![]() ![]() This book is both an important scholarly contribution to the philosophy of logic and a systematic survey of the standard (and not so standard) logical systems that were established during the short history of modern logic. Jaroslav Peregrin analyzes the rationale behind the introduction of the artificial languages of logic classifies the various tools which were adopted to build such languages gives an overview of the various kinds of languages introduced in the course of modern logic and the motifs of their employment discusses what can actually be achieved by relocating the problems of logic from natural language into them and reaches certain conclusions with respect to the possibilities and limitations of this "formal turn" of logic. Philosophy of Logical Systems addresses these new kinds of philosophical problems that are intertwined with the development of modern logic. Hence, this movement has generated brand new kinds of philosophical problems that have still not been dealt with systematically. However, the change that logic underwent in this way was in no way insignificant, and it is also far from an insignificant matter to determine to what extent the "new logic" only engaged new and more powerful instruments to answer the questions posed by the "old" one, and to what extent it replaced these questions with new ones. This shift seemed extremely helpful and managed to elevate logic to a new level of rigor and clarity. Proceedings of The London Mathematical Society, 42: 230–265, 1937.ĭiagonal arguments is licensed under a Creative Commons Attribution 4.0 International License.This book addresses the hasty development of modern logic, especially its introducing and embracing various kinds of artificial languages and moving from the study of natural languages to that of artificial ones. On computable numbers, with an application to the entscheidungsproblem. Anzeiger der Österreichischen Akademie der Wissenschaften, Mathematisch-Naturwissenschaftliche Klasse, 69: 23–25, 1932.ġ0. Der Wahrheitsbegriff in den Sprachen der deduktiven Disziplinen. American Journal of Mathematics, XXX: 222–262, 1908.Ĩ. Mathematical logic as based on the theory of types. What is so bad about contradictions? The Journal of Philosophy, 95: 410–426, 1998.ħ. Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. What, outside of our logical theories, makes us believe that the theories are reliable, and what is it that. Naming and diagonalization, from Cantor to Gödel to Kleene. Jahresbericht der Deutschen Mathematiker-Vereingumg, 1: 75–78, 1890.Ĥ. Über eine elementare Frage der Mannigfaltigkeitslehre. Journal für die reine und angewandte Mathematik, 77: 258–262, 1874.ģ. ![]() Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen. Peregrin writes in Czech, English, German and Portuguese. He has published almost a hundred books and articles in several languages. Klíčová slova: diagonalization cardinality Russell’s paradox incompleteness of arithmetic halting problem reference (10)ġ. Jaroslav Peregrin (born 1957) is a professor of logic at Charles University in Prague and also a faculty member at the Academy of Sciences of the Czech Republic. Institute of Philosophy of the Czech Academy of Sciences, Jilska 1, 110 00 Prague 1, Czech Republic. Finally, we show how this fact yields the unsolvability of the halting problem for Turing machines. Institute of Philosophy of the Czech Academy of Sciences. We explain how this fact can be used to show that there are more sequences of natural numbers than there are natural numbers, that there are more real numbers than natural numbers and that every set has more subsets than elements (all results due to Cantor) we indicate how this fact can be seen as underlying the celebrated Russell’s paradox and we show how it can be employed to expose the most fundamental result of mathematical logic of the twentieth century, Gödel’s incompleteness theorem. Despite its apparent triviality, this fact can lead us the most of the path-breaking results of logic in the second half of the nineteenth and the first half of the twentieth century. It is a trivial fact that if we have a square table filled with numbers, we can always form a column which is not yet contained in the table.
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