1. Deductive and Inductive Inference. Within the traditional treatments of scientific method, e.g., in and, it was customary to divide scientific inference into two parts: deductive and inductive. Deductive inference was taken to mean the activity of deducing theorems from postulates and definitions, whereas inductive inference represented the activity of constructing a general statement from a set of particular “facts.” Deductive inference was relegated to the mathematical sciences, and inductive inference to the empirical sciences. As a consequence, the whole of (...) science was split into two quite distinct parts: deductive science was conceived to start with precise axioms, postulates, and definitions, and its method consisted in drawing inferences from these “givens” in such a way that if the original assumptions are taken as true, then the theorems must be taken as true also. The obligation behind this “must” of the mathematical sciences was an obligation based on strict rules of deductive inference; in the earlier analyses, it was supposed that these rules were all aspects of the general theory of the syllogism, as it was described in an almost complete form in but in later work the rules have been formalized in more general terms. Inductive inference, on the other hand, was supposed to start with observed facts; these facts, or “data,” were presumably given by the senses, and described particular aspects of the external world. If the facts were given in a certain way, then the empirical scientist could “infer” a generalized description; this generalization had the characteristic that if it were granted as true, then all the facts could be deduced as consequences. The inductive process admittedly does not lead to unique generalizations, and the philosopher of science searched for other defining characteristics of good inference, such as “simplicity” and “convenience.” These empirical generalizations were taken to be “descriptions of the phenomenal world of the scientist”; a further inductive step might be taken by constructing a set of very general principles out of the more specialized generalizations within specific research problems. These “higher” inductive inferences were regarded as “theories,” which could be studied by themselves within the method of deductive inference. The scientist was then described as “checking” theory by determining whether or not the predicted consequences deduced from theory actually hold in the phenomenal world. (shrink)

CL diagrams – the abbreviation of Cubus Logicus – are inspired by J.C. Lange’s logic machine from 1714. In recent times, Lange’s diagrams have been used for extended syllogistics, bitstring semantics, analogical reasoning and many more. The paper presents a method for testing statistical syllogisms (also called proportional syllogisms or inductive syllogisms) by using CL diagrams.

A general form is proposed for epistemological theories, the relevant factors being: the family of epistemic judgments, the epistemic state, the epistemic commitment , and the family of possible epistemic inputs . First a simple theory is examined in which the states are probability functions, and the subject of probability kinematics introduced by Richard Jeffrey is explored. Then a second theory is examined in which the state has as constituents a body of information and a recipe that determines the accepted (...) epistemic judgments on the basis of this corpus. Through an examination of several approaches to the statistical syllogism, a relation is again established with Jeffrey's generalized conditionalization. (shrink)

A general form is proposed for epistemological theories, the relevant factors being: the family of epistemic judgments, the epistemic state, the epistemic commitment, and the family of possible epistemic inputs. First a simple theory is examined in which the states are probability functions, and the subject of probability kinematics introduced by Richard Jeffrey is explored. Then a second theory is examined in which the state has as constituents a body of information and a recipe that determines the accepted epistemic judgments (...) on the basis of this corpus. Through an examination of several approaches to the statistical syllogism, a relation is again established with Jeffrey's generalized conditionalization. (shrink)

Probabilities are important in belief updating, but probabilistic reasoning does not subsume everything else (as the Bayesian would have it). On the contrary, Bayesian reasoning presupposes knowledge that cannot itself be obtained by Bayesian reasoning, making generic Bayesianism an incoherent theory of belief updating. Instead, it is indefinite probabilities that are of principal importance in belief updating. Knowledge of such indefinite probabilities is obtained by some form of statistical induction, and inferences to non-probabilistic conclusions are carried out in accordance (...) with the statistical syllogism. Such inferences have been the focus of much attention in the nonmonotonic reasoning literature, but the logical complexity of such inference has not been adequately appreciated. (shrink)

