In his recent book The Advancement of Science, Philip Kitcher endorses eliminative induction, or the view that confirmation of hypotheses proceeds by the elimination of alternatives. My intention here is to critically examine Kitcher's eliminativist view of confirmation, and his rejection of the widely held Bayesian position, according to which an hypothesis H is confirmed by evidence E just in case the probability of H conditional on E is greater than the simple unconditional probability of H [i.e. p (...) > p]. Here, I will maintain that while there are aspects of the eliminative approach which Bayesianism must incorporate, as has been argued by John Earman, the eliminativism advocated by Kitcher is unsatisfactory. In addition, I will suggest that Kitcher's reasons for rejecting Bayesian confirmation theory are unconvincing and depend on an overly restrictive version of the position and that indeed Bayesianism has resources needed by an eliminativist account of confirmation. (shrink)

In his recent bookThe Advancement of Science,Philip Kitcher endorses eliminative induction, or the view that confirmation of hypotheses proceeds by the elimination of alternatives. My intention here is to critically examine Kitcher's eliminativist view of confirmation, and his rejection of the widely held Bayesian position, according to which an hypothesis H is confirmed by evidence E just in case the probability of H conditional on E is greater than the simple unconditional probability of H [i.e. p(H/E) > p(H)]. (...) Here, I will maintain that while there are aspects of the eliminative approach which Bayesianism must incorporate, as has been argued by John Earman, the eliminativism advocated by Kitcher is unsatisfactory. In addition, I will suggest that Kitcher's reasons for rejecting Bayesian confirmation theory are unconvincing and depend on an overly restrictive version of the position and that indeed Bayesianism has resources needed by an eliminativist account of confirmation. (shrink)

Eliminative induction is a method for finding the truth by using evidence to eliminate false competitors. It is often characterized as "induction by means of deduction"; the accumulating evidence eliminates false hypotheses by logically contradicting them, while the true hypothesis logically entails the evidence, or at least remains logically consistent with it. If enough evidence is available to eliminate all but the most implausible competitors of a hypothesis, then (and only then) will the hypothesis become highly confirmed. (...) I will argue that, with regard to the evaluation of hypotheses, Bayesian inductive inference is essentially a probabilistic form of induction by elimination. Bayesian induction is an extension of eliminativism to cases where, rather than contradict the evidence, false hypotheses imply that the evidence is very unlikely, much less likely than the evidence would be if some competing hypothesis were true. This is not, I think, how Bayesian induction is usually understood. The recent book by Howson and Urbach, for example, provides an excellent, comprehensive explanation and defense of the Bayesian approach; but this book scarcely remarks on Bayesian induction's eliminative nature. Nevertheless, the very essence of Bayesian induction is the refutation of false competitors of a true hypothesis, or so I will argue. (shrink)

It is argued that in deterministic contexts evidence for causal relations states whether a boundary condition makes a difference or not to a phenomenon. In order to substantiate the analysis, I show that this difference/indifference making is the basic type of evidence required for eliminative induction in the tradition of Francis Bacon and John Stuart Mill. To this purpose, an account of eliminative induction is proposed with two distinguishing features: it includes a method to establish the (...) causal irrelevance of boundary conditions by means of indifference making, which is called strict method of agreement, and it introduces the notion of a background against which causal statements are evaluated. Causal statements thus become three-place-relations postulating the relevance or irrelevance of a circumstance C to the examined phenomenon P with respect to a background B of further conditions. To underline the importance of evidence in terms of difference/indifference making, I sketch two areas, in which eliminative induction is extensively used in natural and engineering sciences. One concerns exploratory experiments, the other engineering design methods. Given that a method is discussed that has been used for centuries, I make no claims to novelty in this paper, but hope that the combined discussion of several topics that are still somewhat underrepresented in the philosophy of science literature is of some merit. (shrink)

We gather the following miscellaneous results in proof theory from the attic.1. 1. A provably well-founded elementary ordering admits an elementary order preserving map.2. 2. A simple proof of an elementary bound for cut elimination in propositional calculus and its applications to separation problem in relativized bounded arithmetic below S21.3. 3. Equivalents for Bar Induction, e.g., reflection schema for ω logic.4. 4. Direct computations in an equational calculus PRE and a decidability problem for provable inequations in PRE.5. 5. Intuitionistic (...) fixed point theories which are conservative extensions of HA.6. 6. Proof theoretic strengths of classical fixed points theories.7. 7. An equivalence between transfinite induction rule and iterated reflection schema over IΣn.8. 8. Derivation lengths of finite rewrite rules reducing under lexicographic path orders and multiply recursive functions.Each section can be read separately in principle. (shrink)

