I set up two axiomatic theories of inductive support within the framework of Kolmogorovian probability theory. I call these theories ‘Popperian theories of inductive support’ because I think that their specific axioms express the core meaning of the word ‘inductive support’ as used by Popper (and, presumably, by many others, including some inductivists). As is to be expected from Popperian theories of inductive support, the main theorem of each of them is an (...) anti-induction theorem, the stronger one of them saying, in fact, that the relation of inductive support is identical with the empty relation. It seems to me that an axiomatic treatment of the idea(s) of inductive support within orthodox probability theory could be worthwhile for at least three reasons. Firstly, an axiomatic treatment demands from the builder of a theory of inductive support to state clearly in the form of specific axioms what he means by ‘inductive support’. Perhaps the discussion of the new anti-induction proofs of Karl Popper and David Miller would have been more fruitful if they had given an explicit definition of what inductive support is or should be. Secondly, an axiomatic treatment of the idea(s) of inductive support within Kolmogorovian probability theory might be accommodating to those philosophers who do not completely trust Popperian probability theory for having theorems which orthodox Kolmogorovian probability theory lacks; a transparent derivation of anti-induction theorems within a Kolmogorovian frame might bring additional persuasive power to the original anti-induction proofs of Popper and Miller, developed within the framework of Popperian probability theory. Thirdly, one of the main advantages of the axiomatic method is that it facilitates criticism of its products: the axiomatic theories. On the one hand, it is much easier than usual to check whether those statements which have been distinguished as theorems really are theorems of the theory under examination. On the other hand, after we have convinced ourselves that these statements are indeed theorems, we can take a critical look at the axioms—especially if we have a negative attitude towards one of the theorems. Since anti-induction theorems are not popular at all, the adequacy of some of the axioms they are derived from will certainly be doubted. If doubt should lead to a search for alternative axioms, sheer negative attitudes might develop into constructive criticism and even lead to new discoveries. -/- I proceed as follows. In section 1, I start with a small but sufficiently strong axiomatic theory of deductive dependence, closely following Popper and Miller (1987). In section 2, I extend that starting theory to an elementary Kolmogorovian theory of unconditional probability, which I extend, in section 3, to an elementary Kolmogorovian theory of conditional probability, which in its turn gets extended, in section 4, to a standard theory of probabilistic dependence, which also gets extended, in section 5, to a standard theory of probabilistic support, the main theorem of which will be a theorem about the incompatibility of probabilistic support and deductive independence. In section 6, I extend the theory of probabilistic support to a weak Popperian theory of inductive support, which I extend, in section 7, to a strong Popperian theory of inductive support. In section 8, I reconsider Popper's anti-inductivist theses in the light of the anti-induction theorems. I conclude the paper with a short discussion of possible objections to our anti-induction theorems, paying special attention to the topic of deductive relevance, which has so far been neglected in the discussion of the anti-induction proofs of Popper and Miller. (shrink)

Overall, Max Black's defense of the inductive support of inductive rules succeeds. Circularity is best explained in terms of epistemic conditions of inference. When an inference is circular, another inference token of the same type may, because of a difference of surrounding circumstances, not be circular. Black's inductive arguments in support of inductive rules fit this pattern: a token circular in some circumstances may be noncircular in other circumstances.

We perceive relevance by virtue of inference habits, which may be expressed as Pierce's leading principles or as Toulmin's warrants. Hence relevance in a descriptive sense is a ternary relation between two statements and a set of inference rules. For a normative sense, the warrants must be properly backed. Different types of warrant to empirical generalizations, we introduce L.J. Cohen's notion of inductive support. A to empirical generalizations, we introduce L.J. Cohen's notion of inductive support. A (...) generalization H is supported by evidence E to degree i/in iff E indicates that H passes canonical test i, where there are n canonical tests. In a canonical test, one or more relevant variables, factors which may falsify H, are varied. H passes a test if it is not falsified. The tests are cumulative. Degree of support is relative to the canonical test, and may be modeled as relative to a point in a dialectical situation. A value of a variable at which H is falsified is a rebutting value. A is normatively relevant to B with respect to W iff sup[associated generalization(W), E] = i/n and for j > i, there is a presumption that the values of j are non-rebuting. (shrink)

Wolfgang Spohn’s paper I think clearly places him in the forefront of research on the theory of lawlikeness, and simultaneously on the methodology of inductive reasoning.