The objective Bayesian view of proof (or logical probability, or evidential support) is explained and defended: that the relation of evidence to hypothesis (in legal trials, science etc) is a strictly logical one, comparable to deductive logic. This view is distinguished from the thesis, which had some popularity in law in the 1980s, that legal evidence ought to be evaluated using numerical probabilities and formulas. While numbers are not always useful, a central role is played in uncertain reasoning by the (...) ‘proportional syllogism’, or argument from frequencies, such as ‘nearly all aeroplane flights arrive safely, so my flight is very likely to arrive safely’. Such arguments raise the ‘problem of the reference class’, arising from the fact that an individual case may be a member of many different classes in which frequencies differ. For example, if 15 per cent of swans are black and 60 per cent of fauna in the zoo is black, what should I think about the likelihood of a swan in the zoo being black? The nature of the problem is explained, and legal cases where it arises are given. It is explained how recent work in data mining on the relevance of features for prediction provides a solution to the reference class problem. (shrink)

This article sketches a theory of objective probability focusing on nomic probability, which is supposed to be the kind of probability figuring in statistical laws of nature. The theory is based upon a strengthened probability calculus and some epistemological principles that formulate a precise version of the statistical syllogism. It is shown that from this rather minimal basis it is possible to derive theorems comprising (1) a theory of direct inference, and (2) a theory of induction. The (...) theory of induction is not of the familiar Bayesian variety, but consists of a precise version of the traditional Nicod Principle and its statistical analogues. (shrink)

In attempting to form rational personal probabilities by direct inference, it is usually assumed that one should prefer frequency information concerning more specific reference classes. While the preceding assumption is intuitively plausible, little energy has been expended in explaining why it should be accepted. In the present article, I address this omission by showing that, among the principled policies that may be used in setting one’s personal probabilities, the policy of making direct inferences with a preference for frequency information for (...) more specific reference classes yields personal probabilities whose accuracy is optimal, according to all proper scoring rules, in situations where all of the relevant frequency information is point-valued. Assuming that frequency information for narrower reference classes is preferred, when the relevant frequency statements are point-valued, a dilemma arises when choosing whether to make a direct inference based upon relatively precise-valued frequency information for a broad reference class, R, or upon relatively imprecise-valued frequency information for a more specific reference class, R*. I address such cases, by showing that it is often possible to make a precise-valued frequency judgment regarding R* based on precise-valued frequency information for R, using standard principles of direct inference. Having made such a frequency judgment, the dilemma of choosing between and is removed, and one may proceed by using the precise-valued frequency estimate for the more specific reference class as a premise for direct inference. (shrink)

It is well known that there are, at least, two sorts of cases where one should not prefer a direct inference based on a narrower reference class, in particular: cases where the narrower reference class is gerrymandered, and cases where one lacks an evidential basis for forming a precise-valued frequency judgment for the narrower reference class. I here propose (1) that the preceding exceptions exhaust the circumstances where one should not prefer direct inference based on a narrower reference class, and (...) (2) that minimal frequency information for a narrower (non-gerrymandered) reference class is sufficient to yield the defeat of a direct inference for a broader reference class. By the application of a method for inferring relatively informative expected frequencies, I argue that the latter claim does not result in an overly incredulous approach to direct inference. The method introduced here permits one to infer a relatively informative expected frequency for a reference class R', given frequency information for a superset of R' and/or frequency information for a sample drawn from R'. (shrink)

Probabilistic inference from frequencies, such as "Most Quakers are pacifists; Nixon is a Quaker, so probably Nixon is a pacifist" suffer from the problem that an individual is typically a member of many "reference classes" (such as Quakers, Republicans, Californians, etc) in which the frequency of the target attribute varies. How to choose the best class or combine the information? The article argues that the problem can be solved by the feature selection methods used in contemporary Big Data science: the (...) correct reference class is that determined by the features relevant to the target, and relevance is measured by correlation (that is, a feature is relevant if it makes a difference to the frequency of the target). (shrink)

