Principle of Inferential Justification (PIJ):
To be justified in believing P on the basis of E one must be (1) justified in believing E, and (2) justified in believing that E makes probable P.
One might note that in the palm reading example there actually is no significant, objective probability between the length of Fred’s so-called “life-line” and his life span. Perhaps this is why my belief that he is going to die soon is unjustified, and not that I don’t satisfy clause (2). Against this, the proponent of PIJ might ask us to consider an amendment to the case. Suppose that, surprisingly, it turns out that there is some objective, significant probabilistic connection between “life-lines” and the life spans of the individuals who have them, though again, suppose that I do not have any justification for believing that there is such a connection. This possibility seems coherent: the fact that the relevant objective probabilistic relation obtains is not sufficient for one to have justification for believing that it obtains. But then, intuitively, I remain unjustified in believing that Fred is going to die soon. Or consider the possibility that I believe Fred will die because he has just ingested a lot of hemlock, and when you ask me why I think hemlock would lead to death, I say that I’m not sure, that it is just a hunch on my part that it is going to kill him. Again, if I lack justification for believing that hemlock is a deadly poison, or that it is likely to have this effect, then intuitively, I lack justification for believing that Fred will die soon. What more, then, is needed? A natural though controversial suggestion is that one must satisfy something like clause (2).
With the first clause of PIJ, one can present a relatively straightforward epistemic regress argument for foundationalism. That clause basically says that one cannot acquire justification for a belief by inferring it from an unjustified belief. It also seems that one cannot acquire justification for a belief by way of a circular, inferential justification—one cannot rely even in part on a proposition as a premise in an inference in support of that very proposition. We seem left with two options: allow that some beliefs have justification without depending on other beliefs, or suppose that all justification is inferential. If all justification is inferential, then for someone S to be justified in believing some proposition P, S must be in a position to legitimately infer it from some other proposition E1. But E1 could justify S in believing P only if S were justified in believing E1, and if all justification were inferential, S would have to infer it (or at least be able to infer it) from some other proposition justifiably believed, E2, a proposition which in turn would have to be inferred from some other proposition justifiably believed, E3, and so on, ad infinitum. But finite beings cannot complete an infinitely long chain of reasoning—arguably, even an infinite being cannot complete an infinitely long chain of reasoning; if it were completed, it would no longer be infinite. And so, if all justification were inferential, no one could be justified in believing anything at all to any extent whatsoever.