Inductive Reasoning

The paper demonstrates that falsifiability is fundamental to learning. We prove the following theorem for statistical learning and sequential prediction: If a theory is falsifiable then it is learnable -- i.e. admits a strategy that predicts optimally. An analogous result is shown for universal induction.

We information-theoretically reformulate two measures of capacity from statistical learning theory: empirical VC-entropy and empirical Rademacher complexity. We show these capacity measures count the number of hypotheses about a dataset that a learning algorithm falsifies when it finds the classifier in its repertoire minimizing empirical risk. It then follows from that the future performance of predictors on unseen data is controlled in part by how many hypotheses the learner falsifies. As a corollary we show that empirical VC-entropy quantifies the message (...) length of the true hypothesis in the optimal code of a particular probability distribution, the so-called actual repertoire. (shrink)

We argue that a particular approach to satisfying the broad predictive ambitions of the sciences demands law confirmation. On this approach we confirm non-nomic generalizations by confirming there are no actually realized ways of causing disconfirming cases. This gives causal generalizations a crucial role in prediction. We then show how rational judgements of relevant causal similarity can be used to confirm that causal generalizations themselves have no actual disconfirmers, providing a distinctive and clearly viable methodology for inductively confirming them. Finally, (...) we argue that for agents in our epistemic position using this methodology to confirm causal generalizations of adequate breadth will commonly demand law confirmation. We make a prima facie assessment of the methodology’s fit with scientific practice and briefly consider the prospects for an associated analysis of laws. (shrink)

The grue paradox, also called the new riddle of induction, posed a great challenge to the common understanding about induction. This paper shows that there is a close relation between the grue paradox and the problem of conditionals. This paper presents a general form of the grue predicate. Based on the general form, this paper argues that this kind of predicates can not be used for induction and prediction.

There are (at least) three approaches to quantifying information. The first, algorithmic information or Kolmogorov complexity, takes events as strings and, given a universal Turing machine, quantifies the information content of a string as the length of the shortest program producing it [1]. The second, Shannon information, takes events as belonging to ensembles and quantifies the information resulting from observing the given event in terms of the number of alternate events that have been ruled out [2]. The third, statistical learning (...) theory, has introduced measures of capacity that control (in part) the expected risk of classifiers [3]. These capacities quantify the expectations regarding future data that learning algorithms embed into classifiers. Solomonoff and Hutter have applied algorithmic information to prove remarkable results on universal induction. Shannon information provides the mathematical foundation for communication and coding theory. However, both approaches have shortcomings. Algorithmic information is not computable, severely limiting its practical usefulness. Shannon information refers to ensembles rather than actual events: it makes no sense to compute the Shannon information of a single string – or rather, there are many answers to this question depending on how a related ensemble is constructed. Although there are asymptotic results linking algorithmic and Shannon information, it is unsatisfying that there is such a large gap – a difference in kind – between the two measures. This note describes a new method of quantifying information, effective information, that links algorithmic information to Shannon information, and also links both to capacities arising in statistical learning theory [4, 5]. After introducing the measure, we show that it provides a non-universal analog of Kolmogorov complexity. We then apply it to derive basic capacities in statistical learning theory: empirical VC-entropy and empirical Rademacher complexity. A nice byproduct of our approach is an interpretation of the explanatory power of a learning algorithm in terms of the number of hypotheses it falsifies [6], counted in two different ways for the two capacities. We also discuss how effective information relates to information gain, Shannon and mutual information. (shrink)

In this paper, I argue that explaining cognitive behavior can be achieved through what I call hybrid explanatory inferences: inferences that posit mechanisms, but also draw on observed regularities. Moreover, these inferences can be used to achieve unification, in the sense developed by Allen Newel in his work on cognitive architectures. Thus, it seems that explanatory pluralism and unification do not rule out each other in cognitive science, but rather that the former represents a way to achieve the latter.

All else being equal, can granting the objective purport of moral experience support a presumption in favor of some form of moral objectivism? Don Loeb (2007) has argued that even if we grant that moral experience appears to present us with a realm of objective moral fact—something he denies we have reason to do in the first place—the objective purport of moral experience cannot by itself provide even prima facie support for moral objectivism. In this paper, I contend against Loeb (...) that granting the objective purport of ordinary moral experience is sufficient to support a defeasible presumption in favor of moral objectivism, and this by constituting non-explanatory, comparative confirmation that incrementally raises the prima facie likelihood that moral facts exist. More specifically, I appeal to a modest confirmation principle shared by Likelihoodists and Bayesieans - namely, the Weak Law of Likelihood - in an effort to show that (i) at a minimum, moral experience establishes a middling scrutable probability for a sufficient but not necessary condition of moral objectivism being true, and that (ii) this moderate probability in turn constitutes evidence that makes it prima facie more probable than not that some form of moral objectivism is true. (shrink)

A standard way to challenge convergence-based accounts of inductive success is to claim that they are too weak to constrain inductive inferences in the short run. We respond to such a challenge by answering some questions raised by Juhl (1994). When it comes to predicting limiting relative frequencies in the framework of Reichenbach, we show that speed-optimal convergence—a long-run success condition—induces dynamic coherence in the short run.