In this study, we examine the belief bias effect in syllogistic reasoning under both standard presentation and in a condition where participants are required to respond within 10 seconds. As predicted, the requirement for rapid responding increased the amount of belief bias observed on the task and reduced the number of logically correct decisions, both effects being substantial and statistically significant. These findings were predicted by the dual-process account of reasoning, which posits that fast heuristic processes, responsible for belief bias, (...) compete with slower analytic processes that can lead to correct logical decisions. Requiring rapid responding thus differentially inhibits the operation of analytic reasoning processes, leading to the results observed. (shrink)

We present an analytical study that puts forward a hypothesis about the role of analogy in thinking. The article presents a critique of the structural mapping hypothesis in analogy as an explanation of the analogical argument and will offer an alternative explanation — the functional hypothesis of the analogical argument. It will also be shown how such functions of thinking as recognition and memory, metaphor and syllogism, generalization and ontology, deduction and induction can be realized with the help of (...) the analogy method developed by the author. The article puts forward a hypothesis that these different functions are nothing more than different manifestations of one mechanism for the dissemination of thinking patterns through analogy.In the previous article [1] we described the results of experiments on obtaining analogs of words based on the statistics of predicates extracted from texts by a simple parser. In this article, continuing the topic of analogy, we will analyze two aspects:- how similar expressions (analogous argument) are found when solving problems and learning;- what is the role of analogy in thinking, namely, what thinking processes are realized with the help of analogy.The article critically examines the most well-known approaches to explaining and attempting to implement analogy. The authors propose another hypothesis, called functional analogy, which is distinguished by the simplicity of explaining the analogical argument, greater correspondence to examples of analogy, in the authors’ opinion, and the possibility of programmatic implementation. (shrink)

