Sunday


In several earlier posts I have made a trial of distinct definitions of naturalism. These posts include:

A Formulation of Naturalism
Two Thoughts on Naturalism
Naturalism: Yet Another Formulation, and
Naturalism and Object Oriented Ontology

I regard all of these formulations of tentative, but there may be something to learn from these tentative formulations if we employ them as a kind of experiment for understanding methodological naturalism. That is to say, each of these attempts to formulate naturalism implies a formulation of methodological naturalism. Furthermore, in so far as methodological naturalism is definitive of contemporary science, each formulation of methodological naturalism implies a distinct conception of science.

In A Formulation of Naturalism I suggested that, “Naturalism is on a par with materialism, and philosophically is to be treated as far as possible like materialism.”

In Two Thoughts on Naturalism I suggested that “Naturalism is on a par with mechanism, and philosophically is to be treated as far as possible like mechanism.” I also suggested that, “Naturalism entails that all ideas will first be manifest in embodied form… there are no abstract ideas that are given to us as abstract ideas; all ideas are ultimately derived from experience.”

In Naturalism: Yet Another Formulation I noted that these earlier efforts at formulations of naturalism are implicitly parsimonious, tending toward conceptual minimalism, and further suggested that, “we can characterize naturalism in terms of a quantitative parsimony, following quantitative formulations as far as they will go, and only appealing to qualitative formulations when quantitative formulations break down.” There is a sense, then, in which we can speak of deflationary naturalism. In so far as these formulations of naturalism embody the principle of parsimony, we need not separately formulate the principle of parsimony as a regulative norm of science.

In Naturalism and Object Oriented Ontology I suggested that an approach to naturalism might be made by way of object oriented ontology, which I there compared to Colin McGinn’s transcendental naturalism thesis, i.e., that the world is “flatly natural” though we are unable to see this for what it is because of our perceptual and cognitive limitations.

While when I first formulated naturalism such that, “Naturalism is on a par with materialism, and philosophically is to be treated as far as possible like materialism,” I intended naturalism as consisting of a more comprehensive scope than materialism, though when applied to the scientific method I see that it can be taken as a doctrine of limiting one’s scope to the problem at hand. This approach to science is as familiar as Newton’s aphorism, Hypotheses non fingo. Science often proceeds by providing a very limited explanation for a very limited range of phenomena. This leaves many explanatory gaps, but the iteration of the scientific method means that subsequent scientists return to the gaps time and again, and when they do so they do so from the perspective of the success of the earlier explanation of surrounding phenomena. Once a species of explanation becomes generally received as valid, the perception of the later extension of this species of explanation (perhaps already considered radical in its initial formulation) becomes more acceptable, and more explanatory power can be derived from the explanation.

Similar considerations to those above hold for the same formulation in terms of mechanism rather than materialism, or in terms of quantification rather than materialism. Initial formulations of mechanism (or quantification) can be crude and seem only to apply to macroscopic features, and is possibly seen as impossibly awkward to explain the fine-grained features of the world. As the mechanistic explanation becomes more refined and flexible, the idea of its application to more delicate matters appears less problematic.

An object-oriented ontological account of naturalism would be the most difficult to formulate and would take us the farthest from methodological concerns and the deepest into ontological concerns, so I will not pursue this at present (as I write this I can feel that my mind is not up to the task at the moment), but I will only mention it here as a viable possibility.

In any case, our formulations of methodological naturalism based on these formulations of naturalism would run something like this:

Methodological materialism pursued as far as possible, leaving any non-material account aside

Methodological mechanism pursued as far as possible, leaving any non-mechanistic account aside

Methodological quantification pursued as far as possible, leaving any qualitative account aside

Methodological flat naturalism, or transcendental naturalism, pursued as fas a possible, leaving any non-flat or non-transcendental account aside

I think that all of these approaches do, in fact, closely describe the methodology of the scientific method, especially as I mentioned above considered from the perspective of the growth of knowledge through the iteration of the scientific method.

The growth of knowledge through the iteration of the scientific method is a formulation of the historicity of scientific knowledge in terms of the future of that knowledge. The formulation of the historicity of scientific knowledge in terms of the past is nothing other than that embodied in the Foucault quote that, “A real science recognizes and accepts its own history without feeling attacked.” (from “Truth, Power, Self: An Interview with Michel Foucault”)

All present scientific knowledge will eventually become past scientific knowledge, and it will become past knowledge through the continued pursuit of the scientific method, which is to say, methodological naturalism in some form or another.

The distant future of scientific knowledge, if only we had access to it, would seem as unlikely and as improbable as the distant past of scientific knowledge, but the past, present, and future of scientific knowledge are all connected in a continuum of iterated method.

It is ultimately the task of philosophy of see scientific knowledge whole, and to this end we must see the whole temporal continuum as the expression of science, and not any one, single point on the continuum as definitive of science. The unity of science, then, is the unity of the scientific method that is the connective tissue between these diverse epochs of science, part, present, and future.

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Parsimonious Formulations

30 December 2009

Wednesday


William of Ockham was one of the greatest philosophers of the Western tradition, who more-or-less single-handedly inaugurated the tradition of philosophical parsimony that still reigns today.