As our epistemic ambitions grow, the common and scientific endeavours are becoming increasingly dependent on Machine Learning (ML). The field rests on a single experimental paradigm, which consists of splitting the available data into a training and testing set and using the latter to measure how well the trained ML model generalises to unseen samples. If the model reaches acceptable accuracy, an a posteriori contract comes into effect between humans and the model, supposedly allowing its deployment to target environments. Yet (...) the latter part of the contract depends on human inductive predictions or generalisations, which infer a uniformity between the trained ML model and the targets. The paper asks how we justify the contract between human and machine learning. It is argued that the justification becomes a pressing issue when we use ML to reach ‘elsewheres’ in space and time or deploy ML models in non-benign environments. The paper argues that the only viable version of the contract can be based on optimality (instead of on reliability which cannot be justified without circularity) and aligns this position with Schurz’s optimality justification. It is shown that when dealing with inaccessible/unstable ground-truths (‘elsewheres’ and non-benign targets), the optimality justification undergoes a slight change, which should reflect critically on our epistemic ambitions. Therefore, the study of ML robustness should involve not only heuristics that lead to acceptable accuracies on testing sets. The justification of human inductive predictions or generalisations about the uniformity between ML models and targets should be included as well. Without it, the assumptions about inductive risk minimisation in ML are not addressed in full. (shrink)

This chapter presents a typology of the different kinds of inductive inferences we can draw from our evidence, based on the explanatory relationship between evidence and conclusion. Drawing on the literature on graphical models of explanation, I divide inductive inferences into (a) downwards inferences, which proceed from cause to effect, (b) upwards inferences, which proceed from effect to cause, and (c) sideways inferences, which proceed first from effect to cause and then from that cause to an additional effect. I further (...) distinguish between direct and indirect forms of downwards and upwards inferences. I then show how we can subsume canonical forms of inductive inference mentioned in the literature, such as inference to the best explanation, enumerative induction, and analogical inference, under this typology. Along the way, I explore connections with probability and confirmation, epistemic defeat, the relation between abduction and enumerative induction, the compatibility of IBE and Bayesianism, and theories of epistemic justification. (shrink)

A growing number of philosophers are concerned with the epistemic status of culturally nurtured beliefs, beliefs found especially in domains of morals, politics, philosophy, and religion. Plausibly, worries about the deep impact of cultural contingencies on beliefs in these domains of controversial views is a question about well-foundedness: Does it defeat well-foundedness if the agent is rationally convinced that she would take her own reasons for belief as insufficiently well-founded, or would take her own belief as biased, had she been (...) nurtured in a different psychographic community? This chapter will examine the proper scope and force of this epistemic location problem. It sketches an account of well and ill-founded nurtured belief based upon the many markers of doxastic strategies exhibiting low to high degrees of inductive risk: the moral and epistemic risk of ‘getting it wrong’ in an inductive context of inquiry. (shrink)

Privileged-perspective realism (PPR) is a version of metaphysical realism that takes certain irreducibly perspectival facts to be partly constitutive of reality. PPR asserts that there is a single metaphysically privileged standpoint from which these perspectival facts obtain. This chapter discusses several views that fall under the category of privileged-perspective realism. These include presentism, which is PPR about tensed facts, and non-multiverse interpretations of quantum mechanics, which the chapter argues, constitute PPR about world-indexed facts. Using the framework of the bird perspective (...) and the frog perspective, it argues that PPR views methodologically treat the frog perspective as metaphysically primary. This chapter considers case studies of metaphysical interpretations of special relativity and quantum mechanics in order to demonstrate that such motivations for PPR are non-naturalistic. Further, it considers psychological factors that motivate the appeal of PPR views and offers naturalistic explanations of why we should not expect them to produce an adequate metaphysics of science. (shrink)