The aim of the article is to present the results of research conducted as part of the project Polonica Philosophica Orientalia: namely, to give an overview of the most important logical and metaphysical treatises written in Vilnius between the sixteenth and eighteenth centuries that are currently accessible in some of the Vilnius libraries. Although the research focused primarily on the Vilnius University Library and its resources, some interesting results were also obtained while researching the Wróblewski Library of the Lithuanian Academy (...) of Sciences. Most sources containing information about the state and the nature of metaphysical and logical investigations conducted in Vilnius during the period discussed are the manuscripts of lecture courses delivered for the students of Vilnius University and other schools. The analysis of those manuscripts has revealed a strong and long-lasting influence of scholastic Aristotelianism in both logic and metaphysics. Namely, up to the mid-eighteenth century, the main questions discussed in logic were Aristotelian syllogism, the square of opposition and the medieval topics of semantical antinomies, modalities and supposition theory, while investigations into metaphysical issues were limited to commentaries on Aristotle’s theoretical treatises without seriously questioning their main theses. In the second part of the eighteenth century, a moderate shift towards subjectivism and psychologism was observed in both of these disciplines. This was influenced by modern epistemologists. Logicians and metaphysicians of Vilnius University developed an interest in the topics of human understanding and cognition. However, this shift did not take a radical form – while the majority of eighteenth-century authors sought a combination of scholastic and modern ideas, a critical and even hostile stance towards modern philosophy and science is still noticeable in many of the analysed sources. An overview of the research supported by statistical data is followed by some preliminary remarks on how and where investigation of this topic might be continued in the future. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:@ @ Notes and Dlscussaons A NOTE ON CHARLES PEIRCE'S THEORY OF INDUCTION By "Peirce's theory of induction," I refer to a system or collection of ideas which Peirce formulated about the nature and validity of inductive inference or inductive reasoning. This system or collection of ideas covers Peirce's writings from 1867 to 1905.1 During this period of his long philosophical career from 1857 to 1914, Peirce wrote his (...) most important papers on the logic of science and probability. ~ These papers, though only a minor portion of Peirce's philosophical works, constitute a self-explanatory unit of study, simply because they deal with one single subject: the validity of synthetic inference. In the year 1867, Peirce wrote his paper "On the Natural Classification of Arguments," which provides a natural introduction to his treatment of inference and its validity in syllogistic terms and to his trichotomy of inference into deduction, induction, and hypothesis. Through the year 1877 to 1878, Peirce wrote a series of papers on "Illustrations of the Logic of Science." Beside the well-known "The Fixation of Belief" and "How to Make our Ideas Clear," there are four other important but comparatively little discussed papers which are essentially concerned with the logic of science and probability. They are in the following order: "Doctrine of Chances" (with corrections, 1893 and notes, 1910), "The Probability of Induction" (with corrections, 1893), "Deduction, Induction, and Hypothesis" (with corrections, 1893), and "The Order of Nature." In these papers, Peirce laid out his rationale for the validity of ampliative or synthetic inference and indicated a justification of induction in terms of probability. He also made explicit his conception of probabilty in terms of empirical frequency. But very often his ideas concerning the validity of synthetic inference appear disconnected and do not fit into a consistent, not to say wellorganized, whole. It was not until 1883 that Peirce wrote a comparatively systematic treatise on his general theory concerning the validity of ampliative or synthetic inference. This is his "A Theory of Probable inference," in which we find Peirce's statement of what a probable inference is and his argument that inductive inference is valid on account of its being a probable inference. After the year 1883, Peirce's philosophical writings appear to bear little upon his earlier problems in logic of science and probubility. But here and there we find a variety of topics under which Peirce touched the problem of justifying kinds of inference. One significant feature among these is Peirce's recurrent distinction between kinds of induction, a distinction which he had never made in his earlier writings. The distinction is between a "crude induction" (or "pooh-pooh" argument ), a "quantitative induction," and a "qualitative induction." This distinc1See the "Chronological Listing of Peirce's Papers Directly Bearing upon Induction and Probability" in the appendix. 2The earfiest of his papers which we have is dated 1857,and his philosophical activity continued until his death in 1914. [361] 362 HISTORY OF PHILOSOPHY tion is found in the following three short papers: "Three Kinds of Induction" (from "The Logic of Drawing History from Ancient Documents," 1901), "Kinds of Induction" (1903), and "The Varieties and Validity of Induction," (c. 1905). What Peiree calls a "crude induction" is an inference which concludes a universal generalization from what has been found in common in a group of instances. It is induction by simple enumeration. A quantitative induction is an inference from our knowledge of a statistical proportion of individual things having a certain character in a given sample to a conclusion regarding that in the population, from which the sample is chosen. ~ A qualitative induction, on the other hand, is a method of ascertaining factual truths by postulating hypotheses and confirming them on the basis of relevant evidences. That all these three forms of inference are considered induction by Peirce is due to the fact that they do not usually have the form of deduction, and they usually give rise to generalizations which are not deductively warranted by their premises. They differ, nevertheless, because they have different bases for generalizations and their generalizations have different contents. 4 In the light of Peirce's distinction between these three forms... (shrink)

This article explores the domain of legal analysis and its methodologies, emphasising the significance of generalisation in legal systems. It discusses the process of generalisation in relation to legal concepts and the development of ideal concepts that form the foundation of law. The article examines the role of logical induction and its similarities with semantic generalisation, highlighting their importance in legal decision-making. It also critiques the formal-deductive approach in legal practice and advocates for more adaptable models, incorporating fuzzy logic, non-monotonic (...) defeasible reasoning, and artificial intelligence. The potential application of neural networks, specifically deep learning algorithms, in legal theory is also discussed. The article discusses how neural networks encode legal knowledge in their synaptic connections, while the syllogistic model condenses legal information into axioms. The article also highlights how neural networks assimilate novel experiences and exhibit evolutionary progression, unlike the deductive model of law. Additionally, the article examines the historical and theoretical foundations of jurisprudence that align with the basic principles of neural networks. It delves into the statistical analysis of legal phenomena and theories that view legal development as an evolutionary process. The article then explores Friedrich Hayek’s theory of law as an autonomous self-organising system and its compatibility with neural network models. It concludes by discussing the implications of Hayek’s theory on the role of a lawyer and the precision of neural networks. (shrink)

