The mathematical theory of communication.

The focus of this study is cognitive choice: the selection of one cognitive option (a hypothesis, a theory, or an axiom, for instance) rather than another. The study proposes that cognitive choice should be based on the plausibilities of states posited by rival cognitive options and the utilities of these options' information outcomes. The proposal introduces a form of decision theory that is novel because comparative; it permits many choices among cognitive options to be based on merely comparative plausibilities and (...) utilities. This form of decision theory intersects with recommendations by advocates of decision theory for cognitive choice, on the one hand, and defenders of comparative evaluation of scientific hypotheses and theories, on the other. But it differs from prior decision-theoretic proposals because it requires no more than minimal precision in specifying plausibilities and utilities. And it differs from comparative proposals because none has shown how comparative evaluations can be carried out within a decision-theoretic framework. (shrink)

That some propositions are testable, while others are not, was a fundamental idea in the philosophical program known as logical empiricism. That program is now widely thought to be defunct. Quine’s (1953) “Two Dogmas of Empiricism” and Hempel’s (1950) “Problems and Changes in the Empiricist Criterion of Meaning” are among its most notable epitaphs. Yet, as we know from Mark Twain’s comment on an obituary that he once had the pleasure of reading about himself, the report of a death can (...) be an exaggeration. The research program that began in Vienna and Berlin continues, even though many of the specific formulations that came out of those circles are flawed and need to be replaced. (shrink)

Akaike’s framework for thinking about model selection in terms of the goal of predictive accuracy and his criterion for model selection have important philosophical implications. Scientists often test models whose truth values they already know, and they often decline to reject models that they know full well are false. Instrumentalism helps explain this pervasive feature of scientific practice, and Akaike’s framework helps provide instrumentalism with the epistemology it needs. Akaike’s criterion for model selection also throws light on the role of (...) parsimony considerations in hypothesis evaluation. I explain the basic ideas behind Akaike’s framework and criterion; several biological examples, including the use of maximum likelihood methods in phylogenetic inference, are considered. (shrink)

Nelson Goodman has constructed two theories of simplicity: one of predicates; one of hypotheses. I offer a simpler theory by generalization and abstraction from his. Generalization comes by dropping special conditions Goodman imposes on which unexcluded extensions count as complicating and which excluded extensions count as simplifying. Abstraction is achieved by counting only nonisomorphic models and subinterpretations. The new theory takes into account all the hypotheses of a theory in assessing its complexity, whether they were projected prior to, or result (...) from, projection of a given hypothesis. It assigns simplicity post-projection priority over simplicity pre-projection. It better orders compound conditionals than does the theory of simplicity of hypotheses, and it does not inherit an anomaly of the theory of simplicity of predicates — its failure to order the ordering relations. Drop Goodman's special conditions, and the problems fall away with them. (shrink)

The philosophical significance of the procedure of applying Akaike Information Criterion (AIC) to curve-fitting problems is evaluated. The theoretical justification for using AIC (the so-called Akaike's theorem) is presented in a rigorous way, and its range of validity is assessed by presenting both instances in which it is valid and counter-examples in which it is invalid. The philosophical relevance of the justification that this result gives for making one particular choice between simple and complicated hypotheses is emphasized. In addition, recent (...) claims that the methods based on Akaike's theorem are relevant to other philosophical problems associated with the notion of simplicity are presented and evaluated. (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)

It is not possible to dismiss the atomistic paradigm because the proposed elementary particles are too many (and, hence, it is claimed, they do not provide a simple account of nature) or because it is not possible to observe quarks in an isolated manner. The developments in particle physics have brought about radical changes to our notions of simplicity and observability, and in this paper we elaborate on these changes. It is as a result of these changes that the present (...) situation in elementary particle physics justify us to claim that we have indeed reached a level of explanation where the constituent particles (quarks, leptons, gluons, and intermediate bosons) used for the explanation of the various phenomena considered to be delineating a particular level in the descriptive framework of the physical phenomena and a specific stratum in the organization of nature, can be regarded as elementary. (shrink)

Mathematicians often speak of conjectures as being confirmed by evidence that falls short of proof. For their own conjectures, evidence justifies further work in looking for a proof. Those conjectures of mathematics that have long resisted proof, such as Fermat's Last Theorem and the Riemann Hypothesis, have had to be considered in terms of the evidence for and against them. It is argued here that it is not adequate to describe the relation of evidence to hypothesis as `subjective', `heuristic' or (...) `pragmatic', but that there must be an element of what it is rational to believe on the evidence, that is, of non-deductive logic. (shrink)

Traditional analyses of the curve fitting problem maintain that the data do not indicate what form the fitted curve should take. Rather, this issue is said to be settled by prior probabilities, by simplicity, or by a background theory. In this paper, we describe a result due to Akaike [1973], which shows how the data can underwrite an inference concerning the curve's form based on an estimate of how predictively accurate it will be. We argue that this approach throws light (...) on the theoretical virtues of parsimoniousness, unification, and non ad hocness, on the dispute about Bayesianism, and on empiricism and scientific realism. * Both of us gratefully acknowledge support from the Graduate School at the University of Wisconsin-Madison, and NSF grant DIR-8822278 (M.F.) and NSF grant SBE-9212294 (E.S.). Special thanks go to A. W. F. Edwards.William Harper. Martin Leckey. Brian Skyrms, and especially Peter Turney for helpful comments on an earlier draft. (shrink)