To demarcate the limits of experimental knowledge, we probe the limits of what might be called an experiment. By appeal to examples of scientific practice from astrophysics and analogue gravity, we demonstrate that the reliability of knowledge regarding certain phenomena gained from an experiment is not circumscribed by the manipulability or accessibility of the target phenomena. Rather, the limits of experimental knowledge are set by the extent to which strategies for what we call ‘inductive triangulation’ are available: that is, the (...) validation of the mode of inductive reasoning involved in the source-target inference via appeal to one or more distinct and independent modes of inductive reasoning. When such strategies are able to partially mitigate reasonable doubt, we can take a theory regarding the phenomena to be well supported by experiment. When such strategies are able to fully mitigate reasonable doubt, we can take a theory regarding the phenomena to be established by experiment. There are good reasons to expect the next generation of analogue experiments to provide genuine knowledge of unmanipulable and inaccessible phenomena such that the relevant theories can be understood as well supported. This article is part of a discussion meeting issue ‘The next generation of analogue gravity experiments’. (shrink)

After long arguments between positivism and falsificationism, the verification of universal hypotheses was replaced with the confirmation of uncertain major premises. Unfortunately, Hemple proposed the Raven Paradox. Then, Carnap used the increment of logical probability as the confirmation measure. So far, many confirmation measures have been proposed. Measure F proposed by Kemeny and Oppenheim among them possesses symmetries and asymmetries proposed by Elles and Fitelson, monotonicity proposed by Greco et al., and normalizing property suggested by many researchers. Based on the (...) semantic information theory, a measure b* similar to F is derived from the medical test. Like the likelihood ratio, measures b* and F can only indicate the quality of channels or the testing means instead of the quality of probability predictions. Furthermore, it is still not easy to use b*, F, or another measure to clarify the Raven Paradox. For this reason, measure c* similar to the correct rate is derived. Measure c* supports the Nicod Criterion and undermines the Equivalence Condition, and hence, can be used to eliminate the Raven Paradox. An example indicates that measures F and b* are helpful for diagnosing the infection of Novel Coronavirus, whereas most popular confirmation measures are not. Another example reveals that all popular confirmation measures cannot be used to explain that a black raven can confirm “Ravens are black” more strongly than a piece of chalk. Measures F, b*, and c* indicate that the existence of fewer counterexamples is more important than more positive examples’ existence, and hence, are compatible with Popper’s falsification thought. (shrink)

It is generally assumed that relations of necessity cannot be known by induction on experience. In this paper, I propose a notion of situated possibilities, weaker than nomic possibilities, that is compatible with an inductivist epistemology for modalities. I show that assuming this notion, not only can relations of necessity be known by induction on our experience, but such relations cannot be any more underdetermined by experience than universal regularities. This means that any one believing in a universal regularity is (...) as well warranted to believe in the corresponding relation of necessity. (shrink)

John D. Norton is responsible for a number of influential views in contemporary philosophy of science. This paper will discuss two of them. The material theory of induction claims that inductive arguments are ultimately justified by their material features, not their formal features. Thus, while a deductive argument can be valid irrespective of the content of the propositions that make up the argument, an inductive argument about, say, apples, will be justified (or not) depending on facts about apples. The argument (...) view of thought experiments claims that thought experiments are arguments, and that they function epistemically however arguments do. These two views have generated a great deal of discussion, although there hasn’t been much written about their combination. I argue that despite some interesting harmonies, there is a serious tension between them. I consider several options for easing this tension, before suggesting a set of changes to the argument view that I take to be consistent with Norton’s fundamental philosophical commitments, and which retain what seems intuitively correct about the argument view. These changes require that we move away from a unitary epistemology of thought experiments and towards a more pluralist position. (shrink)

Gözlemlenenlerden gözlemlen(e)meyenlere diğer bir deyişle genel yasalara ulaşma imkânı veren çıkarım yöntemi olarak tümevarımsal ya da endüktif akıl yürütmenin rasyonel olarak temellendirilmesinin imkanına yönelik soruşturma tarih içerisinde tümevarım sorunu ya da endüksiyon problemi olarak tezahür etmiştir. Bu sorunun temel argümanı tarihsel okumalara baktığımızda İskoç ampirist filozof David Hume tarafından öne sürülmüştür. Hume, tümevarımsal çıkarımlar temelinde, gözlenmeyen meseleler hakkındaki inançlarımıza hangi gerekçelerle ulaştığımızı soruşturmaktadır. Hume soruşturmasının sonucunda gözlemlenenden gözlemlen(e)meyen durumlara ilişkin yapılan olgu meseleleri ile ilgili bütün tümevarımsal akıl yürütmelerin dolaylı ya (...) da dolaysız olarak nedensellik ilişkisine ve bu ilişkinin temelinde yer alan doğanın düzenliliği ilkesi ya da “gelecek her zaman geçmişe benzer” önermesine dayandığını ifade ederek bütün tümevarımsal akıl yürütmelerde ortak olan geleceğin her zaman geçmişe benzeyeceği ifadesinin rasyonel olarak temellendirilmesinin mümkün olmadığını belirtmektedir. Bu bağlamda, çalışmada tümevarımsal akıl yürütme sonucunda ulaşılan sonuca inanmanın hiçbir rasyonel temelinin olamayacağı yönündeki Hume’un görüşü argüman formunda yeniden yapılandırılarak ortaya konulacaktır. (shrink)

