Tuesday, 17 September 2013

"Naturalism" in Metaphysics

Naturalistic metaphysics is fashionable amongst philosophers. A recent article,
Maclaurin, J., and Dyke, H. 2012.  "What is Analytic Metaphysics For?", Australasian Journal of Philosophy 90.
aims to articulate the concept of naturalistic metaphysics and to criticize its (alleged) opponent. The abstract begins:
Abstract
We divide analytic metaphysics into naturalistic and non-naturalistic metaphysics. The latter we define as any philosophical theory that makes some ontological claim (as opposed to conceptual claim), where that ontological claim has no observable consequences.
McLeod, M., and Parsons, J. 2013. “Maclaurin and Dyke on Analytic Metaphysics”, Australasian Journal of Philosophy 91.
whose abstract begins:
Abstract:
We argue that Maclaurin and Dyke's recent critique of non-naturalistic metaphysics suffers from difficulties analogous to those that caused trouble for earlier positivist critiques of metaphysics. Maclaurin and Dyke say that a theory is naturalistic iff it has observable consequences. Depending on the details of this criterion, either no theory counts as naturalistic or every theory does.
This seems right to me. The examples discussed by McLeod and Parsons come from basic philosophy of science: for example, auxiliary hypotheses and the difficulties involved in formulating some principle of verifiability. So, what is being promoted as "naturalistic metaphysics" looks like reheated positivism and faces exactly similar objections.

Here is a bit more to consider:
(1) $\nabla \cdot B = 0$
(2) $\exists X \forall y (y \in X \leftrightarrow \phi(y))$
Neither of these has "observable consequences". Since the magnetic field $B$ is not observable (not observable to the human eye), it follows that Maxwell's equation, $\nabla \cdot B = 0$, has no observable consequences (for this, we need to show its consistency). And one can show that any consequence of the (predicative version of) Comprehension Principle (2), in the restricted language (i.e., without the set/class quantifiers), is a logical truth. (The Comprehension Principle is what makes mathematics applicable. In addition to asserting the existence of objects of pure mathematics, e.g., $\mathbb{R}^3$ and $SU(3)$, we can also assert the existence of the objects of physics: (mixed) functions on spacetime (such as wavefunctions and fields), and sets of spacetime points, and sets of more mundane concreta, etc.).

Observing iron filings, the readings on a Hall probe, etc., doesn't count. One needs to state auxiliary claims about how the unobservable magnetic field $B$ is locally coupled to point charges and dipoles, along with a complicated network of idealized assumptions about how Hall probes work, etc.

In the linked video, you hear (1:02) the announcer say,
"As you see, the magnetic field forces the iron filings to line up along the lines of force ..."
This is an auxiliary assumption. This is how science works.

A number of basic, explanatory fundamental principles are given which do not refer to "observables" and have no observable consequences. To obtain observable consequences, one needs to add very complicated networks of auxiliary hypotheses.

Auxiliary hypotheses are deductively indispensable. It is usually safe to assume their truth, because the experimental setup normally---but after a lot of work, usually---ensures that the required idealizations are ok. But there are always cases where a failure of observation does not imply the law predicting it false. Rather, one of the auxiliaries is to blame. (This is called the Duhem-Quine Problem/Thesis.) This is not just logically obvious, it's also obvious to anyone who has worked with, e.g., an oscilloscope or pretty much any measuring device. For example:
Is the oscilloscope plugged in?
If you press a light switch and the light doesn't come on, the reasonable explanation is not that James Clark Maxwell has been refuted after all, but rather than some wire is not connected, or the bulb has blown, etc.

Similarly in the case of applicable mathematics and every physical principle of any interest (Maxwell's laws, Euler-Lagrange equations, laws of gravitation, principles of quantum theory, etc.). Although the basic principles of applicable mathematics have no observable consequences, it's still an interesting question to examine how the axioms of applicable mathematics interact with the mixed laws of physics to obtain measurable consequences. This is a non-trivial and not well-understood problem. It is more or less equivalent to Hilbert's 6th Problem:
6. Mathematical Treatment of the Axioms of Physics. The investigations on the foundations of geometry suggest the problem: To treat in the same manner, by means of axioms, those physical sciences in which already today mathematics plays an important part; in the first rank are the theory of probabilities and mechanics.
Overall, why not simply accept that there is no opposition between analytic metaphysics---which I'm inclined to define, by ostension, as the writings of Frege, Moore and Russell + some similarity sphere---and science, or anything close to that? For example, look at the table of contents of Russell's Principles of Mathematics (1903).