Is Transparent Intensional Logic a non-classical logic?
DOI:
https://doi.org/10.12775/LLP.2013.032Keywords
TIL, bivalence, classicality, construction, expressivity, extensions, intensions, hyperintensionality, procedure, realism, anti-realismAbstract
It is shown that:
(a) classicality is connected with various criteria some of which are fulfilled by TIL while some other are not;
(b) some more general characteristic of classicality connects it with philosophical realism whereas (radical) anti-realism is connected with non-classical logics;
(c) TIL is highly expressive due to its hyperintensionality, which makes it possible to handle procedures as objects sui generis.
Thus TIL is classical in obeying principles of realism and non-classical in transcending some principles taught by textbooks of classical logic.
References
Banks, P., 1950, “On the philosophical interpretation of logic: an Aristotelian dialogue”, pages 139–153 in Dominican Studies, Oxford, III/2. DOI: 10.1007/978-94-010-3649-8_1
Bealer, G., 1982, Quality and Concept, Oxford: Clarendon Press.
Carnap, R., 1947, Meaning and Necessity, Chicago: Chicago University Press.
Carnap, R., 1950, Logical Foundations of Probability, Chicago: Chicago University Press.
Dummett, M., 1991, The Logica Basis of Metaphysics, London, G. Duckworth.
Duží, M., 2003, “Do we have to deal with partiality?”, pages 45–76 in Miscellanea Logica, vol. 5, K. Bendová and P. Jirků (eds.), Praha: Karolinum.
Duží, M., B. Jespersen and P. Materna, 2010, Procedural Semantics for Hyperintiensional Logic, Springer.
Kolmogorov, A., 1932, “Zur Deutung der intuitionistischen Logik”, Mathematische Zeitschrift, 35: 58–65. DOI: 10.1007/BF01186549
Strawson, P.F., 1950, “On referring”, Mind, 59: 320–344.
Tichý, P., 1988, The Foundations of Frege’s Logic, Berlin, New York: De Gruyter.
Tichý, P., 1995, “Constructions as the subject-matter of mathematics”, pages 175–185 in The Foundational Debate: Complexity and Constructivity in Mathematics and Physics, W. DePauli-Schimanovich, E. Köhler and F. Stadler (eds.), Dordrecht, Boston, London, and Viena: Kluwer. CrossRef
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