Again, with special reference to the mind-body problem

One of the obvious weaknesses in the distinction that I made between that which is strongly distinct and that which is weakly distinct in Of Distinctions, Weak and Strong, was the fact that I provided no way to distinguish between weak distinctions and strong distinctions. Without some principle to identify the distinction between weak and strong distinctions, the distinction is arbitrary, and will be made differently by different persons.
Of course, any distinction whatsoever can be made, whether it is principled or arbitrary, but, as J. L. Austin put it in Sense and Sensibilia, “A distinction which we are not in fact able to draw is — to put it politely — not worth making.” I think that there is a way to coherently disagree with Austin, and I will try to show how this is possible.
Every principle implies a distinction. In fact, we could make a principle of the idea that, while every principle implies a distinction (viz. between the principle holding and the principle not holding), it is not the case that every distinction implies a principle. Often there is, in fact, a principle implicit in a distinction, but if we acknowledge the possibility of arbitrary sets, it seems to me that we must also acknowledge the possibility of arbitrary distinctions, for what is an arbitrary set but an arbitrary distinction?
There doesn’t seem to be much problem with strong distinctions such as the Cartesian distinction between body and mind. In fact, this distinction is so strong that overcoming the distinction is the problem, and not the other way around. When we place the mind-body distinction in the context of a mind-body continuum, acknowledging weak distinctions within that continuum, matters become much more problematic.
A strong distinction such as that between body and mind seems to be rooted in the very fabric of the world. Such distinctions could be said to be natural distinctions. Natural distinctions occur between natural kinds. What exactly constitutes a natural kind is, of course, philosophically controversial. The weaker the distinction in question, the less likely it is to be accounted a natural distinction based on obviously distinct natural kinds.
While weak distinctions are problematic in this sense, precisely their problematic character makes it possible to interpolate weak distinctions virtually at will. In so far as a weak distinction can be so difficult to discern that no principle is evident in making the distinction, and we can erect these weak distinctions almost arbitrarily, there is no question of the continuity of whatever is so distinguished. This can be a virtue, and it might also be employed as the distinguishing criterion of a weak distinction.
A strong distinction creates an explanatory gap. There is no explanatory gap with a weak distinction. Moreover, the uniformity and continuity of nature implies that the explanatory gap of a strong distinction can be bridged by a chain of weak distinctions. In other contexts this bridging of an explanatory gap resulting from a strong distinction by a chain of weak distinctions would be called, “the gradual ascent up Mount Improbable.” As it is, we are not talking so much about an ascent as about bridging a chasm, so that we might call this the gradual building out from each bridgehead until the structure meets at the keystone in the middle.