Patrick Maher

Subjective and objective confirmation

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 Carnaps 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 Achinsteins criticisms of the relevance concept of confirmation.

Joyce’s Argument for Probabilism

James Joyce’s ‘Nonpragmatic Vindication of Probabilism’ gives a new argument for the conclusion that a person’s credences ought to satisfy the laws of probability. The premises of Joyce’s argument include six axioms about what counts as an adequate measure of the distance of a credence function from the truth. This paper shows that (a) Joyce’s argument for one of these axioms is invalid, (b) his argument for another axiom has a false premise, (c) neither axiom is plausible, and (d) without these implausible axioms Joyce’s vindication of probabilism fails.

Inductive Logic and the Ravens Paradox

Hempels paradox of the ravens arises from the inconsistency of three prima facie plausible principles of confirmation. This paper uses Carnapian inductive logic to (a) identify which of the principles is false, (b) give insight into why this principle is false, and (c) identify a true principle that is sufficiently similar to the false one that failure to distinguish the two might explain why the false principle is prima facie plausible. This solution to the paradox is compared with a variety of other responses and is shown to differ from all of them.

Probabilities for two properties

Let R(X, B) denote the class of probability functions that are defined on algebra X and that represent rationally permissible degrees of certainty for a person whose total relevant background evidence is B. This paper is concerned with characterizing R(X, B) for the case in whichX is an algebra of propositions involving two properties and B is empty. It proposes necessary conditions for a probability function to be in R(X, B), some of which involve the notion of statistical dependence. The class of probability functions that satisfy these conditions, here denoted PI, includes a class that Carnap once proposed for the same situation. Probability functions in PI violate Carnaps axiom of analogy but, it is argued, that axiom should be rejected. A derivation of Carnaps model by Hesse has limitations that are not present in the derivation of PI given here. Various alternative probability models are considered and rejected.

Depragmatized Dutch book arguments

Recently a number of authors have tried to avoid the failures of traditional Dutch book arguments by separating them from pragmatic concerns of avoiding a sure loss. In this paper I examine defenses of this kind by Howson and Urbach, Hellman, and Christensen. I construct rigorous explications of their arguments and show that they are not cogent. I advocate abandoning Dutch book arguments in favor of a representation theorem.

PROBABILITIES FOR MULTIPLE PROPERTIES: THE MODELS OF HESSE AND CARNAP AND KEMENY

In 1959 Carnap published a probability model that was meant to allow forreasoning by analogy involving two independent properties. Maher (2000)derived a generalized version of this model axiomatically and defended themodels adequacy. It is thus natural to now consider how the model mightbe extended to the case of more than two properties. A simple extension waspublished by Hess (1964); this paper argues that it is inadequate. Amore sophisticated one was developed jointly by Carnap and Kemeny in theearly 1950s but never published; this paper gives the first published descriptionof Carnap and Kemenys model and argues that it too is inadequate. Since noother way of extending the two-property model is currently known, the conclusionof this paper is that a satisfactory extension to multiple properties requires somenew approach.

Howson and Franklin on Prediction

Evidence for a hypothesis typically confirms the hypothesis more if the evidence was predicted than if it was accommodated. Or so I argued in previous papers, where I also developed an analysis of why this should be so. But this was all a mistake if Howson and Franklin (1991) are to be believed. In this paper, I show why they are not to be believed. I also identify a grain of truth that may have been dimly grasped by those Bayesians who deny the confirmatory value of prediction.

Why Scientists Gather Evidence

One of the most pervasive features of scientific practice is that scientists gather evidence, by making observations and conducting experiments. This fact provides reason to believe that evidence gathering is a rational means for pursuing scientific goals. Consequently, a philosophy of science which can explain why evidence gathering is a rational means for pursuing scientific goals is (ceteris paribus) to be preferred to one that has no such explanation. In this paper I will test several different philosophies of science by examining whether they are able to give such an explanation of why scientists gather evidence.

Explication of Inductive Probability

Inductive probability is the logical concept of probability in ordinary language. It is vague but it can be explicated by defining a clear and precise concept that can serve some of the same purposes. This paper presents a general method for doing such an explication and then a particular explication due to Carnap. Common criticisms of Carnap’s inductive logic are examined; it is shown that most of them are spurious and the others are not fundamental.

Bayesianism and Irrelevant Conjunction

Bayesian confirmation theory offers an explicatum for a pretheoretic concept of confirmation. The “problem of irrelevant conjunction” for this theory is that, according to some people’s intuitions, the pretheoretic concept differs from the explicatum with regard to conjunctions involving irrelevant propositions. Previous Bayesian solutions to this problem consist in showing that irrelevant conjuncts reduce the degree of confirmation; they have the drawbacks that (i) they don’t hold for all ways of measuring degree of confirmation and (ii) they don’t remove the conflict with intuition but merely “soften the impact” (as Fitelson has written). A better solution, which avoids both these drawbacks, is to show that the intuition is wrong.