Three experiments examined the influence of argument length on plausibility judgements, in a category-based induction task. The general results were that when arguments were logically invalid they were considered stronger when they were longer, but for logically valid arguments longer arguments were considered weaker. In Experiments 1a and 1b when participants were forewarned to avoid using length as a cue to judging plausibility, they still did so. Indeed, participants given the opposite instructions did not follow those instructions either. In Experiment (...) 2 arguments came from a reliable or unreliable speaker. This manipulation affected accuracy as well as response bias, but the effects of argument length for both reliable and unreliable speakers replicated Experiments 1a and 1b. The results were analysed using receiver operating characteristic (ROC) curves and modelled using multidimensional signal detection theory (SDT). Implications for models of category-based inductive reasoning, and theories of reasoning more generally, are discussed. (shrink)

Proponents of the value ladenness of science rely primarily on arguments from underdetermination or inductive risk, which share the premise that we should only consider values where the evidence runs out or leaves uncertainty; they adopt a criterion of lexical priority of evidence over values. The motivation behind lexical priority is to avoid reaching conclusions on the basis of wishful thinking rather than good evidence. This is a real concern, however, that giving lexical priority to evidential considerations over values (...) is a mistake and unnecessary for avoiding the wishful thinking. Values have a deeper role to play in science. (shrink)

More than a decade of exacting scientific research involving paleontological fragments and ancient DNA has lately produced a series of pronouncements about a purportedly novel population of archaic hominins dubbed “the Denisova.” The science involved in these matters is both technically stunning and, socially, at times a bit reckless. Here I discuss the responsibilities which scientists incur when they make inductively risky pronouncements about the different relative contributions by Denisovans to genomes of members of apparent subpopulations of current humans. This (...) science is sensational: it is science which empirically speculates, to the public delight’s and entertainment, about scintillating topics such as when humans evolved, where we came from, and who else we were having sex with during our early hominin history. An initial characterization of sensational science emerges from my discussion of the case, as well as a diagnosis of an interactive phenomenon termed amplified inductive risk. (shrink)

We apply methods of abduction derived from propositional probabilistic reasoning to predicate probabilistic reasoning, in particular inductive logic, by treating finite predicate knowledge bases as potentially infinite propositional knowledge bases. It is shown that for a range of predicate knowledge bases and several key propositional inference processes this procedure is well defined, and furthermore yields an explanation for the validity of the induction in terms of 'reasons'.

The ‘death of evidence’ issue in Canada raises the spectre of politicized science, and thus the question of what role social values may have in science and how this meshes with objectivity and evidence. I first criticize philosophical accounts that have to separate different steps of research to restrict the influence of social and other non-epistemic values. A prominent account that social values may play a role even in the context of theory acceptance is the argument from inductive risk. (...) It maintains that the more severe the social consequences of erroneously accepting a theory would be, the more evidence is needed before the theory may be accepted. However, an implication of this position is that increasing evidence makes the impact of social values converge to zero; and I argue for a stronger role for social values. On this position, social values may determine a theory’s conditions of adequacy, which among other things can include co.. (shrink)

An argument, different from the Newman objection, against the view that the cognitive content of a theory is exhausted by its Ramsey sentence is reviewed. The crux of the argument is that Ramsification may ruin inductive systematization between theory and observation. The argument also has some implications concerning the issue of underdetermination.

Among the various meanings in which the word ‘probability’ is used in everyday language, in the discussion of scientists, and in the theories of probability, there are especially two which must be clearly distinguished. We shall use for them the terms ‘probability1’ and ‘probability2'. Probability1 is a logical concept, a certain logical relation between two sentences ; it is the same as the concept of degree of confirmation. I shall write briefly “c” for “degree of confirmation,” and “c” for “the (...) degree of confirmation of the hypothesis h on the evidence e“; the evidence is usually a report on the results of our observations. On the other hand, probability2 is an empirical concept; it is the relative frequency in the long run of one property with respect to another. The controversy between the so-called logical conception of probability, as represented e.g. by Keynes, and Jeffreys, and others, and the frequency conception, maintained e.g. by v. Mises and Reichenbach, seems to me futile. These two theories deal with two different probability concepts which are both of great importance for science. Therefore, the theories are not incompatible, but rather supplement each other. (shrink)

English summary: Bachelards fundamental 1929 text takes mathematics as the means for constructing and investigating physical reality, anticipating many of the great theories developed over the course of the next century. French description: Quatorze ans apres la theorie de la relativite generale (1915), Bachelard publie La Valeur inductive de la relativite (1929). Cet ouvrage qu'on reduit souvent a sa polemique avec Meyerson, auteur de La Deduction relativiste (1925), est en realite un eloge des mathematiques - et notamment du calcul (...) tensoriel - comme mode de construction et d'investigation du reel physique. Dans ce livre non reedite, qui minimise l'experience mais qui contient aussi en germe nombre de themes ulterieurement developpes par l'auteur, Bachelard apparait retrospectivement beaucoup plus prophetique qu'il ne pouvait le penser lui-meme. Les grandes theories physiques du XXe et du XXIe siecle ne cesseront de lui donner raison. (shrink)

