Confirmation, Misc

Can some evidence confirm a conjunction of two hypotheses more than it confirms either of the hypotheses separately? We show that it can, moreover under conditions that are the same for ten different measures of confirmation. Further we demonstrate that it is even possible for the conjunction of two disconfirmed hypotheses to be confirmed by the same evidence.

Watkins proposes a neo-Popperian solution to the pragmatic problem of induction. He asserts that evidence can be used non-Inductively to prefer the principle that corroboration is more successful over all human history than that, Say, Counter-Corroboration is more successful either over this same period or in the future. Watkins's argument for rejecting the first counter-Corroborationist alternative is beside the point, However, As whatever is the best strategy over all human history is irrelevant to the pragmatic problem of induction since we (...) are not required to act in the past, And his argument for rejecting the second presupposes induction. (shrink)

In Ockham's Razors: A User's Guide, Elliott Sober argues that parsimony considerations are epistemically relevant on the grounds that certain methods of model selection, such as the Akaike Information Criterion, exhibit good asymptotic behaviour and take the number of adjustable parameters in a model into account. I raise some worries about this form of argument.

Schervish (1985b) showed that every forecasting system is noncalibrated for uncountably many data sequences that it might see. This result is strengthened here: from a topological point of view, failure of calibration is typical and calibration rare. Meanwhile, Bayesian forecasters are certain that they are calibrated---this invites worries about the connection between Bayesianism and rationality.

We use recently developed approaches in argumentation theory in order to revamp the hypothetico-deductive model of confirmation, thus alleviating the well-known paradoxes the H-D account faces. More specifically, we introduce the concept of dialectic confirmation on the background of the so-called theory of dialectical structures (Betz 2010, 2012b). Dialectic confirmation generalises hypothetico-deductive confirmation and mitigates the raven paradox, the grue paradox, the tacking paradox, the paradox from conceptual difference, and the problem of surprising evidence.

Probabilistic dependence and independence are among the key concepts of Bayesian epistemology. This paper focuses on the study of one specific quantitative notion of probabilistic dependence. More specifically, section 1 introduces Keynes’s coefficient of dependence and shows how it is related to pivotal aspects of scientific reasoning such as confirmation, coherence, the explanatory and unificatory power of theories, and the diversity of evidence. The intimate connection between Keynes’s coefficient of dependence and scientific reasoning raises the question of how Keynes’s coefficient (...) of dependence is related to truth, and how it can be made fruitful for epistemological considerations. This question is answered in section 2 of the paper. Section 3 outlines the consequences the results have for epistemology and the philosophy of science from a Bayesian point of view. (shrink)

Fitelson (1999) demonstrates that the validity of various arguments within Bayesian confirmation theory depends on which confirmation measure is adopted. The present paper adds to the results set out in Fitelson (1999), expanding on them in two principal respects. First, it considers more confirmation measures. Second, it shows that there are important arguments within Bayesian confirmation theory and that there is no confirmation measure that renders them all valid. Finally, the paper reviews the ramifications that this "strengthened problem of measure (...) sensitivity" has for Bayesian confirmation theory and discusses whether it points at pluralism about notions of confirmation. (shrink)

The Linda paradox is a key topic in current debates on the rationality of human reasoning and its limitations. We present a novel analysis of this paradox, based on the notion of verisimilitude as studied in the philosophy of science. The comparison with an alternative analysis based on probabilistic confirmation suggests how to overcome some problems of our account by introducing an adequately defined notion of verisimilitudinarian confirmation.

The main appeal of the currently popular "bootstrap" account of confirmation developed by Clark Glymour is that it seems to provide an account of evidential relevance. This account has, however, had severe problems; and Glymour has revised his original account in an attempt to solve them. I argue that this attempt fails completely, and that any similar modifications must also fail. If the problems can be solved, it will only be by radical revisions which involve jettisoning bootstrapping's basic approach to (...) theories. Finally, I argue that there is little reason to think that even such drastic modifications will lead to a satisfactory account of relevance. (shrink)

Glymour's "bootstrap" account of confirmation is designed to provide an analysis of evidential relevance, which has been a serious problem for hypothetico-deductivism. As set out in Theory and Evidence, however, the "bootstrap" condition allows confirmation in clear cases of evidential irrelevance. The difficulties with Glymour's account seem to be due to a basic feature which it shares with hypothetico-deductive accounts, and which may explain why neither can give a satisfactory analysis of evidential relevance.

