Recently my post of a few years back, Of Distinctions, Weak and Strong, was reblogged by studentsofphilosophy. I was pleased to have this older post noticed, as I think there is a lot of potential in this idea for applications throughout philosophy (and I had followed it with Of Distinctions, Principled and Otherwise, as first step toward these applications).

It is one of the most familiar themes of mysticism that the world is ultimately somehow one and whole, and that everything is connected. Because we are talking about mysticism, none of this can be made fully explicit, but is resigned to the ineffable. Ironically, the worldview of science holds exactly the same proposition, but science can make the ultimate unity of the world explicit.

In the scientific worldview, observation and evidence connects all things. The world is reticulate in structure, so that while it is not the case that each individual object is connected to every other individual object, any one object recognized by science is connected to any other object recognized by science by way of a definable chain of evidence that can be observed and quantified. (Quine employed the phrase “the web of belief” to describe our epistemic structure; the web of belief mirrors the web-like causality that connects the various parts of the world.)

Here is where the distinction between strong and weak distinctions is relevant: where any two objects are in direct evidentiary conjunction -- perhaps a causal connection -- the distinction between them is weak. A corollary of weak distinction is that an alternative ontology might classify the two weakly distinct objects as one. On the other hand, where any two objects are not in direct evidentiary connection, the distinction between them is strong. Strongly distinct objects are not likely to be classed together in any alternative ontology.

One way to think of this reticulate ontology is that it is simply a displacement into ontology of the idea of degrees of separation. Weakly distinct objects have fewer degrees of separation; strongly distinct objects have a greater number of degrees of separation.

Another way to think of this is in terms of the Platonic conception of being (which I wrote about in Extrapolating Plato’s Definition of Being and Agents and Sufferants). If we think of affecting or being affected in Plato’s definition of being in terms of causality, then Plato’s definition of being coincides with the scientific ontology. This is as ironic as scientific ontology maintaining the same unity of the world as mysticism, as Plato was certainly the most mystical of the great philosophers. Plato has indeed become associated with a certain obscurantism, partly because of his social views propounded in the Republic and the Laws, and partly because of the peculiarities of Platonic realism as a metaphysic.

For much of Western history, Platonic realism was identified with metaphysics per se, so that a denial of Platonic realism, or some form of realism that recognizes the reality of properties independent of their existential instantiation, was considered a denial of metaphysics. I remarked in my The Recrudescence of Metaphysics that almost every philosopher has denounced metaphysics even while practising metaphysics, but this is easy to do when you identify metaphysics with Platonic realism. You may engage in all kinds of artful ontological theories, but if you avoid Platonic realism you could, until recently, still condemn metaphysics with a clean conscience.

This is changing. The idea of scientific realism (in contradistinction to Platonic realism) has moved philosophers in the direction of recognizing the “ontological commitments” of a given theory or theories. The unity of the world according to science is the ontology of scientific realism that recognizes either the most parsimonious or the most permissive ontological commitments. If we say that the world according to science is one and whole, then we recognize only the single ontological commitment of the world, whereas if we recognize all of the ways in which science analyzes the world as independent objects ultimately connected to all of the other objects of the world by webs of causal connections that constitute observable evidence, then the inferior species (to invoke an Aristotelian concept) of every scientific analysis are all objects to be equally recognized as constituents of scientific realism and these objects jointly constitute the ontological commitments of science.   

If we recognize mathematics as a part of science, and mathematical ontology as a part of scientific realism (in accordance with indispensability arguments, i.e., that mathematics is indispensable to science, which it is), then the ontological commitments of scientific realism are not merely infinite, but a higher order or infinity, though I suppose that a parsimonious philosopher might argue that we can have the indispensable portions of mathematics without the higher infinities of set theory. However, if we set the ontological commitments of scientific realism in the context of infinitistic historiography and infinitistic cosmology, it would be more difficult to avoid the ontological commitments of higher infinities.  

Infinitistic historiography and infinitistic cosmology have the advantage of excluding nothing from scientific realism, and so avoiding the possibility of an ontological “outside” to the world, which was once the province of Platonic metaphysics and supernaturalistic theology alike. But at our current state of scientific knowledge the Big Bang represents a hard earliest bound to possible observation, and therefore a boundary to what can be connected to everything else in the scientific unification of the world. By following the argument to this extent we come to the limits of the scientific unity of the world; the unity of science is also the limit of science. Thus positing an infinitistic historiography and cosmology may constitute the authentic metaphysical position of our time. In that sense, I must count myself a metaphysician.