Intuition in medical and moral reasoning -- Moral intuitionism -- The place of Aristotelian phronesis in clinical reasoning -- Aristotle's practical syllogism: accounting for the individual through a theory of action and cognition -- Individual and statistical physiognomy: the art and science of making the invisible visible -- Clinical intuition versus statistical reasoning -- Contingency and correlation: the significance of modeling clinical reasoning on statistics -- Abduction: the intuitive support of clinical induction -- Conclusion: medical ethics beyond (...) ontology. (shrink)

What good is logic? -- Seventeen ways this book is different -- The two logics -- All of logic in two pages : an overview -- The three acts of the mind -- I. The first act of the mind : understanding -- Understanding : the thing that distinguishes man from both beast and computer -- Concepts, terms and words -- The problem of universals -- The comprehension and extension of terms -- II. Terms -- Classifying terms -- Categories -- (...) Predicables -- Division -- III. Material fallacies -- Fallacies of language -- Fallacies of diversion -- Fallacies of oversimplification -- Fallacies of argumentation -- Inductive fallacies -- Procedural fallacies -- Metaphysical fallacies -- Short story : love is a fallacy -- IV. Definition -- The nature of definition -- The rules of definition -- The kinds of definition -- The limits of definition -- V. Second act of the mind : judgment -- Judgments, propositions, and sentences -- What is truth? -- The four kinds of categorical propositions -- Logical form -- Euler's circles -- Tricky propositions -- The distribution of terms -- VI. Changing propositions -- Immediate inference -- Conversion -- Obversion -- Contraposition -- VII. Contradiction -- What is contradiction? -- The square of opposition -- Existential import -- Tricky propositions on the square -- Some practical uses of the square of opposition -- VIII. The third act of the mind : reasoning -- What does reason mean? -- The ultimate foundations of the syllogism -- How to detect arguments -- Arguments vs. explanations -- Truth and validity -- IX. Different kinds of arguments -- Three meanings of because -- The four causes -- A classification of arguments -- Simple argument maps -- Deductive and inductive arguments -- Combining deduction and induction : socratic method -- X. Syllogisms -- The structure and strategy of the syllogism -- The skeptics objection to the syllogism -- The empiricist's objection to the syllogism -- Demonstrative syllogisms -- How to construct convincing syllogisms -- XI. Checking syllogisms for validity -- By Euler's circles -- By Aristotle's six rules -- Barbara Celarent : mood and figure -- Venn diagrams -- XII. More difficult syllogisms -- Enthymemes : abbreviated syllogisms -- Sorites : chain syllogisms -- Epicheiremas : multiple syllogisms -- Complex argument maps -- XIII. Compound syllogisms -- Hypothetical syllogisms -- Reductio ad absurdum arguments -- The practical syllogism : arguing about means and ends -- Disjunctive syllogisms -- Conjunctive syllogisms -- Dilemmas -- XIV. Induction -- What is induction? -- Generalization -- Causal induction : Mill's methods -- Scientific hypotheses -- Statistical probability -- Arguments from analogy -- A fortiori and a minore arguments -- XV. Some practical applications of logic -- How to write a logical essay -- How to write a socratic dialogue -- How to have a socratic debate -- How to use socratic method on difficult people -- How to read a book socratically -- XVI. Some philosophical applications of logic -- Logic and theology -- Logic and metaphysics -- Logic and cosmology -- Logic and philosophical anthropology -- Logic and epistemology -- Logic and ethics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Medieval Heritage in Early Modern Metaphysics and Modal Theory, 1400–1700Jean-Pascal AnfrayRussell L. Friedman and Lauge O. Nielsen, editors. The Medieval Heritage in Early Modern Metaphysics and Modal Theory, 1400–1700. Dordrecht: Kluwer, 2003. Pp. vi + 346. Cloth, $149.00.This volume contains contributions that aim to show the continuity between late medieval thought and early modern