Robert Stalnaker has argued that mathematical information is information about the sentences and expressions of mathematics. I argue that this metalinguistic account is open to a variant of Alonzo Church's translation objection and that Stalnaker's attempt to get around this objection is not successful. If correct, this tells not only against Stalnaker's account of mathematical truths, but against any metalinguistic account of truths that are both necessary and informative.

I am grateful to Peter Achinstein, Don Howard, and the other participants at the conference, 'The Role of Experiments in Scientific Changer', Virginia Polytechnic Institute and State University, 30 March to 1 April, 1990, for helpful discussion, and especially to Ron Laymon for his discussion comments presented at the conference on an earlier version of this paper.

The use of the material theory of induction to vindicate a scientist's claims of evidential warrant is illustrated with the cases of Einstein's thermodynamic argument for light quanta of 1905 and his recovery of the anomalous motion of Mercury from general relativity in 1915. In a survey of other accounts of inductive inference applied to these examples, I show that, if it is to succeed, each account must presume the same material facts as the material theory and, in addition, some (...) general principle of inductive inference not invoked by the material theory. Hence these principles are superfluous and the material theory superior in being more parsimonious. (shrink)

The use of the material theory of induction to vindicate a scientist’s claims of evidential warrant is illustrated with the cases of Einstein’s thermodynamic argument for light quanta of 1905 and his recovery of the anomalous motion of Mercury from general relativity in 1915. In a survey of other accounts of inductive inference applied to these examples, I show that, if it is to succeed, each account must presume the same material facts as the material theory and, in addition, some (...) general principle of inductive inference not invoked by the material theory. Hence these principles are superfluous and the material theory superior in being more parsimonious. (shrink)

Investigating random homicides involves constructing models of an odd sort. While the differences between these models and scientific models are radical, calling them models is justified both by functional and structural similarities. Serial homicide investigations illustrate the marked difference between theoretical models in science and the models applied in these criminal investigations. This is further illustrated by considering Glymourian bootstrapping in attempts to solve such homicides. The solutions that result differ radically from explanations in science that are confirmed or disconfirmed (...) by occurrences. Unlike the scientist, the flatfoot gumshoe is also barefoot: he is bereft of a general, determinative theoretical frame. This result shows that criminal investigations do not apply science in the Galilean sense. (shrink)

Contrary to formal theories of induction, I argue that there are no universal inductive inference schemas. The inductive inferences of science are grounded in matters of fact that hold only in particular domains, so that all inductive inference is local. Some are so localized as to defy familiar characterization. Since inductive inference schemas are underwritten by facts, we can assess and control the inductive risk taken in an induction by investigating the warrant for its underwriting facts. In learning more facts, (...) we extend our inductive reach by supplying more localized inductive inference schemes. Since a material theory no longer separates the factual and schematic parts of an induction, it proves not to be vulnerable to Hume's problem of the justification of induction. (shrink)

In this paper a bootstrap theory of rationality is presented. Such a theory is an attempt to explain how standards of rational inquiry may be rationally revised — without assuming that there are any basic and fixed standards for evaluating such revisions. The general bootstrap idea is briefly presented in the first sections. The main part of the paper consists of a discussion of what normative requirements a bootstrap theory should contain, and a number of requirements on rational revisions are (...) proposed. The final section deals with the question of whether a bootstrap theory is self-referentially coherent. (shrink)

For two ideally rational agents, does learning a finite amount of shared evidence necessitate agreement? No. But does it at least guard against belief polarization, the case in which their opinions get further apart? No. OK, but are rational agents guaranteed to avoid polarization if they have access to an infinite, increasing stream of shared evidence? No.

This is a brief, personal retrospective on developments in the treatment of scientific discovery by philosophers, since about 1970.

I follow Hájek (Synthese 137:273–323, 2003c) by taking objective probability to be a function of two propositional arguments—that is, I take conditional probability as primitive. Writing the objective probability of q given r as P(q, r), I argue that r may be chosen to provide less than a complete and exact description of the world’s history or of its state at any time. It follows that nontrivial objective probabilities are possible in deterministic worlds and about the past. A very simple (...) chance–credence relation is also then natural, namely that reasonable credence equals objective probability. In other words, we should set our actual credence in a proposition equal to the proposition’s objective probability conditional on available background information. One advantage of that approach is that the background information is not subject to an admissibility requirement, as it is in standard formulations of the Principal Principle. Another advantage is that the “undermining” usually thought to follow from Humean supervenience can be avoided. Taking objective probability to be a two-argument function is not merely a technical matter, but provides us with vital flexibility in addressing significant philosophical issues. (shrink)

Gott (Nature 363:315–319, 1993) considers the problem of obtaining a probabilistic prediction for the duration of a process, given the observation that the process is currently underway and began a time t ago. He uses a temporal Copernican principle according to which the observation time can be treated as a random variable with uniform probability density. A simple rule follows: with a 95% probability.

