Confirmation, Misc

We conceptualize observation selection effects (OSEs) by considering how a shift from one process of observation to another affects discrimination-conduciveness, by which we mean the degree to which possible observations discriminate between hypotheses, given the observation process at work. OSEs in this sense come in degrees and are causal, where the cause is the shift in process, and the effect is a change in degree of discrimination-conduciveness. We contrast our understanding of OSEs with others that have appeared in the literature. (...) After describing conditions of adequacy that an acceptable measure of degree of discrimination-conduciveness must satisfy, we use those conditions of adequacy to evaluate several possible measures. We also discuss how the effect of shifting from one observation process to another might be measured. We apply our framework to several examples, including the ravens paradox and the phenomenon of publication bias. (shrink)

It is an under-appreciated fact that Quine's rejection of the analytic/synthetic distinction, when coupled with some other plausible and related views, implies that there are serious difficulties in demarcating empirical theories from pure mathematical theories within the Quinean framework. This is a serious problem because there seems to be a principled difference between the two disciplines that cannot apparently be captured in the orthodox Quienan framework. For the purpose of simplicity let us call this Quine's problem of demarcation. In this (...) paper this problem will be articulated and it will be shown that the typical sorts of responses to this problem are all unworkable within the Quinean framework. It will then be shown that the lack of resources to solve this problem within the Quinean framework implies that Quine’s version of the indispensability argument cannot get off the ground, for it presupposes the possibility of making such a distinction. (shrink)

Freitag (2015) and Schramm (2014) have proposed different, although converging, solutions of Goodman’s New Riddle of Induction. Answering their proposals, Dorst (2016 and 2018) has used the fictitious character of a ‘grue-speaker’ as his principal device for criticizing counterfactual-based treatments of the Riddle. In this paper, I argue that Dorst’s arguments fail: On the observation of no other than green emeralds, the ‘grue-speaker’ cannot use the symmetry between the ‘green’- and ‘grue’-languages for claiming ‘grue’- instead of ‘green’-evidence, and the counterfactuals (...) involved (explicitly by Schramm and implicitly by Freitag) remain unaffected by Dorst’s proposal for how to evaluate them. (shrink)

Data from medical research are typically summarized with various types of outcome measures. We present three arguments in favor of absolute over relative outcome measures. The first argument is from cognitive bias: relative measures promote the reference class fallacy and the overestimation of treatment effectiveness. The second argument is decision-theoretic: absolute measures are superior to relative measures for making a decision between interventions. The third argument is causal: interpreted as measures of causal strength, absolute measures satisfy a set of desirable (...) properties, but relative measures do not. Absolute outcome measures outperform relative measures on all counts. (shrink)

In engineering, as in other scientific fields, researchers seek to confirm their models with real-world data. It is common practice to assess models in terms of the distance between the model outputs and the corresponding experimental observations. An important question that arises is whether the model should then be ‘tuned’, in the sense of estimating the values of free parameters to get a better fit with the data, and furthermore whether the tuned model can be confirmed with the same data (...) used to tune it. This dual use of data is often disparagingly referred to as ‘double-counting’. Here, we analyse these issues, with reference to selected research articles in engineering. Our example studies illustrate more and less controversial practices of model tuning and double-counting, both of which, we argue, can be shown to be legitimate within a Bayesian framework. The question nonetheless remains as to whether the implied scientific assumptions in each case are apt from the engineering point of view. (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)

The reward system of science is the priority rule. The first scientist making a new discovery is rewarded with prestige, while second runners get little or nothing. Michael Strevens, following Philip Kitcher, defends this reward system, arguing that it incentivizes an efficient division of cognitive labor. I argue that this assessment depends on strong implicit assumptions about the replicability of findings. I question these assumptions on the basis of metascientific evidence and argue that the priority rule systematically discourages replication. My (...) analysis leads us to qualify Kitcher and Strevens’s contention that a priority-based reward system is normatively desirable for science. (shrink)

Bayesian confirmation theory is rife with confirmation measures. Zalabardo focuses on the probability difference measure, the probability ratio measure, the likelihood difference measure, and the likelihood ratio measure. He argues that the likelihood ratio measure is adequate, but each of the other three measures is not. He argues for this by setting out three adequacy conditions on confirmation measures and arguing in effect that all of them are met by the likelihood ratio measure but not by any of the other (...) three measures. Glass and McCartney, hereafter “G&M,” accept the conclusion of Zalabardo’s argument along with each of the premises in it. They nonetheless try to improve on Zalabardo’s argument by replacing his third adequacy condition with a weaker condition. They do this because of a worry to the effect that Zalabardo’s third adequacy condition runs counter to the idea behind his first adequacy condition. G&M have in mind confirmation in the sense of increase in probability: the degree to which E confirms H is a matter of the degree to which E increases H’s probability. I call this sense of confirmation “IP.” I set out four ways of precisifying IP. I call them “IP1,” “IP2,” “IP3,” and “IP4.” Each of them is based on the assumption that the degree to which E increases H’s probability is a matter of the distance between p and a certain other probability involving H. I then evaluate G&M’s argument in light of them. (shrink)

I argue elsewhere (Roche 2014) that evidence of evidence is evidence under screening-off. Tal and Comesaña (2017) argue that my appeal to screening-off is subject to two objections. They then propose an evidence of evidence thesis involving the notion of a defeater. There is much to learn from their very careful discussion. I argue, though, that their objections fail and that their evidence of evidence thesis is open to counterexample.

