Math

Doing category, one might be lead to think that it is all about a blank canvas of possibilities, and discovering exactly what is necessary to model certain mathematical objects already seen -- as opposed to, say, set theory, in which one only deals with intricate mathematical objects themselves, and tries to find out directly how they relate. But one should not forget, that the two methods of research are essentially the same -- you cannot distantiate yourself from the way that the mathematics presents its objects, be it certain (properties of) sets or certain (properties of) categorical concepts. But why try to model coherent objects? Because these models tell us why the objects are meaningful in the first place, it being the case that there are also non-objects, making this method useful of itself. Non-objects would be falsities, things that are contradictory. One should beware of them before building mighty structures on top of concepts that themselves do not exist -- the mighty structures would collapse. But, is not the essential character of this method, that every object, nonsensical as per the current models, can be turned into something interesting -- the only actual question beforehand being whether this object might be an essential coherence as per the current architecture, or just a slight whim of accidental info. Thus, the uninvestigated, possibly nonsensical, object lends its importance mainly to the current architecture, and hence our (mode of) understanding. Nonsensicality, or falsity, is carved out, bit by bit. The question as to the notion of nonsensicality is whether, after this carving, something remains or not. Or, worded differently, whether our understanding reaches full stop, or will never grasp certain objects, which will ever stay nonsensical.