philosophy, or, as the editors say, to investigate "the way that medieval thought (...) served as a fertile basis for developments in the early modern period" (3). As the title indicates, most papers treat topics more or less connected to modalities, either from a logical or from an ontological point of view. The nature of modalities is indeed at the core of metaphysics and philosophical theology. Ludger Honnefelder, Joël Biard, and Fabrizio Mondori all show the influence of Duns Scotus on the setting of modern metaphysics. The importance of theological matters in the development of philosophical thought has been acknowledged for a long time. Thus Chris Schabel ("Divine Foreknowledge and Human Freedom: Auriol, Pomponazzi, and Luther on 'Scholastic Subtleties'") sketches the story of the controversy over God's foreknowledge and future contingents from its setting in the early fourteenth century to Lutheran Reformation. He stresses the underestimated influence of Peter Auriol in this continuing debate. Still, revealed theology too exercised influence on the philosophy of logic. Trinity constitutes an until now little studied case, which is the subject matter of Simo Knuuttila's contribution ("The Question of the Validity of Logic in Late Medieval Thought"). He partly rehearses some of his well-known theses about the source of logical truths and modalities and analyses the constructivist aspects of Descartes's position, in so far as the laws of logic are said to depend on God's will. But the most original part of the study bears on the effects of Trinitarian constraints within the field of logic, especially in syllogistics. Medieval thinkers had to cope with syllogisms like: "The divine essence is the father; the divine essence is the Son; therefore the Son is the Father." In order to avoid the absurdity of the conclusion, many answers were elaborated: Robert Holcot removed the Trinity from the domain of validity of syllogistics, thereby relativizing it. Luther's claim that the principles of theology contradict those of logic looks like a radical version of this position. Adam Wodeham maintained contrariwise the universality of syllogistics: he held that the premisses are not syllogistic if they are interpreted as true (130). His account is based on the identity theory of predication and on the distinction between intensional and extensional identity, which both date back to Abelard.In the period covered by the volume, early modern scholastic, chiefly the Jesuit scholastic, holds a central place. Two articles insist on its originality and intrinsic value. Jeffrey Coombs ("The Ontological Source of Logical Possibility in Catholic Second Scholasticism") [End Page 208] analyzes the various metaphysics of modalities. He claims that three theories of the source of logical modalities were entertained during the early seventeenth century, which he labels respectively "transcendentalism," "modal voluntarism," and "divine conceptualism." All of these positions can be traced back to medieval theories; however, they received an extensive treatment in late scholastic thought. Coombs is especially illuminating when he emphasizes the importance of the grounding metaphysical structure: essences and their systematic relations through "Porphyrian trees." This generated two different accounts of the ontological status of essences: according to essentialist theories, complete Porphyrian trees are the basis of necessity and possibility, while according to a "string theories," only the logical connections between the components of the essential structure are available eternally (196).Yet the most striking novelty of the time lies in the systematization of a statistical interpretation of modalities through the "moral modalities," originating in post-Tridentine Catholic theology. In contrast to Hacking's thesis (see The Taming of Chance [Cambridge, 1990]), Sven Knebel ("The Renaissance of Statistical Modalities in Early Modern Scholasticism") contends that the concept of aleatory probability was first developed within this context. That an event-type Q is morally necessary means that Q is always the case, and that not-Q actually is never the case (236... (shrink)