That the concepts of confirmation and requirement are very similar has recently been suggested by the discovery of four analogies between them. This conjecture is tested by comparing examples of each relation. I show that both of these relations can be "defeated" in two similar ways. But I also argue for two important dissimilarities between them: 1) when faced with certain inconsistencies, requirement suffers much more drastically than confirmation, and 2) confirmation is partiresultant in a sense in which requirement is (...) not. (shrink)

That the concepts of confirmation and requirement are very similar has recently been suggested by the discovery of four analogies between them. This conjecture is tested by comparing examples of each relation. I show that both of these relations can be "defeated" in two similar ways. But I also argue for two important dissimilarities between them: 1) when faced with certain inconsistencies, requirement suffers much more drastically than confirmation, and 2) confirmation is partiresultant in a sense in which requirement is (...) not. (shrink)

This paper seeks to defend the following conclusions: The program advanced by Carnap and other necessarians for probability logic has little to recommend it except for one important point. Credal probability judgments ought to be adapted to changes in evidence or states of full belief in a principled manner in conformity with the inquirer’s confirmational commitments—except when the inquirer has good reason to modify his or her confirmational commitment. Probability logic ought to spell out the constraints on rationally coherent confirmational (...) commitments. In the case where credal judgments are numerically determinate confirmational commitments correspond to Carnap’s credibility functions mathematically represented by so—called confirmation functions. Serious investigation of the conditions under which confirmational commitments should be changed ought to be a prime target for critical reflection. The necessarians were mistaken in thinking that confirmational commitments are immune to legitimate modification altogether. But their personalist or subjectivist critics went too far in suggesting that we might dispense with confirmational commitments. There is room for serious reflection on conditions under which changes in confirmational commitments may be brought under critical control. Undertaking such reflection need not become embroiled in the anti inductivism that has characterized the work of Popper, Carnap and Jeffrey and narrowed the focus of students of logical and methodological issues pertaining to inquiry. (shrink)

During the periods when logical positivism and ordinary language philosophy were ascendant, Brand Blanshard was defending necessity in his writing and in his teaching. The last five chapters of the second volume of The Nature of Thought, published in 1940, were devoted to necessity, and no less than four chapters of Reason and Analysis, appearing in 1962, were on the same subject. The new realism that has supplanted positivism and language philosophy on the American scene should, it would seem, be (...) sympathetic to Blanshard’s insistence that there are physical necessities. For, according to the new realism, the constituents of gross things are real entities that account for the behavior of these things. One would think that it would be recognized that this is possible only if that behavior were a necessary outcome of having those constituents. For, were it only contingent, the behavior could not genuinely be laid at the feet of those constituents. All expectations have been disappointed here, for the new realism remains uncompromisingly Humean when it comes to necessity. Necessity is still, as in the days of positivism and language philosophy, a matter of concepts or linguistic terms and not a matter of things. But if I am right that the new realism is thus far developed only in a one-sided way, then in the near future we shall see a more coherent realism that has embodied many of the features of the doctrine of necessity elaborated by Blanshard. (shrink)

Necessity holds that, if a proposition A supports another B, then it must support B. John Greco contends that one can resolve Hume's Problem of Induction only if she rejects Necessity in favor of reliabilism. If Greco's contention is correct, we would have good reason to reject Necessity and endorse reliabilism about inferential justification. Unfortunately, Greco's contention is mistaken. I argue that there is a plausible reply to Hume's Problem that both endorses Necessity and is at least as good (...) as Greco's alternative. Hence, Greco provides a good reason for neither rejecting Necessity nor endorsing inferential reliabilism. (shrink)

