validity is insufficiently motivated. We begin (Section 1) by showing that a plausible and natural account of validity for intensional languages can be based on a single model structure, and that validity so defined is analogous in important respects to the standard account of validity for extensional languages. We call this notion of validity "validity!", and in Section 2 we contrast it with the standard notion, which we call "validity2". Several attempts are made to discover a rationale for the almost universal acceptance of validity2, but in most of these attempts we come up empty-handed. So in Section 3 we investigate validity! for some intensional languages. Our investigation includes providing axiomatizations for several propositional and predicate logics, most of which are provably complete. The completeness proofs are given in the Appendix, which also contains a sketch of a compactness proof for one of the predicate logics. (shrink)

Frege's intention in section 31 of Grundgesetze is to show that every well-formed expression in his formal system denotes. But it has been obscure why he wants to do this and how he intends to do it. It is argued here that, in large part, Frege's purpose is to show that the smooth breathing, from which names of value-ranges are formed, denotes; that his proof that his other primitive expressions denote is sound and anticipates Tarski's theory of truth; and that (...) the proof that the smooth breathing denotes, while flawed, rests upon an idea now familiar from the completeness proof for first-order logic. The main work of the paper consists in defending a new understanding of the semantics Frege offers for the quantifiers: one which is objectual, but which does not make use of the notion of an assignment to a free variable. (shrink)

Stig Kanger (1924--1988) made important contributions to logic and formal philosophy. Kanger's most original achievements were in the areas of general proof theory, the semantics of modal and deontic logic, and the logical analysis of the concept of rights. But he contributed significantly to action theory, preference logic and the theory of measurement as well. The first volume is a complete collection of Kanger's philosophical papers. The second volume contains critical essays on the various aspects of Kanger's work as well (...) as some biographical sketches. (shrink)

An account of the logic of bivalent languages with truth-value gaps is given. This account is keyed to the use of tables introduced by S. C. Kleene. The account has two guiding ideas. First, that the bivalence property insures that the language satisfies classical logic. Second, that the general concepts of a valid sentence and an inconsistent sentence are, respectively, as sentences which are not false in any model and sentences which are not true in any model. What recommends this (...) approach is (1) its relative simplicity, and (2) the fact that it leaves the fundamental features of classical logic intact. (shrink)

A strong and weak version of the redundancy theory of truth are distinguished. An argument put forth by Michael Dummett concludes that the weak version is vitiated by truth-value gaps. The weak version is defended against this argument. The strong version, however, is vitiated by truth-value gaps.

Suppose there is a domain of discourse of English, then everything of which any predicate is true is a member of that domain. If English has a domain of discourse, then, since ‘is a domain of discourse of English’ is itself a predicate of English and true of that domain, that domain is a member of itself. But nothing is a member of itself. Thus English has no domain of discourse. We defend this argument and go on to argue to (...) the same conclusion without relying on the supposition that English is a language which contains the predicate ‘is a domain of discourse of English’. (shrink)

The aim of this paper is to provide a nondenotational semantics for first-order languages which will match one for one each distribution of truth-values available in terms of a denotational semantics.

In this paper the authors argue that if Tarski’s definition of truth for the calculus of classes is correct, then set theories which assert the existence of proper classes (classes which are not the member of anything) are incorrect.

A plausible line of thought runs as follows. If P is a semantically primitive predicate of a first order language L, then P requires its own clause in the definition of satisfaction integral to a definition of truth for L. Thus if L has infinitely many such P the satisfaction clause cannot be completed nor can a theory of truth for L. Robert Cummins takes issue with this line of argument. This paper takes issue with Cummins.