Peter Lipton argues that inference to the best explanation involves the selection of a hypothesis on the basis of its loveliness. I argue that in optimal cases of IBE we may be able to eliminate all but one of the hypotheses. In such cases we have a form of eliminative induction takes place, which I call ‘Holmesian inference’. I argue that Lipton’s example in which Ignaz Semmelweis identified a cause of puerperal fever better illustrates Holmesian inference than Liptonian (...) IBE. I consider in detail the conditions under which Holmesian inference is possible and conclude by considering the epistemological relations between Holmesian inference and Liptonian IBE.Keywords: Inference to the best explanation; Peter Lipton; Abduction; Holmesian inference; Eliminative induction. (shrink)

This article offers a simple technical resolution to the problem of induction, which is to say that general facts are not always inferred from observations of particular facts, but are themselves sometimes defeasibly observed. The article suggests a holistic account of observation that allows for general statements in empirical theories to be interpreted as observation reports, in place of the common but arguably obsolete idea that observations are exclusively particular. Predictions and other particular statements about unobservable facts can then (...) appear as deductive consequences of such general observation statements, rather than inductive consequences of other particular statements. This semantic shift resolves the problem by eliminating induction as a basic form of inference, and folding the justification of general beliefs into the more basic problem of perception. (shrink)

Induction–recursion is a powerful definition method in intuitionistic type theory. It extends inductive definitions and allows us to define all standard sets of Martin-Löf type theory as well as a large collection of commonly occurring inductive data structures. It also includes a variety of universes which are constructive analogues of inaccessibles and other large cardinals below the first Mahlo cardinal. In this article we give a new compact formalization of inductive–recursive definitions by modeling them as initial algebras in slice (...) categories. We give generic formation, introduction, elimination, and equality rules generalizing the usual rules of type theory. Moreover, we prove that the elimination and equality rules are equivalent to the principle of the existence of initial algebras for certain endofunctors. We also show the equivalence of the current formulation with the formulation of induction–recursion as a reflection principle given in Dybjer and Setzer 93). Finally, we discuss two type-theoretic analogues of Mahlo cardinals in set theory: an external Mahlo universe which is defined by induction–recursion and captured by our formalization, and an internal Mahlo universe, which goes beyond induction–recursion. We show that the external Mahlo universe, and therefore also the theory of inductive–recursive definitions, have proof-theoretical strength of at least Rathjen's theory KPM. (shrink)

In 1958, to refute the argument known as the theoretician's dilemma, Hempel suggested that theoretical terms might be logically indispensable for inductive systematization of observational statements. This thesis, in some form or another, has later been supported by Scheffler, Lehrer, and Tuomela, and opposed by Bohnert, Hooker, Stegmüller, and Cornman. In this paper, a critical survey of this discussion is given. Several different putative definitions of the crucial notion inductive systematization achieved by a theory are discussed by reference to the (...) properties of inductive inference. The consequences of the following differences between deductive and inductive inference are emphasized: the lack of simple transitivity properties (even in a modified sense) of inductive inference, and the failure of the inductive analogue of the converse of The Deduction Theorem. The main conclusions are: (i) Hempel's original thesis may very well be right but his argument for it is unsatisfactory, (ii) theoretical terms can be logically indispensable for a non-Hempelian kind of inductive systematization, relative to both Craigian and Ramseyan elimination, (iii) Lehrer's attempt to prove the indispensability of theoretical terms for inductive-probabilistic systematization is, as a modification of Hempelian kind of inductive-deterministic systematization, unsatisfactory, and (iv) there does not seem to be much hope of escaping the conclusion (ii), if it is true, by extending the Craigian replacement programme along the lines suggested by Cornman. (shrink)

Backward induction was one of the earliest methods developed for solving finite sequential games with perfect information. It proved to be especially useful in the context of Tom Schelling’s ideas of credible versus incredible threats. BI can be also extended to solve complex games that include an infinite number of actions or an infinite number of periods. However, some more complex empirical or experimental predictions remain dramatically at odds with theoretical predictions obtained by BI. The primary example of such (...) a troublesome game is Centipede. The problems appear in other long games with sufficiently complex structure. BI also shares the problems of subgame perfect equilibrium and fails to eliminate certain unreasonable Nash equilibria. (shrink)

In Tulving’s initial characterization, episodic memory was one of multiple memory systems. It was postulated, in pursuit of explanatory depth, as displaying proprietary operations, representations, and substrates such as to explain a range of cognitive, behavioural, and experiential phenomena. Yet the subsequent development of this research program has, paradoxically, introduced surprising doubts about the nature, and indeed existence, of episodic memory. On dominant versions of the ‘common system’ view, on which a single simulation system underlies both remembering and imagining, there (...) are no processes unique to memory to support robust generalizations with inductive potential. Eliminativism about episodic memory seems to follow from the claim that it has no dedicated neurocognitive system of its own. After identifying this under-noticed threat, we push back against modern eliminativists by surveying recent evidence that still indicates specialized mechanisms, computations, and representations that are distinctly mnemic in character. We argue that contemporary realists about episodic memory can retain lessons of the common system approach while resisting the further move to eliminativism. (shrink)