Predictive algorithms are playing an increasingly prominent role in society, being used to predict recidivism, loan repayment, job performance, and so on. With this increasing influence has come an increasing concern with the ways in which they might be unfair or biased against individuals in virtue of their race, gender, or, more generally, their group membership. Many purported criteria of algorithmic fairness concern statistical relationships between the algorithm’s predictions and the actual outcomes, for instance requiring that the rate of (...) false positives be equal across the relevant groups. We might seek to ensure that algorithms satisfy all of these purported fairness criteria. But a series of impossibility results shows that this is impossible, unless base rates are equal across the relevant groups. What are we to make of these pessimistic results? I argue that none of the purported criteria, except for a calibration criterion, are necessary conditions for fairness, on the grounds that they can all be simultaneously violated by a manifestly fair and uniquely optimal predictive algorithm, even when base rates are equal. I conclude with some general reflections on algorithmic fairness. (shrink)

The paper presents a numerical interpretation of the quantifiers of traditional categorical propositions and then offers a generalization to accommodate all other numerical values. Next, it considers the implications possible on the basis of both minimum and maximum existential presuppositions; and finally, it shows that every pair of categorical premises yields multiple conclusions when appropriate minimum and maximum presuppositions are made for the terms of the premises.

This Element has two main aims. The first one is an historically informed review of the philosophy of probability. It describes recent historiography, lays out the distinction between subjective and objective notions, and concludes by applying the historical lessons to the main interpretations of probability. The second aim focuses entirely on objective probability, and advances a number of novel theses regarding its role in scientific practice. A distinction is drawn between traditional attempts to interpret chance, and a novel methodological study (...) of its application. A radical form of pluralism is then introduced, advocating a tripartite distinction between propensities, probabilities and frequencies. Finally, a distinction is drawn between two different applications of chance in statistical modelling which, it is argued, vindicates the overall methodological approach. The ensuing conception of objective probability in practice is the 'complex nexus of chance'. (shrink)

Many philosophers have pointed out that statistical evidence, or at least some forms of it, lack desirable epistemic or non-epistemic properties, and that this should make us wary of litigations in which the case against the defendant rests in whole or in part on statistical evidence. Others have responded that such broad reservations about statistical evidence are overly restrictive since appellate courts have expressed nuanced views about statistical evidence. In an effort to clarify and reconcile, I (...) put forward an interpretive analysis of why statistical evidence should raise concerns in some cases but not others. I argue that when there is a mismatch between the specificity of the evidence and the expected specificity of the accusation, statistical evidence—as any other kind of evidence—should be considered insufficient to sustain a conviction. I rely on different stylized court cases to illustrate the explanatory power of this analysis. (shrink)

This article argues that most of the approaches to the foundations of statistical mechanics have severed their link with the original foundational project, the project of demonstrating how real mechanical systems can behave thermodynamically.

This paper argues that a notion of statistical explanation, based on Salmon’s statistical relevance model, can help us better understand deep neural networks. It is proved that homogeneous partitions, the core notion of Salmon’s model, are equivalent to minimal sufficient statistics, an important notion from statistical inference. This establishes a link to deep neural networks via the so-called Information Bottleneck method, an information-theoretic framework, according to which deep neural networks implicitly solve an optimization problem that generalizes minimal (...) sufficient statistics. The resulting notion of statistical explanation is general, mathematical, and subcausal. (shrink)

The growing availability of computer power and statistical software has greatly increased the ease with which practitioners apply statistical methods, but this has not been accompanied by attention to checking the assumptions on which these methods are based. At the same time, disagreements about inferences based on statistical research frequently revolve around whether the assumptions are actually met in the studies available, e.g., in psychology, ecology, biology, risk assessment. Philosophical scrutiny can help disentangle 'practical' problems of model (...) validation, and conversely, a methodology of statistical model validation can shed light on a number of issues of interest to philosophers of science. (shrink)

These essays critically reassess the widely accepted view that statistical methods of analysis can, and do, yield causal understanding of social phenomena. They emphasize the historical, philosophical and conceptual perspectives that underlie and inform current methodological controversies.

