We can’t bridge the difference we call contradiction

In the moment we humans began slicing the world with words, we created an aisle between the two possible approaches of conceptualizing the world, called realism and nominalism,  by founding the slicing on difference, that is, the slicing itself. This foundation means that these two approaches are fundamentally incompatible, since the difference between them actually is the foundation of conceptualization itself, and that they thus instead are forever separated by contradiction.

Both these approaches ultimately end in Russell’s paradox, but with the fundamental difference that whereas realism interprets the this paradox as a real thing, nominalism instead interprets it as an abstraction. It means that whereas realism gets stuck in paradox as an impossible “real” thing (as cladistics’ “true tree of life” and particle physics’ “Higgs particle”), nominalism instead rounds the paradox simply by an axiom (as in axiomatic set theory). For nominalism, Russell’s paradox is thus not an end, as it is for realism, but merely a rounding mark.

This basis has today led to that realism by one branch claims that Russell’s paradox can be found (ie, cladistics), and by another that it moreover has found it (particle physics), whereas nominalism instead has found the consistent fusion of logic and mathematics by rounding the paradox. All these conclusions can’t, however, be correct, because the difference between realism and nominalism can’t be bridged – ie, paradoxes can’t be both real and abstract at the same time – since it would bridge the founding difference  of conceptualization, ie, would turn “difference” into “similarity” and thus also “contradiction” into “consistency”. Instead, realism (eg, cladistics and particle physics) actually contradicts mathematics (and is thus contradictory).

Much can we do, but we can’t bridge the difference we call contradiction (on the contrary to what realists like cladists and particle physicists believe and claim).

Another contribution to understanding of conceptualization http://menvall.wordpress.com/