This page wants to provide a connection between General Logic and Hegel's Logic. At first, they not seem to have any relationship whatsoever; but, starting from Aristotle's "tradition", specially in De Interpretatione , we can find clues that Hegel departs from there to build his system, and, for that reason, there should be a connection to other kinds of logical thinking that seems more "rigorous". The Thesis-Antithesis-Synthesis mostly devoted to Karl Marx's interpretation, is not the only one possible in Hegel's construction. It seems that Marx's view, a very simplistic view, so to speak, has had influence in the subsequent existentialists, specially the French, like Jean-Paul Sartre, that seems to contradict the Aristotelian "tradition", when, as it will become clear in my view, that Hegel never departed from the tradition he was immersed in, the Aristotelic-Kantian one, which was greatly denied by the French socialist philosophers, that adhered, without questioning, to the Marxist interpretation of Hegel's Science of Logic.
Incidental Axioms about being.
(1) The Being is / (contr.) The Being is not
(2) The non-Being is / (contr.) The non-Being is not
(3) The Nothing is what it is not.
(4) The Absolute is not what it is not.
Further improvement of the axioms (1a) The Being is what it is.
(2a) The non-Being is not what it is.
(3a) The Nothing(ness) is what it is not.
(4a) The Absolute is not what it is not.
Hegel's Definitions
(HD1) The Being is undetermined and void.
(HD2) The Nothing/ness is undetermined and void.
From HD1 and HD2 we derive the first relationship, the meaning of Equality
Being = Nothing.
proof: As both are initially void and undetermined both concepts they are equal by vacuity. In logic, we would have
\(Being = \{ \} \implies Nothing = \{ \} \wedge Nothing = \{ \} \implies Being = \{ \}\)
, it means both are empty concepts is contained in an empty concepts. Therefore, the equality is true by vacuity.
A first proposition by axioms the axioms (3a) and (4a)
(P1) The Absolute is not Nothing(ness).
Many other propositions can be derived directly from the axioms and definitions.
There are an Aristotelian principle to be aware of
The principle that or one thing is or it is not. Represented by
(5) \(P \vee \neg P\)
Therefore, if we have to account that Being = Nothing is true, then one thing could not be and be nothing at the same time. Thus Being = Nothing are really equal according to Hegel's definitions HD1 and HD2, and by the axiom (5). Ensuring that Hegel is aware of the Aristotelian logic, he has inherited.