In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit pull in opposite directions. To solve this problem, two proposals, the first one based on Bayes's theorem criterion (BTC) and the second one advocated by Forster and Sober based on Akaike's Information Criterion (AIC) are discussed. We show that AIC, which is frequentist in spirit, is logically equivalent to BTC, provided that a suitable choice of priors is made. We evaluate the charges against Bayesianism and contend that AIC approach (...) has shortcomings. We also discuss the relationship between Schwarz's Bayesian Information Criterion and BTC. (shrink)
The notion of a severe test has played an important methodological role in the history of science. But it has not until recently been analyzed in any detail. We develop a generally Bayesian analysis of the notion, compare it with Deborah Mayo’s error-statistical approach by way of sample diagnostic tests in the medical sciences, and consider various objections to both. At the core of our analysis is a distinction between evidence and confirmation or belief. These notions must be kept separate (...) if mistakes are to be avoided; combined in the right way, they provide an adequate understanding of severity. Those who think that the weight of the evidence always enables you to choose between hypotheses “ignore one of the factors (the prior probability) altogether, and treat the other (the likelihood) as though it ...meant something other than it actually does. This is the same mistake as is made by someone who has scruples about measuring the arms of a balance (having only a tape measure at his disposal ...), but is willing to assert that the heavier load will always tilt the balance (thereby implicitly assuming, although without admitting it, that the arms are of equal length!). (Bruno de Finetti, Theory of Probability)2. (shrink)
There are three questions associated with Simpson’s Paradox (SP): (i) Why is SP paradoxical? (ii) What conditions generate SP?, and (iii) What should be done about SP? By developing a logic-based account of SP, it is argued that (i) and (ii) must be divorced from (iii). This account shows that (i) and (ii) have nothing to do with causality, which plays a role only in addressing (iii). A counterexample is also presented against the causal account. Finally, the causal and logic-based (...) approaches are compared by means of an experiment to show that SP is not basically causal. (shrink)
We introduce a distinction, unnoticed in the literature, between four varieties of objective Bayesianism. What we call ' strong objective Bayesianism' is characterized by two claims, that all scientific inference is 'logical' and that, given the same background information two agents will ascribe a unique probability to their priors. We think that neither of these claims can be sustained; in this sense, they are 'dogmatic'. The first fails to recognize that some scientific inference, in particular that concerning evidential relations, is (...) not (in the appropriate sense) logical, the second fails to provide a non-question-begging account of 'same background information'. We urge that a suitably objective Bayesian account of scientific inference does not require either of the claims. Finally, we argue that Bayesianism needs to be fine-grained in the same way that Bayesians fine-grain their beliefs. (shrink)
We investigate the epistemological consequences of a positive polymerase chain reaction SARS-CoV test for two relevant hypotheses: V is the hypothesis that an individual has been infected with SARS-CoV-2; C is the hypothesis that SARS-CoV-2 is the cause of flu-like symptoms in a given patient. We ask two fundamental epistemological questions regarding each hypothesis: First, how much confirmation does a positive test lend to each hypothesis? Second, how much evidence does a positive test provide for each hypothesis against its negation? (...) We respond to each question within a formal Bayesian framework. We construe degree of confirmation as the difference between the posterior probability of the hypothesis and its prior, and the strength of evidence for a hypothesis against its alternative in terms of their likelihood ratio. We find that test specificity—and coinfection probabilities when making inferences about C—were key determinants of confirmation and evidence. Tests with 8) for V against ¬V regardless of sensitivity. Accordingly, low specificity tests could not provide strong evidence in favor of C in all plausible scenarios modeled. We also show how a positive influenza A test disconfirms C and provides weak evidence against C in dependence on the probability that the patient is influenza A infected given that his/her symptoms are not caused by SARS-CoV-2. Our analysis points out some caveats that should be considered when attributing symptoms or death of a positively tested patient to SARS-CoV-2. (shrink)
There is a debate in Bayesian confirmation theory between subjective and non-subjective accounts of evidence. Colin Howson has provided a counterexample to our non-subjective account of evidence: the counterexample refers to a case in which there is strong evidence for a hypothesis, but the hypothesis is highly implausible. In this article, we contend that, by supposing that strong evidence for a hypothesis makes the hypothesis more believable, Howson conflates the distinction between confirmation and evidence. We demonstrate that Howson’s counterexample fails (...) for a different pair of hypotheses. (shrink)
In his book “Medical Philosophy: Conceptual issues in Medicine”, Mario Bunge provides a unique account of medical philosophy that is deeply rooted in a realist ontology he calls “systemism”. According to systemism, the world consists of systems and their parts, and systems possess emergent properties that their parts lack. Events within systems may form causes and effects that are constantly conjoined via particular mechanisms. Bunge supports the views of the evidence-based medicine movement that randomized controlled trials provide the best evidence (...) to establish the truth of causal hypothesis; in fact, he argues that _only_ RCTs have this ability. Here, we argue that Bunge neglects the important feature of patients being open systems which are in steady interaction with their environment. We show that accepting this feature leads to counter-intuitive consequences for his account of medical hypothesis testing. In particular, we point out that the confirmation of hypotheses is inherently stochastic and affords a probabilistic account of both confirmation and evidence which we provide here; RCTs are neither necessary nor sufficient to establish the truth of a causal claim; testing of causal hypotheses requires taking into account background knowledge and the context within which an intervention is applied. We conclude that there is no “best” research methodology in medicine, but that different methodologies should coexist in a complementary fashion. (shrink)
There are three questions associated with Simpson’s paradox (SP): (i) Why is SP paradoxical? (ii) What conditions generate SP? and (iii) How to proceed when confronted with SP? An adequate analysis of the paradox starts by distinguishing these three questions. Then, by developing a formal account of SP, and substantiating it with a counterexample to causal accounts, we argue that there are no causal factors at play in answering questions (i) and (ii). Causality enters only in connection with action.
