| Автор | Jané, Ignacio |
| Дата выпуска | 1993 |
| dc.description | Because of its capacity to characterize mathematical concepts and structures—a capacity which first-order languages clearly lack—second-order languages recommend themselves as a convenient framework for much of mathematics, including set theory. This paper is about the credentials of second-order logic:the reasons for it to be considered logic, its relations with set theory, and especially the efficacy with which it performs its role of the underlying logic of set theory |
| Формат | application.pdf |
| Издатель | Taylor & Francis |
| Копирайт | Copyright Taylor and Francis Group, LLC |
| Название | A critical appraisal of second-order logic |
| Тип | research-article |
| DOI | 10.1080/01445349308837210 |
| Electronic ISSN | 1464-5149 |
| Print ISSN | 0144-5340 |
| Журнал | History and Philosophy of Logic |
| Том | 14 |
| Первая страница | 67 |
| Последняя страница | 86 |
| Аффилиация | Jané, Ignacio; Departamento de Lögica, Universidad de Barcelona |
| Выпуск | 1 |
| Библиографическая ссылка | Bernays, P. 1934. “On Platonism in mathematics”. In Philosophy of mathematics. Selected readings, Edited by: Benacerraf, P. and Putnam, H. 258–271. London: Cambridge University Press. |
| Библиографическая ссылка | Boolos, G. 1975. On second-order logic. The journal of philosophy, 72: 509–527. |
| Библиографическая ссылка | Boolos, G. 1984. To be is to be the value of a variable (or to be some values of some variables). The journal of philosophy, 81: 430–449. |
| Библиографическая ссылка | Boolos, G. and Jeffrey, R. 1980. Computability and logic, London: Cambridge University Press. |
| Библиографическая ссылка | Church, A. 1956. Introduction to mathematical logic, Princeton: Princeton University Press. |
| Библиографическая ссылка | Corcoran, J. 1973. “Gaps between logical theory and mathematical practice”. In The methodological unity of science, Edited by: Bunge, M. 23–50. Dordrecht: Reidel. |
| Библиографическая ссылка | Drake, F. 1974. “Set theory”. In An introduction to large cardinals, Amsterdam: North-Holland. |
| Библиографическая ссылка | Frege, G. 1984. “Collected papers”. Oxford: Basil Blackwell. |
| Библиографическая ссылка | Friedman, H. 1971. Higher set theory and mathematical practice. Annals of mathematical logic, 2: 326–357. |
| Библиографическая ссылка | Hallett, M. 1984. Cantorian set theory and limitation of size, Oxford: Clarendon Press. |
| Библиографическая ссылка | Gödel, K. 1990. Collected works, Vol. II, Oxford: Oxford University Press. |
| Библиографическая ссылка | Lewis, D. 1991. Parts of classes, Oxford: Basil Blackwell. |
| Библиографическая ссылка | Moore, G. 1980. Beyond first-order logic:the historical interplay between logic and set theory. History and philosophy of logic, 1: 95–137. |
| Библиографическая ссылка | Quine, W. 1963. Set theory and its logic, London: Cambridge University Press. |
| Библиографическая ссылка | Quine, W. 1970. “Philosophy of logic”. Englewood Cliffs, N.J: Prentice-Hall. |
| Библиографическая ссылка | Quine, W. 1987. Quiddities. An intermittently philosophical dictionary, London: Harvard University Press. |
| Библиографическая ссылка | Russell, B. 1919. Introduction to mathematical philosophy, London: Allen & Unwin. |
| Библиографическая ссылка | Shapiro, S. 1985. Second-order languages and mathematical practice. The journal of symbolic logic, 50: 714–742. |
| Библиографическая ссылка | Shapiro, S. 1990. Second-order logic, foundations and rules. The journal of philosophy, 87: 234–261. |
| Библиографическая ссылка | Shapiro, S. 1991. Foundations without foundationalism, Oxford: Clarendon Press. |
| Библиографическая ссылка | Solovay, S. 1969. “On the cardinality of ∑ ½ sets of reals”. In Foundations of mathematics, Edited by: Bulloff, J. 58–73. Berlin: Springer. |
| Библиографическая ссылка | Solovay, S. 1970. A model of set theory in which every set of reals is Lebesgue measurable. Annals of mathematics, 92: 1–56. |
| Библиографическая ссылка | Weston, T. 1976. Kreisel, the continuum hypothesis and second-order set theory. Journal of philosophical logic, 5: 281–298. |
| Библиографическая ссылка | Zermelo, E. 1930. Über Grenzzahlen und Mengenbereiche. Fundamenta mathematica, 16: 29–47. |
