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.

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)

Die Grundlagen gehören zu den klassischen Texten der Sprachphilosophie, Logik und Mathematik. Frege stützt sein Programm einer Begründung von Arithmetik und Analysis auf reine Logik, indem er die natürlichen Zahlen als bestimmte Begriffsumfänge definiert. Die philosophische Fundierung des Fregeschen Ansatzes bilden erkenntnistheoretische und sprachphilosophische Analysen und Begriffserklärungen. Studienausgabe aufgrund der textkritisch herausgegebenen Jubiläumsausgabe (Centenarausgabe). Mit Einleitung, Anmerkungen, Literaturverzeichnis und Namenregister.

Noam Chomsky's book on syntactic structures is a serious attempts on the part of a linguist to construct within the tradition of scientific theory-construction ...

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)

This volume contains a collection of research papers centered around the concept of quantifier. Recently this concept has become the central point of research in logic. It is one of the important logical concepts whose exact domain and applications have so far been insufficiently explored, especially in the area of inferential and semantic properties of languages. It should thus remain the central point of research in the future. Moreover, during the last twenty years generalized quantifiers and logical technics based on (...) them have proved their utility in various applications. The example of natu rallanguage semantics has been partcularly striking. For a long time it has been belived that elementary logic also called first-order logic was an ade quate theory of logical forms of natural language sentences. Recently it has been accepted that semantics of many natural language constructions can not be properly represented in elementary logic. It has turned out, however, that they can be described by means of generalized quantifiers. As far as computational applications oflogic are concerned, particulary interesting are semantics restricted to finite models. Under this restriction elementary logic looses several of its advantages such as axiomatizability and compactness. And for various purposes we can use equally well some semantically richer languages of which generalized quantifiers offer the most universal methods of describing extensions of elementary logic. Moreover we can look at generalized quantifiers as an explication of some specific mathematical concepts, e. g. (shrink)

Die Grundlagen gehören zu den klassischen Texten der Sprachphilosophie, Logik und Mathematik. Frege stützt sein Programm einer Begründung von Arithmetik und Analysis auf reine Logik, indem er die natürlichen Zahlen als bestimmte Begriffsumfänge definiert. Die philosophische Fundierung des Fregeschen Ansatzes bilden erkenntnistheoretische und sprachphilosophische Analysen und Begriffserklärungen. Studienausgabe aufgrund der textkritisch herausgegebenen Jubiläumsausgabe (Centenarausgabe). Mit Einleitung, Anmerkungen, Literaturverzeichnis und Namenregister.

Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens / von Dr. Gottlob Frege,...Date de l'edition originale : 1879Ce livre est la reproduction fidele d'une oeuvre publiee avant 1920 et fait partie d'une collection de livres reimprimes a la demande editee par Hachette Livre, dans le cadre d'un partenariat avec la Bibliotheque nationale de France, offrant l'opportunite d'acceder a des ouvrages anciens et souvent rares issus des fonds patrimoniaux de la BnF.Les oeuvres faisant partie de cette collection ont ete numerisees (...) par la BnF et sont presentes sur Gallica, sa bibliotheque numerique.En entreprenant de redonner vie a ces ouvrages au travers d'une collection de livres reimprimes a la demande, nous leur donnons la possibilite de rencontrer un public elargi et participons a la transmission de connaissances et de savoirs parfois difficilement accessibles.Nous avons cherche a concilier la reproduction fidele d'un livre ancien a partir de sa version numerisee avec le souci d'un confort de lecture optimal. Nous esperons que les ouvrages de cette nouvelle collection vous apporteront entiere satisfaction.Pour plus d'informations, rendez-vous sur www.hachettebnf.frhttp://gallica.bnf.fr/ark:/12148/bpt6k65658c. (shrink)

By logical foundations of language syntax ontology we understand here the construction of formalized linguistic theories based on widely conceived mathematical logic and dependent on two trends in language ontology. The formalization includes exclusively the syntactic aspect of logical analysis of language characterized categorially according to Ajdukiewicz's approach [1935, 1960]. Any categorial language L is characterized formally on two levels: on one of them it concerns the language of expression-tokens, on the other one - that of expression-types. Accepting the view (...) that expression-concretes, that is expression-tokens - thus, physical objects are fundamental language layer, whereas the secondary layer for L are expression-abstracts, that is expression-types - thus, ideal objects, it is the nominalistic, concretistic philosophical view on the ontological nature of language entities that is adhered to. Supporting the view that expression-types are the basic language layer, while expression-concretes are the secondary one, we take the opposite standpoint - platonizing one. We prove that the two dual approaches towards the two-level syntax theory of language are logically eqivalent. In the scope of language syntax, both conceptions deriving from two different existential assumption are equivalent. This statement is philosophical significance, since it proves that in syntactical studies on language the assumption of the existence of abstract language beings (interpreted as classes equiform tokens) can be neglected. The idea was signalized by author in ealier paper "On the type-token relationships'' [1986) and than, in a slighly diffrent form in English "On the eliminatibility of ideal linguistic entities, Studia Logica 48,no 4 (1989), pp. 587-615. (shrink)