Entailment relations, introduced by Scott in the early 1970s, provide an abstract generalisation of Gentzen’s multi-conclusion logical inference. Originally applied to the study of multi-valued logics, this notion has then found plenty of applications, ranging from computer science to abstract algebra. In particular, an entailment relation can be regarded as a constructive presentation of a distributive lattice and in this guise it has proven to be a useful tool for the constructive reformulation of several classical theorems in commutative algebra. In (...) this paper, motivated by these concrete applications, we state and prove a cut-elimination result for inductively generated entailment relations. We analyse some of its consequences and describe the existing connections with analogous results in the literature. (shrink)

We apply Mints’ technique for proving the termination of the epsilon substitution method via cut-elimination to the system of Peano Arithmetic with Transfinite Induction given by Arai.

Over the last few decades Michael Dummett developed a rich program for assessing logic and the meaning of the terms of a language. He is also a major exponent of Frege's version of logicism in the philosophy of mathematics. Over the last decade, Neil Tennant developed an extensive version of logicism in Dummettian terms, and Dummett influenced other contemporary logicists such as Crispin Wright and Bob Hale. The purpose of this paper is to explore the prospects for Fregean logicism within (...) a broadly Dummettian framework. The conclusions are mostly negative: Dummett's views on analyticity and the logical/non-logical boundary leave little room for logicism. Dummett's considerations concerning manifestation and separability lead to a conservative extension requirement: if a sentence S is logically true, then there is a proof of S which uses only the introduction and elimination rules of the logical terms that occur in S. If basic arithmetic propositions are logically true-as the logicist contends-then there is tension between this conservation requirement and the ontological commitments of arithmetic. It follows from Dummett's manifestation requirements that if a sentence S is composed entirely of logical terminology, then there is a formal deductive system D such that S is analytic, or logically true, if and only if S is a theorem of D. There is a deep conflict between this result and the essential incompleteness, or as Dummett puts it, the indefinite extensibility, of arithmetic truth. (shrink)

The structure of derivations in natural deduction is analyzed through isomorphism with a suitable sequent calculus, with twelve hidden convertibilities revealed in usual natural deduction. A general formulation of conjunction and implication elimination rules is given, analogous to disjunction elimination. Normalization through permutative conversions now applies in all cases. Derivations in normal form have all major premisses of elimination rules as assumptions. Conversion in any order terminates.Through the condition that in a cut-free derivation of the sequent Γ⇒C, no inactive weakening (...) or contraction formulas remain in Γ, a correspondence with the formal derivability relation of natural deduction is obtained: All formulas of Γ become open assumptions in natural deduction, through an inductively defined translation. Weakenings are interpreted as vacuous discharges, and contractions as multiple discharges. In the other direction, non-normal derivations translate into derivations with cuts having the cut formula principal either in both premisses or in the right premiss only. (shrink)

In 1983, Valentini presented a syntactic proof of cut elimination for a sequent calculus GLSV for the provability logic GL where we have added the subscript V for “Valentini”. The sequents in GLSV were built from sets, as opposed to multisets, thus avoiding an explicit contraction rule. From a syntactic point of view, it is more satisfying and formal to explicitly identify the applications of the contraction rule that are ‘hidden’ in these set based proofs of cut elimination. There is (...) often an underly ing assumption that the move to a proof of cut elimination for sequents built from multisets is easy. Recently, however, it has been claimed that Valentini’s arguments to eliminate cut do not terminate when applied to a multiset formulation of GLSV with an explicit rule of contraction. The claim has led to much confusion and various authors have sought new proofs of cut elimination for GL in a multiset setting. Here we refute this claim by placing Valentini’s arguments in a formal setting and proving cut elimination for sequents built from multisets. The formal setting is particularly important for sequents built from multisets, in order to accurately account for the interplay between the weakening and contraction rules. Furthermore, Valentini’s original proof relies on a novel induction parameter called “width” which is computed ‘globally’. It is diffi cult to verify the correctness of his induction argument based on “width”. In our formulation however, verification of the induction argument is straight forward. Finally, the multiset setting also introduces a new complication in the the case of contractions above cut when the cut formula is boxed. We deal with this using a new transformation based on Valentini’s original arguments. Finally, we show that the algorithm purporting to show the non termi nation of Valentini’s arguments is not a faithful representation of the original arguments, but is instead a transformation already known to be insufficient. (shrink)

Abstract Theories of induction in psychology and artificial intelligence assume that the process leads from observation and knowledge to the formulation of linguistic conjectures. This paper proposes instead that the process yields mental models of phenomena. It uses this hypothesis to distinguish between deduction, induction, and creative forms of thought. It shows how models could underlie inductions about specific matters. In the domain of linguistic conjectures, there are many possible inductive generalizations of a conjecture. In the domain of (...) models, however, generalization calls for only a single operation: the addition of information to a model. If the information to be added is inconsistent with the model, then it eliminates the model as false: this operation suffices for all generalizations in a Boolean domain. Otherwise, the information that is added may have effects equivalent (a) to the replacement of an existential quantifier by a universal quantifier, or (b) to the promotion of an existential quantifier from inside to outside the scope of a universal quantifier. The latter operation is novel, and does not seem to have been used in any linguistic theory of induction. Finally, the paper describes a set of constraints on human induction, and outlines the evidence in favor of a model theory of induction. (shrink)