I evaluate Schurz's proposed meta-inductive justification of induction, a refinement of Reichenbach's pragmatic justification that rests on results from the machine learning branch of prediction with expert advice. My conclusion is that the argument, suitably explicated, comes remarkably close to its grand aim: an actual justification of induction. This finding, however, is subject to two main qualifications, and still disregards one important challenge. The first qualification concerns the empirical success of induction. Even though, I argue, Schurz's argument does not (...) need to spell out what inductive method actually consists in, it does need to postulate that there is something like the inductive or scientific prediction strategy that has so far been significantly more successful than alternative approaches. The second qualification concerns the difference between having a justification for inductive method and for sticking with induction for now. Schurz's argument can only provide the latter. Finally, the remaining challenge concerns the pool of alternative strategies, and the relevant notion of a meta-inductivist's optimality that features in the analytic step of Schurz's argument. Building on the work done here, I will argue in a follow-up paper that the argument needs a stronger dynamic notion of a meta-inductivist's optimality. (shrink)

Peter Achinstein gives in his papers [1] and [2] interesting analyses of some problems of inductive logic and of some approaches I have proposed. I shall discuss here some of these problems in order to clarify my present position. My comments will mainly concern the variety of instances, and only briefly the analogy influence, and the inductive methods for a coordinate language.

C-Inductive arguments are arguments that increase the probability of a hypothesis. This can be contrasted with what is called a P-Inductive argument. A P-inductive argument is an argument that shows the overall probability of a hypothesis to be more probable than not. In this paper, we put forth a C-inductive argument for the truth of the Catholic hypothesis (CH). Roughly, we take CH to be the hypothesis that the core creedal beliefs found within the Catholic Tradition (...) are true. Specifically, we argue that we would expect the Miracle of Fátima on CH, but, we wouldn’t expect it as much on ~CH. In order to establish this thesis, we first discuss the basics of confirmation theory. Second, we give the historical context of the Miracle of Fátima. Third, we briefly survey and then reject two possible non-supernatural explanations of the apparent miracle. Doing this will help make plausible that the Miracle of Fátima is actual evidence that a hypothesis needs to predict. Fourth, we give the details as to why we should expect the Miracle of Fátima more on CH than ~CH. Finally, we argue that miracles that occur in Protestant contexts, generally don’t carry the same evidential weight for a Protestant hypothesis as the Miracle of Fátima carries for CH. (shrink)

Then, in 1960, Carnap drew up a plan of articles for Studies in Inductive Logic and Probability — a surrogate for Volume II of the ...

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)

Bayesian inference is limited in scope because it cannot be applied in idealized contexts where none of the hypotheses under consideration is true and because it is committed to always using the likelihood as a measure of evidential favouring, even when that is inappropriate. The purpose of this article is to study inductive inference in a very general setting where finding the truth is not necessarily the goal and where the measure of evidential favouring is not necessarily the likelihood. (...) I use an accuracy argument to argue for probabilism and I develop a new kind of argument to argue for two general updating rules, both of which are reasonable in different contexts. One of the updating rules has standard Bayesian updating, Bissiri et al.’s general Bayesian updating, Douven’s IBE-based updating, and Vassend’s ]) quasi-Bayesian updating as special cases. The other updating rule is novel. (shrink)

It is widely recognized that computational theories of learning must posit the existence of a priori constraints on hypothesis selection. The present article surveys the theoretical options available for modelling the dynamic process whereby the constraints have their effect. According to the 'simplicity' theory (exemplified by Fodor's treatment), hypotheses are preference-ordered in terms of their syntactic or semantic properties. It is argued that the same explanatory power can be obtained with a weaker (hence better) theory, the 'minimalist' theory, which dispenses (...) with the preference ordering. According to the 'finitistic' theory, the learner is capable of generating only finitely many hypotheses for evaluation. Chomsky maintains that the occurrence of errorless learning in language acquisition necessitates a finististic explanation. Once again, there is a weaker theory that explains the same data. Finally, Goodman's argument to the effect that there cannot be a computational theory of learning is examined and rejected. (shrink)

L. Jonathan Cohen has written a number of important books and articles in which he argues that mathematical probability provides a poor model of much of what paradigmatically passes for sound reasoning, whether this be in the sciences, in common discourse, or in the law. In his book, The Probable and the Provable, Cohen elaborates six paradoxes faced by advocates of mathematical probability (PM) when treating issues of evidence as they would arise in a court of law. He argues that (...) his system of inductive probability (PI) satisfactorily handles the issues that proved paradoxical for mathematical probability, and consequently PI deserves to be thought of as an important standard of rational thinking. I argue that a careful look at each of the alleged paradoxes shows that there is no conflict between mathematical probability and the law, except when for reasons of policy we opt for values in addition to accuracy maximization. Recognizing the role of such policies provides no basis for questioning the adequacy of PM. The significance of this critical treatment of Cohen's work is that those interested in revising the laws of evidence to allow for more explicitly mathematical approaches ought to feel that such revisions will not violate the spirit of forensic rationality. (shrink)

This text focuses on basic topics and problems of logic, as well as decision theory and topics related to the philosophy of science and statistics. Topics covered include inductive inference; causal inferrence; probability calculus; expected value; confirmation theory; the justification of induction; the riddle of induction and theories of probability. It also includes coverage, in both historical and contemporary terms, of the traditional problem of induction raised by Hume.