Xu and Tenebaum, in Word Learning as Bayesian Inference (Psychological Review, 2007), develop a very simple Bayesian model of how children (and even adults) build semantic associations based on accumulated evidence. In short, they find contrastive elimination approaches as well as connectionist methods unable to explain the patterns that are observed. Specifically, the most salient problem with these other methods is that they lack the rapid transition that is seen when three exemplars are presented for a class of objects associated with a word versus one exemplar. Adults and kids (the former even more so) just get word meanings faster than those other models can easily show. Moreover, a space of contending hypotheses that are weighted according to their Bayesian statistics, provides an escape from the all-or-nothing of hypothesis elimination and some of the “soft” commitment properties that connectionist models provide.
The mathematical trick for the rapid transition is rather interesting. They formulate a “size principle” that weights the likelihood of a given hypothesis (this object is most similar to a “feb,” for instance, rather than the many other object sets that are available) according to a scaling that is exponential in the number of exposures. Hence the rapid transition:
Hypotheses with smaller extensions assign greater probability than do larger hypotheses to the same data, and they assign exponentially greater probability as the number of consistent examples increases.
It should be noted that they don’t claim that the psychological or brain machinery implements exactly this algorithm. As is usual in these matters, it is instead likely that whatever machinery is involved, it simply has at least these properties. It may very well be that connectionist architectures can do the same but that existing approaches to connectionism simply don’t do it quite the right way. So other methods may need to be tweaked to get closer to the observed learning of people in these word tasks.
So what can this tell us about epistemology and belief? Classical foundationalism might be formulated as something is a “basic” or “justified” belief if it is self-evident or evident to our senses. Other beliefs may therefore be grounded by those basic beliefs. And a more modern reformulation might substitute “incorrigible” for “justified” with the layered meaning of incorrigibility built on the necessity that given the proposition it is in fact true.
Here’s Alvin Plantinga laying out a case for why justified and incorrigibility have a range of problems, problems serious enough for Plantinga that he suspects that god belief could just as easily be a basic belief, allowing for the kinds of presuppositional Natural Theology (think: I look around me and the hand of God is obvious) that is at the heart of some of the loftier claims concerning the viability or non-irrationality of god belief. It even provides a kind of coherent interpretative framework for historical interpretation.
Plantinga positions the problem of properly basic belief then as an inductive problem:
And hence the proper way to arrive at such a criterion is, broadly speaking, inductive. We must assemble examples of beliefs and conditions such that the former are obviously properly basic in the latter, and examples of beliefs and conditions such that the former are obviously not properly basic in the latter. We must then frame hypotheses as to the necessary and sufficient conditions of proper basicality and test these hypothesis by reference to those examples. Under the right conditions, for example, it is clearly rational to believe that you see a human person before you: a being who has thoughts and feelings, who knows and believes things, who makes decisions and acts. It is clear, furthermore, that you are under no obligation to reason to this belief from others you hold; under those conditions that belief is properly basic for you.
He goes on to conclude that this opens up the god hypothesis as providing this kind of coherence mechanism:
By way of conclusion then: being self-evident, or incorrigible, or evident to the senses is not a necessary condition of proper basicality. Furthermore, one who holds that belief in God is properly basic is not thereby committed to the idea that belief in God is groundless or gratuitous or without justifying circumstances. And even if he lacks a general criterion of proper basicality, he is not obliged to suppose that just any or nearly any belief—belief in the Great Pumpkin, for example—is properly basic. Like everyone should, he begins with examples; and he may take belief in the Great Pumpkin as a paradigm of irrational basic belief.
So let’s assume that the word learning mechanism based on this Bayesian scaling is representative of our human inductive capacities. Now this may or may not be broadly true. It is possible that it is true of words but not other domains of perceptual phenomena. Nevertheless, given this scaling property, the relative inductive truth of a given proposition (a meaning hypothesis) is strictly Bayesian. Moreover, this doesn’t succumb to problems of verificationalism because it only claims relative truth. Properly basic or basic is then the scaled contending explanatory hypotheses and the god hypothesis has to compete with other explanations like evolutionary theory (for human origins), empirical evidence of materialism (for explanations contra supernatural ones), perceptual mistakes (ditto), myth scholarship, textual analysis, influence of parental belief exposure, the psychology of wish fulfillment, the pragmatic triumph of science, etc. etc.
And so we can stick to a relative scaling of hypotheses as to what constitutes basicality or justified true belief. That’s fine. We can continue to argue the previous points as to whether they support or override one hypothesis or another. But the question Plantinga raises as to what ethics to apply in making those decisions is important. He distinguishes different reasons why one might want to believe more true things than others (broadly) or maybe some things as properly basic rather than others, or, more correctly, why philosophers feel the need to pin god-belief as irrational. But we succumb to a kind of unsatisfying relativism insofar as the space of these hypotheses is not, in fact, weighted in a manner that most reflects the known facts. The relativism gets deeper when the weighting is washed out by wish fulfillment, pragmatism, aspirations, and personal insights that lack falsifiability. That is at least distasteful, maybe aretetically so (in Plantinga’s framework) but probably more teleologically so in that it influences other decision-making and the conflicts and real harms societies may cause.