ancestors and relatives

NOT.04.LeibnizOppositional Geometry (OG), the mathematical theory of opposition, was created/discovered in 2004 (by Moretti, later followed by Smessaert, Pellissier and Luzeaux). But it has several “ancestors” : these range from Aristotle (he himself relying on previous studies by Parmenides and Plato) – who is the founder of opposition theory, formally represented by the logical square (or square of opposition) – through people having felt uneasy with the square (as Vasil’ev and many others before him), and people having discovered either successors to the square (like Jacoby, Sesmat, Blanché and Joerden) or compositions of these successors (like Blanché, Sauriol and Béziau). In some sense the successors of the logical square and the compositions of these successors are some of the most important ingredients of OG (they are respectively the α-structures and the β-structures). OG also has “relatives”, i.e. people having explored fields, if not identical, at least very similar to those of OG : like squares slightly other than the logical one (as Gottschalk, Piaget and Greimas) or applications of the logical square and of the logical hexagon more or less unexpected but very stimulating (as Lacan, Gallais and Seuren). In some sense, this intelligence of the possible applications (of the α-structures and of the β-structures) constitutes another fundamental ingredient of OG. It is therefore quite important for OG to be aware of its own ancestors and relatives.

  • Relatives of OG (27):

    • Peirce C.S. (1839/1914)
    • Frege G. (1848/1925)
    • Keynes J.N. (1852/1949)
    • Piaget J. (1896/1980)
    • Lacan J. (1901/1981)
    • Greimas A.J. (1917/1992)
    • Gottschalk W.H. (1918/2004)
    • Grothendieck A. (1928/2014)
    • Gallais P. (1929/2001)
    • Englebretsen G. (?/)
    • Seuren P. (1934/)
    • Badiou A. (1937/)
    • Petitot J. (1944/)
    • Pizzi (1944/)
    • Guitart R. (1947/)
    • Sion A. (?/)
    • Max (?/)
    • Dubois D. (1952/)
    • Prade H. (1953/)
    • Schröder-Heister P. (1953/)
    • Jaspers D. (1957/)
    • Varzi A. (1958/)
    • Warglien M. (?/)
    • Cavaliere F. (1960/)
    • Diaconescu (1964/)
    • Chow K.-F. (1965/)
    • Marcos J. (1974/)

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