Online research in philosophy

According to the Doomsday Argument the probability of an impending extinction of mankind is much higher than we think. The adduced reason is that in our assignment of probabilities to soon or not so soon doom we have not fully taken into account that we live in the specific year 2001. This is relevant information, because if I consider myself as an arbitrary member of the human race I have a much higher probability of finding myself living in 2001 on the hypothesis of a soon extinction, Doom Soon, than on the hypothesis of Doom Late---according to the latter hypothesis there are so many more years I could have found myself living in. Accordingly, Bayesian reasoning leads to a posterior probability of the Doom Soon hypothesis, after I have taken the evidence of my birth date fully into account, that is much higher than the prior probability. I show that the Argument is nothing but a rather trivial mathematical exercise in the calculation of posterior from prior probabilities; it is only about the relation between these probabilities and is silent about the concrete values these probabilities should have. Nothing in the Argument supports the conclusion its proponents think it supports, namely that Doom Soon is much more probable than we ordinarily think. The Argument is formally valid, but ineffective.

This paper critically analyzes Sherrilyn Roush’s (Tracking truth: knowledge, evidence and science, 2005) definition of evidence and especially her powerful defence that in the ideal, a claim should be probable to be evidence for anything. We suggest that Roush treats not one sense of ‘evidence’ but three: relevance, leveraging and grounds for knowledge; and that different parts of her argument fare differently with respect to different senses. For relevance, we argue that probable evidence is sufficient but not necessary for Roush’s own two criteria of evidence to be met. With respect to grounds for knowledge, we agree that high probability evidence is indeed ideal for the central reason Roush gives: When believing a hypothesis on the basis of e it is desirable that e be probable. But we maintain that her further argument that Bayesians need probable evidence to warrant the method they recommend for belief revision rests on a mistaken interpretation of Bayesian conditionalization. Moreover, we argue that attempts to reconcile Roush’s arguments with Bayesianism fail. For leveraging, which we agree is a matter of great importance, the requirement that evidence be probable suffices for leveraging to the probability of the hypothesis if either one of Roush’s two criteria for evidence are met. Insisting on both then seems excessive. To finish, we show how evidence, as Roush defines it, can fail to track the hypothesis. This can remedied by adding a requirement that evidence be probable, suggesting another rationale for taking probable evidence as ideal—but only for a grounds-for-knowledge sense of evidence.

The burden of this theorem, stated informally, is that when a hypothesis h is maximally independent of the evidence — that is, it goes wholly beyond the evidence —, then the probability p(h, e) increases when the evidence e is weakened; and hence, the weaker is the evidence, the greater is the probabilistic support.

In Bayesian epistemology, the concept of one proposition’s being evidence for another is explained along the following lines. Given a measure of degrees of confidence, con(...), that conforms to standard probability axioms: (EV) a proposition e is evidence for a proposition h iff con(h|e) is greater than con(h). (Con(h|e) is the degree of confidence in h given e, and is defined as con(h and e)/con(e).) Proposals along these lines, however, have been dogged by what Clark Glymour called the Problem of Old Evidence.[i] (EV) apparently precludes a theory being confirmed by evidence that is already in. For if a potentially evidential proposition, e, is already known, then con(e)=1. One can be subjectively certain of propositions already known to be true. But by definition of con(h|e), where con(e)=1, con(h|e) will always be equal to, and hence never greater than, con(h). Not only does (EV) preclude one from confirming new theories on the basis of information already gathered. Suppose Q is some proposition of which we are now uncertain, but which is evidence for a scientific hypothesis P. That is, con(P|Q) is greater than con(P). If we now devise an experiment to test whether Q, perform the experiment, and become certain that Q, it will no longer count as evidence for P. Thus, if we accept (EV), gathering new evidence to support a theory actually has quite the opposite effect. Gathering the evidence destroys its quality as evidence.

A theory of evidential probability is developed from two assumptions:(1) the evidential probability of a proposition is its probability conditional on the total evidence;(2) one's total evidence is one's total knowledge. Evidential probability is distinguished from both subjective and objective probability. Loss as well as gain of evidence is permitted. Evidential probability is embedded within epistemic logic by means of possible worlds semantics for modal logic; this allows a natural theory of higher-order probability to be developed. In particular, it is emphasized that it is sometimes uncertain which propositions are part of one's total evidence; some surprising implications of this fact are drawn out.

Bayesian epistemology suggests various ways of measuring the support that a piece of evidence provides a hypothesis. Such measures are defined in terms of a subjective probability assignment, pr, over propositions entertained by an agent. The most standard measure (where “H” stands for “hypothesis” and “E” stands for “evidence”) is.

P(H|E): posterior probability of H. That is, the probability of the hypothesis H given the evidence E. P(E|H): likelihood of H. That is, the probability of the evidence E given the hypothesis H.

This paper aims to reconcile (i) the intuitively plausible view that a higher degree of coherence among independent pieces of evidence makes the hypothesis they support more probable, and (ii) the negative results in Bayesian epistemology to the effect that there is no probabilistic measure of coherence such that a higher degree of coherence among independent pieces of evidence makes the hypothesis they support more probable. I consider a simple model in which the negative result appears in a stark form: the prior probability of the hypothesis and the individual vertical relations between each piece of evidence and the hypothesis completely determine the conditional probability of the hypothesis given the total evidence, leaving no room for the lateral relation (such as coherence) among the pieces of evidence to play any role. Despite this negative result, the model also reveals that a higher degree of coherence is indirectly associated with a higher conditional probability of the hypothesis because a higher degree of coherence indicates stronger individual supports. This analysis explains why coherence appears truth-conducive but in such a way that it defeats the idea of coherentism since the lateral relation (such as coherence) plays no independent role in the confirmation of the hypothesis.

The running debate between Peter Achinstein and his critics concerning the nature of scientific evidence is misguided as each side attempts to explicate a distinct notion of evidence. Achinstein's approach, however, is valuable in helping to point out a problem with Carnap's statistical relevance model. By claiming an increase in probability to be necessary for evidence, the received view is incapable of accounting for evidence which is statistically irrelevant but explanatorily relevant. A broader view of evidence which can account for pragmatic concerns such as explanation is thereby required.

This paper addresses two examples due to Peter Achinstein purporting to show that the positive relevance view of evidence is too strong, that is, that evidence need not raise the probability of what it is evidence for. The first example can work only if it makes a false assumption. The second example fails because what Achinstein claims is evidence is redundant with information we already have. Without these examples Achinstein is left without motivation for his account of evidence, which uses the concept of explanation in addition to that of probability.