Schurz proposed a justification of creative abduction on the basis of the Reichenbachian principle of the common cause. In this paper we take up the idea of combining creative abduction with causal principles and model instances of successful creative abduction within a Bayes net framework. We identify necessary conditions for such inferences and investigate their unificatory power. We also sketch several interesting applications of modeling creative abduction Bayesian style. In particular, we discuss use-novel predictions, confirmation, and the problem of underdetermination (...) in the context of abductive inferences. (shrink)

If the laws of nature are as the Humean believes, it is an unexplained cosmic coincidence that the actual Humean mosaic is as extremely regular as it is. This is a strong and well-known objection to the Humean account of laws. Yet, as reasonable as this objection may seem, it is nowadays sometimes dismissed. The reason: its unjustified implicit assignment of equiprobability to each possible Humean mosaic; that is, its assumption of the principle of indifference, which has been attacked on (...) many grounds ever since it was first proposed. In place of equiprobability, recent formal models represent the doxastic state of total ignorance as suspension of judgment. In this paper I revisit the cosmic coincidence objection to Humean laws by assessing which doxastic state we should endorse. By focusing on specific features of our scenario I conclude that suspending judgment results in an unnecessarily weak doxastic state. First, I point out that recent literature in epistemology has provided independent justifications of the principle of indifference. Second, given that the argument is framed within a Humean metaphysics, it turns out that we are warranted to appeal to these justifications and assign a uniform and additive credence distribution among Humean mosaics. This leads us to conclude that, contrary to widespread opinion, we should not dismiss the cosmic coincidence objection to the Humean account of laws. (shrink)

This book is the result of rethinking the standard playbook for critical thinking courses, to include only the most useful skills from the toolkits of philosophy, cognitive psychology, and behavioral economics. -/- The text focuses on: -/- - a mindset that avoids systematic error, more than the ability to persuade others - the logic of probability and decisions, more than than the logic of deductive arguments - a unified treatment of evidence, covering statistical, causal, and best-explanation inferences -/- The unified (...) account of evidence I offer is a broadly Bayesian one, but there aren’t any daunting theorems. (Without knowing it, students are taught to use a gentle form of the Bayes factor to measure the strength of evidence and to update.) It’s also shown how this framework illuminates aspects of the scientific method, such as the proper design of experiments. -/- The link above allows Anonymous Guest Access without an account. (shrink)

In a paper and a reply to critics published in _Informal Logic_, I argue that arguments from expert opinion are weak arguments. To appeal to expert opinion is to take an expert’s judgment that _p_ is the case as evidence for _p_. Such appeals to expert opinion are weak, I argue, because the fact that an expert judges that _p_ does not make it significantly more likely that _p_ is true or probable, as evidence from empirical studies on expert performance (...) suggests. Unlike other critics of this argument, who take issue with the empirical evidence on expert performance, David Botting says that he wants to take issue with the premise that reliability is a necessary condition for the strength of appeals to expert opinion. I respond to Botting’s objections and argue that they miss their intended target. I also argue that his attempt to show that arguments from expert opinion are strong is unsuccessful. (shrink)

