We walk around the world with a bewildering network of opinions, beliefs and judgments, some of them ephemeral (I think that I won’t need an umbrella today) and some vital (I trust that person).

Why is the sky blue? Why do you believe you are mortal? Why is four twice two? How do you know that George Washington actually existed?

If we have an opinion about such a question, then when we are challenged, we offer what we think counts for evidence. We hope, of course, that our evidence persuades our challenger (i.e., we hope that our rhetoric is up to the task), but, more importantly, we hope that our evidence really justifies our opinion.

It is striking, though, how different branches of knowledge — the humanities, the sciences, mathematics — justify their findings so very differently; they have, one might say, quite incommensurate rules of evidence. Often a shift of emphasis, or framing, of one of these disciplines goes along with, or derives from, a change of these rules, or of the repertoire of sources of evidence, for justifying claims and findings in that field. Law has, of course, its own precise rules explicitly formulated.

1 As is perfectly reasonable, Darwin reserves the word “fact” for those pieces of data or opinion that have been, in some sense, vetted, and are not currently in dispute. The word “evidence” in “On the Origin of Species” can refer to something more preliminary that is yet to be tested and deemed admissible or not. Sometimes, if evidence is firmer than that, Darwin will supply it with an adjective such as “clear” or “plainest”; it may come as a negative, such as “there isn’t a shadow of evidence.”
Even the way the word “evidence” is used can already tell us much about the profile of an intellectual discipline. To take a simple example, consider Charles Darwin’s language in “On the Origin of Species”— specifically, his use of the words “fact” and “evidence” — as offering us clues about the types of argumentation that Darwin counts in support, or in critique, of his emerging theory of evolution.1 Sometimes Darwin provides us with a sotto voce commentary on what shouldn’t count — or should only marginally count — as evidence, such as when he writes, “But we have better evidence on this subject than mere theoretical calculations.”

Darwin spends much time offering his assessment of what one can expect — or not expect — to glean from the fossil record. He gives quick characterizations of types of evidence — “historical evidence” he calls “indirect” (as, indeed, it is in comparison with the evidence one gets by having an actual bone in one’s actual hands). These types of judgments frame the project of evolution.

The subsequent changes in Darwin’s initial repertoire, such as evidence obtained by formulating various mathematical models, or the formidable technology of gene sequencing, and so on, mark changes in the types of argument evolutionary biologists regard as constituting a genuine result in the field — in effect, changes in what they regard evolutionary biology to be.

If we accept that the shape and mood of a field of inquiry is largely, or even just somewhat, determined by the specific kinds of evidence needed to have consensually agreed-upon findings or results in that field, it becomes important to study the perhaps peculiar nature of evidence in different domains to appreciate how these distinct domains fit into the greater constellation of intellectual effort.

Mathematics — a realm in which one might think the issue of evidence to be fairly straightforward (you prove a theorem or you don’t) — will, as we shall see, turn out to be not at all clear, and it has its own history of the shaping of types of evidence.

In the fall semester of 2012 I had the pleasure of co-running a seminar course, “The Nature of Evidence,” in the Harvard Law School with Professor Noah Feldman. It was structured as an extended conversation between different practitioners and our students. A number