Two kinds of individuals are distinguished: abstract and concrete. Whereas abstract individuals belong to our conceptual sphere, concrete individuals (i.e. particulars) individuate the world of matter. A subject investigating the external world projects abstract individuals onto concrete ones. The proposal offers a solution to various metaphysical and epistemological puzzles concerned with individuals, e.g., the Ship of Theseus, the Polish Logician, problems with reidentification, or proper names.

This paper discusses empty quotation (‘’ is an empty string) and lexical quotation (his praise was, quote, fulsome, unquote), it challenges the minimal theory of quotation (‘ “x” ’ quotes ‘x’) and it defends the identity theory of quotation. In the process it illuminates disciplinary differences between the science of language and the philosophy of language. First, most philosophers assume, without argument, that language includes writing, whereas linguists have reason to identify language with speech (plus sign language). Second, philosophers tend (...) to think of languages as abstract objects whereas linguists tend to think of them as natural objects. These foundational differences help to explain disagreements in grammaticality judgments and consequent disagreements in semantic theory. (shrink)

This paper presents a new approach to the class-theoretic paradoxes. In the first part of the paper, I will distinguish classes from sets, describe the function of class talk, and present several reasons for postulating type-free classes. This involves applications to the problem of unrestricted quantification, reduction of properties, natural language semantics, and the epistemology of mathematics. In the second part of the paper, I will present some axioms for type-free classes. My approach is loosely based on the Gödel–Russell idea (...) of limited ranges of significance. It is shown how to derive the second-order Dedekind–Peano axioms within that theory. I conclude by discussing whether the theory can be used as a solution to the problem of unrestricted quantification. In an appendix, I prove the consistency of the class theory relative to Zermelo–Fraenkel set theory. (shrink)

Esta enciclopédia abrange, de uma forma introdutória mas desejavelmente rigorosa, uma diversidade de conceitos, temas, problemas, argumentos e teorias localizados numa área relativamente recente de estudos, os quais tem sido habitual qualificar como «estudos lógico-filosóficos». De uma forma apropriadamente genérica, e apesar de o território teórico abrangido ser extenso e de contornos por vezes difusos, podemos dizer que na área se investiga um conjunto de questões fundamentais acerca da natureza da linguagem, da mente, da cognição e do raciocínio humanos, bem (...) como questões acerca das conexões destes com a realidade não mental e extralinguística. A razão daquela qualificação é a seguinte: por um lado, a investigação em questão é qualificada como filosófica em virtude do elevado grau de generalidade e abstracção das questões examinadas (entre outras coisas); por outro, a investigação é qualificada como lógica em virtude de ser uma investigação logicamente disciplinada, no sentido de nela se fazer um uso intenso de conceitos, técnicas e métodos provenientes da disciplina de lógica. O agregado de tópicos que constitui a área de estudos lógico-filosóficos é já visível, pelo menos em parte, no Tractatus Logico-Philosophicus de Ludwig Wittgenstein, uma obra publicada em 1921. E uma boa maneira de ter uma ideia sinóptica do território disciplinar abrangido por esta enciclopédia, ou pelo menos de uma porção substancial dele, é extrair do Tractatus uma lista dos tópicos mais salientes aí discutidos; a lista incluirá certamente tópicos do seguinte género, muitos dos quais se podem encontrar ao longo desta enciclopédia: factos e estados de coisas; objectos; representação; crenças e estados mentais; pensamentos; a proposição; nomes próprios; valores de verdade e bivalência; quantificação; funções de verdade; verdade lógica; identidade; tautologia; o raciocínio matemático; a natureza da inferência; o cepticismo e o solipsismo; a indução; as constantes lógicas; a negação; a forma lógica; as leis da ciência; o número. (shrink)