Hans Reichenbach’s pragmatic treatment of the problem of induction in his later works on inductive inference was, and still is, of great interest. However, it has been dismissed as a pseudo-solution and it has been regarded as problematically obscure. This is, in large part, due to the difficulty in understanding exactly what Reichenbach’s solution is supposed to amount to, especially as it appears to offer no response to the inductive skeptic. For entirely different reasons, the significance of Bertrand Russell’s classic (...) attempt to solve Hume’s problem is also both obscure and controversial. Russell accepted that Hume’s reasoning about induction was basically correct, but he argued that given the centrality of induction in our cognitive endeavors something must be wrong with Hume’s basic assumptions. What Russell effectively identified as Hume’s (and Reichenbach’s) failure was the commitment to a purely extensional empiricism. So, Russell’s solution to the problem of induction was to concede extensional empiricism and to accept that induction is grounded by accepting both a robust essentialism and a form of rationalism that allowed for a priori knowledge of universals. So, neither of those doctrines is without its critics. On the one hand, Reichenbach’s solution faces the charges of obscurity and of offering no response to the inductive skeptic. On the other hand, Russell’s solution looks to be objectionably ad hoc absent some non-controversial and independent argument that the universals that are necessary to ground the uniformity of nature actually exist and are knowable. This particular charge is especially likely to arise from those inclined towards purely extensional forms of empiricism. In this paper the significance of Reichenbach’s solution to the problem of induction will be made clearer via the comparison of these two historically important views about the problem of induction. The modest but important contention that will be made here is that the comparison of Reichenbach’s and Russell’s solutions calls attention to the opposition between extensional and intensional metaphysical presuppositions in the context of attempts to solve the problem of induction. It will be show that, in effect, what Reichenbach does is to establish an important epistemic limitation of extensional empiricism. So, it will be argued here that there is nothing really obscure about Reichenbach’s thoughts on induction at all. He was simply working out the limits of extensional empiricism with respect to inductive inference in opposition to the sort of metaphysics favored by Russell and like-minded thinkers. (shrink)

This textbook is not a textbook in the traditional sense. Here, what we have attempted is compile a set of assignments and exercise that may be used in critical thinking courses. To that end, we have tried to make these assignments as diverse as possible while leaving flexibility in their application within the classroom. Of course these assignments and exercises could certainly be used in other classes as well. Our view is that critical thinking courses work best when they are (...) presented as skills based learning opportunities. We hope that these assignments speak to that desire and can foster the kinds of critical thinking skills that are both engaging and fun Please feel free to contact us with comments and suggestions. We will strive to correct errors when pointed out, add necessary material, and make other additional and needed changes as they arise. Please check back for the most up to date version. Rebeka Ferreira and Anthony Ferrucci. (shrink)

This paper defends the naïve thesis that the method of experiment has per se an epistemic superiority over the method of computer simulation, a view that has been rejected by some philosophers writing about simulation, and whose grounds have been hard to pin down by its defenders. I further argue that this superiority does not come from the experiment’s object being materially similar to the target in the world that the investigator is trying to learn about, as both sides of (...) dispute over the epistemic superiority thesis have assumed. The superiority depends on features of the question and on a property of natural kinds that has been mistaken for material similarity. Seeing this requires holding other things equal in the comparison of the two methods, thereby exposing that, under the conditions that will be specified, the simulation is necessarily epistemically one step behind the corresponding experiment. Practical constraints like feasibility and morality mean that scientists do not often face an other-things- equal comparison when they choose between experiment and simulation. Nevertheless, I argue, awareness of this superiority and of the general distinction between experiment and simulation is important for maintaining motivation to seek answers to new questions. (shrink)

A. W. F. Edwards is one of the most influential mathematical geneticists in the history of the discipline. One of the last students of R. A. Fisher, Edwards pioneered the statistical analysis of phylogeny in collaboration with L. L. Cavalli-Sforza, and helped establish Fisher's concept of likelihood as a standard of statistical and scientific inference. In this book, edited by philosopher of science Rasmus Grønfeldt Winther, Edwards's key papers are assembled alongside commentaries by leading scientists, discussing Edwards's influence on their (...) own research and on thinking in their field overall. In an extensive interview with Winther, Edwards offers his thoughts on his contributions, their legacy, and the context in which they emerged. This book is a resource both for anyone interested in the history and philosophy of genetics, statistics, and science, and for scientists seeking to develop new algorithmic and statistical methods for understanding the genetic relationships between and among species both extant and extinct. (shrink)

As it is standardly conceived, Inference to the Best Explanation (IBE) is a form of ampliative inference in which one infers a hypothesis because it provides a better potential explanation of one’s evidence than any other available, competing explanatory hypothesis. Bas van Fraassen famously objected to IBE thus formulated that we may have no reason to think that any of the available, competing explanatory hypotheses are true. While revisionary responses to the Bad Lot Objection concede that IBE needs to be (...) reformulated in light of this problem, reactionary responses argue that the Bad Lot Objection is fallacious, incoherent, or misguided. This paper shows that the most influential reactionary responses to the Bad Lot Objection do nothing to undermine the original objection. This strongly suggests that proponents of IBE should focus their efforts on revisionary responses, i.e. on finding a more sophisticated characterization of IBE for which the Bad Lot Objection loses its bite. (shrink)

Book review of Paul Horwich, Probability and Evidence (Cambridge Philosophy Classics edition), Cambridge: Cambridge University Press, 2016, 147pp, £14.99 (paperback).

