In 1907 Luitzen Egbertus Jan Brouwer defended his doctoral dissertation on the foundations of mathematics and with this event the modem version of mathematical intuitionism came into being.
Like the journal TOPOl, the TOPOl Library is based on the assumption that philosophy is a lively, provocative, delightful activity, which constantly challenges our inherited habits, painstakingly elaborates on how things could be different, in other stories, in counterfactual situations, in alternative possible worlds.
Recent major advances in model theory include connections between model theory and Diophantine and real analytic geometry, permutation groups, and finite algebras.
Intensional logic has emerged, since the 1960' s, as a powerful theoretical and practical tool in such diverse disciplines as computer science, artificial intelligence, linguistics, philosophy and even the foundations of mathematics.
The purpose of this book is to provide the reader who is interested in applications of fuzzy set theory, in the first place with a text to which he or she can refer for the basic theoretical ideas, concepts and techniques in this field and in the second place with a vast and up to date account of the literature.
Discussions of the foundations of mathematics and their history are frequently restricted to logical issues in a narrow sense, or else to traditional problems of analytic philosophy.
Doing Worlds with Words throws light on the problem of meaning as the meeting point of linguistics, logic and philosophy, and critically assesses the possibilities and limitations of elucidating the nature of meaning by means of formal logic, model theory and model-theoretical semantics.
without a properly developed inconsistent calculus based on infinitesimals, then in- consistent claims from the history of the calculus might well simply be symptoms of confusion.
With the vision that machines can be rendered smarter, we have witnessed for more than a decade tremendous engineering efforts to implement intelligent sys- tems.
The International Congresses of Logic, Methodology and Philosophy of Science, which are held every fourth year, give a cross-section of ongoing research in logic and philosophy of science.
A partially ordered group is an algebraic object having the structure of a group and the structure of a partially ordered set which are connected in some natural way.
Since their appearance in the late 19th century, the Cantor--Dedekind theory of real numbers and philosophy of the continuum have emerged as pillars of standard mathematical philosophy.
This volume contains a selection of papers presented at a Seminar on Intensional Logic held at the University of Amsterdam during the period September 1990-May 1991.
Between the two world wars, Stanislaw Lesniewski (1886-1939), created the famous and important system of foundations of mathematics that comprises three deductive theories: Protothetic, Ontology, and Mereology.
Modal Logic is a branch of logic with applications in many related disciplines such as computer science, philosophy, linguistics and artificial intelligence.
On January 22, 1990, the late John Bell held at CERN (European Laboratory for Particle Physics), Geneva a seminar organized by the Center of Quantum Philosophy, that at this time was an association of scientists interested in the interpretation of quantum mechanics.
The conference on Ordered Algebraic Structures held in Curat;ao, from the 26th of June through the 30th of June, 1995, at the Avila Beach Hotel, marked the eighth year of ac- tivities by the Caribbean Mathematics Foundation (abbr.
Mathematics is often considered as a body of knowledge that is essen- tially independent of linguistic formulations, in the sense that, once the content of this knowledge has been grasped, there remains only the problem of professional ability, that of clearly formulating and correctly proving it.
Belief change is an emerging field of artificial intelligence and information science dedicated to the dynamics of information and the present book provides a state-of-the-art picture of its formal foundations.
Nonstandard methods of analysis consist generally in comparative study of two interpretations of a mathematical claim or construction given as a formal symbolic expression by means of two different set-theoretic models: one, a "e;standard"e; model and the other, a "e;nonstandard"e; model.