Elementary results concerning the connections between deductive relations and probabilistic support are given. These are used to show that Popper-Miller's result is a special case of a more general result, and that their result is not very unexpected as claimed. According to Popper-Miller, a purely inductively supports b only if they are deductively independent — but this means that a b. Hence, it is argued that viewing induction as occurring only in the absence of deductive relations, as Popper-Miller sometimes (...) do, is untenable. Finally, it is shown that Popper-Miller's claim that deductive relations determine probabilistic support is untrue. In general, probabilistic support can vary greatly with fixed deductive relations as determined by the relevant Lindenbaum algebra. (shrink)

We investigate the relative probabilistic support afforded by the combination of two analogies based on possibly different, structural similarity (as opposed to e.g. shared predicates) within the context of Pure Inductive Logic and under the assumption of Language Invariance. We show that whilst repeated analogies grounded on the same structural similarity only strengthen the probabilistic support this need not be the case when combining analogies based on different structural similarities. That is, two analogies may provide less (...) class='Hi'>support than each would individually. (shrink)

This note makes a contribution to the issue raised in a paper by Popper and Miller (1983) in which it was claimed that probabilistic support is purely deductive. Developing R. C. Jeffrey's remarks, a new general approach to the crucial concept of "going beyond" is here proposed. By means of it a quantitative measure of the inductive component of a probabilistic inference is reached. This proposal leads to vindicating the view that typical predictive probabilistic inferences by enumeration and (...) analogy are purely inductive. (shrink)

The inaugural title in the new, Open Access series BSPS Open, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference. The fundamental burden of a theory of inductive inference is to determine which are the good inductive inferences or relations of inductive support and why it is that they are so. The traditional approach is modeled on that taken in accounts of deductive inference. It seeks universally applicable schemas (...) or rules or a single formal device, such as the probability calculus. After millennia of halting efforts, none of these approaches has been unequivocally successful and debates between approaches persist. The Material Theory of Induction identifies the source of these enduring problems in the assumption taken at the outset: that inductive inference can be accommodated by a single formal account with universal applicability. Instead, it argues that that there is no single, universally applicable formal account. Rather, each domain has an inductive logic native to it. Which that is, and its extent, is determined by the facts prevailing in that domain. Paying close attention to how inductive inference is conducted in science and copiously illustrated with real-world examples, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference. (shrink)

Sections 1 through 3 present all of the main ideas behind the probabilistic logic of evidential support. For most readers these three sections will suffice to provide an adequate understanding of the subject. Those readers who want to know more about how the logic applies when the implications of hypotheses about evidence claims (called likelihoods) are vague or imprecise may, after reading sections 1-3, skip to section 6. Sections 4 and 5 are for the more advanced reader who wants (...) a detailed understanding of some telling results about how this logic may bring about convergence to the truth. (shrink)

Brouwer’s view on induction has relatively recently been characterised as one on which it is not only intuitive (as expected) but functional, by van Dalen. He claims that Brouwer’s ‘Ur-intuition’ also yields the recursor. Appealing to Husserl’s phenomenology, I offer an analysis of Brouwer’s view that supports this characterisation and claim, even if assigning the primary role to the iterator instead. Contrasts are drawn to accounts of induction by Poincaré, Heyting, and Kreisel. On the phenomenological side, the analysis provides an (...) alternative to that in Tieszen’s Mathematical Intuition, and confirms a view of Gödel on his Dialectica Interpretation. (shrink)

In this article, I argue that arguments from the history of science against scientific realism, like the arguments advanced by P. Kyle Stanford and Peter Vickers, are fallacious. The so-called Old Induction, like Vickers's, and New Induction, like Stanford's, are both guilty of confirmation bias—specifically, of cherry-picking evidence that allegedly challenges scientific realism while ignoring evidence to the contrary. I also show that the historical episodes that Stanford adduces in support of his New Induction are indeterminate between a pessimistic (...) and an optimistic interpretation. For these reasons, these arguments are fallacious, and thus do not pose a serious challenge to scientific realism. (shrink)

The basic idea by means of which Popper and Miller proved the non-existence of inductive probabilistic support in 1983/1985/1987, is used to prove that inductive probabilistic countersupport does exist. So it seems that after falsification has won over verification on the deductive side of science, countersupport wins over support on the inductive side.

