This book is intended to be used as a textbook by students of mathematics, and also within limitations as a reference work.

"This book is valuable as expounding in full a theory of meaning that has its roots in the work of Frege and has been of the widest influence.

This paper reminds, puts in order, sketches and also initiates some researches from the field of logic and philosophy of language. It lays emphasis on the logical-linguistic and ontological developmental lines originated with Polish researchers. The author discusses two opposite orientations of the former line in the process of formalization of language, called here nominalistic and Platonistic. The paper mentions the author's result (1989; 1991) concerning theoretical equivalence of two axiomatic approaches to language syntax which take into consideration these two (...) different philosophical orientations, respectively. It also introduces certain formal-logical foundations of language semantics, discusses and develops the problem of the syntactic and semantic categorial agreement, i.e. the agreement of the syntactic category of each language expression with the ontological category assigned to the reference of this expression. The author, in particular, gives a solution to this problem for quantifiers. (shrink)

With reference to Polish logico-philosophical tradition two formal theories of language syntax have been sketched and then compared with each other. The first theory is based on the assumption that the basic linguistic stratum is constituted by object-tokens (concrete objects perceived through the senses) and that the types of such objects (ideal objects) are derivative constructs. The other is founded on an opposite philosophical orientation. The two theories are equivalent. The main conclusion is that in syntactic researches it is redundant (...) to postulate the existence of abstract linguistic entities. Earlier, in a slightly different form, the idea was presented in [27] and signalled in [26] and [25]. (shrink)

Husserls »Logische Untersuchungen« sind eines der folgenreichsten Werke der neueren Philosophiegeschichte. Mit dem ersten Erscheinen in den Jahren 1900 und 1901 (Max Niemeyer Verlag, Halle/Saale) nimmt jene Schule ihren Anfang, deren Name im Untertitel des zweiten Bandes zum ersten Mal sinnfällig wird: die Phänomenologie. Husserl sah damals in diesem Werk »Versuche zur Neubegründung der reinen Logik und Erkenntnistheorie«, die den Grund zu einem größeren Gedankengebäude zu legen imstande waren. Sie wollten freilich kein bloßes Programm sein, sondern »Fundamentalarbeit an den unmittelbar (...) erschauten und ergriffenen Sachen« darstellen. Die weitere Arbeit an der Ausprägung der phänomenologischen Philosophie führte schon nach wenigen Jahren zu neuen Problemen, zu vertieften Erkenntnissen und zu schärferen Formulierungen. Ihnen trägt die zweite, zum Teil tiefgreifend umgearbeitete Auflage Rechnung, deren Text seither in unveränderter Form immer wieder nachgedruckt wurde. (shrink)

In "Truth and the Past, " Dummett, best known as a proponent of antirealism, clarifies his current positions on the metaphysical issue of realism and the ...

Michael Dummett's three John Dewey Lectures--"The Concept of Truth," "Statements About the Past," and "The Metaphysics of Time"--were delivered at Columbia University in the spring of 2002. Revised and expanded, the lectures are presented here along with two new essays by Dummett, "Truth: Deniers and Defenders" and "The Indispensability of the Concept of Truth." In _Truth and the Past,_ Dummett clarifies his current positions on the metaphysical issue of realism and the philosophy of language. He is best known as a (...) proponent of antirealism, which loosely characterizes truth as what we are capable of knowing. The events of the past and statements about them are critical tests of an antirealist position. These essays continue and significantly contribute to Dummett's work. (shrink)

Originally published in 1973, this book shows that methods developed for the semantics of systems of formal logic can be successfully applied to problems about the semantics of natural languages; and, moreover, that such methods can take account of features of natural language which have often been thought incapable of formal treatment, such as vagueness, context dependence and metaphorical meaning. Parts 1 and 2 set out a class of formal languages and their semantics. Parts 3 and 4 show that these (...) formal languages are rich enought to be used in the precise description of natural languages. Appendices describe some of the concepts discussed in the text. (shrink)

Two chief problems of the theory of knowledge are the question of meaning and the question of verification. The first question asks under what conditions a sentence has meaning, in the sense of cognitive, factual meaning. The second one asks how we get to know something, how we can find out whether a given sentence is true or false. The second question presupposes the first one. Obviously we must understand a sentence, i.e. we must know its meaning, before we can (...) try to find out whether it is true or not. But, from the point of view of empiricism, there is a still closer connection between the two problems. In a certain sense, there is only one answer to the two questions. If we knew what it would be for a given sentence to be found true then we would know what its meaning is. And if for two sentences the conditions under which we would have to take them as true are the same, then they have the same meaning. Thus the meaning of a sentence is in a certain sense identical with the way we determine its truth or falsehood; and a sentence has meaning only if such a determination is possible. (shrink)

