A NON-PROBABILISTIC A PRIORI VIEW
I turn to a view according to which simplicity is “built into” the very concept of inductive reasoning. Reasoning inductively just is reasoning to the simplest hypothesis compatible with the evidence.
This is what it means to reason inductively. The idea can also be expressed using a more standard definition of induction, according to which if from the fact that all observed As are Bs you infer that all As are Bs, you are making an inductive inference. Some inductive inferences are valid, some are not. You are making a valid inductive inference if and only if the hypothesis that all As are Bs is the simplest one compatible with all your data. That is part of the meaning of “valid induction.”This view is just too simple to be true. To begin with, your sample of As observed may be much too small or too unvaried to justify an inference to the hypothesis that all As are Bs, even if that hypothesis is the simplest one compatible with the data. The As may have been selected in a way biased toward being B. This can be so even if all the observed As are Bs. And whether the size, variation, or methods of selection are adequate is a matter to be determined empirically, not a priori, depending on the nature of the As and Bs in question. For J. J. Thomson in 1897, a few experiments showing that cathode rays are attracted to a positively charged plate was sufficient to justify his general claim that cathode rays are negatively charged. For pollsters in 2016, showing that the majority of the people in their poll said they would vote for Hillary Clinton was not enough to justify the claim that Hillary would win—it depends on the size, variation, and location of the sample, and on the degree of commitment of those sampled. In these cases, one evaluates the strength of the inference by reference to empirical facts about the case, not by an appeal to simplicity.
An a priorist may reply by saying, “Yes, in cases of these sorts, empirical factors enter into determining whether the inductive inference is justified. But so does simplicity, and that is a priori.” Suppose the election pollsters did a very good job: the size, variation, location, and commitment of those sampled are empirically impeccable. And suppose, given their impeccable polling, done say two weeks prior to the election, they concluded that Hillary would win by a margin of at least 5 points. Let's say that was the simplest hypothesis given the polling and all other information available at the time. Now, there were more complex hypotheses that were also compatible with the data— e.g., that the director of the FBI would announce a further investigation of Hillary, and that the Russians would hack into the computers of the DNC, which would cause Hillary to lose. We have, then, two competing hypotheses, each of which is compatible with all the well-gathered information. On the present viewpoint, the pollsters were supposed to say that the inference to the “Hillary wins” hypothesis was justified and the “FBI-Russian hack-Hillary loses” hypothesis was not, because the former was the simplest one compatible with the data and the latter is too complex.
My response is that simplicity has nothing to do with it. The reason is that two weeks prior to the election, the pollsters had no evidence at all for the more complex hypothesis and a lot of evidence for the simpler one. Yes, both hypotheses are “compatible” with the polling evidence two weeks prior to the election. But this is “logical” compatibility. There is no contradiction in conjoining either hypothesis with the polling results. But given the information available at that time, the polling results constituted evidence for the “Hillary wins” hypothesis and none for the “FBI-Russian hack-Hillary loses” one. Simplicity is irrelevant.
So let's change the case a little to give simplicity a chance.
Let us change the “Hillary wins” hypothesis in a way that makes it more comparable to the rival I have introduced. The hypothesis is now “No FBI-No Russian hack-Hillary wins.” I will suppose that this hypothesis is simpler than the “FBI-Russian hack-Hillary loses” hypothesis because the latter introduces external causes that will interfere with the outcome, while the former denies the existence of such external causes. Now, suppose that two weeks prior to the election, the polling results were dead-even and that no other empirical information was obtained that favored one candidate over the other or that provided evidence for or against the FBI-Russian hack idea. We might even suppose that the experts put the probability of the FBI-Russian hack idea at 50%, since they learned that Director James Comey of the FBI and President Vladimir Putin are, surprisingly, in collusion and will flip a coin in deciding whether to reopen the investigation of Hillary and to hack the DNC. Should the pollsters have said: “Well, the fact that the new hypothesis involving Hillary winning is simpler than the hypothesis involving Hillary losing makes the former more believable than the latter. It is ‘a priori evidence' for the former hypothesis.” No, under these circumstances the pollsters should say: “Yes, one hypothesis is simpler than the other, but there is no evidence favoring one rather than the other. There is no more reason to believe one rather than the other. So, suspend belief or, if you are a betting person, assign the same odds for both hypotheses.”11.