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On Gluts, Gauges, & Gaps

Non–classical Logic offers a menu of truth values. A “glut” is of the form A ^ –A: unlike the classical case, it is accepted. Dually, a “gap” is of the form A v –A: unlike the classical case, it is rejected. In the middle, I suggest, is a “gauge” of the form A => –A: *like* the classical case, its truth value is contingent.

The real question is the interrelation between these three values. To tie them together one can weave them in this manner: a glut is both a gap & a gauge; a gap is neither a glut nor a gauge; while a gauge is a transformation of a gap into a glut. The last definition is crucial, as we cannot think of a gauge as some kind of “confusion” of gluts & gaps, as that would be akin to being a glut. But also we cannot think of a gauge as some kind of “diffusion” of gluts & gaps, as that would be akin to being a gap. 

So it is not the case that a gauge is neither a glut nor a gap, because that presents a gap-like value; it is equally not the case that a gauge is both a glut & a gap, because that presents a glut-like value. Moreover, the grammar of the previous sentence would suggest that we can characterize gauges as neither gap-like nor glut-like, but, again, that would have to fail due to its gap-like nature! (& symmetrically so were we to describe it as both gap-like & glut-like.)

Nay, a gauge is its very own contingency, the logical measuring-stick of space itself. Thus the lefthand & righthand appearances of “A” in what classically was the “law of identity” now become different events, meaningless master signifiers that can relate to each other through the decision of the gauge value. The sides of implication become polarized: indices abound, location ruling the Game.

Priest & Garfield call this “emptiness”; but crucially, this emptiness has a Name. For us, this is Hegelian Essence, Peircean Secondness, brutal-relationality-in-itself.

#philosophy #peirce #logic #categories #truthvalues #nonclassical