It is not the aim of the present essay to defend the principle of empiricism against apriorism or anti-empiricist metaphysics. Taking empirism for granted, we wish to discuss, the question what is meaningful. The word ‘meaning’ will here be taken in its empiricist sense; an expression of language has meaning in this sense if we know how to use it in speaking about empirical facts, either actual or possible ones. Now our problem is what expressions are meaningful in this sense. (...) We may restrict this question to sentences because expressions other than sentences are meaningful if and only if they can occur in a meaningful sentence. (shrink)

Two chief problems of the theory of knowledge are the question of meaning and the question of verification. The first question asks under what conditions a sentence has meaning, in the sense of cognitive, factual meaning. The second one asks how we get to know something, how we can find out whether a given sentence is true or false. The second question presupposes the first one. Obviously we must understand a sentence, i.e. we must know its meaning, before we can (...) try to find out whether it is true or not. But, from the point of view of empiricism, there is a still closer connection between the two problems. In a certain sense, there is only one answer to the two questions. If we knew what it would be for a given sentence to be found true then we would know what its meaning is. And if for two sentences the conditions under which we would have to take them as true are the same, then they have the same meaning. Thus the meaning of a sentence is in a certain sense identical with the way we determine its truth or falsehood; and a sentence has meaning only if such a determination is possible. (shrink)

This book presents a formal and philosophical analysis of language syntax. It refers to some ideas of E.Husserl and G. Frege, to S. Leśniewski's theory of syntactic categories and K. Ajdukiewicz's conception of formal grammar, also to Ch.S. Pierces's distinction between tokens (concrete linguistic entities) and types (ideal linguistic entities) and to A.A. Markov's theory of algorithms. The central aim of the book is - in the spirit of these ideas - to provide both strict yet comprehensive lectures on two (...) axiomatic theories of languages (grammars) irrespective of specific structure of their expression and the notation used in them. The main feature of these theories are that definitions of well-formed expression allow the formulation of algorithms for the examination of syntactic correctness of expressions and that their formalizations are bi-level, in reference to opposite philosophical orientations: nominalistic and idealistic. The theoretical considerations in the book speak in favour of the former. The book contains a translation of the basic contents of the book in Polish "Teorie języków syntaktycznie kategorialnych ("Theories of syntactically categorial languages"), PWN, Warszawa-Wrocław 1985, and extensive Introduction and Final Remarks. In Introduction are discussed the main assumptions, objectives and conditionings of presented theories and intuitive foundations of these theories. Final Remarks are connected with the subject-matter of the book and the ability to build syntax theories in the opposition spirit, because of the Platonic approach to language syntax. -/- . (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 ...

Charles Sanders Peirce has been characterized as the greatest American philosophic genius. He is the creator of pragmatism and one of the founders of modern logic. James, Royce, Schroder, and Dewey have acknowledged their great indebtedness to him. A laboratory scientist, he made notable contributions to geodesy, astronomy, psychology, induction, probability, and scientific method. He introduced into modern philosophy the doctrine of scholastic realism, developed the concepts of chance, continuity, and objective law, and showed the philosophical significance of the theory (...) of signs and mathematical logic. The present series is the first published edition of his systematic works. (shrink)

Now in a new edition, this volume updates Davidson's exceptional Inquiries into Truth and Interpretation (1984), which set out his enormously influential philosophy of language. The original volume remains a central point of reference, and a focus of controversy, with its impact extending into linguistic theory, philosophy of mind, and epistemology. Addressing a central question--what it is for words to mean what they do--and featuring a previously uncollected, additional essay, this work will appeal to a wide audience of philosophers, linguists, (...) and psychologists. (shrink)

I reject the contention that an important theoretical difference exists between formal and natural languages.

This note is based on a lecture delivered at the Conference on the Scien- tic Research of the Mathematical Center of Opole, Turawa, May 10-11th, 1980. A somewhat extended version will be published in the Proceedings of the Conference. At the same time it is an abstract of a part of a planned larger paper, which will involve the theory of label-tokens. The theory is included into the author's monograph in Polish "Teorie Językow Syntaktycznie Kategorialnych", PWN, Warszawa-Wrocław 1985 and into (...) its English version: Theory of Language Syntax. Categorial Approach, Kluwer Academic Publishers, Boston-London-Dordrecht 1991. (shrink)