I have a tendency to speak in a way that conflates “evidence” and “reasons.” I’m pretty sure they are interchangeable. When we discover evidence, we discover a reason to believe some proposition. At the same time, reason-giving is the exchange of evidence, even when it is nothing more than the exchange of priors and ungrounded convictions.
Neither evidence nor reasons constitute proof, alone: instead we speak of “proving” something according to some evidentiary standard, as when we distinguish, in law, between the standards of “reasonable suspicion,” “probable cause,” “preponderance of the evidence,” and “beyond a reasonable doubt.” In that sense, proof, too, is a matter of satisfying some evidentiary standard by sharing evidence and thus reasons to believe a proposition.
Of course, this stands in opposition to the use of proof in a priori situations, like logical and geometric proofs. In such instances, we seek irrefutable evidence as the only acceptable reason to believe a conclusion. The task in such instances to achieve epistemic closure: to explicitly consider the implicit conclusions entailed by our current set of beliefs. Rather than achieving an evidentiary standard, we look to go beyond evidence to “the things themselves,” which raises all of the concerns of Humean skepticism and Kant’s Critiques.
In light of those concerns, we can consider an alternative. We can reject this formulation of proving as categorically distinct from reason-giving and evidence-appraisal. In that case, we’d take a logical “proof” as evidence of some claim, but nothing more. This requires us to re-evaluate our relationship to the necessity called upon in logic and mathematics.
That re-evaluation is at the heart of the project in naturalized epistemology: when we begin with the assumption that our very reasoning is the product of natural evolutionary forces, and thus perhaps it is not “fit to purpose” for metaphysical reflections, or set theory, or ontological interrogation. Yet when we set out with a purely or preferentially descriptive approach to the habits of belief and and reason-giving in our thinking and knowing, other trouble arises, not the least that, descriptively, we seem to be burdened with a number of epistemic prescriptions and norms. We cannot help but notice that believing is shot through with justification and warrant, that we find ourselves constantly aspiring more than a description of what we find ourselves believing.
In particular, I think it is notable that a description of epistemic behaviors includes the aspiration to demonstrate epistemic virtues, and that those epistemic virtues are said to be warranted by their capacity to achieve the truth. When a particular epistemic habit is shown to be worse than we first thought at achieving the truth, it seems like we tend to reject it, or at least try to reject it by rooting it out in some of the glaring places where we find it. In that sense, my tendency to use “evidence,” “reasons,” and even “proof” interchangeably reflects what I take to be the current state of the art in epistemology: the remarkable proximity between naturalism, reliabilism, and virtue epistemology.
One question that continues to trouble me is a variation of the one first described by Plato’s Meno: are epistemic virtues teachable? That is, is it possible to transmit the habits of responsible, reliable, and truth-sensitive believing? Alternatively, do we as teachers only select and sort reliable knowers from unreliable knowers through a process of assessment and recognition? Or worse, do we select and sort like-minded believers from those who we do not recognize because of the flawed, prejudicial, or biased methods built into our metrics for selection and sorting? Note that teaching as “selection and sorting” is not incommensurable with a subsequent process by which we cultivate virtuous epistemic habits in those who show native talent, but nor is it incommensurable with a process of sorting that merely groups like-minded believers and then privileges some over others through estimable associations.