Philosophical and Mathematical Logic

Cham: Springer Verlag (2014)
  Copy   BIBTEX

Abstract

Having studied mathematics, in particular foundations and philosophy of mathematics, it happened that I was asked to teach logic to the students in the Faculty of Philosophy of the Radboud University Nijmegen. It was there that I discovered that logic is much more than just a mathematical discipline consisting of definitions, theorems and proofs, and that logic can and should be embedded in a philosophical context. After ten years of teaching logic at the Faculty of Philosophy at the Radboud University Nijmegen, thirty years at the Faculty of Philosophy of Tilburg University and nine years at the Faculty of Philosophy of the Erasmus University Rotterdam, I got many ideas how to improve my LOGIC book which was published twenty five years ago in 1993 by Verlag Peter Lang. Although the amount of work was enormous, I felt I should do it. It is like working on a large painting where you put some extra color in one corner, add a little detail at another place, shed some more light on a particular face, etc.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,386

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Chapters

Applications: Prolog; Relational Databases and SQL; Social Choice Theory

The language of logic can be used as a declarative programming language, i.e., the programmer has to describe what the problem is, not how it should be solved. We introduce logic programming by means of an example and explain how the system answers questions given a certain program. The possibility ... see more

Intuitionism and Intuitionistic Logic

Brouwer’s intuitionism is based on quite different philosophical ideas about the nature of mathematical objects than classical mathematics. This intuitionistic point of view results in a different use of language and in a corresponding different intuitionistic logic which is far more subtle than the... see more

Philosophy of Language

This chapter aims to be an introduction to the philosophy of language and presents some major topics belonging to this field: the difference between use and mention, Frege’s notions of Sinn and Bedeutung , Mannoury’s significs, speech acts, definite descriptions, Berry’s and Grelling’s paradox, the ... see more

Modal Logic

Modal operators, like ‘it is necessary that’ or ‘John knows that’, express an attitude about the proposition to which they are applied. Modal logic studies the reasoning in modal contexts, extending classical logic in which only connectives and quantifiers are taken into account. There are many syst... see more

Arithmetic: Gödel’s Incompleteness Theorems

We formalize elementary number theory, i.e., we introduce a formal language L for expressing properties of addition and multiplication of natural numbers, and a set P of non-logical axioms in order to be able to formally deduce those properties fromP.

Predicate Logic

In this chapter we extend the language of propositional logic to the one of predicate logic, in which we also can analyse arguments containing subjects and predicates, such as in, for example: All men are mortal; therefore: Socrates is mortal; and in: Socrates is a philosopher; therefore: someone is... see more

Sets: finite and infinite

Sets occur abundantly in mathematics and in daily life. But what is a set? Cantor defined a set as a collection of all objects which have a certain property in common. Russell showed in 1902 that this assumption yields a contradiction, known as Russell’s paradox, and hence is untenable. In 1908 Zerm... see more

Propositional Logic

In this chapter we analyse reasoning patterns of which the validity only depends on the meaning of the propositional connectives ‘if..., then...’, ‘and’, ‘or’ and ‘not’. By giving a precise description of the meaning of these propositional connectives one is able to give a precise definition of the ... see more

Logic; a First Impression

In this introductory chapter the topic of the book is explained: distinguishing valid patterns of reasoning from invalid ones. The validity may depend on the meaning of connectives like ‘if..., then... ’, ‘and’, ‘or’ and ‘not’, in which case one speaks of propositional logic. But the validity may al... see more

Fallacies and Unfair Discussion Methods

Many discussions and meetings are led perfectly from a formal and procedural perspective, but the quality of the in-depth discussion is nevertheless poor. The cause of poor thinking should be sought in the weakness of human nature, rather than in the limitations of our intelligence. Among the weakne... see more

Similar books and articles

Mathematical Logic and Modern Formal Logic.A. A. Vetrov - 1964 - Russian Studies in Philosophy 3 (1):24-33.
19th century logic between philosophy and mathematics.Volker Peckhaus - 1999 - Bulletin of Symbolic Logic 5 (4):433-450.
On The Concept of Dialectical Logic.S. B. Tsereteli - 1966 - Russian Studies in Philosophy 5 (2):15-22.
Formal logic: Classical problems and proofs.Luis M. Augusto - 2019 - London, UK: College Publications.
Mathematical epistemology and psychology.Evert Willem Beth - 1966 - New York,: Gordon & Breach. Edited by Jean Piaget.
On the use (and abuse) of Logic in Game Theory.Eric Pacuit - 2015 - Journal of Philosophical Logic 44 (6):741-753.
Mathematical logic.Willard Van Orman Quine - 1951 - Cambridge,: Harvard University Press.
A course in mathematical logic.J. L. Bell - 1977 - New York: sole distributors for the U.S.A. and Canada American Elsevier Pub. Co.. Edited by Moshé Machover.
The development of mathematical logic.Peter Harold Nidditch - 1962 - New York,: Free Press of Glencoe.
Mathematical existence.Penelope Maddy - 2005 - Bulletin of Symbolic Logic 11 (3):351-376.

Analytics

Added to PP
2020-02-02

Downloads
6 (#1,430,516)

6 months
2 (#1,232,442)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Harrie De De Swart
Erasmus University Rotterdam

Citations of this work

Slippery Slopes Revisited.Martin Hinton - 2020 - Studia Semiotyczne 34 (2):9-24.

Add more citations

References found in this work

No references found.

Add more references