Tuesday, July 12, 2011

the causal closure of nature: a mathematical concept

Immanent Transcendence hits it again.  What does it mean to say that "nature is closed"?  See this post.  When I was working on my dissertation, and I honestly forget if this made its way into the Peirce book or not, I had alot to say about set theory and how it fits into the picture of thinking about nature ...

Some would like to say that nature is "closed," as in "finite," a bound "set of all sets," a container of some sort that holds all things.  But, then, does this make nature (being a container) the ultimate thing?  Is nature thus a thing or not?  And so by treating nature as an object we are left with Russell's paradox.  Nature is not an object. Without an explanation of change, nature itself (whatever that means) is drawn asunder into the Newtonian pile of objects.  To have an account of the closure (or non-closure) of nature is to take a position on whether nature is an object or not.

If nature is *not* an object (my position), does it follow that nature can be "closed" in *any* sense?  This may play out on two levels: the categorical (I'll call this the general, as in applying universally) and on the level of objects themselves, as in particulars.  The layout may look something like this ... I hypothesize:

Categorical closure, as in fundamental modes of being (there are three: ontological or real possibility, sometimes called existential possibility - what is first; actuality - what is second, as in a reaction, what exists; and generality - what is third, established as the meaning of the interaction of the first two, or generality and law, this seems to evolve over time); where in total these modes are closed only in that they hold to what reality does (process) and is (objects), as part of what reality means - its own nature.  This is the universal.

Nature may be causally closed in that objects, being discreta, are indeed finite and capable of being totaled, numbered at any given time, and thus by having some present existence of being actualized carry a current actual material and efficient cause.  So there is closure in that sense; meaning that those causal limits have been defined and are now individuated through particulars, through objects as finite singulars.  Formal and final causes would be categorized as open (though they may be looked at as closed in the respect that *being causes* they are what they are): why?  Thinking Whitehead (and Deleuze) here: the Ideas, though being specific, contain an infinite degree of power in their generativity - and that power is indeed what makes for the openess, i.e. processural nature of nature.  It would seem that at the very least formal cause applies here, with short range final cause being malleable to the evolutionary selective pressures introduced by the ongoing actualization and change of materials and their efficient causes.  

Jason mentions Tom Alexander quite abit with reference to naturalism (and naturalism's apparently closed ontology - but for some forms of naturalism the ontology is open). I quite explicitly remember Alexander remarking during a Dewey seminar once, something to the effect of, "Once we forget that the forms change, we begin to forget God and God dies." 

Nature, I believe, is closed in some respects yet open in others.  Just as its quite misinformed to maintain *only* a "flat ontology" without depth, it is as equally naive to maintain all depth, all hierarchy, without a proper sense of univocity.