Falsificationism has dominated 20th century philosophy of science. It seemed to have eclipsed all forms of inductivism. Yet recent debates have revived a specific form of eliminative inductivism, the basic ideas of which go back to F. Bacon and J.S. Mill. These modern endorsements of eliminative inductivism claim to show that progressive problem solving is possible using induction, rather than falsification as a method of justification. But this common ground between falsificationism and eliminative inductivism has not (...) led to a detailed investigation into the relationship, if any, which may exist between these two methodologies. This paper reviews several versions of eliminative inductivism, establishes a natural relation between eliminative inductivism and falsificationism, which derives from the distinction between models and theories, and carries out this investigation against a case study of the construction of atom models. The result of the investigation is that falsificationism is a form of eliminative inductivism in the limit of certain constraints. (shrink)

An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Gödel-Gentzen translation of classical into intuitionistic logic, natural deduction and the normalization theorems, the sequent calculus, including cut-elimination and mid-sequent theorems, and various applications of these (...) results. The second half examines ordinal proof theory, specifically Gentzen's consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach's introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics. (shrink)

Mr. Barker examines the efforts of Keynes, Reichenbach, Carnap, Williams, Popper, Kemeny and others in their search for the rationale of experimental inference. On what paradigm of reasoning does empirical knowledge depend? Some philosophers suppose it to be induction by enumeration, others induction by elimination, but Mr. Barker sees hope in a modified version of the hypothetico-deductive method. Our knowledge, he explains, forms a’ system ‘in which the fates of various bits are bound together. Philosophers are misled when (...) they speak as if we could confirm a hypothesis that stands alone. Instead, we ought to count one hypothesis better confirmed than its rival ‘if and only if there is some system including the former and the evidence which is somehow than any system including the latter and the evidence’. Here he brings in Kemeny’s ‘logical measure’ of simplicity, read in terms of the number of ways in which two systems of hypotheses can be true in an membered universe. Mr. Barker does not go into the application of this enormous Apparat, nor does he explain the sense of ‘system’ which is supposed to go with his examples of hypotheses, e.g., ‘There’s a cat behind the sofa’. (shrink)

Mr. Barker examines the efforts of Keynes, Reichenbach, Carnap, Williams, Popper, Kemeny and others in their search for the rationale of experimental inference. On what paradigm of reasoning does empirical knowledge depend? Some philosophers suppose it to be induction by enumeration, others induction by elimination, but Mr. Barker sees hope in a modified version of the hypothetico-deductive method. Our knowledge, he explains, forms a’ system ‘in which the fates of various bits are bound together. Philosophers are misled when (...) they speak as if we could confirm a hypothesis that stands alone. Instead, we ought to count one hypothesis better confirmed than its rival ‘if and only if there is some system including the former and the evidence which is somehow than any system including the latter and the evidence’. Here he brings in Kemeny’s ‘logical measure’ of simplicity, read in terms of the number of ways in which two systems of hypotheses can be true in an membered universe. Mr. Barker does not go into the application of this enormous Apparat, nor does he explain the sense of ‘system’ which is supposed to go with his examples of hypotheses, e.g., ‘There’s a cat behind the sofa’. (shrink)

I argue for the causal character of modeling in data-intensive science, contrary to widespread claims that big data is only concerned with the search for correlations. After discussing the concept of data-intensive science and introducing two examples as illustration, several algorithms are examined. It is shown how they are able to identify causal relevance on the basis of eliminative induction and a related difference-making account of causation. I then situate data-intensive modeling within a broader framework of an epistemology (...) of scientific knowledge. In particular, it is shown to lack a pronounced hierarchical, nested structure. The significance of the transition to such “horizontal” modeling is underlined by the concurrent emergence of novel inductive methodology in statistics such as non-parametric statistics. Data-intensive modeling is well equipped to deal with various aspects of causal complexity arising especially in the higher level and applied sciences. (shrink)

