Keith Douglas
Last time, I challenged the reader to grapple with a question in method — hence, think of it as a puzzle in epistemology. I am sad to report nobody answered the call, but no matter.
Possibility and Necessity
This time I would like to discuss possibility and necessity again. Philosophical tradition has it that the domain of possibilities is propositions or perhaps sentences. This allows for a neat hierarchy. Logically possible sentences include physically possible ones, where the latter is also regarded logically — “consistency with the laws of nature.” But to a “metaphysics-first” person like me, laws of nature are the objective patterns in reality, and only law statements (i.e., their partial reconstruction or representation in thought and language) are capable of being consistent or inconsistent. To my mind, since we want to know what can actually happen (or fail to happen), the idea that “physically possible” gets understood in language-like terms “epistemicizes” what should be regarded as metaphysics. At first glance this may be just regarded as a warning that the physically possible can be imperfectly known. So far so good. However, there’s a further problem.
Consider a simple case of falling bodies in an assumed-to-be-constant gravitational field, where the small body is much smaller than the larger one. The proverbial cannon ball off a shortish tower, with small air resistance, for example. Galileo studied this problem as stated, and concluded that the distance traveled by the smaller body was proportional to the square of the time. (We formalize this as s = ct2 in modern notation.) Now, consider a predictive task. We want to know if it is possible that a body will hit the ground in 10 seconds without bothering to drop it.
In order to do this we have to have a value for c. If we do, we can then calculate that the body will hit the ground within 10 seconds if it is dropped from such-and-such a height or lower. Where in all of that was the possibility of a proposition, a “language-like possibility”?
There are several further questions that result from this reflection on what is now grade 10 physics. One more: What in the philosopher’s understanding of possibility corresponds to the height from which the smaller body is dropped? In science, this is an example of what is called a boundary condition. Only some heights lend themselves to the “physical possibility.” Some heights would be too far off the ground to allow the smaller body to reach it in the time asked about. The “law” does not tell us this alone. So both semantically and practically, the view that physical possibility is understood as “consistency with the laws of nature” seems wrong.
Yet why does the common view appear in recent discussions — e.g., Bob Hale’s Necessary Beings from 2015? Here we have to try to steelman our opponent. I think this author would suggest that the theoretical unification that results from having all possibilities similar is important. Does that suggest we should perhaps adopt both viewpoints? That mine is not in opposition, so maybe we can and should use both? I would have no trouble with that, except…
Suppose I wanted to use it to determine whether or not something were physically possible. The view would first require me to regard the something to be language-like as already stated. So, what do I take up? A general sentence? If so, which do I use? Do I use the “Galileo’s law of falling bodies” mentioned above? Do I use the generalization that Galileo himself offered, the one that studies what happens if the smaller body has a small but non-zero initial relative velocity? This is so-called “projectile motion.” Which do I use? Do I try the Newtonian further generalization, usable when the bodies are approximately the same size (e.g., two planets)? Einstein’s, in general relativity, for bodies with very large masses? Each one is truer, but even the last is not going to be quite correct, presumably, under some circumstance or other.
Next I need to create a list of the known laws of nature, so as to check consistency. I am not sure what this would include, but at some point it would include another item from the list. Philosophers often think laws also have to be true. None of these generalizations are completely true, as I just stated. OK, so then, I have to use an approximation. Fair enough, but what approximation? How much error is tolerable?
Both of us have to worry about error. However, saying the body can fall X meters in 10 seconds contradicts the prediction that it can fall X’ meters in 10 seconds. This is all that consistency gets you. Now, one could then give my opponent the error bars I tacitly made use of myself. But the error bars are not part of the laws!
Those who know some of the philosophy of science literature can connect this puzzle to that proposed by Nancy Cartwright’s 1983 book, How the Laws of Physics Lie.
That’s all for now. See you in the new year!
Yes, that is something worth thinking about!