New light on the square. Of oppositions and its nameless corner


J.-Y. Beziau


It has been pointed out that there is no primitive name in natural and formal languages for one corner o f the famous square o f oppositions. We have all, some and no, but no primitive name for not all It is true also in the modal version o f the square, we have necessary, possible and impossible, but no primitive name for not necessary.






A.I. Amida. N.A.Vasiliev e a logica paraconsistente. Center o f Logic o f the Univer sity o f Campinas, Campinas, 1990.

J.-Y.Beziau. «What is paraconsistent logic? » // Frontiers o f paraconsistent logic , D.Batens et al. (eds) Research Studies Press, Badlock, 2000, pp.95-112.

J.-Y.Beziau. «Are paraconsistent negations negations? » in Paraconsistency, the logical way to the inconsistent. W.Camielli et al. (eds). Marcel Dekker, New York, 2002.

J.-Y.Beziau. «S5 is a paraconsistent logic and so is first-order classical logic» // Logical Investigations. 9 (2002). P.23-31.

J.-Y.Beziau. «Paraconsistent logic from a modal viewpoint»: Talk presented at the ESSLI 2002. Trento, August 2002, 16.html. To appear in the Journal o f Applied Logic. J.-Y.Beziau. «Paraconsistent logic! (A reply to Slater)», submitted. R.Blanche. «Sur Г opposition des concepts» // Theoria, 19 (1953). P.89-130.

R.Blanche. «Opposition et negation» // Revue Philosophique, 167 (1957).

P. 187-216.

R.Blanche. «Sur la structuration du tableau des connectifs interpropositionnels

binaires» // Journal o f Symbolic Logic, 22 (1957). P.17-18.

R.Blanch c.ructures intellectuelles. Essai sur Vorganisation systematique des

concepts. Vrin, Paris, 1966.

W .Camielli and C.Pizzi. Modalit_ e multimodalit_. Franco Angeli, Milan,

2001 .

R.M.Chisholm. «Supererogation and offence: a conceptual scheme for ethics» П Ratio 5 (1963). P.1-14.

M . J.Cresswell. «Necessity and contingency», Studia Logica , 47 (1988), pp. 145-149.

K.Dosen. «Negation ,and impossibility»: in Essays on philosophy and logic, J.Perzanowski (ed), Jagellonian University Press, Cracow, 1987. P.85-91. K.Dosen. «Negation in the light of modal logic»: in What is negation?, D.Gabbay and H.Wansing (eds). Kluwer, Dordrecht, 1999. P.77-86.

J. -L.Gardies. Essai sur la logique des modalites, PUF, Paris, 1979.

K. G_del. «Eine Interpretation des intuitionistischen Aussagenkalk_ls» Ergebnisse eines mathematischen Kolloquiums, 4 (1933). P.34-40.

N . Grana. Contradizzione e incompletezza , Liguori, Naples, 1990.

J.-B.Grize. «Des canes qui ne toument pas rond et de quelques autres» // Travaux du centre de recherches semiologiques , 56 (1988). P. 139-152.

J.Hoeksema. «Blocking Effects and Polarity Sensitivity»: in: JFAK Essaysdedicated to Johan van Benthem on the Occasion o f his 50th Birthday. Vossiuspers/Amsterdam University Press, 1999.

L. R.Hom. A natural history o f negation, UCP, Chicago, 1989. I.L.Humberstone. «The logic of non-contingency» // Notre Dame Journal o f Formal Logic , 36 (1995). P.214-229.

I.L.Humberstone. «M odality»: in Handbook o f Analytical Philosophy, F.Jackson and M.Smith, Oxford University Press, forthcoming.

O. Jespersen. «Negation in English and other languages» // Historiskfdologiske Meddeleser, 1 (1917). P.1-151.

A.Loparic and N.C.A. da Costa. «Paraconsistency, paracompleteness and valuations» 11 Logique et Analyse, 106 (1984). P.l 19-139.

I. Lucchese and N.Grana. Attraverso lo specchio , LOrientale Editrice, Naples, 2000 .

J. Lukasiewicz. 1953, «A system o f modal logic» // Journal o f Computing Systems, 1, P.l 11-149.

H.Montgomery and R.Routley. «Contingency and non-contingency bases for normal modal logics»// Logique et Analyse, 9 (1966). P.341-344.

T.Parsons. «The traditional square o f opposition» // Stanford Encyclopedia o f Philosophy, 1999.

D.H.Sanford. «Contraries and subcontraries» // Nous, 2 (1968). P.95-96. A . Sion. Future logic. Geneva, 1996.

B . H.Slater, «Paraconsistent logics? » // Journal o f Philosophical Logic, 24 (1995). P.451-454.

N.Vasiliev. On particular judgments, the triangle o f oppositions and the law o f the excluded fourth (Russian)10. Kazan University Press., 1910.

M.Wajsberg. «Ein erweiteter Klassenkalkiil» // Monatschefte fu r Mathematik undPhysik , 40 (1933). P.l 13-126.