Neuroeconomics is a research programme founded on the thesis that cognitive and neurobiological data constitute evidence for answering economic questions. I employ confirmation theory in order to reject arguments both for and against neuroeconomics. I also emphasize that some arguments for neuroeconomics will not convince the skeptics because these arguments make a contentious assumption: economics aims for predictions and deep explanations of choices in general. I then argue for neuroeconomics by appealing to a much more restrictive (and thereby skeptic-friendly) characterization (...) of the aims of economics. (shrink)

Where E is the proposition that [If H and O were true, H would explain O], William Roche and Elliot Sober have argued that P(H|O&E) = P(H|O). In this paper I argue that not only is this equality not generally true, it is false in the very kinds of cases that Roche and Sober focus on, involving frequency data. In fact, in such cases O raises the probability of H only given that there is an explanatory connection between them.

Among Bayesian confirmation theorists, several quantitative measures of the degree to which an evidential proposition E confirms a hypothesis H have been proposed. According to one popular recent measure, s, the degree to which E confirms H is a function of the equation P(H|E) − P(H|~E). A consequence of s is that when we have two evidential propositions, E1 and E2, such that P(H|E1) = P(H|E2), and P(H|~E1) ≠ P(H|~E2), the confirmation afforded to H by E1 does not equal the (...) confirmation afforded to H by E2. I present several examples that demonstrate the unacceptability of this result, and conclude that we should reject s (and other measures that share this feature) as a measure of confirmation. (shrink)

How should the information that a proposition p is a mystery impact your credence in p? To answer this question, we first provide a taxonomy of mysteries; then, we develop a test to distinguish two types of mysteries. When faced with mysteries of the first type, rational epistemic agents should lower their credence in p upon learning that p is a mystery. The same information should not impact agents’ credence in p, when they face mysteries of the second type. Our (...) account of mystery complements existing explications of abduction. We illustrate its significance by examining the mystery of consciousness. (shrink)

The main point of the paper is to show how popular probabilistic measures of incremental confirmation and statistical relevance with qualitatively different features can be embedded smoothly in generalized parametric families. In particular, I will show that the probability difference, log probability ratio, log likelihood ratio, odds difference, so-called improbability difference, and Gaifman’s measures of confirmation can all be subsumed within a convenient biparametric continuum. One intermediate step of this project may have interest on its own, as it provides a (...) unified representation of graded belief of which both probabilities and odds are special cases. (shrink)

In this paper, we identify a new and mathematically well-defined sense in which the coherence of a set of hypotheses can be truth-conducive. Our focus is not, as usually, on the probability but on the confirmation of a coherent set and its members. We show that, if evidence confirms a hypothesis, confirmation is "transmitted" to any hypotheses that are sufficiently coherent with the former hypothesis, according to some appropriate probabilistic coherence measure such as Olsson’s or Fitelson’s measure. Our findings have (...) implications for scientific methodology, as they provide a formal rationale for the method of indirect confirmation and the method of confirming theories by confirming their parts. (shrink)

To clarify and illuminate the place of probability in science Ellery Eells and James H. Fetzer have brought together some of the most distinguished philosophers ...

The Paradox of the Ravens (a.k.a,, The Paradox of Confirmation) is indeed an old chestnut. A great many things have been written and said about this paradox and its implications for the logic of evidential support. The first part of this paper will provide a brief survey of the early history of the paradox. This will include the original formulation of the paradox and the early responses of Hempel, Goodman, and Quine. The second part of the paper will describe attempts (...) to resolve the paradox within a Bayesian framework, and show how to improve upon them. This part begins with a discussion of how probabilistic methods can help to clarify the statement of the paradox itself. And it describes some of the early responses to probabilistic explications. We then inspect the assumptions employed by traditional (canonical) Bayesian approaches to the paradox. These assumptions may appear to be overly strong. So, drawing on weaker assumptions, we formulate a new-and-improved Bayesian confirmation-theoretic resolution of the Paradox of the Ravens. (shrink)