As a way of dealing with the semantical paradoxes Quine has suggested: that semantical expressions such as ‘true’ and ‘true of’ be used with numerical subscripts; that when a truth locution T is applied to a sentence S, the subscript on T is greater than any within S; otherwise, the result of applying T to S is ill formed. A problem is that this introduces infinitely many semantical primitives. The paper suggests a way around the problem. The paper raises a (...) further problem, leaving it open whether this further problem has a satisfactory solution. (shrink)

A formal, computational, semantically clean representation of natural language is presented. This representation captures the fact that logical inferences in natural language crucially depend on the semantic relation of entailment between sentential constituents such as determiner, noun, adjective, adverb, preposition, and verb phrases.The representation parallels natural language in that it accounts for human intuition about entailment of sentences, it preserves its structure, it reflects the semantics of different syntactic categories, it simulates conjunction, disjunction, and negation in natural language by computable (...) operations with provable mathematical properties, and it allows one to represent coordination on different syntactic levels. (shrink)

Central to discussion of supervaluationist accounts of vagueness is the extent to which they require revisions of classical logic and if so, whether those revisions are objectionable. In an important recent Journal of Philosophy article, J.R.G. Williams presents a powerful challenge to the orthodox view that supervaluationism is objectionably revisionary. Williams argues both that supervaluationism is non-revisionary and that even if it were, those revisions would be unobjectionable. This note shows that his arguments for both claims fail.

Philosophy is the science of the science; it is the analysis of the assumptions underlying empirical inquiry. Given that these assumptions cannot possibly be examined or even identified on the basis of empirical data, it follows that philosophy is a non-empirical discipline. And given that our linguistic and cultural practices cannot possibly be examined or even identified except on the basis of empirical data, it follows that philosophical questions are not linguistic questions and do not otherwise concern our conventions or (...) our cultural practices. This entails that philosophical truths are not tautologous or otherwise trivial. It also entails that empiricism is false and, therefore, that Platonism is correct. Given a clear understanding of why Platonism is correct and of what this implies, a number of shibboleths of contemporary analytic philosophy are speedily demolished and are no less speedily replaced with independently corroborated and intuitively plausible alternatives. New answers are given to age-old questions concerning scientific explanation, causal and logical dependence, linguistic meaning, personal identity, the structure of the psyche, and the nature of personal responsibility. Existing answers to these question are thoroughly considered and duly extended, modified, or replaced. Every technical term is defined; every philosophy-specific concept is explained; and the positions defended are consistent with commonsense, so far as their being consistent with the relevant data allows them to be. Therefore, this book is intelligible to philosophically minded laymen. At the same time, it is appropriate for advanced scholars, given that it defends original viewpoints and given also that, even though it discusses old viewpoints, it does so in new ways. Because it is clearly written, it is intelligible to neophytes; but it is not an introductory text and it is not a textbook. There are two appendices: the first, a thorough exposition of the rudiments of formal logic, along with the conceptual underpinnings of that discipline; the second, a definition and analytic discussion of each technical term that occurs in the text. Most of the chapters are followed by study-questions and by practice tests. (shrink)

This paper analyzes the logical truths as (very roughly) those truths that would still have been true under a certain range of counterfactual perturbations.What’s nice is that the relevant range is characterized without relying (overtly, at least) upon the notion of logical truth. This approach suggests a conception of necessity that explains what the different varieties of necessity (logical, physical, etc.) have in common, in virtue of which they are all varieties of necessity. However, this approach places the counterfactual conditionals (...) in an unfamiliar foundational role. (shrink)

This paper offers an expressivist account of logical form, arguing that in order to fully understand it one must examine what valid arguments make us do (or: what Achilles does and the Tortoise doesn’t, in Carroll’s famed fable). It introduces Charles Peirce’s distinction between symbols, indices and icons as three different kinds of signification whereby the sign picks out its object by learned convention, by unmediated indication, and by resemblance respectively. It is then argued that logical form is represented by (...) the third, iconic, kind of sign. It is noted that icons uniquely enjoy partial identity between sign and object, and argued that this holds the key to Carroll’s puzzle. Finally, from this examination of sign-types metaphysical morals are drawn: that the traditional foes metaphysical realism and conventionalism constitute a false dichotomy, and that reality contains intriguingly inference-binding structures. (shrink)

Robert Brandom’s expressivism argues that not all semantic content may be made fully explicit. This view connects in interesting ways with recent movements in philosophy of mathematics and logic (e.g. Brown, Shin, Giaquinto) to take diagrams seriously - as more than a mere “heuristic aid” to proof, but either proofs themselves, or irreducible components of such. However what exactly is a diagram in logic? Does this constitute a semiotic natural kind? The paper will argue that such a natural kind does (...) exist in Charles Peirce’s conception of iconic signs, but that fully understood, logical diagrams involve a structured array of normative reasoning practices, as well as just a “picture on a page”. (shrink)