Inference to the Best Explanation (IBE) is widely criticized for being an unreliable form of ampliative inference – partly because the explanatory hypotheses we have considered at a given time may all be false, and partly because there is an asymmetry between the comparative judgment on which an IBE is based and the absolute verdict that IBE is meant to license. In this paper, I present a further reason to doubt the epistemic merits of IBE and argue that it motivates (...) moving to an inferential pattern in which IBE emerges as a degenerate limiting case. Since this inferential pattern is structurally similar to an argumentative strategy known as Inferential Robustness Analysis (IRA), it effectively combines the most attractive features of IBE and IRA into a unified approach to non-deductive inference. (shrink)

We explore the grammar of Bayesian confirmation by focusing on some likelihood principles, including the Weak Law of Likelihood. We show that none of the likelihood principles proposed so far is satisfied by all incremental measures of confirmation, and we argue that some of these measures indeed obey new, prima facie strange, antilikelihood principles. To prove this, we introduce a new measure that violates the Weak Law of Likelihood while satisfying a strong antilikelihood condition. We conclude by hinting at some (...) relevant links between the likelihood principles considered here and other properties of Bayesian confirmation recently explored in the literature. (shrink)

My topic is moderate modal skepticism in the spirit of Peter van Inwagen. Here understood, this is a conservative version of modal empiricism that severely limits the extent to which an ordinary agent can reasonably believe “exotic” possibility claims. I offer a novel argument in support of this brand of skepticism: modal skepticism grounds an attractive (and novel) reply to Humean skepticism. Thus, I propose that modal skepticism be accepted on the basis of its theoretical utility as a tool for (...) dissolving philosophical paradox. (shrink)

The justificatory force of empirical reasoning always depends upon the existence of some synthetic, a priori justification. The reasoner must begin with justified, substantive constraints on both the prior probability of the conclusion and certain conditional probabilities; otherwise, all possible degrees of belief in the conclusion are left open given the premises. Such constraints cannot in general be empirically justified, on pain of infinite regress. Nor does subjective Bayesianism offer a way out for the empiricist. Despite often-cited convergence theorems, subjective (...) Bayesians cannot hold that any empirical hypothesis is ever objectively justified in the relevant sense. Rationalism is thus the only alternative to an implausible skepticism. (shrink)

Modern scientific cosmology pushes the boundaries of knowledge and the knowable. This is prompting questions on the nature of scientific knowledge. A central issue is what defines a 'good' model. When addressing global properties of the Universe or its initial state this becomes a particularly pressing issue. How to assess the probability of the Universe as a whole is empirically ambiguous, since we can examine only part of a single realisation of the system under investigation: at some point, data will (...) run out. We review the basics of applying Bayesian statistical explanation to the Universe as a whole. We argue that a conventional Bayesian approach to model inference generally fails in such circumstances, and cannot resolve, e.g., the so-called 'measure problem' in inflationary cosmology. Implicit and non-empirical valuations inevitably enter model assessment in these cases. This undermines the possibility to perform Bayesian model comparison. One must therefore either stay silent, or pursue a more general form of systematic and rational model assessment. We outline a generalised axiological Bayesian model inference framework, based on mathematical lattices. This extends inference based on empirical data (evidence) to additionally consider the properties of model structure (elegance) and model possibility space (beneficence). We propose this as a natural and theoretically well-motivated framework for introducing an explicit, rational approach to theoretical model prejudice and inference beyond data. (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 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.

Research into the cognition of conditionals has predominantly focused on conditional reasoning, producing a range of theories which explain associated phenomena with considerable success. However, such theories have been less successful in accommodating experimental data concerning how agents assess the probability of indicative conditionals. Since an acceptable account of conditional reasoning should be compatible with evidence regarding how we evaluate conditionals’ likelihoods, this constitutes a failing of such theories. Section 1 introduces the most dominant established approach to conditional reasoning: mental (...) models theory. Surveying a range of experimental results, I show that mental models theory (along with competing theories) is incapable of fully accounting for findings regarding judgements about conditionals’ probabilities. Section 2 introduces an alternative account of deductive reasoning, the erotetic theory, recently proposed by Koralus and Mascarenhas (2013). Section 3 argues that, given a natural extension, this theory is able to explain the otherwise unaccounted for data. (shrink)

In this paper, I argue that, other things being equal, simpler arguments are better. In other words, I argue that, other things being equal, it is rational to prefer simpler arguments over less simple ones. I sketch three arguments in support of this claim: an argument from mathematical proofs, an argument from scientific theories, and an argument from the conjunction rule.