In the face of continuing assumptions by many scientists and journal editors that p-values provide a gold standard for inference, counter warnings are published periodically. But the core problem is not with p-values, per se. A finding that “p-value is less than α” could merely signal that a critical value has been exceeded. The question is why, when estimating a parameter, we provide a range (a confidence interval), but when testing a hypothesis about a parameter (e.g. µ = x) we (...) proceed as if “=” entails exact equality of the parameter with x. That standard is hard to meet, and is not a standard expected for power calculations, where we are satisfied to reject a null hypothesis H0 if the result is merely “detectably” different from (exact) H0. This paper explores, with resampling (simulation) methods, the impacts on p-values, and alternatives, if the null hypothesis is defined as a thick or thin range of values. It also examines, empirically, the extent to which the p-value may or may not be a good predictor of the probability that H0 is true, given the distribution of the data. (shrink)

Intertheoretic relations are an important topic in the philosophy of science. However, since their classical discussion by Ernest Nagel, such relations have mostly been restricted to relations between pairs of theories in the natural sciences. In this paper, we present a model of a new type of intertheoretic relation, called 'Montague Reduction', which is assumed in Montague's framework for the analysis and interpretation of natural language syntax. To motivate the adoption of our new model, we show that this model extends (...) the scope of application of the Nagelian (or related) models, and that it shares the epistemological advantages of the Nagelian model. The latter is achieved in a Bayesian framework. (shrink)

Sections 1 through 3 present all of the main ideas behind the probabilistic logic of evidential support. For most readers these three sections will suffice to provide an adequate understanding of the subject. Those readers who want to know more about how the logic applies when the implications of hypotheses about evidence claims (called likelihoods) are vague or imprecise may, after reading sections 1-3, skip to section 6. Sections 4 and 5 are for the more advanced reader who wants a (...) detailed understanding of some telling results about how this logic may bring about convergence to the truth. (shrink)

Scientifi c theories and hypotheses make claims that go well beyond what we can immediately observe. How can we come to know whether such claims are true? The obvious approach is to see what a hypothesis says about the observationally accessible parts of the world. If it gets that wrong, then it must be false; if it gets that right, then it may have some claim to being true. Any sensible a empt to construct a logic that captures how we (...) may come to reasonably believe the falsehood or truth of scientifi c hypotheses must be built on this idea. Philosophers refer to such logics as logics of confi rmation or as confi rmation theories. (shrink)

Confirmation theory is the study of the logic by which scientific hypotheses may be confirmed or disconfirmed, or even refuted by evidence. A specific theory of confirmation is a proposal for such a logic. Presumably the epistemic evaluation of scientific hypotheses should largely depend on their empirical content – on what they say the evidentially accessible parts of the world are like, and on the extent to which they turn out to be right about that. Thus, all theories of confirmation (...) rely on measures of how well various alternative hypotheses account for the evidence.1 Most contemporary confirmation theories employ probability functions to provide such a measure. They measure how well the evidence fits what the hypothesis says about the world in terms of how likely it is that the evidence should occur were the hypothesis true. Such hypothesis-based probabilities of evidence claims are called likelihoods. Clearly, when the evidence is more likely according to one hypothesis than according to an alternative, that should redound to the credit of the former hypothesis and the discredit of the later. But various theories of confirmation diverge on precisely how this credit is to be measured? (shrink)

The objectivity of Bayesian induction relies on the ability of evidence to produce a convergence to agreement among agents who initially disagree about the plausibilities of hypotheses. I will describe three sorts of Bayesian convergence. The first reduces the objectivity of inductions about simple "occurrent events" to the objectivity of posterior probabilities for theoretical hypotheses. The second reveals that evidence will generally induce converge to agreement among agents on the posterior probabilities of theories only if the convergence is 0 or (...) 1. The third establishes conditions under which evidence will very probably compel posterior probabilities of theories to converge to 0 or 1. (shrink)

