Non-Classical Stems from Classical: N. A. Vasiliev’s Approach to Logic and his Reassessment of the Square of Opposition
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In the XIXth century there was a persistent opposition to Aristotelian logic. Nicolai A. Vasiliev (1880–1940) noted this opposition and stressed that the way for the novel – non-Aristotelian – logic was already paved. He made an attempt to construct non-Aristotelian logic (1910) within, so to speak, the form (but not in the spirit) of the Aristotelian paradigm (mode of reasoning). What reasons forced him to reassess the status of particular propositions and to replace the square of opposition by the triangle of opposition? What arguments did Vasiliev use for the introduction of new classes of propositions and statement of existence of various levels in logic? What was the meaning and role of the “method of Lobachevsky” which was implemented in construction of imaginary logic? Why did psychologism in the case of Vasiliev happen to be an important factor in the composition of the new ‘imaginary’ logic, as he called it?
Mathematics Subject Classification (2000).03-03 03A05 03B50 03G20 03G25 01A55-01A60 01A70
Keywords.Non-Aristotelian logic square of opposition triangle of opposition classifications of propositions the law of non-self-contradiction metalogic
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