The principle of parsimony — also called Ockham’s Razor, after William of Ockham who gave the principle some of its most compelling formulations — is among the most venerable of principles in human thought. This must be one of the few medieval philosophical principles that remains a staple of thought even today. Few but Thomists would be able to make it through the bulk of the Summa Theologiae, and far fewer still would find much in it with which they could agree, but there are parts of Ockham that can be read like a contemporary. Ockham is among the very few medieval writers of whom we can say this, and he shares this status with the canonical texts of classical antiquity.

I can't think of much of anything in Saint Thomas Aquinas that we can read while nodding with approval.

Not long ago in A Formulation of Naturalism I cited Hallett’s book Cantorian Set Theory and Limitation of Size for its treatment of what Hallett called Cantor’s finitism, i.e., Cantor’s treatment of transfinite numbers as being like finite numbers as far as this methodological analogy could be made to hold. I suggested that a similar approach could be used to characterize naturalism in terms of materialism: we can treat naturalism like materialism by way of a methodological analogy that is employed as long as it can be made to work. Later, in Two Thoughts on Naturalism, I suggested that naturalism could be given a similar treatment vis-à-vis mechanism.

Such formulations — the transfinite in terms of the finite, and naturalism in terms of materialism or mechanism — are minimalist formulations. Conceptual minimalism makes the most it can from the fewest resources. This is an application of the principle of parsimony. It has always been felt most strongly in the formal sciences. Axiomatization is an expression of this spirit of minimalism. Łukasiewicz’s reduction of the propositional calculus to a single axiom is another expression of the spirit of parsimony, as is the Polish notation for symbolic logic that he first formulated. The later Russell’s formulations in terms of “minimum vocabularies” must be counted a part of the same tradition, though Russell’s parsimonious roots go much deeper and are perhaps expressed most profoundly in his theory of descriptions.

Russell's theory of descriptions, called a 'paradigm of philosophy' by Frank Ramsey, is a classically parsimonious theory.

The language of parsimony is pervasive throughout contemporary logic and mathematics, such as when one says that, for example, Von Neumann–Bernays–Gödel set theory is a conservative extension of Zermelo–Fraenkel set theory (ZF). There is even a conservativity theorem of mathematical logic that formalizes this approach to parsimony. Perhaps counter-intuitively, a conservative extension of a theory extends the language of a theory without extending the theorems that can be derived from the original (unextended) theory. Michael Dummett is sometimes credited with originating the idea of a conservative extension (by Neil Tennant, for example), and he wrote in his Frege: Philosophy of Mathematics that:

“The notion of a conservative extension makes sense only if the theory to be extended is formulated in a language more restricted than that of the extended theory.” (p. 297)

It sounds puzzling at first, but it shouldn’t surprise us. Quine noted that the more we conserve on the elements of our theory, the larger the apparatus of derivation must become, and vice versa: there is an inverse relationship between the two.

dummett michael

The short Wikipedia article on conservative extensions observes as follows:

“a conservative extension of a consistent theory is consistent. Hence, conservative extensions do not bear the risk of introducing new inconsistencies. This can also be seen as a methodology for writing and structuring large theories: start with a theory, T0, that is known (or assumed) to be consistent, and successively build conservative extensions T1, T2, … of it.”

Thus the methodologically parsimonious tool of conservative extensions has implications for theoretical work over all. One can imagine an entire theoretical discipline given over to gradual and incremental extensions of an originally modest theory, which implies a model of theoretical thought innocent of Kuhnian paradigm shifts and revolutions in knowledge.

Sufficiently gradual (and sufficiently conservative) extensions of an existing theory may obviate the need for a Kuhnian paradigm shift.

Sufficiently gradual (and sufficiently conservative) extensions of an existing theory may obviate the need for a Kuhnian paradigm shift.

Of course, all parsimonious theories must rely upon some original bold insight upon which later conservative extensions can build. Cantor’s informal insights into set theory and transfinite numbers begat such an embarrassment of riches that almost all subsequent mathematical thought has consisted of various restrictions and codifications of Cantor’s intuitive and informal ideas. There is scarcely anything in the history of science to compare with it, except for Darwin’s conceptual breakthrough to natural selection. But mathematical theory and biological theory are developed so differently that the resemblance of these two insights followed by decades (and, I would guess, coming centuries) and elaboration and qualification is easier to miss than to see.

There is an implicit recognition in the conceptualization of parsimonious formulations of the power of more sweeping formulations, the proactive character of conceptual innovation that goes beyond accepted formulations, even while there is at the same time an implicit recognition of the danger and perhaps also irresponsibility of such theorizing.

Some time ago I noted in Exaptation of the Law that the law has an intrinsic bias in favor of the past that makes it a conservative force in society. With the law, this influence is concrete and immediate, often deciding the fates of individuals. It strikes me now that the minimalism and parsimony of much (if not most) formal thought is intrinsically conservative in an intellectual sense, and constitutes the ontological equivalent of bias in favor of the past. This intrinsic bias of formal thought is likely to be less concrete and immediate than that of the law, but no less pervasive.

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