What is the relation or connection between formalizations of induction and the actual inductive inferences of scientists? Building from recent works in the philosophy of logic, this paper argues that these formalizations of induction are best viewed as models and not literal descriptions of inductive inferences in science. Three arguments are put forward to support this claim. First, I argue that inductive support is the kind of phenomenon that can be justifiably modeled. Second, I argue (...) that these formalizations have the features that define models—that they have representors, artefacts, and idealizations. Third, I argue that these formalizations being models explains their plurality and revisability. (shrink)

In this paper I adduce a new argument in support of the claim that IBE is an autonomous form of inference, based on a familiar, yet surprisingly, under-discussed, problem for Hume’s theory of induction. I then use some insights thereby gleaned to argue for the claim that induction is really IBE, and draw some normative conclusions.

This work is in two parts. The main aim of part 1 is a systematic examination of deductive, probabilistic, inductive and purely inductive dependence relations within the framework of Kolmogorov probability semantics. The main aim of part 2 is a systematic comparison of (in all) 20 different relations of probabilistic (in)dependence within the framework of Popper probability semantics (for Kolmogorov probability semantics does not allow such a comparison). Added to this comparison is an examination of (in all) 15 (...) purely inductive dependence relations. ————Part 1 leads in an axiomatic step-by-step development from the elementary classical truth value semantics of a sentential-logical language, called ‘L’, (chapter 1) to the elementary Kolmogorov probability semantics of L (chapter 2), which is then extended to four axiomatic semantical theories of dependence relations between the formulae of L. First the elementary Kolmogorov probability semantics of L is extended to a theory, called ‘Kdd’, of the relations of deductive dependence and deductive independence between formulae of L (chapter 3). Then Kdd is extended to a theory, called ‘Kpd1’, of the degree to which formulae of L probabilistically depend on each other in regard to a given probability distribution on the set of all formulae of L (chapter 4). Kpd1, in its turn, gets extended to a theory, called ‘Kpd2’, of the relations of probabilistic dependence and independence, relativized to unary Kolmogorov probability functions defined on L (chapter 5). Then Kpd2 is extended to a theory, called ‘Kid’, of the relations of inductive dependence and inductive independence, again relativized to unary Kolmogorov probability functions defined on L (chapter 6). Finally, Kid is extended to a theory, called ‘Kpid’, of the relations of purely inductive positive and negative dependence, relativized to unary Kolmogorov probability functions defined on L (chapter 7). ——Chapter 1, which deals with the familiar notions of truth value functions, tautologies, consequence relations and relations of logical opposition, is naturally the shortest chapter of part 1.——In chapter 2, the elementary classical semantics of L is extended to the elementary Kolmogorov probability semantics of L, i.e. to an axiomatic theory of unary and of binary Kolmogorov probability functions defined on the set of formulae of L. Because of the elementary character of this theory, chapter 2 is also rather short.——Chapter 3 introduces the first theory on dependence relations, to wit: Kdd, the theory of deductive (in)dependence between formulae of L. I follow here the well-known idea of Popper and Miller, who have used it in a famous discussion on the nature of probabilistic support for their arguments that probabilistic support is deductive, not inductive. I develop Kdd in the form of about 100 theorems, making ample use of the fact that deductive independence is nothing but subcontrary opposition, and close with a remark on the fundamental difference between deductive and logical dependence—two relations the ideas of which are all too easily mixed up.——Chapters 4 and 5 deal extensively with the traditional ideas of probabilistic (in)dependence, applied to formulae rather than to events. As always, I proceed axiomatically in a step-by-step process under systematic viewpoints and obtain about 300 theorems in this way. In the formulation of the theorems, I took special care to state clearly and expressly so-called tacit assumptions, especially those concerning the probability values of the formulae said to be dependent on each other. These assumptions are usually missing in the literature, due either to economy of writing or to sloppiness of thinking. Presumably, both chapters contain little that is new, their value lying more in the systematic grouping and organic development of the theorems than in the newness of these.