The common account of the analog vs digital distinction is based on features of physical systems, being related to the usage of continuous vs discrete supports respectively. It is proposed here to alternatively characterize the concepts of analog and digital as related to coding systems, of which a formal definition is given, by suggesting that the distinction refers to the strategy adopted to define the coding function: extensional in digital systems, isomorphic intensional in analog systems. This thesis is supported by (...) examples, in particular of analog systems exploiting discrete supports, and is discussed to explain why digital coding is currently so widespread in technological and social practice. (shrink)

This article proposes a four-layer semantic structure for common nouns. Each layer matches up with a semantic entity of a certain type in Montague’s intensional semantics. It is argued that a common noun denotes a sense and a concept, which are functions. For any given context, the sense of a term determines its extensions and the concept denoted by the term specifies its intensions. Intensions are treated as sets of senses. The membership relation between a sense and an intension is (...) a soft kind and is expressed in the form of a generic sentence. Such a layered structure explains various “degrees of publicity” of a language. The result we present clarifies the confusions existing in the ordinary understanding of “sense,” “intension,” and “concept.” It also has promising applications in interpreting metaphors and revealing the relationship between generics and metaphors. (shrink)

The foregoing set of theorems forms an effective foundation for the theory of situations and worlds. All twenty-five theorems seem to be basic, reasonable principles that structure the domains of properties, relations, states of affairs, situations, and worlds in true and philosophically interesting ways. They resolve 15 of the 19 choice points defined in Barwise (1989) (see Notes 22, 27, 31, 32, 35, 36, 39, 43, and 45). Moreover, important axioms and principles stipulated by situation theorists are derived (see Notes (...) 33, 37, and 38). This is convincing evidence that the foregoing constitutes a theory of situations. Note that worlds are just a special kind of situation, and that the basic theorems of world theory, which were derived in previous work, can still be derived in this situation-theoretic setting. So there seems to be no fundamental incompatibility between situations and worlds — they may peacably coexist in the foundations of metaphysics. The theory may therefore reconcile two research programs that appeared to be heading off in different directions. And we must remind the reader that the general metaphysical principles underlying our theory were not designed with the application to situation theory in mind. This suggests that the general theory and the underlying distinction have explanatory power, for they seem to relate and systematize apparently unrelated phenomena. (shrink)

The author examines the differences between the general intensional logic defined in his recent book and Montague's intensional logic. Whereas Montague assigned extensions and intensions to expressions (and employed set theory to construct these values as certain sets), the author assigns denotations to terms and relies upon an axiomatic theory of intensional entities that covers properties, relations, propositions, worlds, and other abstract objects. It is then shown that the puzzles for Montague's analyses of modality and descriptions, propositional attitudes, and directedness (...) towards nonexistents can be solved using the author's logic. (shrink)

This paper was written with two aims in mind. A large part of it is just an exposition of Tarski's theory of truth. Philosophers do not agree on how Tarski's theory is related to their investigations. Some of them doubt whether that theory has any relevance to philosophical issues and in particular whether it can be applied in dealing with the problems of philosophy (theory) of science.In this paper I argue that Tarski's chief concern was the following question. Suppose a (...) language L belongs to the class of languages for which, in full accordance with some formal conditions set in advance, we are able to define the class of all the semantic interpretations the language may acquire. Every interpretation of L can be viewed as a certain structure to which the expressions of the language may refer. Suppose that a specific interpretation of the language L was singled out as the intended one. Suppose, moreover, that the intended interpretation can be characterized in a metalanguage L +. If the above assumptions are satisfied, can the notion of truth for L be defined in the metalanguage L + and, if it can, how can this be done? (shrink)

Your story is there waiting for you, it has been waiting for you there a hundred years, long before you were born and you cannot change a comma of it. Everything you do you have to do. You are the twig, and the water you float on swept you here. You are the leaf, and the breeze you were borne on blew you here. This is your story and you cannot escape it.—Cornell Woolrich, I Married a Dead Man.

Your story is there waiting for you, it has been waiting for you there a hundred years, long before you were born and you cannot change a comma of it. Everything you do you have to do. You are the twig, and the water you float on swept you here. You are the leaf, and the breeze you were borne on blew you here. This is your story and you cannot escape it.—Cornell Woolrich, I Married a Dead Man.