Medical diagnosis has been traditionally recognized as a privileged field of application for so called probabilistic induction. Consequently, the Bayesian theorem, which mathematically formalizes this form of inference, has been seen as the most adequate tool for quantifying the uncertainty surrounding the diagnosis by providing probabilities of different diagnostic hypotheses, given symptomatic or laboratory data. On the other side, it has also been remarked that differential diagnosis rather works by exclusion, e.g. by modus tollens, i.e. deductively. By drawing on (...) a case history, this paper aims at clarifying some points on the issue. Namely: 1) Medical diagnosis does not represent, strictly speaking, a form of induction, but a type, of what in Peircean terms should be called ‘abduction’ (identifying a case as the token of a specific type); 2) in performing the single diagnostic steps, however, different inferential methods are used for both inductive and deductive nature: modus tollens, hypothetical-deductive method, abduction; 3) Bayes’ theorem is a probabilized form of abduction which uses mathematics in order to justify the degree of confidence which can be entertained on a hypothesis given the available evidence; 4) although theoretically irreconcilable, in practice, both the hypothetical- deductive method and the Bayesian one, are used in the same diagnosis with no serious compromise for its correctness; 5) Medical diagnosis, especially differential diagnosis, also uses a kind of “probabilistic modus tollens”, in that, signs (symptoms or laboratory data) are taken as strong evidence for a given hypothesis not to be true: the focus is not on hypothesis confirmation, but instead on its refutation [Pr (¬ H/E1, E2, …, En)]. Especially at the beginning of a complicated case, odds are between the hypothesis that is potentially being excluded and a vague “other”. This procedure has the advantage of providing a clue of what evidence to look for and to eventually reduce the set of candidate hypotheses if conclusive negative evidence is found. 6) Bayes’ theorem in the hypothesis-confirmation form can more faithfully, although idealistically, represent the medical diagnosis when the diagnostic itinerary has come to a reduced set of plausible hypotheses after a process of progressive elimination of candidate hypotheses; 7) Bayes’ theorem is however indispensable in the case of litigation in order to assess doctor’s responsibility for medical error by taking into account the weight of the evidence at his disposal. (shrink)

A constructivisation of the cut-elimination proof for sequent calculi for classical, intuitionistic and minimal infinitary logics with geometric rules—given in earlier work by the second author—is presented. This is achieved through a procedure where the non-constructive transfinite induction on the commutative sum of ordinals is replaced by two instances of Brouwer’s Bar Induction. The proof of admissibility of the structural rules is made ordinal-free by introducing a new well-founded relation based on a notion of embeddability of derivations. Additionally, (...) conservativity for classical over intuitionistic/minimal logic for the seven (finitary) Glivenko sequent classes is here shown to hold also for the corresponding infinitary classes. (shrink)

In this response, I begin by defending and clarifying the notion of concept proposed in Doing without Concepts (Machery 2009) against the alternatives proposed by several commentators. I then discuss whether psychologists and philosophers who theorize about concepts are talking about distinct phenomena or about different aspects of the same phenomenon, as argued in some commentaries. Next, I criticize the idea that the cognitive-scientific findings about induction, categorization, concept combination, and so on, could be explained by positing a single (...) kind of concept, and I insist that many categories (substances, types of events, etc.) are represented by distinct coreferential concepts that belong to very different kinds of concept. This is followed by an assessment of the hybrid theories of concepts offered by commentators, according to which categories, substances, and types of events are represented by hybrid concepts made of several parts. Finally, I defend the proposal that it may be useful to eliminate concept from the theoretical vocabulary of psychology. (shrink)

In this paper I discuss Newton's first optical paper. My aim is to examine the type of argument which Newton uses in order to convince his readers of the truth of his theory of colors. My claim is that this argument is an induction by elimination, and that the Newtonian method of justification is a kind of “generative justification”, a term due to T. Nickles. To achieve my aim I analyze in some detail the arguments in Newton's first optical (...) paper, relating the paper with Newton's other writings in optics, and especially his early correspondence in defence of his theory of colors. (shrink)

La théorie des jeux évolutionnaires s'oppose à la théorie des jeux classique en ce qu 'elle élimine les raisonnements des joueurs. Peut-elle dépasser les apories de la théorie classique ? Mais en reconsidérant le raisonnement classique d'induction rétrograde, en y introduisant des possibilités de révision, on évite son aspect paradoxal. L'intérêt de la théorie des jeux évolutionnaires est donc surtout de simuler l'évolution d'interactions dans des populations.Evolutionary game theory does not take into account reasoning players, in contrast with classical (...) game theory. Can it overcome some drawbacks of classical theory ? If we reconsider the backward induction reasoning, and if introduce the possibility of revising, paradoxes and drawbacks disappear. So the main interest of evolutionary game theoiy consists in the simulation of evolution of interactions among populations. (shrink)

An ongoing debate in Catholic bioethical circles today centers around the liceity of inducing labor in a woman with a healthy previable fetus in order to save her life. Many Catholic bioethicists have defended the view that such inductions are morally licit even though the fetus itself has no medical issues and it is the combination of the pregnancy along with a weakened heart of the mother that is causing problems. Typically the basis for this view is the procedure’s satisfaction (...) of the four criteria of the principle of double effect, namely: the act itself is not evil, the evil effect is not intended, the evil effect is not produced by means of the good effect, and there is proportionate reason for the procedure. A few Catholic bioethicists have worried that the procedure does not satisfy the fourth criterion, the principle of proportionate reason. Here I present arguments showing that it is also unlikely to satisfy the first criterion, that the act itself is not evil. This hinges on the principle that it is only permissible to perform acts from which evil effects follow necessarily when such acts only directly target a pathology. Fortunately such vital conflict cases are rare and hopefully medical advances will eliminate them. (shrink)

