Online research in philosophy

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: the difference measure: d(H,E) = pr(H/E) - pr(H).0 This may be called a “positive (probabilistic) relevance measure” of confirmation, since, according to it, a piece of evidence E qualitatively confirms a hypothesis H if and only if pr(H/E) > pr(H), where qualitative disconfirmation is characterized by replacing “>” with “ “ with “=”. Other more or less standard positive relevance measures that have been proposed are: the log-ratio measure: r(H,E) = log[pr(H/E)/pr(H)] and the log-likelihood-ratio measure: l(H,E) = log[pr(E/H)/pr(E/~H)].

This paper investigates the adequacy of evidential relevance relations proposed by Glymour and others. These accounts incorporate, as a necessary condition, what I call the Positive Instance Condition (PIC): the evidence statement and auxiliary assumptions entail a "positive instance" of the hypothesis. I argue that any account which incorporates PIC as a necessary condition while allowing "bootstrap testing" is doomed to fail. A nonbootstrapping evidential relevance relation of similar form is proposed, and it is argued that, in addition to avoiding published counter examples, this new relation meets two general requirements which, if not met, would undermine the ability of any account that incorporates PIC to accord with our intuitions of evidential relevance.

According to a standard account of evidence, one piece of information is stronger evidence for an hypothesis than is another iff the probability of the hypothesis on the one is greater than it is on the other. This condition, I argue, is neither necessary nor sufficient because various factors can strengthen the evidence for an hypothesis without increasing (and even decreasing) its probability. Contrary to what probabilists claim, I show that this obtains even if a probability function can take these evidential factors into account in ways they suggest and yield a unique probability value. Nor will the problem be solved by appealing to second-order probabilities.

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.

In this note, I consider various precisifications of the slogan ‘evidence of evidence is evidence’. I provide counter-examples to each of these precisifications (assuming an epistemic probabilistic relevance notion of ‘evidential support’).

, Peter Achinstein argues against the long-standing claim that ‘evidence’ is ambiguous in possessing a sense of confirming evidence and a sense of supporting evidence. He argues that explications of supporting evidence will necessarily violate his contentions that evidence is a discontinuous ‘threshold concept’ and that any philosophical account of supporting evidence will be too weak to be useful to working scientists. But an account of supporting evidence may be formulated which includes Achinstein's notion of epistemic thresholds that finds examples in Achinstein's own historical case studies. Thresholds and the denial of ambiguity Achinstein's new account of confirming evidence Achinstein's argument against the ‘ambiguity response’ A threshold-based approach for restoring the ambiguity Maxwell and ‘a subject of rational curiosity’ Bohr and ‘future development of our understanding’ Perrin and the edge of reasonable belief Restoring ambiguity.

Confirmation is commonly identified with positive relevance, E being said to confirm H if and only if E increases the probability of H. Today, analyses of this general kind are usually Bayesian ones that take the relevant probabilities to be subjective. I argue that these subjective Bayesian analyses are irremediably flawed. In their place I propose a relevance analysis that makes confirmation objective and which, I show, avoids the flaws of the subjective analyses. What I am proposing is in some ways a return to Carnap's conception of confirmation, though there are also important differences between my analysis and his. My analysis includes new accounts of what evidence is and of the indexicality of confirmation claims. Finally, I defend my analysis against Achinstein's criticisms of the relevance concept of confirmation.

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.

Recently in this journal Sherrilyn Roush (2004) defends positive relevance as a necessary (albeit not a sufficient) condition for evidence by rejecting two of the counterexamples from my earlier (2001) work. In this reply I argue that Roush's critique is not successful.

Two notions of evidence are focused on in this essay, Carnap's positive-relevance notion of evidence (1962, pp. 462 ff.), and Achinstein's notion of potential evidence (1978; and 1983, pp. 322–350). Achinstein creates several interesting examples in his attempt to find faults in Carnap's notion of evidence; his motive, ultimately, is to impel us towards potential evidence. The purpose of this essay is to show that positive relevance is significantly more promising than potential evidence with respect to capturing the scientific sense of the term evidence. This is accomplished by finding faults in the notion of potential evidence, and by defending positive relevance against Achinstein's examples.