Bibliography (1) Alechina, N., Mendler, M., De Paiva, V., & Ritter, E. (2001, September). Categorical and Kripke semantics for constructive S4 modal logic. En International Workshop on Computer Science Logic (pp. 292–307). Springer Berlin Heidelberg. (2) Van Benthem, J. (1976). Modal correspondence theory [Ph.D. Thesis]. University of Amsterdam, Netherlands . (3) Blackburn, P., De Rijke, M., & Venema, Y. (2001). Modal logic , volume 53 of Cambridge tracts in theoretical computer science. (4) Van Ditmarsch, H., van Der Hoek, W., & Kooi, B. (2007). Dynamic

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Ierodiakonou and Benjamin Morison. Oxford: Oxford University Press, 189-212. Bobzien, Susanne. 2013. Higher-order Vagueness and Borderline Nestings — a Persistent Confusion. Analytic Philosophy 54: 1-43. Carnielli, Walter and Pizzi, Claudio. 2009. Modalities and Multimodalities . New York: Springer. Chellas, Brian F. 1980. Modal Logic: An Introduction . Cambridge: Cambridge University Press. Fara, Delia Graff. 2003. Gap principles, penumbral consequence and infinitely higher-order vagueness. In Liars and Heaps: New Essays on Paradox . Edited by J. C. Beall

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## Abstract

My aim in this paper is to critically assess Plantinga’s modal ontological argument for existence of God, such as it is presented in the book “The Nature of Necessity” (1974). Plantinga tries to show that this argument is (i) valid and (ii) it is rational to believe in his main premise, namely “there is a possible world in which maximal greatness is instantiated”. On the one hand, I want to show that this argument is logically valid in both systems B and S5 of modal logic. On the other hand, I think that this argument is not a good argument to show that God exists or that it is rational to believe in God.

References 1. Bobzien, S. Determinism and Freedom in Stoic Philosophy , Oxford: Clarendon Press, 1998. 2. Garson, J. W. Modal Logic for Philosophers , Cambridge: Cambridge University Press, 2006. 3. Łukasiewicz, J. O logice trójwartościowej, Ruch filozoficzny 5, 1920, pp. 170–171б; English translation: On three-valued logic, In L. Borkowski (ed.), Selected works by Jan Łukasiewicz , Amsterdam: North–Holland, 1970, pp. 87-88.

References [1] SOLOVAY R.M., Provability interpretations of modal logic // Israel J. Math., 1975, 25, p. 287 - 304. [2] Post E.L. Introduction to a general theory of elementary propositions // Amer. J. Math., 1921, v. 43, p. 163 - 185. [3] Post E.L. Two-valued iterative systems of mathematical logic. Princeton, 1941. [4] KUZNETSOV A. V., On detecting non-deducibility and non-expressibility in: Locical deduction, Nauka, Moscow (1979), 5-33 (in russian) [5] DANIL'čENCO A. F. Parametric expressibility of functions of three-valued logic // Algebra i Logika, 16

## Abstract

A paradox of our time is identified: on the one hand – the development of one global system (ecological, technological and social), on the other hand – the still increasing “balkanization” of science. The dynamics of this systems is a source of well-known numerous global problems. Its possibly effective solution needs adequate knowledge about the system. For this reason, counteraction to “balkanization” of science is of great practical importance. And this counteraction should comprise not only development of “transboundary” sciences (such as biochemistry or social psychology) but also establishing and developing links between very distant disciplines. This text is intended as a contribution to linking social and engineering sciences. The notion of design plays the central role in this text. Its meaning in the engineering sciences. The notion of utopia has been chosen as a partial counterpart to the term of engineering design. This notion was defined using a concept of possible world – taken from modal logic. It encompasses two ideas: this of design and that of prediction, It is claimed that we need many utopias and that their plurality is of fundamental importance for protecting us against the threats of utopianism. The paper suggests that social utopias can play a heuristic role in engineering design (particularly in the initial phase of defining technological problems), and – on the other hand – that the theory of engineering design can be supportive for, badly needed, development of methodology of utopias creation.

References Correia, Fabrice. 2005. Existential Dependence and Cognate Notions . Munich: Philosophia Verlag. Everett, Anthony. 2005. Against fictional realism. Journal of Philosophy 102(12): 624–49. Everett, Anthony. 2013 The Nonexistent . Oxford: Oxford University Press. Fine, Kit. 1995. Ontological dependence. Proceedings of the Aristotelian Society 95: 269–90. Fitting, Melvin; and Mendelsohn, Richard. 1998. First-Order Modal Logic . Dordrecht: Kluwer. Fontaine, Matthieu. 2019. Hintikka, free logician—singular terms in world lines semantic. Logica

References Arieli, O., Avron, A., & Zamansky, A. (2011). Ideal Paraconsistent Logics. Studia Logica, 99(1-3), 31-60. Béziau, J.-Y. (2006). The paraconsistent logic Z. A possible solution to Jaśkowski’s problem. Logic and Logical Philosophy, 15(2), 99-111. Chellas, B. F. (1980). Modal Logic: An Introduction. Cambridge: Cambridge University Press. Ciuciura, J. (2008). Negations in the Adjunctive Discursive Logic. Bulletin of the Section of Logic, 3 7(3-4), 143-160. Ciuciura, J. (2005). On the da Costa, Dubikajtis and Kotas’ system of the discursive logic, D∗ 2