RATIONALE, AIMS AND OBJECTIVES: Increased awareness of the gap between controlled research and medical practice has raised concerns over whether the special attention of doctors to probability estimates from clinical trials really improves the care of individuals. Evidence-based medicine has acknowledged that research results are not applicable to all kinds of patients, and consequently, has attempted to overcome this limitation by introducing improvements in the design and analysis of clinical trials. METHODS: A clinical case is used to highlight the premises (...) required to support reasonable extrapolations from controlled research to individuals. Then, the prospects of two key methodological improvements - pragmatic randomized controlled trials and subgroup analysis - are critically appraised. RESULTS: A principle to guide therapeutic inferences is suggested. According to this principle, the probabilities of interest for purposes of therapeutic decision making are those of the set defined by everything that is relevant to the patient and the outcome of interest at the time of the decision. It is argued that the conditions necessary to authorize automatic extrapolations of research results to specific patients are highly demanding. Furthermore, these requirements are rarely accomplished in real practice, even in the event that probability estimates come from samples generally taken as representative and are derived from specific subsets of patients. CONCLUSIONS: Clinicians should generally avoid unreflective extrapolations from research and address, as explicitly as possible, the challenge of estimating probabilities for individual patients. A key element of this task is the integration of data from research and non-research sources. (shrink)

Many philosophers have wrongly assumed that there is an asymmetry between the problem of induction and the logocentric predicament (the justification of deductive inferences). This paper will show that the demand for justification, for the very inferences that are required for justification, is deeply problematic. Using a Wittgensteinian approach, I will argue that justification has an internal relation with deductive and inductive inferences. For Wittgenstein, two concepts are internally related if my understanding of one is predicated on my understanding of (...) the other. Separating the two concepts so that one can be applied to the other is then a misunderstanding of role that these concepts play. (shrink)

This paper argues that all apparently special forces characteristically reduce to a few fundamental physical forces which conserve energy and operate throughout nature. Consequently, there are probably no special mental forces originating from souls and acting upon bodies and brains in addition to the basic, energy-conserving physical forces. Moreover, physiological and biochemical research have failed to uncover any evidence of forces over and above the basic physical forces acting on living bodies. It is as if all organic processes can be (...) fully accounted for in terms of normal physical forces—that is, as if there are no souls or ethereal doubles interacting with living bodies. -/- 1. The Argument from Fundamental Forces -- 2. The Argument from Physiology -- 3. Conclusion. (shrink)

Formal and empirical work on the Wisdom of Crowds has extolled the virtue of diverse and independent judgment as essential to the maintenance of ‘wise crowds’. In other words, com-munication and imitation among members of a group may have the negative effect of decreasing the aggregate wisdom of the group. In contrast, it is demonstrable that certain meta-inductive methods provide optimal means for predicting unknown events. Such meta-inductive methods are essentially imitative, where the predictions of other agents are imitated to (...) the extent that those agents have proven successful in the past. Despite the (self-serving) optimality of meta-inductive methods, their imitative nature may undermine the ‘wisdom of the crowd’, since these methods recommend that agents imitate the predictions of other agents. In this paper, I present a replication of selected results of Thorn and Schurz, illustrating the effect on a group’s performance that may result from having members of a group adopt meta-inductive methods. I then expand on the work of Thorn and Schurz by considering three simple measures by which meta-inductive prediction methods may improve their own performance, while simultaneously mitigating their negative impact on group performance. The effects of adopting these maneuvers are investigated using computer simulations. (shrink)

‘Reasoning’ can be considered a general concept that, upon speaking, is the ‘enraonar’, a Catalan word that should not be mistaken with ‘explain’ nor with ‘discuss’ which imply more detail, and cover different situations. This article is presented as an essay on the ancient ideal of ‘enraonar’. To that end, it is explained in what sense ‘enraonar’ and reason are one of the most complex phenomena thought has to deal with. Here it is argued that these natural phenomena require a (...) systematic and ‘scientific’ study, and that withoutthis knowledge computer science cannot simulate people’s every-day ‘enraonar’. (shrink)