Auguste Comte's doctrine of the three phases through which sciences pass (the theological, the metaphysical, and the positive) allows us to explain what John Stuart Mill was attempting in his magnum opus, the System of Logic: namely, to move the science of logic to its terminal and 'positive' stage. Both Mill's startling account of deduction and his unremarked solution to the Humean problem of induction eliminate the notions of necessity or force—in this case, the 'logical must'—characteristic of a science's (...) metaphysical stage. Mill's treatment had a further surprising payoff: his solution to the Problem of Necessity (what today we call the problem of determinism and freedom of the will). (shrink)

Roy A. Sorensen has advanced an ingenious variation of the prediction or surprise event paradox, which he calls the designated student paradox. Sorensen reduces the temporal dimension of the problem by eliminating reference to future occasions on which an announced surprise event might occur, and substituting a surprise location to which epistemic agents have progressively limited spatial-perceptual access, in order to sidestep what he regards as inessential solutions to the standard formulation.

This chapter contains sections titled: Introduction The Reform of Philosophy and its Practitioners A Method of Discovery: From Rhetoric to Science The Doctrine of Idols Eliminative Induction Truth.

English abstract: Feminist philosophers of science have argued that various biases can and do influence the results of scientific investigations. Two kinds of arguments have been most influential: On the one hand, it has been argued that biased assumptions frequently bridge the gap between observation and theory associated with ‘the underdetermination thesis’. On the other hand, it has been argued that biased value judgments determine when the evidence in favor of a particular theory is considered sufficiently strong for the theory (...) to be accepted as true. This paper argues that bias can influence the results of scientific investigations via a third route. Briefly, biases can and do influence which theories are seriously proposed and considered in scientific communities, which in turn leads to otherwise promising theories being ignored when scientists are choosing between such theories. In the final section, I suggest that this result speaks in favor of taking a quite radical approach to eliminating unwanted biases in science. (shrink)

There is now a well-established distinction recognized in the ways simplicity considerations enter into science. Laws of nature may be graded either with regard to their simplicity of form or with regard to the fewness of the concepts employed to express them. I shall distinguish these as formal simplicity and conceptual simplicity respectively. Dr. J. O. Wisdom suggests that it should be fewness of non-instantial concepts that serves as the guide for making judgements of relative simplicity; a “non-instantial” concept being (...) a concept which is constructed for the purpose of theory, its meaning not being derived simply from experience. Hence non-instantial concepts are, from a logical point of view, to be contrasted with the concepts used to express and record observations directly, that is with instantial concepts representing observables. This seems to be too narrow a restriction on the reduction of concepts. Clearly an advance towards simplicity has been made not only when e.g. a non-instantial concept like “force of gravity” is eliminated from our technical language, but also when the number of instantial concepts is reduced by redefinition, in terms of a smaller number of observables. For example a great simplification was surely made when space-traversed, time taken and mass were chosen as the dynamic “simples”, for the multiplicity of kinds of motion were found to be expressible as functions of these concepts. “Motion” is not non-instantial in the same way as “force of gravity” or “kinetic energy” is non-instantial. However, once this extension to instantial concepts is made there is no need to quarrel with the form/concept distinction as marking a pritma facie difference in criteria of some methodological importance; for a choice say to concentrate on using the fewest concepts does, and one would be inclined to think must , lead to a “decrease” in the formal simplicity of the laws of nature. (shrink)

Almost all words are the names of categories. We can learn most of our words (and hence our categories) from dictionary definitions, but not all of them. Some have to be learned from direct experience. To understand a word from its definition we need to already understand the words used in the definition. This is the “Symbol Grounding Problem” [1]. How many words (and which ones) do we need to ground directly in sensorimotor experience in order to be able to (...) learn all other words via definition alone? The answer may shed some light both on the developmental origin of word meanings and on the evolutionary origin and adaptive value of language. We used an algorithm to reduce each of our dictionaries (Longmans LDOCE, Cambridge CIDE and WordNet) to its “grounding kernel” (“Kernel”) (which turned out to be about 10% of the dictionary) by systematically eliminating.. (shrink)

Francis Bacon’s method of induction is often understood as a form of eliminative induction. The idea, on this interpretation, is to list the possible formal causes of a phenomenon and, by reference to a copious and reliable natural history, to falsify all of them but one. Whatever remains must be the formal cause. Bacon’s crucial instances are often seen as the crowning example of this method. In this article, I argue that this interpretation of crucial instances is (...) mistaken, and it has caused us to lose sight of why Bacon assigns crucial instances a special role in his quest for epistemic certainty about formal causes. If crucial instances are interpreted eliminatively, then they are subject to the two problems related to underdetermination raised by Duhem: (1) that it is impossible to be certain one has specified all of the possible alternatives and (2) that an experiment falsifies a whole theory, not just a single hypothesis in isolation. I show that Bacon anticipates and aims to dodge both of these problems by conceiving of crucial instances as working, in the ideal case, through direct affirmations that are supported by links to more foundational knowledge. (shrink)

