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Abstract

The form of the conditional syllogism resembles that of the categorical syllogism, while its subject matter is at least a conditional premise, but its conclusion is always conditional conjunctive or disjunctive. This mixed structure to which we apply the rules of the categorical syllogism, is a structure of which Aristotle did not have an idea, and which the Stoics did not conceive, and which the non-Arabian logicians did not know until in modern times. But what we have to notice here is the putting of a conditional matter in the form of the categorical syllogism, and it is this kind of hybridization, if we dare to say, which generated this mixed structure which appeared for the first time in the history of logic in the treatise on the logic of Ibn Sina and which can be considered a discovery by this author until proof to the contrary, and that the ancient Arabian logicians have taken the habit of exhibiting in their treatises.

Abstract

In this paper, we are trying to summarize the peak of achievement of the Arabian logicians of the fifteenth century by making a classification and sketching in familiar terms the conditional and subjunctive syllogisms in Muḥammad Ibn Yusūf al-SSinūsī’s (1426-1490) work, i.e. in his explanation of Kitāb al-Muḫtaşar fī al-Manṭiq of al-Imām Muḥammad Ibn ʿArafa (1316- 1401).

PRESENT Proceedings of The 8th International Conference on Cryptology and Network Security, CANS ’09, Springer, New York, 2009, pp. 58-75. [8] OHKUMA, K.: Weak keys of reduced-round PRESENT for linear cryptanalysis , Selected Areas in Cryptography, Lecture Notes in Comput. Sci., Vol. 5867, Springer, New York, 2009, pp. 249-265. [9] RADDUM, H.-SEMAEV, I.: New technique for solving sparse equation systems , Technical Report, Cryptology ePrint Archive, 2006. [10] ZAJAC, P.: On the use of the method of syllogisms in algebraic cryptanalysis , in: Proc. of The 1st Plenary

Abstract

The article presents a proposal of explanation what practical rationality is, how it works and what are its criteria. In order to define practical rationality, the author starts from the general characteristics of reason, and then in the realm or reason activity distinguishes practical rationality from theoretical rationality. The necessary conditions of practical rationality are presented, as well as its standing between freedom and values. Next, the sources and nature of practical reasons are characterized, as well as their relation to values and desires. The problem of practical syllogism is briefly commented on. In the final part of the article the author proposes five criteria of practical rationality.

in Comput. Sci., Vol. 6087, Springer-Verlag, Berlin, 2010, pp. 151-165 [5] SEMAEV, I.: Improved Agreeing-Gluing Algorithm , Cryptology ePrint Archive: Report 2010/140, http://eprint.iacr.org/2010/140. [6] WARSHALL, S.: A theorem on Boolean matrices, J. Assoc. Comput. Mach. 9 (1962), 11-12. [7] ZAJAC, P.: Solving SPN-based system of equations with syllogisms , in: 1st Plenary Conference of the NIL-I-004, Bergen, 2009 (A. Kholosha, K. Nemoga, M. Sýs, eds.), STU Bratislava, 2009, pp. 21-30. [8] ZAJAC, P.: Implementation of the method of syllogisms, (preprint

]. Shijie Hanyu Jiaoxue [Chinese teaching in the world] 1, 20-30. Yin, Shuling. 2009. Xiandai hanyu fanwenju yanjiu [A study of modern Chinese rhetorical questions]. Ha’er’bin: Heilongjiang University Press. Yuan, Ying & Yan Jiang. 2010. Xiuci sanduanlun yu yuyi de yuyong tuidao [Rhetorical syllogism and implicature-drawing in pragmatic inference]. Foreign Language Teaching and Research 42. 97–103. Yuan, Yulin & Bin Liu. 2016. “ Shenme ”ju fouding yiyi de xingcheng yu shijie jizhi [On the formation and construal mechanism of the negative meaning of shenme- sentences

. Lagerlund, Henrik. 2016. Medieval Theories of the Syllogism. In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (Spring 2016 Edition) . [Online] Available from: http://plato.stanford.edu/archives/spr2016/entries/medieval-syllogism/ . [Accessed on: 7 March 2019] Pagin, Peter. 2016. Assertion. In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (Winter 2016 Edition) . [Online] Available from: http://plato.stanford.edu/archives/win2016/entries/assertion/ . [Accessed on: 7 March 2019] Perelman, Chaim and Lucie Olbrechts-Tyteca. 1969. The New

the logic of Arabic and Islamic philosophy and sciences, it is well known that it is a result of the Greek through Syriacs and Hebrews (some argue against the latter). However, both Yagoubi and Fatahine try to prove, in their two papers in this volume, i.e. The Status of Conditional Syllogism in Syllogistics, and Theory of Syllogisms with Categorical, Conditional and Disjunctive Connectives Developed by Arabian Logicians, that Arabs and Muslims added new syllogism(s) to the Greek logical traditions. The second sketches the figures and forms of this new

cipher security , 2012 (preprint). [24] ZAJAC, P.: Solving trivium-based Boolean equations using the method of syllogisms , Fund. Inform. 114 (2012), 359-373. [25] ZAJAC, P.: On the use of the method of syllogisms in algebraic cryptanalysis , in: Proceedings of the 1st Plenary Conference of the NIL-I-004, University of Bergen, 2009, pp. 21-30. [26] ZAJAC, P.: Implementation of the method of syllogisms , 2010 (preprint). [27] ZAJAC, P. - ČAGALA, R.: Local reduction and the algebraic cryptanalysis of the block cipher GOST , Period. Math. Hungar. 65 (2012), 239

simplified NP-complete satisfiability problem , Discrete Appl. Math. 8 (1984), 85–89. [9] ZAJAC, P.: On the use of the method of syllogisms in algebraic cryptanalysis , in: Proc. of the 1st Plenary Conf. of the NIL-I-004, University of Bergen, Norway, 2009, pp. 21–30. [10] ZAJAC, P.: Solving trivium-based Boolean equations using the method of syllogisms , Fund. Inform. 114 (2012), 359–373. [11] ZAJAC, P.: A new method to solve MRHS equation systems and its connection to group factorization , J. Math. Cryptol. 7 (2013), 367–381. [12] ZAJAC, P.: Some notes on MRHS