Bayesian confirmation theory is rife with confirmation measures. Many of them differ from each other in important respects. It turns out, though, that all the standard confirmation measures in the literature run counter to the so-called “Reverse Matthew Effect” (“RME” for short). Suppose, to illustrate, that H1 and H2 are equally successful in predicting E in that p(E | H1)/p(E) = p(E | H2)/p(E) > 1. Suppose, further, that initially H1 is less probable than H2 in that p(H1) < p(H2). (...) Then by RME it follows that the degree to which E confirms H1 is greater than the degree to which it confirms H2. But by all the standard confirmation measures in the literature, in contrast, it follows that the degree to which E confirms H1 is less than or equal to the degree to which it confirms H2. It might seem, then, that RME should be rejected as implausible. Festa (2012), however, argues that there are scientific contexts in which RME holds. If Festa’s argument is sound, it follows that there are scientific contexts in which none of the standard confirmation measures in the literature is adequate. Festa’s argument is thus interesting, important, and deserving of careful examination. I consider five distinct respects in which E can be related to H, use them to construct five distinct ways of understanding confirmation measures, which I call “Increase in Probability”, “Partial Dependence”, “Partial Entailment”, “Partial Discrimination”, and “Popper Corroboration”, and argue that each such way runs counter to RME. The result is that it is not at all clear that there is a place in Bayesian confirmation theory for RME. (shrink)

There are many scientific and everyday cases where each of Pr and Pr is high and it seems that Pr is high. But high probability is not transitive and so it might be in such cases that each of Pr and Pr is high and in fact Pr is not high. There is no issue in the special case where the following condition, which I call “C1”, holds: H 1 entails H 2. This condition is sufficient for transitivity in high (...) probability. But many of the scientific and everyday cases referred to above are cases where it is not the case that H 1 entails H 2. I consider whether there are additional conditions sufficient for transitivity in high probability. I consider three candidate conditions. I call them “C2”, “C3”, and “C2&3”. I argue that C2&3, but neither C2 nor C3, is sufficient for transitivity in high probability. I then set out some further results and relate the discussion to the Bayesian requirement of coherence. (shrink)

We argued that explanatoriness is evidentially irrelevant in the following sense: Let H be a hypothesis, O an observation, and E the proposition that H would explain O if H and O were true. Then our claim is that Pr = Pr. We defended this screening-off thesis by discussing an example concerning smoking and cancer. Climenhaga argues that SOT is mistaken because it delivers the wrong verdict about a slightly different smoking-and-cancer case. He also considers a variant of SOT, called (...) “SOT*”, and contends that it too gives the wrong result. We here reply to Climenhaga’s arguments and suggest that SOT provides a criticism of the widely held theory of inference called “inference to the best explanation”. (shrink)

There are numerous (Bayesian) confirmation measures in the literature. Festa provides a formal characterization of a certain class of such measures. He calls the members of this class “incremental measures”. Festa then introduces six rather interesting properties called “Matthew properties” and puts forward two theses, hereafter “T1” and “T2”, concerning which of the various extant incremental measures have which of the various Matthew properties. Festa’s discussion is potentially helpful with the problem of measure sensitivity. I argue, that, while Festa’s discussion (...) is illuminating on the whole and worthy of careful study, T1 and T2 are strictly speaking incorrect (though on the right track) and should be rejected in favor of two similar but distinct theses. (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)

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.

Coherentism maintains that coherent beliefs are more likely to be true than incoherent beliefs, and that coherent evidence provides more confirmation of a hypothesis when the evidence is made coherent by the explanation provided by that hypothesis. Although probabilistic models of credence ought to be well-suited to justifying such claims, negative results from Bayesian epistemology have suggested otherwise. In this essay we argue that the connection between coherence and confirmation should be understood as a relation mediated by the causal relationships (...) among the evidence and a hypothesis, and we offer a framework for doing so by fitting together probabilistic models of coherence, confirmation, and causation. We show that the causal structure among the evidence and hypothesis is sometimes enough to determine whether the coherence of the evidence boosts confirmation of the hypothesis, makes no difference to it, or even reduces it. We also show that, ceteris paribus, it is not the coherence of the evidence that boosts confirmation, but rather the ratio of the coherence of the evidence to the coherence of the evidence conditional on a hypothesis. (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)

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.

