Thursday, 26 July 2012

Metaphysics as Über-theory and Metaphysics as Meta-theory

1. Understanding how things hang together ...

There is a view of metaphysics -- a very standard view of metaphysics from the pre-Socratics to the post-Quinians -- which takes metaphysics to be trying to say very broad things about reality, at the most abstract and general level. Quine says things along these lines, but not having my books with me means I can't find a nice quote to that effect. But there is a similar formulation due to Sellars, which I take from the SEP article on Wilfrid Sellars (by Willem deVries),
"The aim of philosophy, abstractly formulated, is to understand how things in the broadest possible sense of the term hang together in the broadest possible sense of the term” (Sellars, 1962, "Philosophy and the Scientific Image of Man").
As good as this sounds, I think there's an interesting distinction to be drawn here. Consider the phrase "things in the broadest sense of the term". Does this mean,
"How does everything there is hang together"?
Or does it mean,
"How do our theories and representations of everything there is hang together"?
Sellars is not focussing here on metaphysics, but rather on philosophy as a whole. Still, let's say that the aim to understand how every thing there is hangs together is über-theory; while the aim to understand how our theories, representations and concepts of everything there is hang together I shall call meta-theory.

(I'm not sure if the slightly jokey name "über-theory" has been used much before. I take it from a 2003 Scientific American article, "A Unified Physics by 2050?", by the theoretical physicist, Steven Weinberg.)

Über-theorizing is doctrinal in the sense that it usually concerns competing doctrines as to what there is (in the broadest sense of the term). For example, "are there abstract objects?", "are there possible worlds?", etc. Meta-theorizing is conceptual in the sense that it usually concerns trying to analyse or explicate broad notions - such as existence, identity, indiscernibility, causation, possibility, truth, reference, and so on. (It also counts if one does not explicitly analyse/explicate, but merely relates the concepts.)

This is not to suggest that über-theorizing and meta-theorizing need be disjoint! They may overlap considerably. The metaphysician may be both über-theorist and meta-theorist in what they aim to do and what their work achieves. So, there may be significant overlap. For example:
(i) What is a relation? (über-theory)
(i)* What does "relation" mean? (meta-theory)
(ii) What is truth? (über-theory)
(ii)* What does "true" mean? (meta-theory)
In such cases, it may be quite hard to see a sharp difference between the two. The reason is that there is an intimate link between (knowing) what "F" means and (knowing) what Fs are. If one's semantic theory is suitably disquotational, then x is true iff "true" is true of x, and x is a relation iff "relation" is true of x, and so on.

2. Metaphysics as über-theory

Considering again Sellars's phrase, "to understand how things in the broadest possible sense of the term hang together in the broadest possible sense of the term", the qualifier "in the broadest sense of the term" is what make such understanding philosophical, or metaphysical, rather than merely scientific.

Again, it may be both. If Quine, say, suggests that a scientific theory has less and more philosophical aspects, this doesn't imply that the more philosophical aspects are non-scientific. It might imply that they are less directly empirically checkable. To infer the conclusion that the philosophical or metaphysical parts are non-scientific, one would need further empiricist assumptions.

So, the über-theorist might, and in fact normally does, judge the more mundane parts of physics (e.g., solid state or astrophysics) as lacking much metaphysical import, while focusing on the more fundamental and foundational parts (e.g., getting conservation laws from symmetries of a lagrangian; general relativity; quantum theory; theoretical parts of statistical mechanics) as providing a guide to über-theoretic issues about space, time, identity, objects, causation, etc. In such cases, there is overlap between scientific inquiry and metaphysics as über-theory. Indeed, the projects of interpreting GR and QM (and this includes such programmes as ontic structuralism) are all examples of über-theory. Questions about the nature of time, for example, are über-theoretic, but are linked with foundational parts of general relativity. This is why I would classify work on Gödel spacetimes and hypercomputation/supertasks as belonging to both theoretical physics and metaphysics. For similar reasons, I would classify theories of continuous quantities, infinite sets/structures, and computable functions as belonging to both mathematics and metaphysics. (Examples of these are listed in the list of achievements.)

But there is, in addition, metaphysical über-theory which has no obvious connection with science. Examples include possible worlds, theology, moral facts, and perhaps the metaphysics of abstract objects. Clearly, there is sometimes an antagonism to this, sometimes for allegedly naturalistic reasons. I disagree quite strongly with the suggestion that such work "should be discontinued". It is anti-intellectualism. In fact, I think the naturalistic reasons given are not even good naturalistic reasons, but that would be a topic for another post. (But as a quick example, the best argument we have against nominalism is the indispensability of mathematics in science.)

3. Metaphysics as meta-theory

One might be suspicious of metaphysics as über-theory - perhaps because one thinks that "understanding how things hang together" is the job of science. Full stop. How could one come to know "how things hang together" in an a priori way, without proceeding through empirically-condtioned scientific inquiry? Or perhaps because one has read The Phenomenology of Spirit and drawn the conclusion that Hegel is bonkers. Or perhaps because one accepts some kind of verification principle (identifying meaningfulness with empirical content).

For whatever reason is dominant here, whatever good metaphysics might be in that case, it couldn't be just more scientific theory. For it would just be more speculative scientific theory. For example, Hegel (and German Idealism more generally) is metaphysics, but mathematically, logically and scientifically ignorant metaphysics. Then, what would good metaphysics be?

Thanks to Frege and Russell, followed by Wittgenstein and then Carnap, we do have another way of thinking about all this. Metaphysics, done properly, is meta-theory. I.e., meta-theoretical logical analysis. One finds views like this expressed sometimes by Russell and Carnap. For example, Russell's "Philosophy of Logical Analysis" (from his History of Western Philosophy (1945)) and Carnap's Logische Aufbau.

This sort of view is linked to deflationism. It isn't that metaphysics should be eliminated; rather it is that metaphysical problems should be reconceptualized in a deflationary manner which doesn't have the pretensions of being a kind of über-science: discovering how things are merely from the armchair.

How to characterize deflationary metaphysics is something I thought about for a long time during my PhD between 1994 and 1998, and I focused on truth (though there are analogous approaches relating to abstract objects and possible worlds). Roughly, truth can be deflated by focusing on the principles governing the truth predicate (e.g., the T-scheme; or perhaps compositional principles), and showing that they are conservative with respect to non-truth-theoretic matters. Stewart Shapiro suggested this in a 1998 J. Philosophy article "Proof and Truth - Through Thick and Thin"; I suggested it in a 1999 Mind article "Deflationism and Tarski's Paradise". Shapiro and I both argued in this context (it is well-known, and not a major discovery) that a compositional truth theory (like Tarski's, or modern variants like Kripke-Feferman or Friedman-Sheard) is usually non-conservative, allowing one to prove things like reflection principles and consistency sentence (which the underlying theory cannot prove). Such results are consequences of Gödel's incompleteness theorems.

Arguing that deflationary truth should be conservative is analogous to deflating talk of infinite sets by arguing that infinitary set theory is conservative with respect to finitary matters (i.e., computations on finite objects). Such a result would sanction the inferential use of infinite sets, but while showing this to be merely instrumental -- i.e., merely increasing the usefulness of the theory. The instrumentalist programme in this case was Hilbert's Programme. But this came unstuck when it was recognized, by Kurt Gödel, that finitary arithmetic can encode, but not prove its own consistency, while infinitary set theory can prove the consistency of finitary arithmetic; and so, non-conservatively extends finitary arithmetic.

No comments:

Post a Comment