Negation of the Negation


Within a system of classical logic, double negation, that is, the negation of the negation of a proposition p, reinstates the initial proposition p. Expressed in symbolic terms,  ¬(¬p) ⇔ p.

But in Hegelian dialectical logic a negation of the negation leads to higher form of the original function. While it features the geometry of recurrent motion it also involves a process of progression in that 'being for itself' sublates.

1874 Engels wrote an article in the German Social Democratic newspaper Volk­statt to an explanation of what he and Marx understood by this Hegelian law of dialectics. (This article was later republished as Chapter 13 in his work Anti-Duhring ). According to Engels the Hegelian philosophical notion of negation simulates the process of differentiation in mathematical calculus. Marx in his mathematical manuscripts of 1881 makes a similar point.

In a simple circular function the negation or differentiation of sine is cosine.  Geometrically this represents a 90 degree phase shift which in astrology represents a square aspect.

The negation of the negation is a double differentiation which in the Schrödinger wave equation restores a higher form of the original function.

wave  equation

where H, the Hamiltonian, is a second-order differential operator and ψE, the wavefunction,

The solution of this equation gives rise to series of Eigen states or stable orbits which apply equally from macroscopic planetary orbits to microscopic particles such as the electrons orbits of a nucleas of an atom.

In binary mathematics the negation of a 1 is 0 and the negation of 0 is 1 but negation of the negation of 1 is 10 or 100, etc. In computer science this is bitwise negation. This takes the value given and switches all the binary
1s to 0s and 0s to 1s.

See also  On the Negation of the Negation