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.

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)

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)

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)

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)

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)

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)

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)

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)

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)

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:@ @ 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)

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: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)

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.

One of Ian Hacking's earliest publications, this book showcases his early ideas on the central concepts and questions surrounding statistical reasoning. He explores the basic principles of statistical reasoning and tests them, both at a philosophical level and in terms of their practical consequences for statisticians. Presented in a fresh twenty-first-century series livery, and including a specially commissioned preface written by Jan-Willem Romeijn, illuminating its enduring importance and relevance to philosophical enquiry, Hacking's influential and original work has been (...) revived for a new generation of readers. (shrink)

The conspicuous similarities between interpretive strategies in classical statistical mechanics and in quantum mechanics may be grounded on their employment of common implementations of probability. The objective probabilities which represent the underlying stochasticity of these theories can be naturally associated with three of their common formal features: initial conditions, dynamics, and observables. Various well-known interpretations of the two theories line up with particular choices among these three ways of implementing probability. This perspective has significant application to debates on primitive (...) ontology and to the quantum measurement problem. (shrink)

Recent attempts to resolve the Paradox of the Gatecrasher rest on a now familiar distinction between individual and bare statistical evidence. This paper investigates two such approaches, the causal approach to individual evidence and a recently influential (and award-winning) modal account that explicates individual evidence in terms of Nozick's notion of sensitivity. This paper offers counterexamples to both approaches, explicates a problem concerning necessary truths for the sensitivity account, and argues that either view is implausibly committed to the impossibility (...) of no-fault wrongful convictions. The paper finally concludes that the distinction between individual and bare statistical evidence cannot be maintained in terms of causation or sensitivity. We have to look elsewhere for a solution of the Paradox of the Gatecrasher. (shrink)

Information theory and statistical mechanics II.

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)

In "Counterfactual Dependence and Time's Arrow", David Lewis defends an analysis of counterfactuals intended to yield the asymmetry of counterfactual dependence: that later affairs depend counterfactually on earlier ones, and not the other way around. I argue that careful attention to the dynamical properties of thermodynamically irreversible processes shows that in many ordinary cases, Lewis's analysis fails to yield this asymmetry. Furthermore, the analysis fails in an instructive way: it teaches us something about the connection between the asymmetry of overdetermination (...) and the asymmetry of entropy. (shrink)

The most compelling extant accounts of explanation casts all explanations as causal. Yet there are sciences, theoretical population biology in particular, that explain their phenomena by appeal to statistical, non-causal properties of ensembles. I develop a generalised account of explanation. An explanation serves two functions: metaphysical and cognitive. The metaphysical function is discharged by identifying a counterfactually robust invariance relation between explanans event and explanandum. The cognitive function is discharged by providing an appropriate description of this relation. I offer (...) examples of explanations from portfolio theory and population genetics that meet this characterisation. In each case the invariance relation holds between a statistical property of an ensemble and a change in structure of the ensemble. In neither case, however, does the statistical property cause the outcome it explains. There are genuine statistical, non-causal scientific explanations. (shrink)

In some cases, there appears to be an asymmetry in the evidential value of statistical and more individualized evidence. For example, while I may accept that Alex is guilty based on eyewitness testimony that is 80% likely to be accurate, it does not seem permissible to do so based on the fact that 80% of a group that Alex is a member of are guilty. In this paper I suggest that rather than reflecting a deep defect in statistical (...) evidence, this asymmetry might arise from a general constraint on rational inquiry. Plausibly the degree of evidential support needed to justify taking a proposition to be true depends on the stakes of error. While relying on statistical evidence plausibly raises the stakes by introducing new kinds of risk to members of the reference class, paradigmatically `individualized' evidence---evidence tracing back to A's voluntary behavior---can lower the stakes. The net result explains the apparent evidential asymmetry without positing a deep difference in the brute justificatory power of different types of evidence. (shrink)

