Between writing and picturing: The square of opposition in formal logic and formal axiology of alethic and deontic modalities

Abstract

From some point of view, the famous “Square of Opposition” in the formal logic has
nothing to do with squares and other geometrical objects which can be pictured, shown
and seen. All the rational formal logic contents of the “Square of Opposition” could
be written, read, said and understood without any picturing and showing. The
well-known picture is really useful only in mnemonic relation: the scheme supports
the mimesis. Assuming this abstract-language-form viewpoint in the present paper, and
using the hypothetic-deductive method, below I develop the mentioned assumption
(hypothesis) with respect to one particular case, namely, in relation to alethic and
deontic modality interpretations of the “Square”. According to the hypothesis under
examination, all the formal rules making up the rational contents of the “Square” are
to be adequately formulated and expressed in a written language without
picturing.