Eliminative induction is a method for finding the truth by using evidence to eliminate false competitors. It is often characterized as "induction by means of deduction"; the accumulating evidence eliminates false hypotheses by logically contradicting them, while the true hypothesis logically entails the evidence, or at least remains logically consistent with it. If enough evidence is available to eliminate all but the most implausible competitors of a hypothesis, then (and only then) will the hypothesis become highly confirmed. I will argue (...) that, with regard to the evaluation of hypotheses, Bayesian inductive inference is essentially a probabilistic form of induction by elimination. Bayesian induction is an extension of eliminativism to cases where, rather than contradict the evidence, false hypotheses imply that the evidence is very unlikely, much less likely than the evidence would be if some competing hypothesis were true. This is not, I think, how Bayesian induction is usually understood. The recent book by Howson and Urbach, for example, provides an excellent, comprehensive explanation and defense of the Bayesian approach; but this book scarcely remarks on Bayesian induction's eliminative nature. Nevertheless, the very essence of Bayesian induction is the refutation of false competitors of a true hypothesis, or so I will argue. (shrink)

This essay is an attempt to gain better insight into Russell's positive account of inductive inference. I contend that Russell's postulates play only a supporting role in his overall account. At the center of Russell's positive view is a probabilistic, Bayesian model of inductive inference. Indeed, Russell and Maxwell actually held very similar Bayesian views. But the Bayesian component of Russell's view in Human Knowledge is sparse and easily overlooked. Maxwell was not aware of it when he developed his own (...) view, and I believe he was never fully aware of the extent to which Russell's account anticipates his own. The primary focus of this paper will be the explication of the Bayesian component of the Russell-Maxwell view, and the way in which it undermines judgment empiricism. (shrink)

Think of confirmation in the context of the Ravens Paradox this way. The likelihood ratio measure of incremental confirmation gives us, for an observed Black Raven and for an observed non-Black non-Raven, respectively, the following “full” likelihood ratios.

Naive deductivist accounts of confirmation have the undesirable consequence that if E confirms H, then E also confirms the conjunction H·X, for any X—even if X is completely irrelevant to E and H. Bayesian accounts of confirmation may appear to have the same problem. In a recent article in this journal Fitelson (2002) argued that existing Bayesian attempts to resolve of this problem are inadequate in several important respects. Fitelson then proposes a new‐and‐improved Bayesian account that overcomes the problem of (...) irrelevant conjunction, and does so in a more general setting than past attempts. We will show how to simplify and improve upon Fitelson's solution. (shrink)

The problem addressed in this paper is “the main epistemic problem concerning science”, viz. “the explication of how we compare and evaluate theories [...] in the light of the available evidence” (van Fraassen, BC, 1983, Theory comparison and relevant Evidence. In J. Earman (Ed.), Testing scientific theories (pp. 27–42). Minneapolis: University of Minnesota Press). Sections 1– 3 contain the general plausibility-informativeness theory of theory assessment. In a nutshell, the message is (1) that there are two values a theory should exhibit: (...) truth and informativeness—measured respectively by a truth indicator and a strength indicator; (2) that these two values are conflicting in the sense that the former is a decreasing and the latter an increasing function of the logical strength of the theory to be assessed; and (3) that in assessing a given theory by the available data one should weigh between these two conflicting aspects in such a way that any surplus in informativeness succeeds, if the shortfall in plausibility is small enough. Particular accounts of this general theory arise by inserting particular strength indicators and truth indicators. In Section 4 the theory is spelt out for the Bayesian paradigm of subjective probabilities. It is then compared to incremental Bayesian confirmation theory. Section 4 closes by asking whether it is likely to be lovely. Section 5 discusses a few problems of confirmation theory in the light of the present approach. In particular, it is briefly indicated how the present account gives rise to a new analysis of Hempel’s conditions of adequacy for any relation of confirmation (Hempel, CG, 1945, Studies in the logic of comfirmation. Mind, 54, 1–26, 97–121.), differing from the one Carnap gave in § 87 of his Logical foundations of probability (1962, Chicago: University of Chicago Press). Section 6 adresses the question of justification any theory of theory assessment has to face: why should one stick to theories given high assessment values rather than to any other theories? The answer given by the Bayesian version of the account presented in section 4 is that one should accept theories given high assessment values, because, in the medium run, theory assessment almost surely takes one to the most informative among all true theories when presented separating data. The concluding section 7 continues the comparison between the present account and incremental Bayesian confirmation theory. (shrink)

