Wednesday, January 12, 2011

The Nature of Ontologies

I recently read in a book a statement that quantum theory is not concerned with the question of what exists, and neither is science. It immediately reminded me of the “early” Quine’s dictum, “to be is to be a value of a variable” from his seminal paper “On What There is” of old, back in the days when he’d wield Ockham’s nominalist Razor with ontological fervor. It’s my opinion that there was an irony about this, because what was intended to keep the population of the universe of discourse under control backfired to proliferate theoretical tickets of admission to anything articulable. That’s fine by me, but it’s also no wonder that Quine eventually modified his nominalism, rather drastically.

He came to call it “ontological relativity,” which is to say, simply, that theory θ1’s nonempty universe of discourse Λ has its set of quantifiable objects as does theory θ2 (also nonempty universe Λ ≠ ∅), but operators and quantifiers over θ1’s universe, which are formal apparatuses universally applicable (“covariant”) across the board to all universes of discourse (even to the set of all sets and to the empty set), can potentially yield differing ontologies of quantifiable objects, viz., that what exists for θ1 need not exist for θ2, and vice versa, and so on ad infinitum. This is rather radical, because it does away with the idea of asserting existence or non-existence in general; it looks to paradigms as the foundation of ontology, instead of the classical approach to ontology, viz., of imposing an acceptable universe of discourse to all paradigms in general. Hence θn is in general ontologically answerable solely with respect to its own universe of discourse Λn, and no other. Ontologically speaking, this even implies paradigmatic relativity, and is an elegant argument in its favor.

An example is, say the universe of discourse of a many-worlds interpretation of quantum theory and an e-prime interpretation of quantum theory. The theory is the same (quantum theory based on quantum mechanics) in terms of its subject matter (quanta), but the paradigms vastly differ with respect to ontology, i.e., universe of discourse. There is no homomorphism between the two theories either, as the former is inflated and the latter is stripped bare, down to specifically structured propositions that do not presuppose the realist correlation of assertions to their objects. There is no foundation but Consciousness; all ontologies are comprised of castles in the sky, floating in mid-air, free-falling in the space of Mind.