Thursday, March 29, 2012

Contextual Ontology Bookkeeping

Let an anchored ontology be one in which the only frames of reference (from which laws must hold) are anchored by "objects" x, y, z, ... Each anchor describes (or interacts with) some of the other "objects" in the ontology via the classical laws of physics, probabilistic quantum laws, logical truths, or whatever... An anchored, contextual ontology is more parsimonious than a classical ontology because 1. there is no disembodied frame of reference from which everything must be true 2. not all anchors describe/interact with all the other anchors.

Let (xy) mean x behaves lawfully (even if only probabilistically) or logically, in the terms of the frame of reference of (anchor) y. In a universe with only one "object", x, there is only

1) (xx)

In a contextual ontology like quantum realism the set x-union-y may behave differently from the single composite system x-and-y. So the possibilities for a universe as above with two "objects" x and y is given by a 3x3 table

here e.g. yx is the collection of physical laws that y must satisfy in x's frame of reference. And e.g.,  
just means that from the frame of reference of the combined system x-and-object y behaves according to various laws and rules L1, L2, ... If there is no relation or set of laws, then

For 3 "objects" the table is 7x7, for 4 it is 15x15, etc...

All the information in the universe is given by the elements in the table and relations among the elements in the table, e.g.
denotes whatever physical/logical laws z must obey from the perspective of the combined system (x-and-y-and-w), the values of the same laws about w from the perspective of (y-and-z) is 3i(n)2 as large.  

A case that I predict is going to become important is where two different anchors have ontologically independent notions of time, in which case there is not a simultaneous state of the anchors. 

"Perhaps we should take seriously the possibility of time's consisting of multiple time streams, each one of which is isolated from each other, so that every moment of time stands in temporal relations to other moments in its own time stream, but does not bear any temporal relations to any moment from another time stream." (Markosian, N., "Time", The Stanford Encyclopedia of Philosophy, 2008, )


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