
#1
Nov1907, 02:36 AM

P: 166

The opposite of a great truth is also a great truth  T. Mann
For example, the opposite of empty set {} is a nonempty set, such as the set of integers, or finite sets we experience in our mundane lifes. Also a lesser context can define the greater context, and vice versa.That is, each is defined by what it is not i.e. its antithesis; for example, the antithesis of quanta and spacetime manifold. So what if a physical model such as our universe, or a divergent cyclical set of universes (hence nonempty set with 1:1 correspondence to integers), has a greater context of simplest case i.e. empty set? Might this be indirectly inferred; of course without perturbing such alleged greater context? Such as if there were multiple 'universes'. So could {} be introduced into consideration of a description of a larger context? 



#2
Jul1711, 12:49 AM

P: 4

I've been contemplating this issue lately this is a problem that is *sorta kinda* addressed in the Axiom of Choice and in the theories of Borel, Lebesque and Godel in a big sort of way. The main concern that I have had with this idea is that even a physical model would have to have some sort of set limit and I even have problems with this being a conceptual model of mathematics because Cartesian sensual realism cannot cope with such abstractness. I wish that I could get a good grasp on this notion. :/




#3
Jul1711, 01:23 AM

P: 4,570

In any descriptive language in order to define something you need two definitions: the thing you are describing and its complement. If you can't strictly define both of these, then you have not given a clear definition. When working with sets, the union of a subset and its complement are required to define the "universe" that it exists in. In this sense in order to describe "everything", you need to define "nothing", just like you would make a definition of "hot" and "not hot" or "black" and "not black". In saying this if you had to give a description that corresponded to "everything" as a description of some physical phenomena, then there must also be a description of "not everything" and if a mathematical description of "everything" was written in terms of set and its boundaries were precise, then the definition of "not everything" should be precise. There are probably philosophical arguments about this, but I am not a philosopher: I am looking at this from the point of language since in order to formulate an idea, let alone a model, you have create a descriptive boundary of some sort that describes not only the idea or model, but its complement with respective to the limits of the language used to describe it. 


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