О докладе Владимира Олеговича Лобовикова

23.09.2022

Главным научным сотрудником Института философии и права УрО РАН Владимиром Олеговичем Лобовиковым  9 сентября 2022 г. сделан доклад на английском языке  по теме «A new metatheoretic square and hexagon uniting empirical theories with a priori ones, and uniting theories based on the classical logic with ones based on a nonclassical logic» в рамках 7-го  Международного конгресса по логическому квадрату в Левене (Нидерланды).

The paper submits significant explicating and developing further the metatheoretic square and hexagon published originally in (Lobivikov, 2015; 2016) which square-and-hexagon is a new instantiation of the old idea substantially generalized and represented today as “geometrical logic” (Blanché, 1966; Béziau, 2012a; 2012b).

Let variable “t” stand for a theory having a recursively enumerable set of axioms. “Emp(t)” stands for the metatheoretic property “theory t as a whole is empirical one”. “Apr(t)” stands for the metatheoretic property “theory t is a system of a-priori knowledge exclusively. “Cla(t)” – “theory t is based on the classical logic”. “Con(t)” – “theory t is consistent”. “Com(t)” – “theory t is complete”. “Dec(t)” – “theory t is decidable”. Notions “Emp(t)” and “Apr(t)” are defined as follows. DF-1: Apr(t)  (Cla(t)  Con(t)  Com(t)  Dec(t)). DF-2: Emp(t)  (Cla(t)  Con(t)  Com(t)  Dec(t)). Corollary-1: Apr(t)  (Emp(t). Corollary-2: Emp(t)  Apr(t)).

The system of logical interrelations among the metatheoretic notions is modeled graphically by the following square and hexagon.

References

1) Béziau, J.-Y. (2012a) The New Rising of the Square of Opposition, In: Beziau, J.-Y., Jacqette, D., eds., Around and Beyond the Square of Opposition, Basel, Birkhäuser, 3-19.

2) Béziau, J-Y. (2012b) The Power of the Haxagon, Logica Universalis, 6, No. 1-2, 1-43.

3) Blanché, R. (1966) Structures intellectuelles. Essai sur l’organisation systématique des concepts, Paris, Vrin.

4) Lobovikov, V. (2015) A meta-theoretical interpretation of the logical square and hexagon of opposition. In: Jean-Yves Beziau, Safak Ural, Arthur Buchsbaum, Iskender Tasdelen, Vedat Kamer (Eds.). Handbook of the 5th World Congress and School on Universal Logic (June 20- 30, 2015, Istanbul, Turkey) / Istambul, Turkey: University of Istambul, pp. 346-348.

5) Lobovikov, V. (2016) Submitting a Meta-theoretic Interpretation of the Logic Square and Hexagon of Opposition, Aporia – Revista Internacional de Investigaciones Filosoficas [International Journal for Philosophical Investigations] / Santiago de Chile. № 11, pp. 4-11.