indirectness of moving from a negative (falsity) to a positive (truth). The principle of necessity does not have this particular indirectness, but, as if to compensate, it is much more difficult to use: it is much easier to show that something is a contradiction than it is to show that something is necessary. Thus, even when using these methods, tightly connected to truth as they are, discovering whether a theory is true is always a matter of discovering whether that theory has some other property.
This of course is not somehow a necessary feature of truth discovery. We can imagine a being, God perhaps, who could simply directly assess the truth or falsity of claims, explanations, and theories. But we are not like such beings. To find the truth, we must use methods that connect truth to some other property and then work to discover that property. Methods of evaluating the truth of theories are mediated by a middle term: something we can discover in theories and which is connected to truth. So far, we have found three such middle terms: fit with other truths (which is connected to truth), contradictoriness (which is connected to falsity), and necessity (which is connected to truth). To admit that we need indirect means of truth evaluation for theories is not to undercut the importance of truth or other epistemic value to our theory evaluation. It is instead to be cognizant of our limitations when it comes to evaluating theories for their truth. Assessing the truth or other epistemic value of theories is difficult. Beings like us must utilize different tools—methods that mediate a connection between truth and theories—in our endeavor to evaluate theories.
These relatively straightforward methods will probably be enough to help us in the case above of Rawls’ theory and its competitors. Recall: Rawls’ theory, the libertarian theory, the radical egalitarian theory, and the utilitarian theory are all competing explanations of justice. Using the methods we’ve sketched above, we can work to discover which theory is true or at least which theory we are most justified in believing to be true. It’s unlikely that we’ll discover necessity at the heart of any of these theories or that these theories are entailed by any necessity, so that method is perhaps not helpful. But the method of noncontradiction may be helpful. For instance, one might argue that the libertarian theory has a contradiction at its heart: to give unlimited liberty to any is ipso facto to restrict other people’s liberty (because unlimited liberty includes the liberty to trample on others), and thus the theory which says that justice can countenance no restrictions on liberty whatsoever is contradictory and thus false. If this argument is successful (this of course is just a sketch; a serious attempt to use this method would have to argue in more detail that there is a contradiction here), then we’ve knocked one of the competitors out of the running for being the true theory. There may be an analogous but opposite contradiction at the heart of the radical egalitarian theory, so perhaps we can use the same method to knock that theory out of the running as well. But when it comes to Rawls’ theory and the utilitarian theory, it seems that the method of noncontradiction has given out. We still want to know which of those theories we should think is true, but it doesn’t seem as though either theory involves a contradiction. We thus need a further method if we are to continue to winnow down the competitors until we arrive at the true theory. Fit with other truths is a method that can step in at this point. We know that it is true that justice forbids slavery. But the utilitarian theory allows that slavery can sometimes be compatible with justice (where the program of slavery maximized utility), whereas Rawls’ theory rules out slavery in principle (it’s in violation of both principles of justice and the deeper spirit of Rawls’ theory on which society is to be a fair system of cooperation among free equals). Thus, Rawls’ theory of justice fits better with other things we know to be true about justice and is thus a better theory—an epistemically better theory or a better candidate for being true.4
Problem: Lists and Epicycles
One might think that the question I raised at the outset—how to discover which theories are true—can be solved with only the tools, the methods of theory evaluation, we’ve introduced thus far. Fit with other truths in particular is a powerful method which might seem to be able to resolve all competition between theories such that we can discover which theories are true or which theories are epistemically better.5 But just as the method of noncontradiction gave out at a certain point—there can be competing theories, neither of which involves a contradiction—so too will the method of fit with other truths give out. There can be competing theories both of which fit equally well with the data. To see this, consider another of our example questions above: “Do the planets move according to Copernicus’ model?” Suppose we have two competing theories: first, we have Copernicus’ model which explains the motions of the planets by positing the existence of principled orbits (circles) as well as a model of the relative positions of the bodies (heliocentricism). Second, we have a “theory” which simply lists the positions of the planets in precisely the same way that Copernicus’ model predicts, but with no underlying principles or model that systematizes those movements.6 Now, by stipulation, both of these theories of the motions of the planets fit equally well with the data. They say precisely the same thing about where the planets will be and thus will stand and fall together with respect to fitting with our observations about the planets (Copernicus’ theory, of course, does not fit perfectly well with the data; its circular orbits commit it to significant lack of fit with the data). Both theories fit equally well with the data, but we still need a way to adjudicate between them as to which theory is true or otherwise epistemically better. Notice that we can multiply this problem to infinity: we could have another list of the positions of the planets, identical to our previous list, except that it makes a slightly different prediction about the position of Mars in 10,000 years. We can generate infinite such lists, all of which fit equally well with the data we have available to us, but which make different predictions about future planetary motions. So, we have infinite theories of the motions of the planets from which to choose; how do we evaluate which theory is best from among these? This, of course, is meant to be a silly question: among all these options, Copernicus’ model clearly stands out as the best theory. The others are ad hoc lists built on no underlying system. But this is precisely the point: Copernicus’ theory is the best theory, despite scoring equally well with respect to fit with the data. This tells us that there is some other method of theory evaluation, other than fit with the data, at play. Infinite underdetermination will always plague the method of fit with the data. We need other methods of theory evaluation to break that impasse. If fit with the data were all that were needed, a mere list of data would always be an option, and there are infinite such lists that fit with the data available to us.
What exactly is the method of theory evaluation that Copernicus’ model scores well on as compared to the lists? It’s something like a unity or a simplicity method of theory evaluation: a theory that is simpler or more unified is a better theory, a better candidate for being true. How exactly Copernicus’ theory is more unified or simpler needs spelling out, and we need to know much more about how these methods work.7 But for now, it’s clear enough that something like a method of simplicity gets deployed in our evaluating Copernicus’ theory as better.
But one still might think that fit with the data is still the predominant method of theory evaluation and that the simplicity method of theory evaluation only gets deployed as a tiebreaker, to resolve the underdetermination that remains after the method of fit with the data is exhausted. But further permutations on the Copernicus case show that this is incorrect. Compare Copernicus’ theory of the motions of the planets with its predecessor: Ptolemy’s theory. Copernicus’ theory holds that the sun is the center of the solar system and that the planets (including the earth) move in circular orbits around the sun. Ptolemy’s theory holds that the earth is the center of the solar system and that the planets (including the sun) move in circular orbits around the earth. But Ptolemy’s theory also held that there are epicycles—orbits upon orbits—for each of the planets. By Copernicus’ time, Ptolemy’s theory had been refined to fit the data by adding more and more epicycles, until the theory invoked hundreds upon hundreds of epicycles. But with such epicycles (ad hoc as we recognize them to be now), the theory can fit the data. Indeed, Ptolemy’s theory actually fits better with the data (or at least it could be made to be) than does Copernicus’ theory.8 But Ptolemy’s theory, with its hundreds of epicycles, clearly scores worse than Copernicus’