This paper looks at progressive neurological diseases showing brain decline correlated with the decline of consciousness, as well as the content of consciousness. For instance, a young man’s healthy and fully functional brain generated an intelligent and lovely self, but then an aggressive brain tumor grew deep within his brain. As the tumor grew, it rendered brain tissue dysfunction and direct effects followed. From focal destruction of brain tissue, an aphasia first results. What follows is the dissolution of a functional (...) brain, a mind, a person, and what some call a soul. From more widespread destruction of brain tissue, more functions erode until a minimally conscious state results. Intact and functional brain tissue is required to produce one’s consciousness and personality. When these brain tissues become dysfunctional and die, everything taken as the soul appears to die with them. -/- 1. Left Brain Slow Progressive Decline - 1.1 Behind the Case -- 2. Right Brain Progressive Decline -- 3. Alien Limb -- 4. Fallacious Objections -- 5. Lucid Moments, Coma Recoveries -- 6. The Correlation is Not Causation “Problem”. (shrink)

In this paper we show that the coherence measures of Olsson (J Philos 94:246–272, 2002), Shogenji (Log Anal 59:338–345, 1999), and Fitelson (Log Anal 63:194–199, 2003) satisfy the two most important adequacy requirements for the purpose of assessing theories. Following Hempel (Synthese 12:439–469, 1960), Levi (Gambling with truth, New York, A. A. Knopf, 1967), and recently Huber (Synthese 161:89–118, 2008) we require, as minimal or necessary conditions, that adequate assessment functions favor true theories over false theories and true and informative (...) theories over true but uninformative theories. We then demonstrate that the coherence measures of Olsson, Shogenji, and Fitelson satisfy these minimal conditions if we confront the hypotheses with a separating sequence of observational statements. In the concluding remarks we set out the philosophical relevance, and limitations, of the formal results. Inter alia, we discuss the problematic implications of our precondition that competing hypotheses must be confronted with a separating sequence of observational statements, which also leads us to discuss theory assessment in the context of scientific antirealism. (shrink)

Aristotle said that induction (epagōgē) is a proceeding from particulars to a universal, and the definition has been conventional ever since. But there is an ambiguity here. Induction in the Scholastic and the (so-called) Humean tradition has presumed that Aristotle meant going from particular statements to universal statements. But the alternate view, namely that Aristotle meant going from particular things to universal ideas, prevailed all through antiquity and then again from the time of Francis Bacon until the mid-nineteenth century. Recent (...) scholarship is so steeped in the first-mentioned tradition that we have virtually forgotten the other. In this essay McCaskey seeks to recover that alternate tradition, a tradition whose leading theoreticians were William Whewell, Francis Bacon, Socrates, and in fact Aristotle himself. The examination is both historical and philosophical. The first part of the essay fills out the history. The latter part examines the most mature of the philosophies in the Socratic tradition, specifically Bacon’s and Whewell’s. After tracing out this tradition, McCaskey shows how this alternate view of induction is indeed employed in science, as exemplified by several instances taken from actual scientific practice. In this manner, McCaskey proposes to us that the Humean problem of induction is merely an artifact of a bad conception of induction and that a return to the Socratic conception might be warranted. (shrink)

Over the past decades or so the probabilistic model of rational belief has enjoyed increasing interest from researchers in epistemology and the philosophy of science. Of course, such probabilistic models were used for much longer in economics, in game theory, and in other disciplines concerned with decision making. Moreover, Carnap and co-workers used probability theory to explicate philosophical notions of confirmation and induction, thereby targeting epistemic rather than decision-theoretic aspects of rationality. However, following Carnap’s early applications, philosophy has more recently (...) seen an increased popularity of probabilistic models in other areas concerned with the philosophical analysis of belief: there are models targeting coherence, informativeness, simplicity, and so on.In brief, the probabilistic model of belief comprises of a language, detailing the propositions about which an agent is supposed to have beliefs, and a function over the language that expresses beliefs: .. (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)

The applicability of Bayesian conditionalization in setting one’s posterior probability for a proposition, α, is limited to cases where the value of a corresponding prior probability, PPRI(α|∧E), is available, where ∧E represents one’s complete body of evidence. In order to extend probability updating to cases where the prior probabilities needed for Bayesian conditionalization are unavailable, I introduce an inference schema, defeasible conditionalization, which allows one to update one’s personal probability in a proposition by conditioning on a proposition that represents a (...) proper subset of one’s complete body of evidence. While defeasible conditionalization has wider applicability than standard Bayesian conditionalization (since it may be used when the value of a relevant prior probability, PPRI(α|∧E), is unavailable), there are circumstances under which some instances of defeasible conditionalization are unreasonable. To address this difficulty, I outline the conditions under which instances of defeasible conditionalization are defeated. To conclude the article, I suggest that the prescriptions of direct inference and statistical induction can be encoded within the proposed system of probability updating, by the selection of intuitively reasonable prior probabilities. (shrink)