A first-order language with a defined identity predicate is proposed whose apparatus for atomic predication is sensitive to grammatical categories of natural language. Subatomic natural deduction systems are defined for this naturalistic first-order language. These systems contain subatomic systems which govern the inferential relations which obtain between naturalistic atomic sentences and between their possibly composite components. As a main result it is shown that normal derivations in the defined systems enjoy the subexpression property which subsumes the subformula property with respect (...) to atomic and identity formulae as a special case. The systems admit a proof-theoretic semantics which does not only apply to logically compound but also to atomic and identity formulae—as well as to their components. The potential of the defined systems for a meticulous first-order analysis of natural inferences whose validity crucially depends on expressions of some of the aforementioned categories is demonstrated. (shrink)

A semantics may be compositional and yet partial, in the sense that not all well-formed expressions are assigned meanings by it. Examples come from both natural and formal languages. When can such a semantics be extended to a total one, preserving compositionality? This sort of extension problem was formulated by Hodges, and solved there in a particular case, in which the total extension respects a precise version of the fregean dictum that the meaning of an expression is the contribution it (...) makes to the meanings of complex phrases of which it is a part. Hodges' result presupposes the so-called Husserl property, which says roughly that synonymous expressions must have the same category. Here I solve a different version of the compositional extension problem, corresponding to another type of linguistic situation in which we only have a partial semantics, and without assuming the Husserl property. I also briefly compare Hodges' framework for grammars in terms of partial algebras with more familiar ones, going back to Montague, which use many-sorted algebras instead. (shrink)

Language theorists have recently come to have an increasing appreciation for the fact that context contributes heavily in determining our interpretation of what is said. Indeed, it now seems clear that no complete understanding of a natural language is possible without some account of the way in which context affects our interpretation of discourse. In this paper, I will attempt to explore one facet of the language – context relationship, namely, the relation between conditionals and context. The first part of (...) the paper develops an account of truth for conditionals which allows them to depend on momentary features of the context in which they are uttered. In the second half of the paper, comparisons with other recent theories of the conditional will be considered. Particular attention will be given to the problem of whether the conditional really violates classical inferences such as Hypothetical Syllogism and Contraposition as has often been claimed in recent years. (shrink)

The relation between logic and philosophy of science, often taken for granted, is in fact problematic. Although current fashionable criticisms of the usefulness of logic are usually mistaken, there are indeed difficulties which should be taken seriously -- having to do, amongst other things, with different "scientific mentalities" in the two disciplines. Nevertheless, logic is, or should be, a vital part of the theory of science. To make this clear, the bulk of this paper is devoted to the key notion (...) of a "scientific theory" in a logical perspective. First, various formal explications of this notion are reviewed, then their further logical theory is discussed. In the absence of grand inspiring programs like those of Klein in mathematics or Hilbert in metamathematics, this preparatory ground-work is the best one can do here. The paper ends on a philosophical note, discussing applicability and merits of the formal approach to the study of science. (shrink)

Measures of theory-Distance are defined for theories formalizable within first-Order predicate logic by using distributive normal forms. The account is applied to give measures of verisimilitude.

In his published work and even more in conversations, Tarski emphasized what he thought were important philosophical aspects of his work. The English translation of his more philosophical papers [56m] was dedicated to his teacher Tadeusz Kotarbinski, and in informal discussions of philosophy he often referred to the influence of Kotarbinski. Also, the influence of Leiniewski, his dissertation adviser, is evident in his early papers. Moreover, some of his important papers of the 1930s were initially given to philosophical audiences. For (...) example, the famous monograph on the concepotf truth ([33”], [35b]) was first given as twol ectures to the Logic Section of the Philosophical Society in Warsaw in 1930. Second, his paper [33], which introduced the concepts of co-consistency and co-completeness as well as the rule of infinite induction: was first given at the Second Conference of the Polish Philosophical Society in Warsaw in 1927. Also [35c] was based upon an address given in 1934 to the conference for the Unity of Science in Prague; C361 and [36a] summarize an address given at the International Congress of Scientific Philosophy in Paris in 1935. The article [44a] was published in a philosophical journal and widely reprinted in philosophical texts. This list is of course not exhaustiveb ut only representative of Tarski’s philosophical interactions as reflected in lectures given to philosophical audiences, which were later embodied in substantial papers. After 1945 almost all of Tarski’s publications and presentations are mathematical in character with one or two minor exceptions. This division, occurring about 1945, does not, however, indicate al oss of interest in philosophical questionbsu t is a result of Tarski’s moving to the Department of Mathematics at Berkeley. There he assumed an important role in the development of logic within mathematics in the United States. (shrink)

