Logicians do it with Models

It took me a good while to get through this paper –more than I expected –but here we are.

What has Hellman accomplished?

First he showed us how to build the ontological principle of physical exhaustion, PE, . PE allows us to say that everything is exhausted by the physical without (embarrassingly) implying that everything is in the extension of a basic physical predicate.

Then he introduced the identity of physical indiscernables, IPI, and IPI’, and , respectively.  IPI says that if two objects have the same physical properties, then they are the same thing, while IPI’ says that no two objects are distinct with respect to a property without being distinct with respect to a property.

These three principles neither independently nor in conjunction imply or require reduction to the physical, but they are also too weak to express the physicalist thesis that physical phenomena determine all phenomena.  He then turns his attention to principles of determination. In addition to PE and IPI/IPI’ Hellman introduces the determination of truth, Det-T: in structures truth determines truth if, and only if, , and Det-R: in structures reference determines reference if, and only if, .

Det-T says that once you have given a complete description of things in terms, there is only one correct way to describe them in terms.  Det-R says that if two structures agree in what they assign to the terms, then they agree on what they assign to the terms.

Given a notion of definability, Hellman is able to state the thesis of physical reduction, PE: in structures, reduces , if, and only if, is definable in terms of in structures.

Given that assumptions about the mathematical-physical determination of all truths and, maybe, reference, are regulative principles of scientific theory construction –the assumption in general that all terms and all theories are reducible to mathematical-physical terms is probably false. Hellman’s physicalist materialism is instead composed of PE, DET-T and DET-R, with PE independent of PR and the determination principles.

Because there are non-standard models of the laws of science, our formal systems do not model scientific possibility in a way that permits the move from physical determination to physical reduction –thus Beth’s definibility theorem poses no threat to physicalist materialism.  And any way you cut it, the link between theories as syntactic entities and reductionism doesn’t carry over to determination of reference, ruling out even accidental co-extensiveness between terms.

This sets up the theoretical background for an evaluation of the applications of physicalist materialism across disciplines and problems in philosophy of science, mind and social theory.  In the next updates I  will be covering Hellman’s 1977 “Physicalist Materialism” (Noûs) as well as giving a detailed, critical, evaluation of some of the anti-Materialist claims David Chamers makes in the early chapters of his book The Conscious Mind: In Search of a Fundamental Theory.