Note: Sections at a more advanced level are indicated by ∞. Preface ix Acknowledgments x Introduction 1 I Nicolaus Copernicus: The Loss of Centrality 3 1 Ptolemy and Copernicus 3 2 A Clash of Two Worldviews 4 2.1 The geocentric worldview 5 2.2 Aristotle’s cosmology 5 2.3 Ptolemy’s geocentrism 9 2.4 A philosophical aside: Outlook 14 2.5 Shaking the presuppositions: Some medieval developments 17 3 The Heliocentric Worldview 20 3.1 Nicolaus Copernicus 21 3.2 The explanation of the seasons 25 3.3 (...) Copernicus and the Copernican turn 28 3.3.1 A philosophical aside: From empirical adequacy to theoretical validity 32 3.4 Copernicus consolidated: Kepler and Galileo 32 4 Copernicus was not a Scientifi c Revolutionary 37 4.1 The Copernican method 39 4.2 The relativity of motion 42 5 The Transition to Newton 43 5.1 On hypotheses 45 6 Some Philosophical Lessons 47 6.1 The loss of centrality 48 6.2 Was Copernicus a realist? 51 6.2.1 Lessons for instrumentalism and realism 52 6.3 Modern realism 55 6.4 The underdetermination of theories by evidence 58 6.4.1 The Duhem--Quine thesis 59 ∞ 6.4.2 The power of constraints 61 ∞ 6.5 Theories, models, and laws 64 ∞ 6.5.1 Theories and models 64 ∞ 6.5.2 Laws of nature, laws of science 68 ∞ 6.5.3 Philosophical views of laws 69 ∞ 6.5.3.1 The inference view 69 ∞ 6.5.3.2 The regularity view 70 ∞ 6.5.3.3 The necessitarian view 73 ∞ 6.5.3.4 The structural view 75 7 Copernicus and Scientifi c Revolutions 77 8 The Anthropic Principle: A Reversal of the Copernican Turn? 83 Reading List 87 Essay Questions 91 II Charles Darwin: The Loss of Rational Design 93 1 Darwin and Copernicus 93 2 Views of Organic Life 94 2.1 Teleology 94 2.1.1 The Great Chain of Being 97 2.1.2 Design arguments 99 2.1.3 Jean Baptiste Lamarck 104 3 Fossil Discoveries 106 3.1 Of bones and skeletons 108 3.2 The antiquity of man 110 4 Darwin’s Revolution 112 4.1 The Darwinian view of life 114 4.1.1 Principles of evolution 116 4.2 The descent of man 119 5 Philosophical Matters 124 5.1 Philosophical presuppositions: Mechanical worldview, determinism, materialism 125 5.2 From biology to the philosophy of mind 129 5.2.1 Empiricism 129 5.2.2 Philosophy of mind 132 5.2.3 Emergent minds 134 5.3 The loss of rational design 136 5.4 Intelligent design 139 6 A Question of Method 143 6.1 Darwinian inferences 143 6.2 Philosophical empiricism 147 6.3 Some principles of elimination 149 ∞ 6.4 Essential features of eliminative induction 150 6.5 Falsifi ability or testability? 155 6.6 Explanation and prediction 157 ∞ 6.7 Some models of scientifi c explanation 159 ∞ 6.7.1 Hempel’s models 160 ∞ 6.7.2 Functional models 161 ∞ 6.7.3 Causal models 163 6.7.3.1 A counterfactual-interventionist account 163 6.7.3.2 A conditional model of causation 165 ∞ 6.7.4 Structural explanations 169 6.8 A brief return to realism 172 6.9 Darwin and scientifi c revolutions 174 6.9.1 Philosophical consequences 176 Reading List 177 Essay Questions 183 III Sigmund Freud: The Loss of Transparency 185 1 Copernicus, Darwin, and Freud 185 2 Some Views of Humankind 187 2.1 Enlightenment views of human nature 188 2.2 Nietzsche’s view of human nature 190 3 Scientism and the Freudian Model of Personality 191 3.1 Freud’s model of the mind 192 3.1.1 A summary of psychoanalytic theory 192 3.1.2 Analogy with physics 195 3.1.3 Freud as an Enlightenment thinker 200 3.1.4 The scientifi c status of the Freudian model 202 3.1.4.1 Freud’s methods 202 ∞ 3.1.4.2 The method of eliminative induction, again 205 3.1.5 Freud stands between the empirical and the hermeneutic models 208 3.1.6 The role of mind in the social world 209 4 The Social Sciences beyond Freud 210 4.1 Two standard models of the social sciences -- some history 210 4.1.1 The naturalistic model 211 4.1.2 The hermeneutic model 213 4.2 Essential features of social science models 218 4.2.1 Essential features of the naturalistic model 218 4.2.2 Essential features of the hermeneutic model 221 4.3 Questions of methodology 224 ∞ 4.3.1 What is Verstehen? 225 ∞ 4.3.2 Weber’s methodology of ideal types 229 ∞ 4.3.3 Verstehen and objectivity 234 ∞ 4.4 Causation in the social sciences 236 ∞ 4.4.1 Weber on causation 236 ∞ 4.4.2 On the existence of social laws 239 4.4.3 Explanation and prediction in the social sciences 242 4.4.4 Underdetermination 243 4.4.5 Realism and relativism 244 ∞ 4.4.6 Reductionism and functionalism 248 5 Evolution and the Social Sciences 253 5.1 Sociobiology -- the fourth revolution? 254 5.2 Evolutionary psychology 257 6 Freud and Revolutions in Thought 261 6.1 Revolutions in thought vs. revolutions in science 263 Reading List 263 Essay Questions 269 Name Index 271 Subject Index 274. (shrink)