This paper does not deal with the topic of ‘the generosity of artificial languages from an Asian or a comparative perspective’. Rather, it is concerned with a particular case taken from a development in the Western tradition, when in the wake of the rise of formal logic at the end of the nineteenth and the beginning of the twentieth century people in philosophy and later in linguistics started to use formal languages in the study of the semantics of natural languages. (...) This undertaking rests on certain philosophical assumptions and instantiates a particular methodology, that we want to examine critically. However, that in itself is still too broad a topic for a single paper, so we will focus on a particular aspect, viz., the distinction between grammatical form and logical form and the crucial role it plays in how the relationship between natural languages and formal languages is understood in this tradition. We will uncover two basic assumptions that underlie the standard view on the distinction between grammatical form and logical form, and discuss how they have contributed to the shaping of a particular methodology and a particular view on the status of semantics as a discipline. (shrink)

In the present piece we defend predicate approaches to modality, that is approaches that conceive of modal notions as predicates applicable to names of sentences or propositions, against the challenges raised by Montague’s theorem. Montague’s theorem is often taken to show that the most intuitive modal principles lead to paradox if we conceive of the modal notion as a predicate. Following Schweizer (J Philos Logic 21:1–31, 1992) and others we show this interpretation of Montague’s theorem to be unwarranted unless a (...) further non trivial assumption is made—an assumption which should not be taken as a given. We then move on to showing, elaborating on work of Gupta (J Philos Logic 11:1–60, 1982), Asher and Kamp (Properties, types, and meaning. Vol. I: foundational issues, Kluwer, Dordrecht, pp 85−158, 1989), and Schweizer (J Philos Logic 21:1–31, 1992), that the unrestricted modal principles can be upheld within the predicate approach and that the predicate approach is an adequate approach to modality from the perspective of modal operator logic. To this end we develop a possible world semantics for multiple modal predicates and show that for a wide class of multimodal operator logics we may find a suitable class of models of the predicate approach which satisfies, modulo translation, precisely the theorems of the modal operator logic at stake. (shrink)

The consensus among legal philosophers is probably that rule-based legal expert systems leave much to be desired as aids in legal decision-making. Why? What can we do about it? A bureaucrat administering some set of complex rules will ascertain the facts and apply the rules to them in order to discover their consequences for the case in hand. This process of deductive reasoning is characteristically bureaucratic.

This article introduces three arguments that share a single conclusion: that a comprehensive science of language cannot describe relations of semantic reference, i.e. word–world relations. Spelling this out, if there is to be a genuine science of linguistic meaning, then a theory of meaning cannot involve assigning external, real-world, objects to names, nor sets of external objects to predicates, nor truth values to sentences. Most of the article tries to explain and defend this broad conclusion. The article also presents, in (...) a very limited way, a positive alternative to external-referent semantics for expressions. This alternative has two parts: first, that the meanings of words and sentences are mental instructions, not external things; second, that it is people who refer by using words and sentences, and word/sentence meanings play but a partial role in allowing speakers to talk about the world. (shrink)