In _Reliable Reasoning_, Gilbert Harman and Sanjeev Kulkarni -- a philosopher and an engineer -- argue that philosophy and cognitive science can benefit from statistical learning theory, the theory that lies behind recent advances in machine learning. The philosophical problem of induction, for example, is in part about the reliability of inductive reasoning, where the reliability of a method is measured by its statistically expected percentage of errors -- a central topic in SLT. After discussing philosophical attempts to evade (...) the problem of induction, Harman and Kulkarni provide an admirably clear account of the basic framework of SLT and its implications for inductive reasoning. They explain the Vapnik-Chervonenkis dimension of a set of hypotheses and distinguish two kinds of inductive reasoning. The authors discuss various topics in machine learning, including nearest-neighbor methods, neural networks, and support vector machines. Finally, they describe transductive reasoning and suggest possible new models of human reasoning suggested by developments in SLT. (shrink)

There are many objections to statistical discrimination in general and racial profiling in particular. One objection appeals to the idea that people have a right to be treated as individuals. Statistical discrimination violates this right because, presumably, it involves treating people simply on the basis of statistical facts about groups to which they belong while ignoring non-statistical evidence about them. While there is something to this objection—there are objectionable ways of treating others that seem aptly described (...) as failing to treat them as individuals—it needs to be articulated carefully. First, most people accept that many forms of statistical discrimination are morally unproblematic, let alone morally justified all things considered. Second, even treating people on the basis of putative non-statistical evidence relies on generalizations. Once we construe treating someone as an individual in a way that respects this fact, it becomes apparent: (1) that statistical discrimination is compatible with treating people as individuals, and (2) that one may fail to treat people as individuals even without engaging in statistical discrimination. Finally, there are situations involving the expression of messages of inclusion where we think it is good, morally speaking, that we are not treated as individuals. (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)

In a quantum universe with a strong arrow of time, it is standard to postulate that the initial wave function started in a particular macrostate---the special low-entropy macrostate selected by the Past Hypothesis. Moreover, there is an additional postulate about statistical mechanical probabilities according to which the initial wave function is a ''typical'' choice in the macrostate. Together, they support a probabilistic version of the Second Law of Thermodynamics: typical initial wave functions will increase in entropy. Hence, there are (...) two sources of randomness in such a universe: the quantum-mechanical probabilities of the Born rule and the statistical mechanical probabilities of the Statistical Postulate. I propose a new way to understand time's arrow in a quantum universe. It is based on what I call the Thermodynamic Theories of Quantum Mechanics. According to this perspective, there is a natural choice for the initial quantum state of the universe, which is given by not a wave function but by a density matrix. The density matrix plays a microscopic role: it appears in the fundamental dynamical equations of those theories. The density matrix also plays a macroscopic / thermodynamic role: it is exactly the projection operator onto the Past Hypothesis subspace. Thus, given an initial subspace, we obtain a unique choice of the initial density matrix. I call this property "the conditional uniqueness" of the initial quantum state. The conditional uniqueness provides a new and general strategy to eliminate statistical mechanical probabilities in the fundamental physical theories, by which we can reduce the two sources of randomness to only the quantum mechanical one. I also explore the idea of an absolutely unique initial quantum state, in a way that might realize Penrose's idea of a strongly deterministic universe. (shrink)

Discussions of the foundations of Classical Equilibrium Statistical Mechanics (SM) typically focus on the problem of justifying the use of a certain probability measure (the microcanonical measure) to compute average values of certain functions. One would like to be able to explain why the equilibrium behavior of a wide variety of distinct systems (different sorts of molecules interacting with different potentials) can be described by the same averaging procedure. A standard approach is to appeal to ergodic theory to justify (...) this choice of measure. A different approach, eschewing ergodicity, was initiated by A. I. Khinchin. Both explanatory programs have been subjected to severe criticisms. This paper argues that the Khinchin type program deserves further attention in light of relatively recent results in understanding the physics of universal behavior. (shrink)