A difference-making account of causality is proposed that is based on a counterfactual definition, but differs from traditional counterfactual approaches to causation in a number of crucial respects: it introduces a notion of causal irrelevance; it evaluates the truth-value of counterfactual statements in terms of difference-making; it renders causal statements background-dependent. On the basis of the fundamental notions 'causal relevance' and 'causal irrelevance', further causal concepts are defined including causal factors, alternative causes, and importantly inus-conditions. Problems and advantages of the (...) proposed account are discussed. Finally, it is shown how the account can shed new light on three classic problems in epistemology, the problem of induction, the logic of analogy, and the framing of eliminative induction. (shrink)

Francis Bacon wrote of his method of eliminative induction that it was "a new and certain road for the mind to take" and that it would "establish degrees of certainty". I argue that Bacon's method is not certain in either of two different senses of "certain": (a) resulting in maximally justified conclusions or (b) being as secure as a deductively valid argument.

The idea that a serious threat to scientific realism comes from unconceived alternatives has been proposed by van Fraassen, Sklar, Stanford and Wray among others. Peter Lipton's critique of this threat from underconsideration is examined briefly in terms of its logic and its applicability to the case of space-time and particle physics. The example of space-time and particle physics indicates a generic heuristic for quantitative sciences for constructing potentially serious cases of underdetermination, involving one-parameter family of rivals T_m that work (...) as a team rather than as a single rival against default theory T_0. In important examples this new parameter has a physical meaning and makes a crucial _conceptual_ difference, shrinking the symmetry group and in some case putting gauge freedom, formal indeterminism vs. determinism, the presence of the hole argument, etc., at risk. Methodologies akin to eliminative induction or tempered subjective Bayesianism are more demonstrably reliable than the custom of attending only to "our best theory": they can lead either to a serious rivalry or to improved arguments for the favorite theory. The example of General Relativity vs. massive spin 2 gravity, a recent topic in the physics literature, is discussed. Arguably the General Relativity and philosophy literatures have ignored the most serious rival to General Relativity. (shrink)

The usual, comparative, conception of Inference to the Best Explanation takes it to be ampliative. In this paper I propose a conception of IBE that takes it to be a species of eliminative induction and hence not ampliative. This avoids several problems for comparative IBE. My account of Holmesian inference raises the suspicion that it could never be applied, on the grounds that scientific hypotheses are inevitably underdetermined by the evidence. I argue that this concern may be resisted (...) by acknowledging, as Timothy Williamson has shown, that all knowledge is evidence. This suggests an approach to resisting scepticism different from those that embrace fallibilism. (shrink)

Methodological norms are seen as rules defining a competitive game, and it is argued that rational recognition-seeking scientists can reach a collective agreement about which specific norms serve better their individual interests, especially if the choice is made `under a veil of ignorance', i.e. , before knowing what theory will be proposed by each scientist. Norms for theory assessment are distinguished from norms for theory choice (or inference rules), and it is argued that pursuit of recognition only affects this second (...) type of rule. An inference rule similar to `eliminative induction' is defended on the basis of such a possible agreement. According to this contractarian approach, both the explanation and the justification of scientific norms only need to refer to the preferences of individual scientists, without assuming the existence of `collective' points of view. (shrink)

Epidemiology relies upon a broad interpretation of determinism. This paper discusses analogies with the evolution of the concept of cause in physics, and analyzes the classical nine criteria proposed by Sir Austin Bradford Hill for causal assessment. Such criteria fall into the categories of enumerative induction, eliminative induction, deduction and analogy. All of these four categories are necessary for causal assessment and there is no natural hierarchy among them, although a deductive analysis of the study design is (...) preliminary to any assessment. (shrink)