Van Fraassen argues that explanatory power cannot be a conformational virtue. In this paper I will show that informational features of scientific theories can be positively relevant to their levels of conformation. Thus, in the cases where the explanatory power of a theory is tied to an informational feature of the theory, it can still be the case that the explanatory power of the theory is positively relevant to its level of confirmation.

‘Probability dynamics’ (PD) is a second-order probabilistic theory in which probability distribution d X = (P(X 1), . . . , P(X m )) on partition U m X of sample space Ω is weighted by ‘credence’ (c) ranging from −∞ to +∞. c is the relative degree of certainty of d X in ‘α-evidence’ α X =[c; d X ] on U m X . It is shown that higher-order probabilities cannot provide a theory of PD. PD applies to (...) both subjectivist and frequentist theories. ‘Straight PD’ (SPD) produces associative and commutative mergers of evidence, in which evidences of positive credence are mutually reinforcing. ‘Offsetting PD’ (OPD) sets off conflicting evidences against each other. Subjectivist PD is a quantified second-order logic of action. Frequentist PD relates to descriptions of physical states of affairs. Acceptance of evidence α 1 X = [c 1; d 1 X ] at t 1 updates α 0 X = [c 0; d 0 X ] at t 0 into SPD-merger or OPD-merger . Given ‘co-evidence’ at t 0 < t 1, ‘indirect’ PD accepts evidence at t 1 and produces support for update α 10 X = [c10;d 10 X α 0 X such that in SPD and in OPD. For binary X and Y, with α 0 X = [c 0; P 0(X)] at t 0 (short-hand for ) and the accepted evidence, the support is ; ; where ρ0(X, Y) is the correlation coefficient of X and Y, and update α 10 X of α 0 X is with ‘accord’ λ = 1 in SPD and in OPD. As , tends toward update P 1(Y) of P 0(Y), but P 10(X) does not converge toward ‘ ’ of ‘probability kinematics’. Therefore PD is not compatible with probability kinematics. A process of ‘normalization’ interprets ‘β-evidence’ [[c 1; q 1]& . . . &[c m ; q m ]; U m X ]] with [c j ; q j ] on and m ≥ 3, as an α-evidence on {X 1, . . . , X m }. It is shown that SPD- and OPD-updates can be derived from updated cumulative functions. Time-biased updates are discussed. A PD-based theory of confirmation (PDCT) is presented. (shrink)

This paper proposes a framework for representing in Bayesian terms the idea that analogical arguments of various degrees of strength may provide inductive support to yet untested scientific hypotheses. On this account, contextual information plays a crucial role in determining whether, and to what extent, a given similarity or dissimilarity between source and target may confirm an empirical hypothesis over a rival one. In addition to showing confirmation by analogy compatible with the adoption of a Bayesian standpoint, the proposal outlined (...) in this paper reveals a close agreement between the fulfillment of Hesse’s (Models and analogies in science, University of Notre Dame Press, 1963) criteria for analogical arguments capable of inductive support and the attribution of confirmatory power by the lights of Bayesian confirmation theory. In this sense, the Bayesian representation not only enriches a framework, Hesse’s, of enduring relevance for understanding scientific activity, but may offer something akin to a proof of concept of it. (shrink)

A formal theory of quantity T Q is presented which is realist, Platonist, and syntactically second-order (while logically elementary), in contrast with the existing formal theories of quantity developed within the theory of measurement, which are empiricist, nominalist, and syntactically first-order (while logically non-elementary). T Q is shown to be formally and empirically adequate as a theory of quantity, and is argued to be scientifically superior to the existing first-order theories of quantity in that it does not depend upon empirically (...) unsupported assumptions concerning existence of physical objects (e.g. that any two actual objects have an actual sum). The theory T Q supports and illustrates a form of naturalistic Platonism, for which claims concerning the existence and properties of universals form part of natural science, and the distinction between accidental generalizations and laws of nature has a basis in the second-order structure of the world. (shrink)

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.

This is a very selective survey of developments in epistemology, concentrating on work from the past twenty years that is of interest to philosophers of science. The selection is organized around interesting connections between distinct themes. I first connect issues about skepticism to issues about the reliability of belief-acquiring processes. Next I connect discussions of the defeasibility of reasons for belief to accounts of the theory-independence of evidence. Then I connect doubts about Bayesian epistemology to issues about the content of (...) perception. The last detailed connection is between considerations of the finiteness of cognition and epistemic virtues. To connect the connections I end by briefly discussing the pressure that consideration of social roles in the transmission of belief puts on the purposes of epistemology. (shrink)