We address the need for a model by considering two competing theories regarding the origin of life: (i) the Metabolism First theory, and (ii) the RNA World theory. We discuss two interrelated points, namely: (i) Models are valuable tools for understanding both the processes and intricacies of origin-of-life issues, and (ii) Insights from models also help us to evaluate the core objection to origin-of-life theories, called “the inefficiency objection”, which is commonly raised by proponents of both the Metabolism First theory (...) and the RNA World theory against each other. We use Simpson’s Paradox (SP) as a tool for challenging this objection. We will use models in various senses, ranging from taking them as representations of reality to treating them as theories/accounts that provide heuristics for probing reality. In this paper, we will frequently use models and theories interchangeably. Additionally, we investigate Conway’s Game of Life and contrast it with our SP-based approach to emergence-of-life issues. Finally, we discuss some of the consequences of our view. A scientific model is testable in three senses: (i) a logical sense, (ii) a nomological sense, and (iii) a current technological sense. The SP-based model is testable in the first two senses but it is not feasible to test it using current technology. (shrink)
The underdetermination thesis poses a threat to rational choice of scientific theories. We discuss two arguments for the thesis. One draws its strength from deductivism together with the existence thesis, and the other is defended on the basis of the failure of a reliable inductive method. We adopt a partially subjective/objective pragmatic Bayesian epistemology of science framework, and reject both arguments for the thesis. Thus, in science we are able to reinstate rational choice called into question by the underdetermination thesis.
The major competing statistical paradigms share a common remarkable but unremarked thread: in many of their inferential applications, different probability interpretations are combined. How this plays out in different theories of inference depends on the type of question asked. We distinguish four question types: confirmation, evidence, decision, and prediction. We show that Bayesian confirmation theory mixes what are intuitively “subjective” and “objective” interpretations of probability, whereas the likelihood-based account of evidence melds three conceptions of what constitutes an “objective” probability.
In the Bṛhadāraṇyaka Upaniṣad, one of the principal Upaniṣads, we find a venerable and famous story where the god Prajāpati separately instructs three groups of people (gods, humans, and demons) simply by uttering the syllable “Da.” In this paper, our concern is not with ethics but theories of meaning and interpretation: How can all divergent interpretations of a single expression be correct, and, indeed, endorsed by the speaker? As an exercise in cross-cultural philosophical reflection, we consider some of the leading (...) modern theories of meaning—those of Grice, Quine, and Davidson—in order to see if the Upaniṣadic story receives a natural home in any of them. We conclude that the story is best understood through Grice’s theory of meaning rather than Quine’s or Davidson’s. (shrink)
I show that van Fraassen's empiricism leads to mutually incompatible claims with regard to empirical theories. He is committed to the claim that reasons for accepting a theory and believing it are always identical, insofar as the theory in question is an empirical theory. He also makes a general claim that reasons for accepting a theory are not always reasons for believing it irrespective of whether the theory is an empirical theory.
Elliott Sober is both an empiricist and an instrumentalist. His empiricism rests on a principle called actualism, whereas his instrumentalism violates this. This violation generates a tension in his work. We argue that Sober is committed to a conflicting methodological imperative because of this tension. Our argument illuminates the contemporary debate between realism and empiricism which is increasingly focused on the application of scientific inference to testing scientific theories. Sober’s position illustrates how the principle of actualism drives a wedge between (...) two conceptions of scientific inference and at the same time brings to the surface a deep conflict between empiricism and instrumentalism. (shrink)
I begin chapter I by discussing two key distinctions that constitute the core of van Fraassen's constructive empiricism: a distinction between observables and unobservables and a distinction between acceptance and belief with regard to a theory. To support constructive empiricism, van Fraassen also deploys two epistemological principles: only actual observations are to be taken as evidence and possible evidence is all that can be rationally inferred from the actual evidence. I reject both principle and van Fraassen's construal of observation. As (...) does van Fraassen, I make the distinction between acceptance and belief in chapter II. I contend that one does not need to be an antirealist to espouse this distinction between acceptance and belief. ;In the remaining chapters, I develop a quasi-Bayesian account of acceptance as an alternative to van Fraassen's. In chapter III, I consider three views of acceptance: van Fraassen's, Bayesian views, and the epistemic view. I argue that both van Fraassen's account and the epistemic account are open to Bayesian objections. However, Bayesianism assumes a controversial principle called "maximization of expected utility" , which might mitigate the impact of the Bayesian objections. ;In the final chapter, I consider different decision principles, e.g. Kyburg's decision principle, and Gardenfors and Sahlin's decision principle. I formulate a decision principle called the "weak-dominance-decision principle " based on Kyburg's theory . The interval-based probability yields, as a limiting case, the point-valued probability when we have complete information about the event in question. In this case, my decision principle reduces to MEU. Therefore, the same Bayesian objections against both van Fraassen's theory of acceptance and the epistemic theory of acceptance could be made from the perspective of my decision principle while escaping the perils of strict Bayesianism. My theory of acceptance is quasi-Bayesian, because WDP rests on interval-based probability. (shrink)