This paper presents a new analysis of C.G. Hempel’s conditions of adequacy for any relation of confirmation [Hempel C. G. (1945). Aspects of scientific explanation and other essays in the philosophy of science. New York: The Free Press, pp. 3–51.], differing from the one Carnap gave in §87 of his [1962. Logical foundations of probability (2nd ed.). Chicago: University of Chicago Press.]. Hempel, it is argued, felt the need for two concepts of confirmation: one aiming at true hypotheses and another (...) aiming at informative hypotheses. However, he also realized that these two concepts are conflicting, and he gave up the concept of confirmation aiming at informative hypotheses. I then show that one can have Hempel’s cake and eat it too. There is a logic that takes into account both of these two conflicting aspects. According to this logic, a sentence H is an acceptable hypothesis for evidence E if and only if H is both sufficiently plausible given E and sufficiently informative about E. Finally, the logic sheds new light on Carnap’s analysis. (shrink)

This paper presents a new analysis of C.G. Hempel’s conditions of adequacy for any relation of confirmation [Hempel C. G. (1945). Aspects of scientific explanation and other essays in the philosophy of science. New York: The Free Press, pp. 3–51.], differing from the one Carnap gave in §87 of his [1962. Logical foundations of probability (2nd ed.). Chicago: University of Chicago Press.]. Hempel, it is argued, felt the need for two concepts of confirmation: one aiming at true hypotheses and another (...) aiming at informative hypotheses. However, he also realized that these two concepts are conflicting, and he gave up the concept of confirmation aiming at informative hypotheses. I then show that one can have Hempel’s cake and eat it too. There is a logic that takes into account both of these two conflicting aspects. According to this logic, a sentence H is an acceptable hypothesis for evidence E if and only if H is both sufficiently plausible given E and sufficiently informative about E. Finally, the logic sheds new light on Carnap’s analysis. (shrink)

The paper presents a new analysis of Hempel’s conditions of adequacy, differing from the one in Carnap. Hempel, so it is argued, felt the need for two concepts of confirmation: one aiming at true theories, and another aiming at informative theories. However, so the analysis continues, he also realized that these two concepts were conflicting, and so he gave up the concept of confirmation aiming at informative theories. It is then shown that one can have the cake and eat it: (...) There is a logic of confirmation that accounts for both of these two conflicting aspects. (shrink)

General Relativity and the Standard Model often are touted as the most rigorously and extensively confirmed scientific hypotheses of all time. Nonetheless, these theories appear to have consequences that are inconsistent with evidence about phenomena for which, respectively, quantum effects and gravity matter. This paper suggests an explanation for why the theories are not disconfirmed by such evidence. The key to this explanation is an approach to scientific hypotheses that allows their actual content to differ from their apparent content. This (...) approach does not appeal to ceteris-paribus qualifiers or counterfactuals or similarity relations. And it helps to explain why some highly idealized hypotheses are not treated in the way that a thoroughly refuted theory is treated but instead as hypotheses with limited domains of applicability. (shrink)

The Problem of Old Evidence is a perennial issue for Bayesian confirmation theory. Garber famously argues that the problem can be solved by conditionalizing on the proposition that a hypothesis deductively implies the existence of the old evidence. In recent work, Hartmann and Fitelson :712–717, 2015) and Sprenger :383–401, 2015) aim for similar, but more general, solutions to the Problem of Old Evidence. These solutions are more general because they allow the explanatory relationship between a new hypothesis and old evidence (...) to be inductive, rather than deductive. In this paper, I argue that these solutions are either unsound or under-motivated, depending on the case of inductive explanation that we have in mind. This lends support to the broader claim that Garber–Style Bayesian confirmation cannot capture the sense in which new hypotheses that do not deductively imply old evidence nevertheless seem to be confirmed via old evidence. (shrink)