Confirmation and falsification are different strategies for testing theories and characterizing the outcomes of those tests. Roughly speaking, confirmation is the act of using evidence or reason to verify or certify that a statement is true, definite, or approximately true, whereas falsification is the act of classifying a statement as false in the light of observation reports. After expounding the intellectual history behind confirmation and falsificationism, reaching back to Plato and Aristotle, I survey some of the main controversial issues and (...) arguments that pertain to the choice between these strategies: the Raven Paradox, the Duhem/Quine problem and the Grue Paradox. Finally, I outline an evolutionary criticism of inductive Bayesian approaches based on my assumption of doxastic involuntarism. (shrink)

Crupi et al. propose a generalization of Bayesian confirmation theory that they claim to adequately deal with confirmation by uncertain evidence. Consider a series of points of time t0, . . . , ti, . . . , tn such that the agent’s subjective probability for an atomic proposition E changes from Pr0 at t0 to . . . to Pri at ti to . . . to Prn at tn. It is understood that the agent’s subjective probabilities change for (...) E and no logically stronger proposition, and that the agent updates her subjective probabilities by Jeffrey conditionalization. For this specific scenario the authors propose to take the difference between Pr0 and Pri as the degree to which E confirms H for the agent at time ti , C0,i. This proposal is claimed to be adequate, because. (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)

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)

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)

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)

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)

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.

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)

Amalgamating evidence of different kinds for the same hypothesis into an overall confirmation is analogous, I argue, to amalgamating individuals’ preferences into a group preference. The latter faces well-known impossibility theorems, most famously “Arrow’s Theorem”. Once the analogy between amalgamating evidence and amalgamating preferences is tight, it is obvious that amalgamating evidence might face a theorem similar to Arrow’s. I prove that this is so, and end by discussing the plausibility of the axioms required for the theorem.

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)

Extant literature on Goodman’s ‘New Riddle of Induction’ deals mainly with two versions. I consider both of them, starting from the (‘epistemic’) version of Goodman’s classic of 1954. It turns out that it belongs to the realm of applications of inductive logic, and that it can be resolved by admitting only significant evidence (as I call it) for confirmations of hypotheses. Sect. 1 prepares some ground for the argument. As much of it depends on the notion of evidential significance, this (...) concept is defined and its introduction motivated. Further, I introduce and explain the distinction between support and confirmation: put in a slogan, ‘confirmation is support by significant evidence’. The second section deals with the Riddle itself. I demonstrate that, given the provisions of the first section, not ‘anything confirms anything’: significant green-evidence confirms only green-hypotheses (and no grue-hypotheses), and significant grue-evidence confirms only grue-hypotheses (and no green-hypotheses), whichever terms we use for expressing these evidences or hypotheses. The third section rounds off my treatment. First I show that Frank Jackson’s use of his counterfactual condition is unsuccessful. Further, I argue that no unwanted consequences result, if one starts from the other, ‘objective’, definition of ‘grue’, as it constitutes no more than a mere fact of logic that cannot do any harm. Finally, I present a grue-case involving both kinds of definition, where the exclusive confirmation of either the green- or the grue-hypothesis is shown. (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.

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)

This is an unpublished talk written for a meeting of French philosophers. The paper describes the evolution versus creationism/intelligent design controversy in the U.S. A number of philosophers and scientists try to resolve this issue by sharply distinguishing the realm of science versus any talk of the supernatural. These pro-evolutionists often appeal to science's essential commitment to "methodological naturalism," the view that scientific methodology is essentially committed to naturalism and cannot meaningfully entertain hypotheses concerning the supernatural. I criticize methodological naturalism, (...) suggesting that such an appeal is misguided and counterproductive. I suggest an alternative view of the supernatural consistent with scientific knowledge. (shrink)

Theorists in various scientific disciplines offer radically different accounts of the origin of violent behavior in humans, but it is not clear how the study of violence is to be scientifically grounded. This problem is made more complicated because both what sorts of acts constitute violence and what needs to be appealed to in explaining violence differs according to social scientists, biologists, anthropologists and neurophysiologists, and this generates serious problems with respect to even attempting to ascertain the differential bona fides (...) of these various explanatory programs. As a consequence, there is little theoretical reason to suspect that efforts to prevent violence will have any appreciable effect. In this paper we investigate the general issue of whether any of the general theoretical approaches to violent behavior can reasonably be taken to be the best approach to the explanation of seriously violent behavior. Our more specific aim is to examine the controversial explanation of violent behavior offered by Lonnie Athens in order to ascertain whether it can be seriously considered to be the best explanation of violent behavior. (shrink)