Эпистемологические основания математики в некоторых неологицистских теориях
Neologicism - the trend of modern philosophy of mathematics associated with attempts to resolve the contradictions of Frege’s "Foundations of mathematics" or to develop some other ways of deriving mathematics from logic. We try to examine some neologicist theories (C. Wright , B. Linsky and E. Zalta) and the relative philosophical discussions. Our purpose is to identify the advantages and disadvantages of the different types of neologicism and try to define the concept of neologicism in more precise way.
Edward Zalta's axiomatic metaphysics or Theory of abstract objects is a philosophical theory with powerful logical unit which enables us to analyze a lot of ontological categories, such as non-existent objects, properties and relationships, possible worlds, states of affairs and many others that are in focus of modern analytic philosophy. Rich expressive power of the Theory are directly related to its fundamental premise — the distinction between the two modes of predication: exemplification and encoding. The main concern of the paper is to clarify the structure of the universe which arise on the ground of that distinction and to demonstrate some of its problematic consequences.
E. Zalta and P. Oppenheimer have created non-modal reading of the Anselm’s argument about the existence of God, The Ontological Argument. The authors have deduced the existence of God from his being. For this purpose, the term "that than which none greater can be conceived" used as a definite description. Through the predicate logic with the descriptions and several special axioms Zalta and Oppenheimer have formalized Anselm’s argument and demonstrate that from a formal point of view, his arguments is quite correct. But if we use as a tool the Theory of abstract objects we obtain the ontological argument, consequence of which is fundamentally different from the conclusion that Anselm has made.
This volume presents different conceptions of logic and mathematics and discuss their philosophical foundations and consequences. This concerns first of all topics of Wittgenstein's ideas on logic and mathematics; questions about the structural complexity of propositions; the more recent debate about Neo-Logicism and Neo-Fregeanism; the comparison and translatability of different logics; the foundations of mathematics: intuitionism, mathematical realism, and formalism.
The contributing authors are Matthias Baaz, Francesco Berto, Jean-Yves Beziau, Elena Dragalina-Chernya, Günther Eder, Susan Edwards-McKie, Oliver Feldmann, Juliet Floyd, Norbert Gratzl, Richard Heinrich, Janusz Kaczmarek, Wolfgang Kienzler, Timm Lampert, Itala Maria Loffredo D'Ottaviano, Paolo Mancosu, Matthieu Marion, Felix Mühlhölzer, Charles Parsons, Edi Pavlovic, Christoph Pfisterer, Michael Potter, Richard Raatzsch, Esther Ramharter, Stefan Riegelnik, Gabriel Sandu, Georg Schiemer, Gerhard Schurz, Dana Scott, Stewart Shapiro, Karl Sigmund, William W. Tait, Mark van Atten, Maria van der Schaar, Vladimir Vasyukov, Jan von Plato, Jan Woleński and Richard Zach.
The article describes some of the fundamental features of Edward Zalta’s Theory of abstract objects in connection with the problem of possible worlds, as well as the use of names as rigid designators. The main feature of Zalta’s Theory is the separation of the two types of predication of properties: one for concrete objects and the other for abstract ones. This approach allowed us to avoid certain paradoxes. In the theory of abstract objects possible worlds considered as abstract objects that are associated with propositional properties. Such an approach is not without appeal, but has some syntactical defects, leading to circularity in the definition of modalities and even the definition of identity relation.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.