All Bayesian accounts of evidence, both subjective and objective, share the following principle: For a fact e to be evidence for a hypothesis h in an epistemic context K, it is sufficient that e increases the probability of h. Formally, if p(h|e) > p(h), then e is evidence for h. In this paper I argue that this principle is false. My main claim is that evidence is a threshold concept with respect to probability. There must be a critical mass of probability, so to speak, in order for something to become evidence for a hypothesis.

There are two different threshold accounts in the literature. The first one, which I call the absolute threshold account, states that in order for e to count as evidence for h, e must raise the probability of h from below some threshold r to above it: e is evidence for h only if p(h) £ r and p(h|e) > r. The second view, which I call the relative threshold account, states that in order for e to count as evidence for h, e has to raise the probability of h by at least some threshold value r. In other words, this view says that e is evidence for h only if p(h|e) - p(h) > r.

The threshold view that I advocate, which I call the multiple thresholds account, is a combination of both. Based on the way that evidence is actually judged in different scientific contexts, I argue that evidence comes in degrees that correspond to intervals of probability values. There is an absolute lowest threshold that corresponds to the lower boundary of the lowest degree of evidence, and relative thresholds that determine the degree of evidentiary support of a hypothesis. I use examples taken from evidence-based medicine to illustrate how this approach works in practice.

After presenting my account, I briefly discuss two possible objections to thresholds accounts in general. The first objection is that in a threshold account nothing can raise the probability of a hypothesis that is already above the threshold number. The response to this objection is based on a counterfactual analysis in which the contribution of new evidence can be assessed against an epistemic context in which the probability of the hypothesis is lower than the threshold value. The second objection is a more threatening one. In the orthodox Bayesian approach to evidence, the probability associated with p(h|e) is a continuous measure of degrees of belief. Even if p(h|e) is very low, e provides a justification for believing h to a higher degree than does K alone. My response is based on two claims: (i) to believe that h to a positive degree (to believe positively that h) requires as a necessary and sufficient condition the belief that h; and (ii) belief is a threshold concept with respect to probability. The consequence of combining these two premises is a standpoint which directly opposes orthodox Bayesianism.