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)

Machine learning methods have recently created high expectations in the climate modelling context in view of addressing climate change, but they are often considered as non-physics-based ‘black boxes’ that may not provide any understanding. However, in many ways, understanding seems indispensable to appropriately evaluate climate models and to build confidence in climate projections. Relying on two case studies, we compare how machine learning and standard statistical techniques affect our ability to understand the climate system. For that purpose, we put (...) five evaluative criteria of understanding to work: intelligibility, representational accuracy, empirical accuracy, coherence with background knowledge, and assessment of the domain of validity. We argue that the two families of methods are part of the same continuum where these various criteria of understanding come in degrees, and that therefore machine learning methods do not necessarily constitute a radical departure from standard statistical tools, as far as understanding is concerned. (shrink)

Classifying Madness (Springer, 2005) concerns philosophical problems with the Diagnostic and Statistical Manual of Mental Disorders, more commonly known as the D.S.M. The D.S.M. is published by the American Psychiatric Association and aims to list and describe all mental disorders. The first half of Classifying Madness asks whether the project of constructing a classification of mental disorders that reflects natural distinctions makes sense. Chapters examine the nature of mental illness, and also consider whether mental disorders fall into natural kinds. (...) The second half of the book addresses epistemic worries. Even supposing a natural classification system to be possible in principle, there may be reasons to be suspicious of the categories included in the D.S.M. I examine the extent to which the D.S.M. depends on psychiatric theory, and look at how it has been shaped by social and financial factors. I aim to be critical of the D.S.M. without being antagonistic towards it. Ultimately, however, I am forced to conclude that although the D.S.M. is of immense practical importance, it is unlikely to come to reflect the natural structure of mental disorders. (shrink)

This article is concerned with a statistical proposal due to James R. Beebe for how to solve the generality problem for process reliabilism. The proposal is highlighted by Alvin I. Goldman as an interesting candidate solution. However, Goldman raises the worry that the proposal may not always yield a determinate result. We address this worry by proving a dilemma: either the statistical approach does not yield a determinate result or it leads to trivialization, i.e. reliability collapses into truth (...) (and anti-reliability into falsehood). Various strategies for avoiding this predicament are considered, including revising the statistical rule or restricting its application to natural kinds. All amendments are seen to have serious problems of their own. We conclude that reliabilists need to look elsewhere for a convincing solution to the generality problem. (shrink)

Do privacy rights restrict what is permissible to infer about others based on statistical evidence? This paper replies affirmatively by defending the following symmetry: there is not necessarily a morally relevant difference between directly appropriating people’s private information—say, by using an X-ray device on their private safes—and using predictive technologies to infer the same content, at least in cases where the evidence has a roughly similar probative value. This conclusion is of theoretical interest because a comprehensive justification of the (...) thought that statistical inferences can violate privacy rights is lacking in the current literature. Secondly, the conclusion is of practical interest due to the need for moral assessment of emerging predictive algorithms. (shrink)

Thermodynamic macro variables, such as the temperature or volume macro variable, can take on a continuum of allowable values, called thermodynamic macro values. Although referring to the same macro phenomena, the macro variables of Boltzmannian Statistical Mechanics (BSM) differ from thermodynamic macro variables in an important respect: within the framework of BSM the evolution of macro values of systems with finite available phase space is invariably modelled as discontinuous, due to the method of partitioning phase space into macro regions (...) with sharp, fixed boundaries. Conceptually, this is at odds with the continuous evolution of macro values as described by thermodynamics, as well as with the continuous evolution of the micro state assumed in BSM. This discrepancy I call the discontinuity problem. I show how it arises from BSM’s framework and demonstrate its consequences, in particular for the foundational project of reducing thermodynamics to BSM: thermodynamic macro values are shown to not supervene on the corresponding BSM macro values. With supervenience being a conditio sine qua non for the kind of reduction envisaged by the foundational project, the latter is in jeopardy. (shrink)