This paper is an examination of evidential holism, a prominent position in epistemology and the philosophy of science which claims that experiments only ever confirm or refute entire theories. The position is historically associated with W.V. Quine, and it is at once both popular and notorious, as well as being largely under-described. But even though there’s no univocal statement of what holism is or what it does, philosophers have nevertheless made substantial assumptions about its content and its truth. Moreover they (...) have drawn controversial and important conclusions from these assumptions. In this paper I distinguish three types of evidential holism and argue that the most oft-cited and controversial thesis is entirely unmotivated. The other two theses are much overlooked, but are well-motivated and free from controversial implications. (shrink)

It is well known that the process of scientific inquiry, according to Peirce, is drivenby three types of inference, namely abduction, deduction, and induction. What isbehind these labels is, however, not so clear. In particular, the common identificationof abduction with Inference to the Best Explanation (IBE) begs the question,since IBE appears to be covered by Peirce's concept of induction, not that of abduction.Consequently, abduction ought to be distinguished from IBE, at least on Peirce's account. The main aim of the paper, (...) however, is to show that this distinction is most relevant with respect to current problems in philosophy of science and epistemology (like attempts to supply suitable notions of realism and truth as well as related concepts like coherence and unification). In particular, I also try to show that (and in what way) Peirce's inferential triad can function as a method that ensures both coherence and correspondence. It is in this respect that his careful distinction between abduction and induction (or IBE) ought to be heeded. (shrink)

This paper is an attempt to extend the meaning of the concept of indeterminacy for the human sciences. The authors do this by coining the term methodological indeterminacy and arguing that indeterminacy is better understood when linked to specific methodological techniques. Paradoxically, while specific research techniques demonstrate that the issue of indeterminacy is complex, yielding the possibility of types and degrees, it does not eliminate the problem of translation first raised by Quine. However, the authors go on to argue that, (...) from a research perspective, indeterminacy can and must be approached in such a way that it is possible to reduce cases of it, even though never completely eliminating it in the human sciences. (shrink)

Statistical procedures can be applied to episodes in the history of science in order to weight attributes to predict short-term survival of theories; an asymptotic method is used to show that short-term survival is a valid proxy for ultimate survival; and a theoretical argument is made that ultimate survival is a valid proxy for objective truth. While realists will appreciate this last step, instrumentalists do not need it to benefit from the actuarial procedures of cliometric metatheory. Introduction A plausible proxy (...) for Peircean consensus Assessing the validity of theory attributes as predictors of theory survival 3.1 Linear discriminant function 3.2 Factor analysis 3.3 Taxometric analysis Verisimilitude index Satisfying both instrumentalists and realists Recapitulation Implementation of cliometric metatheory * Correspondence about this article may be addressed to Leslie Yonce at pemeehle{at}umn.edu' + u + '@' + d + ''//--> This article had been completed by Paul Meehl at the time of his death on 14 February 2003. His wife, Leslie J. Yonce, is grateful to Keith Gunderson (University of Minnesota, Center for Philosophy of Science) and Niels G. Waller (Psychology Department, Vanderbilt University) for advice with some final editing details. (shrink)

Charles Peirce’s model of inquiry is supposed to demarcate appropriate methods of inquiry from specious ones. Cheryl Misak points out that Peirce’s explicit account fails, but can nevertheless be rescued by elements of his own system. While Misak’s criticism is a propos, her own attempt to fortify Peirce’s account does not succeed, as it falls prey to the same criticism she raises against Peirce’s explicit account. The account provided in this paper—the ‘open path’ alternative—draws from Peirce’s corollary to his “first (...) rule of reason”, that one should not block the road to inquiry. The ‘open path’ account is able to withstand Misak’s objections, and when combined with other aspects of Peirce’s work, shows us why the optimal way to conduct inquiry is to follow the path of greatest resistance. Inquiry, however, is rarely conducted in optimal conditions. Actual, constrained conditions of inquiry require a measure of economy in terms of what can be reasonably pursued and how. The question, then, is how to conduct our inquiries so that they are as nearly optimal as possible given actual constraints. As a working scientist, Peirce was acutely aware of the need to economize in research. Nicholas Rescher has recognized this issue’s significance for Peirce, and noted its neglect in discussions of Peirce’s work. One issue that has been largely neglected in the literature on Peirce is what specifically he recommends, based on considerations of economy, for how to go about gathering evidence. Kronz & McLaughlin points out that Peirce’s primary recommendation is that in gathering evidence relevant to a particular hypothesis we should test for empirical consequences that would not have been expected otherwise. The view that is developed in this paper is that economy in research, according to Peirce, follows the general line of his theory of inquiry. Peirce’s theory of inquiry implies that pursuit of truth requires maximizing resistance. I argue that his considerations about how to navigate within the constraints introduced in the context of actual research are also best understood as recommendations for maximizing resistance. (shrink)