Since the pioneering work by Kripke and Montague, the term possible world has appeared in most theories of formal semantics for modal logics, natural languages, and knowledge-based systems. Yet that term obscures many questions about the relationships between the real world, various models of the world, and descriptions of those models in either formal languages or natural languages. Each step in that progression is an abstraction from the overwhelming complexity of the world. At the end, nothing is left but a (...) colorful metaphor for an undefined element of a set W called worlds, which are related by an undefined and undefinable primitive relation R called accessibility. For some purposes, the resulting abstraction has proved to be useful, but as a general theory of meaning, the abstraction omits too many significant features. So much information has been lost at each step that many philosophers, linguists, and psychologists have dismissed model-theoretic semantics as irrelevant to the study of meaning. This article examines the steps in the process of extractingthe pair (W,R) from the world and the way people talk about the world. It shows that the Kripke worlds can be reinterpreted as part of a Peircean semiotic theory, which can also include contributions from many other studies in cognitive science. Among them are Dunn’s semantics based on laws and facts, the lexical semantics preferred by manylinguists, psychological models of how the world is perceived, and philosophies of science that relate theories to the world. A full integration of all those sources is far beyond the scope of this article, but an outline of the approach suggests that Peirce’s vision is capable of relating and reconciling the competing sources. (shrink)

This is a study of the epistemology of indexical reference, Or its foundation in the intentionality of the speaker's awareness of the referent. Where the referent is the object of the speaker's acquaintance on that occasion, The sense expressed is the generic content of that awareness. This, Indexical sense determines indexical reference, But indexical sense works by appeal to the context of the speaker's awareness of the referent. It is discussed how, By virtue of indexical sense, Indexical reference is rigid, (...) I.E. Picks out the same referent in any possible world. (shrink)

I have written a number of articles recently that have a rather remarkable character. They all point out trivial grammatical facts that, at great cost, have not been respected in twentieth century Logic. A major continuous strand in my previous work, with this same character, I will first summarise, to locate the kind of fact that is involved. But then I shall present an overview of the more recent, and more varied points I have made, which demonstrate the far larger (...) extent of basic grammar that has been overlooked or suppressed. I end with some remarks about how this phenomenon can have arisen – principally through logicians not being attentive enough to their own language, and occupying themselves, instead, with often quite imaginary languages. (shrink)

This paper contains an argument to the effect that possible worlds semantics renders semantic knowledge impossible, no matter what ontological interpretation is given to possible worlds. The essential contention made is that possible worlds semantic knowledge is unsafe and this is shown by a parallel with the preface paradox.

It is commonly argued that natural language has the expressive power of quantifying over intensional entities, such as times, worlds, or situations. A standard way of modelling this assumes that there are unpronounced but syntactically represented variables of the corresponding type. Not all that much as has been said, however, about the exact syntactic location of these variables. Meanwhile, recent work has highlighted a number of problems that arise because the interpretive options for situation pronouns seem to be subject to (...) various restrictions. This paper is primarily concerned with situation pronouns inside of determiner phrases, arguing that they are introduced as arguments of (certain) determiners. Verbal predicates, on the other hand, are assumed to not combine with a situation pronoun. The various restrictions on their interpretation are shown to fall out from the semantic system that is developed based on that view. Further support for such an account comes from situation semantic analyses of donkey sentences as well as data on the temporal interpretation of nominal predicates. Its ability to account for this full range of data in a unified manner is shown to set it apart from previous proposals. The paper closes with an outlook on further extensions, including an account of quantifier domain restriction based on situation pronouns. (shrink)

This paper proposes a method for computing the temporal aspects of the interpretations of a variety of Germa sentences. The method is strictly modular in the sense that it allows each meaning-bearing sentence constituent to make its own, separate, contribution to the semantic representation of any sentence containing it. The semantic representation of a sentence is reached in several stages. First, an ‘initial semantic representation’ is constructed, using a syntactic analysis of the sentence as input. This initial representation is then (...) transformed into the definitive representation by a series of transformations which reflect the ways in which the contributions from different constituents of the sentence interact. Since the different constituents which make their respective contributions to the meaning of the sentence are in most instances ambiguous, the initial representations are typically of a high degree of underspecification. (shrink)