Even though social scientists continue to discuss the problems posed by self-fulfilling and self-frustrating predictions, philosophers of science have ignored the topic since the 1970s. Back then, the prevailing view was that the methodological problems posed by reflexive predictions are either minor or easily avoided. I believe that this consensus was premature, ultimately relying on an overly narrow understanding of the phenomenon. I present an improved way to understand reflexive predictions (framed in probabilistic terms) and show that, once such predictions (...) are understood this way, the methodological problems they pose may turn out to be neither minor nor easily avoided. (shrink)

I propose a distinct type of robustness, which I suggest can support a confirmatory role in scientific reasoning, contrary to the usual philosophical claims. In model robustness, repeated production of the empirically successful model prediction or retrodiction against a background of independentlysupported and varying model constructions, within a group of models containing a shared causal factor, may suggest how confident we can be in the causal factor and predictions/retrodictions, especially once supported by a variety of evidence framework. I present climate (...) models of greenhouse gas global warming of the 20th Century as an example, and emphasize climate scientists’ discussions of robust models and causal aspects. The account is intended as applicable to a broad array of sciences that use complex modeling techniques. (shrink)

Reference models of the earth’s interior play an important role in the acquisition of knowledge about the earth’s interior and the earth as a whole. Such models are used as a sort of standard reference against which data are compared. I argue that the use of reference models merits more attention than it has gotten so far in the literature on models, for it is an example of a method of doing science that has a long and significant history, and (...) a study of reference models could increase our understanding of this methodology. (shrink)

The paper applies confirmation theory to a famous statement of economics, the law of demand, which says that ceteris paribus, prices and quantities demanded change in opposite directions. Today's economists do not accept the law unless definite restrictions hold, and have shown little interest in deciding whether or not these restrictions were satisfied empirically. However, Hildenbrand (1994) has provided a new derivation of the law of aggregate demand and used this theoretical advance to devise a test that may be the (...) first rigorous one ever performed on the law. The paper accounts for Hildenbrand's and, in less detail, his predecessors' contributions within the philosophical framework of Hempel (1965) and Glymour (1980). Its salient result is that economists have accepted the "consequence condition", and rejected the "converse consequence condition", and thus implicitly adhered to a Hempelian- Glymourian view of confirmation and testability. (shrink)

Recent works in epistemology show that the claim that coherence is truth conducive – in the sense that, given suitable ceteris paribus conditions, more coherent sets of statements are always more probable – is dubious and possibly false. From this, it does not follows that coherence is a useless notion in epistemology and philosophy of science. Dietrich and Moretti (Philosophy of science 72(3): 403–424, 2005) have proposed a formal of account of how coherence is confirmation conducive—that is, of how the (...) coherence of a set of statements facilitates the confirmation of such statements. This account is grounded in two confirmation transmission properties that are satisfied by some of the measures of coherence recently proposed in the literature. These properties explicate everyday and scientific uses of coherence. In his paper, I review the main findings of Dietrich and Moretti (2005) and define two evidence-gathering properties that are satisfied by the same measures of coherence and constitute further ways in which coherence is confirmation conducive. At least one of these properties vindicates important applications of the notion of coherence in everyday life and in science. (shrink)

Hypothetico-deductivists have struggled to develop qualitative confirmation theories not raising the so-called tacking by disjunction paradox. In this paper, I analyze the difficulties yielded by the paradox and I argue that the hypothetico-deductivist solutions given by Gemes (1998) and Kuipers (2000) are questionable because they do not fit such analysis. I then show that the paradox yields no difficulty for the Bayesian who appeals to the Total Evidence Condition. I finally argue that the same strategy is unavailable to the hypothetico-deductivist.

In this paper, I focus on the so-called "tacking by disjunction problem". Namely, the problem to the effect that, if a hypothesis H is confirmed by a statement E, H is confirmed by the disjunction E v F, for whatever statement F. I show that the attempt to settle this difficulty made by Grimes 1990, in a paper apparently forgotten by today methodologists, is irremediably faulty.

Three confirmation principles discussed by Hempel are the Converse Consequence Condition, the Special Consequence Condition and the Entailment Condition. Le Morvan (1999) has argued that, when the choice among confirmation principles is just about them, it is the Converse Consequence Condition that must be rejected. In this paper, I make this argument definitive. In doing that, I will provide an indisputable proof that the simple conjunction of the Converse Consequence Condition and the Entailment Condition yields a disastrous consequence.