Would be fairer to call Peirce’s philosophy of language “extensionalist” or “intensionalist”? The extensionalisms of Carnap and Quine are examined, and Peirce’s view is found to be prima facie similar, except for his commitment to the importance of “hypostatic abstraction”. Rather than dismissing this form of abstraction (famously derided by Molière) as useless scholasticism, Peirce argues that it represents a crucial (though largely unnoticed) step in much working inference. This, it is argued, allows Peirce to transcend the extensionalist-intensionalist dichotomy itself, (...) through his unique triadic analysis of reference and meaning, by transcending the distinction between (as Quine put it) “things” and “attributes”. (shrink)

Call a quantifier unrestricted if it ranges over absolutely all things: not just over all physical things or all things relevant to some particular utterance or discourse but over absolutely everything there is. Prima facie, unrestricted quantification seems to be perfectly coherent. For such quantification appears to be involved in a variety of claims that all normal human beings are capable of understanding. For instance, some basic logical and mathematical truths appear to involve unrestricted quantification, such as the truth that (...) absolutely everything is self-identical and the truth that the empty set has absolutely no members. Various metaphysical views too appear to involve unrestricted quantification, such as the physicalist view that absolutely everything is physical. (shrink)

The Monist’s call for papers for this issue ended: “if formalism is true, then it must be possible in principle to mechanize meaning in a conscious thinking and language-using machine; if intentionalism is true, no such project is intelligible”. We use the Grelling-Nelson paradox to show that natural language is indefinitely extensible, which has two important consequences: it cannot be formalized and model theoretic semantics, standard for formal languages, is not suitable for it. We also point out that object-object mapping (...) theories of semantics, the usual account for the possibility of non intentional semantics, doesn’t seem able to account for the indefinitely extensible productivity of natural language. (shrink)

Assuming the indefinite extensibility of any domain of quantification leads to reasoning with extensible domain semantics. It is showed that some theorems (e.g. Thomson's) in conventional semantics logic are not theorems in a logic provided with this new semantics.

I discuss Quine's claim that anyone denying what we now take to be a logical truth would be using logical words in a novel way. I trace this to a confusions between outright denial and failure to assert, and assertion of a negation. (This abstract is written from memory decades after the article.).

It is a consequence of Quine’s confirmation holism that the logical laws are in principle revisable. Some have worried this is at odds with another dictum in Quine, viz., that any translation which construes speakers as systematically illogical is ipso facto inadequate. In this paper, I try to formulate exactly what the problem is here, and offer a solution to it by (1) disambiguating the term ‘logic,’ and (2) appealing to a Quinean understanding of ‘necessity.’ The result is that the (...) different theses in Quine’s philosophy of logic are to be situated within different contexts of inquiry. (shrink)

This article claims that one has to distinguish between X° reflexives which do not bear phi-features, such as number, and XP complex reflexive - which do bear such features. The presence/vs absence of features, it is argued, explains the behavior of so called long distance reflexives - first observed, within the generative tradition, in scandinavian languages - but present all over. The observation according to which XP reflexives are clause bound, while X° reflexives in argument position are not, is some (...) times refered to as "Pica's generalization" (see Burzio (1987) which stressed correctly that is was the first time that such a correlatiion betwen reflexives structure, binding domains, and the role of a cycle was observed. The behavioir of reflexives it is argued derives from the properties of abstratc movement at the level of Logical Form. (shrink)

Contextual type theories are largely explored in their applications to programming languages, but less investigated for knowledge representation purposes. The combination of a constructive language with a modal extension of contexts appears crucial to explore the attractive idea of a type-theoretical calculus of provability from refutable assumptions for non-monotonic reasoning. This paper introduces such a language: the modal operators are meant to internalize two different modes of correctness, respectively with necessity as the standard notion of constructive verification and possibility as (...) provability up to refutation of contextual conditions. (shrink)