This paper outlines a quantitative theory of strongly semantic information (TSSI) based on truth-values rather than probability distributions. The main hypothesis supported in the paper is that the classic quantitative theory of weakly semantic information (TWSI), based on probability distributions, assumes that truth-values supervene on factual semantic information, yet this principle is too weak and generates a well-known semantic paradox, whereas TSSI, according to which factual semantic information encapsulates truth, can avoid the paradox and is more in line with the (...) standard conception of what generally counts as semantic information. After a brief introduction, section two outlines the semantic paradox implied by TWSI, analysing it in terms of an initial conflict between two requisites of a quantitative theory of semantic information. In section three, three criteria of semantic information equivalence are used to provide a taxonomy of quantitative approaches to semantic information and introduce TSSI. In section four, some further desiderata that should be fulfilled by a quantitative TSSI are explained. From section five to section seven, TSSI is developed on the basis of a calculus of truth-values and semantic discrepancy with respect to a given situation. In section eight, it is shown how TSSI succeeds in solving the paradox. Section nine summarises the main results of the paper and indicates some future developments. (shrink)

Along with such criteria as truth, comprehensiveness, explanatory adequacy, and simplicity, philosophers of science usually also mention predictive accuracy as a criterion of theory choice. But while philosophers have devoted attention to the problem of the logical structure of scientific prediction, it seems that little attention has been devoted to the difficult question of what precisely constitutes predictive accuracy, at least ‘predictive accuracy’ in the sense in which I will discuss it here.I will in this paper discuss the role of (...) predictive accuracy in theory choice. But before that, I will address the problem of what constitutes predictive accuracy more generally and independently of its role in theory choice. I will approach the problem of predictive accuracy from a pragmaticpoint of view, and then try to assess the role of predictive accuracy in theory choice from that perspective. (shrink)

We propose a generalization of expected utility that we call generalized EU (GEU), where a decision maker’s beliefs are represented by plausibility measures and the decision maker’s tastes are represented by general (i.e., not necessarily real-valued) utility functions. We show that every agent, “rational” or not, can be modeled as a GEU maximizer. We then show that we can customize GEU by selectively imposing just the constraints we want. In particular, we show how each of Savage’s postulates corresponds to constraints (...) on GEU. (shrink)

We continue our discussion of the competing arguments in favour of the unified theory and the pluralistic theory of radiation advanced by three nineteenth-century pioneers: Herschel, Melloni, and Draper. Our narrative is structured by a consideration of the epistemic criteria relevant to theory-choice; the epistemic focus highlights many little-known aspects of this relatively well-known episode. We argue that the acceptance of light-heat unity in this period cannot be credibly justified on the basis of common evaluative criteria such as simplicity and (...) standard notions of explanatory power. Whether the consensus was justified by some other criteria remains an open question.Keywords: Theory-choice; Epistemic values; Radiation; Simplicity; Explanatory power; Causal explanation. (shrink)

It is common, though perhaps not correct, to think that practical rationality is strictly instrumental.1 The functions of instrumental reason include finding suitable means to our determinate ends, helping to determine our indeterminate ends, and implementing our principles in appropriate actions. One reason that might be given for adopting instrumentalism with respect to rationality might be that our best scientific evidence offers little support for the idea that our brains have powers to detect good and bad as such in persons, (...) actions, or lives. But whatever one’s reasons for taking up instrumentalism, it remains to specify the relationship means are to have with ends. A natural demand is that instrumentally rational actions implement the best means to one’s given ends. Optimizing conceptions of rationality endorse this demand. A competing conception of rationality—the satisficing conception—weakens this requirement and permits some rational actions to implement (merely) satisfactory means to the agent’s given ends. The present article argues that instrumentalist theories of rationality as commonly understood cannot consistently accommodate this satisficing conception of rationality. (shrink)

Some decisions result in cognitive consequences such as information gained and information lost. The focus of this study, however, is decisions with consequences that are partly or completely noncognitive. These decisions are typically referred to as ‘real-life decisions’. According to a common complaint, the challenges of real-life decision making cannot be met by decision theory. This complaint has at least two principal motives. One is the maximizing objection that to require agents to determine the optimal act under real-world constraints is (...) unrealistic. The other is the precision objection that the numeric requirements for applying decision theory are overly demanding for real-life decisions. Responses to both objections are aired in the History section of this chapter. The maximizing objection is addressed with reference to work by Weirich and Pollock, while the precision objection is countered via a proposal by Kyburg and another by Gärdenfors and Sahlin. However, the Current Research section urges a different response to the precision objection by introducing a comparative version of decision theory. Drawing on Chu and Halpern’s notion of generalized expected utility, this version of decision theory permits many choices to be based on merely comparative plausibilities and utilities. Finally, the Further Research section undertakes an open-ended exploration of three of the assumptions upon which this form of decision theory (and many others) is based: transitivity, independence, and plausibilistic decision rules. (shrink)

This paper claims that adoption of Bayes's theorem as the schema for the appraisal of scientific theories can greatly reduce the distance between Kuhnians and logical empiricists. It is argued that plausibility considerations, which Kuhn considered outside of the logic of science, can be construed as prior probabilities, which play an indispensable role in the logic of science. Problems concerning likelihoods, especially the likelihood on the "catchall," are also considered. Severe difficulties concerning the significance of this probability arise in the (...) evaluation of individual theories, but they can be avoided by restricting our judgments to comparative assessments of competing theories. (shrink)