In this talk, we shall argue that the tarskian structural consequence relation (TSCR) captures the correct idea of consequence relation. This debate is situated within the debate on logical pluralism, especially the debate on pluralism of logical consequence. But, we shall concentrate on the case of Many-valued Logics (MVL’s), i.e., logics which have more than two truth-values. If we defend that TSCR captures this correct idea, then we are compromised with Suszko’s Thesis (ST). According to Suszko [4], there are only two logical values: truth and falsity. This claim is known as ST. In order to defend his position, he proves that any tarskian structural logic is 2-valued. But, Caleiro et al [2] show that the property of structurality can be dispensed. Moreover, they give a constructive method to characterize any MVL with a bivalent semantics. Thus, this thesis becomes quite general. However, ST faces some objections. For example, Woleński [6] argues that the choice of TSCR is arbitrary, i.e., this choice is not based on purely logical reasons. And Wansing et al [5] and da Costa et al [3] argue that we can use alternative consequence relations in order to overcome ST. Finally, we shall argue, in the line of Beall & Restall [1], that ST is compatible with logical pluralism.

References

[1] J. C. Beall and G. Restall. Logical pluralism. Oxford University Press on Demand, 2006.

[2] C. Caleiro, W. Carnielli, M. E. Coniglio, and J. Marcos. Two’s company: “The humbug of many logical values”. In Logica universalis, pages 175–194. Springer, 2007.

[3] N. C. Da Costa, J.-Y. Béziau, O. A. Bueno, et al. Malinowski and Suszko on many - valued logics: on the reduction of many - valuedness to two - valuedness. Modern Logic, 6(3):272–299, 1996.

[4] R. Suszko. The Fregean Axiom and Polish mathematical logic in the 1920 s. Studia Logica, 36(4):377–380, 1977.

[5] H. Wansing and Y. Shramko. Suszko’s Thesis, inferential many - valuedness, and the notion of a logical system. Studia Logica, 88(3):405–429, 2008.

[6] J. Wolenski. The principle of bivalence and Suszko thesis. Bulletin of the Section of Logic, 38(3/4):99–110, 2009.