Are the Propositions of Physics Precise?

It should be noted that Credence to Vagueness makes some surprising predictions about the classification of vagueness. For example, it is often taken to be a platitude among those theorizing about vagueness that the sentences of fundamental physics express precise propositions.

We can illustrate this idea by entertaining a crude version of pre-Socratic physics. According to this picture, there are only four fundamental predicates: earth, wind, fire, and water. Given this account of the physics, the proposition that there is fire ought to be a precise proposition, for it passes our test of being a proposition expressed by a sentence of fundamental physics.

By modern standards the idea that the property of being fire is either fundamental or precise is not particularly plausible. Apply sparks to some kindling and at some point you’ll have a fire, but the point at which there is fire is surely not a precise matter.

From this perspective, the proposition that there is fire is not a precise proposition. However, we can give an argument that even someone who was working under the false assumption that fire was a fundamental property should not consider this proposition to be precise. Since the hypothesis that there are borderline cases of fire is in fact true, it was certainly a hypothesis that was true for all the Aristotelian physicists knew. Thus, there is an epistemically possible hypothesis about fire conditional on which the Aristotelian physicist should have been certain that it was borderline whether there is fire.

If this conclusion does not strike you as particularly surprising, consider instead a proposition that you might find in a modern physics textbook such as the proposition that there are electrons. This might seem like the paradigm example of a precise proposition. Although we presently believe that electrons are basic and not composed of smaller particles, this is an empirical observation. There are consistent scientific hypotheses—hypotheses we might even wish to take seriously—in which electrons are composed of little clouds of smaller, more basic particles. One could also imagine that, just as with real clouds of water vapour, it can sometimes be borderline whether these smaller particles are close enough and dense enough to compose an electron.

It follows, then, that there are physical hypotheses about the world such that conditional on them the proposition that there are electrons has the epistemic profile distinctive to borderline cases. For example, suppose that α is a precise description of a possible arrangement of particles in which it would be borderline whether that arrangement of particles constitute an electron-cloud. Now consider the physical hypothesis that electrons are certain clouds of smaller particles and that there is only one cluster of such particles in the universe and that these particles are arranged in arrangement α. Conditional on this proposition, we should be uncertain in that distinctive way about whether there are electrons, and indeed we should be certain, conditional on this proposition, that it is borderline whether there are electrons. It follows, by Credence to Vagueness, that the proposition that there are electrons is a vague proposition.^[168]

It should be noted that it is completely consistent with this conclusion that the proposition that there are electrons is necessarily determinately true or determinately false. This is not sufficient on our view for a proposition to be precise, however, and this leads to a radically different conception of the vague/precise divide—one that is not fixed by familiarity with particular examples but is instead fixed by the role the distinction plays in thought.

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