Rethinking inconsistent mathematics

This dissertation has two main goals. The first is to provide a practice-based analysis of the field of inconsistent mathematics: what motivates it? what role does logic have in it? what distinguishes it from classical mathematics? is it alternative or revolutionary? The second goal is to introduce and defend a new conception of inconsistent mathematics - queer incomaths - as a particularly effective answer to feminist critiques of classical logic and mathematics. This sets the stage for a genuine revolution in mathematics, insofar as it suggests the need for a shift in mainstream attitudes about the rolee of logic and ethics in the practice of mathematics

Modal Extensions Of Sub-classical Logics For Recovering Classical Logic

In this paper we introduce non-normal modal extensions of the sub-classical logics CLoN, CluN and CLaN, in the same way that S0. 50 extends classical logic. The first modal system is both paraconsistent and paracomplete, while the second one is paraconsistent and the third is paracomplete. Despite being non-normal, these systems are sound and complete for a suitable Kripke semantics. We also show that these systems are appropriate for interpreting □ as "is provable in classical logic". This allows us to recover the theorems of propositional classical logic within three sub-classical modal systems. © 2013 Springer Basel.717186Batens, D., Paraconsistent extensional propositional logics (1980) Logique et Analyse 90/91, pp. 195-234Batens, D., de Clercq, K., Kurtonina, N., Embedding and interpolation for some paralogics (1999) The Propositional Case. Rep. Math. Log., 33, pp. 29-44Boolos, G., (1993) The Logic of Provability, , Cambridge: Cambridge University PressCarnielli, W.A., Coniglio, M.E., Marcos, J., Logics of Formal Inconsistency (2007) Handbook of Philosophical Logic, 14, pp. 1-93. , In: Gabbay, D., Guenthner, F. (eds.), 2nd edn., Springer, BerlinCarnielli, W.A., Pizzi, C., (2008) Modalities and Multimodalities, Vol. 12 of Logic, Epistemology, and the Unity of Science, , Berlin: SpringerConiglio, M.E., Logics of deontic inconsistency (2009) Revista Brasileira de Filosofia, 233, pp. 162-186. , http://www.cle.unicamp.br/e-prints/vol_7,n_4,2007.html, A preliminary version was published in CLE e-Prints 7(4), 2007 Available atCreswell, M.J., The completeness of S0. 5 (1966) Logique et Analyse, 34, pp. 262-266Creswell, M.J., Hughes, G.E., (1968) An Introduction to Modal Logic, , Routledge, London and New YorkGlivenko, V., Sur quelques points de la logique de M. Brouwer. Academie Royale de Belgique (1929) Bulletins de la Classe des Sciences, 5 (15), pp. 183-188Gödel, K., Eine Intepretation des intionistischen Aussagenkalk̈ul (1933) Ergebnisse eines Mathematischen Kolloquiums, 4, pp. 6-7. , English translation in Gödel (1986) pp. 300-303Gödel, K., (1986) Kurt Gödel, Collected Works: Publications 1929-1936, , Cary: Oxford University PressKripke, S., Semantical Analysis of Modal Logic I (1963) Normal Proposicional Calculi. Zeitschrift Fur Mathematische Logik Und Grundlagen Der Mathematik, 9, pp. 67-96Kripke, S., Semantical Analysis of Modal Logic II. Non-Normal Modal Propositional Calculi (1965) The Theory of Models (Proceedings of the 1963 International Symposium at Berkeley), pp. 206-220. , In: Addison, J. W., Henkin, L., Tarski, A. (eds.), Amsterdam, North-HollandLemmon, E.J., New Foundations for Lewis Modal Systems (1957) J. Symb. Logic, 22 (2), pp. 176-186Lemmon, E.J., Algebraic semantics for modal logics I (1966) J. Symb. Logic, 31 (1), pp. 44-65Lewis, C.I., Langford, C.H., (1932) Symbolic Logic, , CenturySegerberg, K.K., (1971) An Essay in Classical Modal Logic, , PhD thesis, Stanford UniversityShoenfield, J.R., (1967) Mathematical Logic, , Addison-Wesley, ReadingWójcicki, R., (1984) Lectures on Propositional Calculi, , http://www.ifispan.waw.pl/studialogica/wojcicki/papers.html, Ossolineum, Wroclaw, Available a