Evidence-based medicine frequently uses statistical hypothesis testing. In this paradigm, data can only disconfirm a research hypothesis’ competitors: One tests the negation of a statistical hypothesis that is supposed to correspond to the research hypothesis. In practice, these hypotheses are often misaligned. For instance, directional research hypotheses are often paired with non-directional statistical hypotheses. Prima facie, one cannot gain proper evidence for one’s research hypothesis employing a misaligned statistical hypothesis. This paper sheds lights on the nature (...) of and the reasons for such misalignments and it provides a thorough analysis of whether they pose a threat to evidence-based medicine. The upshots are that the misalignments are often hidden for clinicians and that although some cases of misalignments can be partially counterbalanced, the overall threat is non-negligible. The counterbalances either lead to methodological inadequacy, loss of statistical power, or involve a lack of information that could be crucial for decision making. This result casts doubt on various findings of medical studies in addition to issues associated with under-powered studies or the replication crisis. (shrink)

The main thesis of the paper is that in the case of modern statistics, the differences between the various concepts of models were the key to its formative controversies. The mathematical theory of statistical inference was mainly developed by Ronald A. Fisher, Jerzy Neyman, and Egon S. Pearson. Fisher on the one side and Neyman–Pearson on the other were involved often in a polemic controversy. The common view is that Neyman and Pearson made Fisher's account more stringent mathematically. It (...) is argued, however, that there is a profound theoretical basis for the controversy: both sides held conflicting views about the role of mathematical modelling. At the end, the influential programme of Exploratory Data Analysis is considered to be advocating another, more instrumental conception of models. Introduction Models in statistics—‘of what population is this a random sample?’ The fundamental lemma Controversy about models Exploratory data analysis as a model-critical approach. (shrink)

This paper is a discussion of David Albert's approach to the foundations of classical statistical menchanics. I point out a respect in which his account makes a stronger claim about the statistical mechanical probabilities than is usually made, and I suggest what might be motivation for this. I outline a less radical approach, which I attribute to Boltzmann, and I give some reasons for thinking that this approach is all we need, and also the most we are likely (...) to get. The issue between the two accounts turns out to be one about the explanatory role probabilities play in statistical mechanics. (shrink)

Statistical mechanics involves probabilities. At the same time, most approaches to the foundations of statistical mechanics--programs whose goal is to understand the macroscopic laws of thermal physics from the point of view of microphysics--are classical; they begin with the assumption that the underlying dynamical laws that govern the microscopic furniture of the world are deterministic. This raises some potential puzzles about the proper interpretation of these probabilities.

In the last quarter of the nineteenth century, Ludwig Boltzmann explained how irreversible macroscopic laws, in particular the second law of thermodynamics, originate in the time-reversible laws of microscopic physics. Boltzmann’s analysis, the essence of which I shall review here, is basically correct. The most famous criticisms of Boltzmann’s later work on the subject have little merit. Most twentieth century innovations – such as the identification of the state of a physical system with a probability distribution on its phase space, (...) of its thermodynamic entropy with the Gibbs entropy of , and the invocation of the notions of ergodicity and mixing for the justification of the foundations of statistical mechanics – are thoroughly misguided. (shrink)

PurposeThis study investigated whether the ability to utilize statistical regularities from fluent speech and map potential words to meaning at 18-months predicts vocabulary at 18- and again at 24-months.MethodEighteen-month-olds were exposed to an artificial language with statistical regularities within the speech stream, then participated in an object-label learning task. Learning was measured using a modified looking-while-listening eye-tracking design. Parents completed vocabulary questionnaires when their child was 18-and 24-months old.ResultsAbility to learn the object-label pairing for words after exposure to (...) the artificial language predicted productive vocabulary at 24-months and amount of vocabulary change from 18- to 24 months, independent of non-verbal cognitive ability, socio-economic status and/or object-label association performance.ConclusionEighteen-month-olds’ ability to use statistical information derived from fluent speech to identify words within the stream of speech and then to map the “words” to meaning directly predicts vocabulary size at 24-months and vocabulary change from 18 to 24 months. The findings support the hypothesis that statistical word segmentation is one of the important aspects of word learning and vocabulary acquisition in toddlers. (shrink)

Routley-Meyer type ternary relational semantics are defined for relevant logics including Routley and Meyer’s basic logic B plus the reductio rule and the disjunctive syllogism. Standard relevant logics such as E and R (plus γ ) and Ackermann’s logics of ‘strenge Implikation’ Π and Π ′ are among the logics considered.