While the common procedure of statistical significance testing and its accompanying concept of p-values have long been surrounded by controversy, renewed concern has been triggered by the replication crisis in science. Many blame statistical significance tests themselves, and some regard them as sufficiently damaging to scientific practice as to warrant being abandoned. We take a contrary position, arguing that the central criticisms arise from misunderstanding and misusing the statistical tools, and that in fact the purported remedies themselves risk damaging science. (...) We argue that banning the use of p-value thresholds in interpreting data does not diminish but rather exacerbates data-dredging and biasing selection effects. If an account cannot specify outcomes that will not be allowed to count as evidence for a claim—if all thresholds are abandoned—then there is no test of that claim. The contributions of this paper are: To explain the rival statistical philosophies underlying the ongoing controversy; To elucidate and reinterpret statistical significance tests, and explain how this reinterpretation ameliorates common misuses and misinterpretations; To argue why recent recommendations to replace, abandon, or retire statistical significance undermine a central function of statistics in science: to test whether observed patterns in the data are genuine or due to background variability. (shrink)

In this paper I argue that aim-oriented empiricism (AOE), a conception of natural science that I have defended at some length elsewhere[1], is a kind of synthesis of the views of Popper, Kuhn and Lakatos, but is also an improvement over the views of all three. Whereas Popper's falsificationism protects metaphysical assumptions implicitly made by science from criticism, AOE exposes all such assumptions to sustained criticism, and furthermore focuses criticism on those assumptions most likely to need revision if science is (...) to make progress. Even though AOE is, in this way, more Popperian than Popper, it is also, in some respects, more like the views of Kuhn and Lakatos than falsificationism is. AOE is able, however, to solve problems which Kuhn's and Lakatos's views cannot solve. [Back to Top]. (shrink)

In this paper I argue that demonstrative induction can deal with the problem ofthe underdetermination of theory by evidence. I present the historical case studyof spectroscopy in the early 1920s, where the choice among different theorieswas apparently underdetermined by spectroscopic evidence concerning the alkalidoublets and their anomalous Zeeman effect. By casting this historical episodewithin the methodological framework of demonstrative induction, the localunderdetermination among Bohr's, Heisenberg's, and Pauli's rival theories isresolved in favour of Pauli's theory of the electron's spin.

“Dutch Book” arguments and references to gambling theorems are typical in the debate between Bayesians and scientists committed to “classical” statistical methods. These arguments have rarely convinced non-Bayesian scientists to abandon certain conventional practices, partially because many scientists feel that gambling theorems have little relevance to their research activities. In other words, scientists “don’t bet.” This article examines one attempt, by Schervish, Seidenfeld, and Kadane, to progress beyond such apparent stalemates by connecting “Dutch Book”–type mathematical results with principles actually endorsed (...) by practicing experimentalists. (shrink)

Confirmation is commonly identified with positive relevance, E being said to confirm H if and only if E increases the probability of H. Today, analyses of this general kind are usually Bayesian ones that take the relevant probabilities to be subjective. I argue that these subjective Bayesian analyses are irremediably flawed. In their place I propose a relevance analysis that makes confirmation objective and which, I show, avoids the flaws of the subjective analyses. What I am proposing is in some (...) ways a return to Carnap's conception of confirmation, though there are also important differences between my analysis and his. My analysis includes new accounts of what evidence is and of the indexicality of confirmation claims. Finally, I defend my analysis against Achinstein's criticisms of the relevance concept of confirmation. (shrink)

If two theory formulations are merely different expressions of the same theory, then any problem of choosing between them cannot be due to the underdetermination of theories by data. So one might suspect that we need to be able to tell distinct theories from mere alternate formulations before we can say anything substantive about underdetermination, that we need to solve the problem of identical rivals before addressing the problem of underdetermination. Here I consider two possible solutions: Quine proposes that we (...) call two theories identical if they are equivalent under a reconstrual of predicates, but this would mishandle important cases. Another proposal is to defer to the particular judgements of actual scientists. Consideration of an historical episodethe alleged equivalence of wave and matrix mechanicsshows that this second proposal also fails. Nevertheless, I suggest, the original suspicion is wrong; there are ways to enquire into underdetermination without having solved the problem of identical rivals. (shrink)

It has been common wisdom for centuries that scientific inference cannot be deductive; if it is inference at all, it must be a distinctive kind of inductive inference. According to demonstrative theories of induction, however, important scientific inferences are not inductive in the sense of requiring ampliative inference rules at all. Rather, they are deductive inferences with sufficiently strong premises. General considerations about inferences suffice to show that there is no difference in justification between an inference construed demonstratively or ampliatively. (...) The inductive risk may be shouldered by premises or rules, but it cannot be shirked. Demonstrative theories of induction might, nevertheless, better describe scientific practice. And there may be good methodological reasons for constructing our inferences one way rather than the other. By exploring the limits of these possible advantages, I argue that scientific inference is neither of essence deductive nor of essence inductive. (shrink)