——In chapter 6, I extend the axiomatic theory about probabilistic (in)dependence which has been elaborated in chapter 5, to an axiomatic theory of inductive (in)dependence by requiring of the relation of inductive (in)dependence that it be probabilistic (in)dependence, but not also logical implication or logical opposition. I point out the differences between probabilistic and inductive (in)dependence by means of some 60 theorems and close my examination of inductive (in)dependence by considering its relationship to the notion of support in the philosophy of science.——Finally, in chapter 7, the last of part 1, I take the step from inductive dependence to what I call ‘purely inductive dependence’ by combining the idea of inductive dependence with that of deductive independence in a way which is suggested by writings of Popper and Miller. I arrive at two noteworthy theorems. Firstly, there is indeed no purely inductive support. But secondly, and perhaps amazingly, countersupport is purely inductive.————Whereas the probabilistic framework of part 1 of the present work is Kolmogorov probability semantics, the framework of part 2 is Popper probability semantics, which is not only worth examining as a fascinating alternative to orthodox Kolmogorov probability semantics, but also allows us to examine dependence relations more deeply, than Kolmogorov probability semantics does. Part 2 leads—again in an axiomatic step-by-step development—from the basic Popper probability semantics of L, called ‘Pb’, (chapter 8) via a probabilistic theory of logical attributes, called ‘Ps’, (chapter 9) to four axiomatic semantical theories of dependence relations between the formulae of L. First, Ps is extended to a theory, called ‘Pdd’, of the relations of deductive dependence and deductive independence between formulae of L (chapter 10). Then Pdd is extended to a theory, called ‘Ppd’, of (in all) 20 relations of probabilistic (in)dependence, relativized to binary Popper probability functions defined on L (chapter 11). Ppd, in its turn, is extended to a theory, called ‘Pid’, of (in all) 10 relations of inductive dependence, again relativized to binary Popper probability functions defined on L (first part of chapter 12). Finally, Pid is extended to a theory, called ‘Ppid’, of (in all) 15 relations of purely inductive positive and negative dependence, relativized to binary Popper probability functions defined on L (second part of chapter 12).——Chapter 8, the first chapter of part 2 of the present work, is entirely preparatory. It introduces the axioms and about 180 theorems (150 of them together with their proofs) of basic Popper probability semantics in order to set this kind of semantics under way.——Then, in chapter 9, basic Popper probability semantics is extended to a probabilistic theory of logical properties of and relations between the formulae of L. Although I think that the way I did this extension is of some interest in itself, the main task of chapter 9 is again a preparatory one: to yield the indispensable lemmata (about 90 in number) for the theorems concerning probabilistic dependence relations in chapter 11 and concerning inductive dependence relations in chapter 12.——Chapter 10 brings the extension of Ps to the theory Pdd of deductive (in)dependence. Only half a dozen theorems are noted here for later use in the Pdd-extensions Ppd and Ppid. In view of the over 100 theorems already gained on this topic in the Kolmogorovian framework (cf. chapter 3), a similar extensive elaboration of Pdd would have been superfluous.——Chapter 11 is the most important one of part 2. It consists of a systematic comparison of 20 probabilistic (in)dependence concepts by means of about 230 theorems, obtained within the axiomatic theory Ppd, which is built up as an extension of Pdd. The main points of comparison were: differences in logical strength; reflexivity and symmetry; behaviour under the condition that the probability values of the formulae in question are extreme. It turned out that each of the examined concepts violates a strong and straightforward version of the intuitive requirement that probabilistic dependence should go with logical dependence. Whereas the corresponding chapter 5 in part 1 of the present work may not have led to new theorems, chapter 11 yields dozens of them in the process of comparison of concepts of dependence and independence which had—as far as I know—never before been treated in a single theoretical framework. With Popper probability semantics, this framework has become available, and here I have simply made full use of it.——In chapter 12, I extend the theory Ppd of probabilistic (in)dependence to the theories Pid and Ppid of inductive and purely inductive dependence, in a way very similar to that in which I have extended the theory Kpd2 to the theories Kid and Kpid in chapters 6 and 7. The first main result of Kpid (roughly: there is no purely inductive support) could be repeated for four of the five purely inductive positive dependence relations considered in chapter 12, whereas the second main result of Kpid (roughly: there is purely inductive countersupport ) could be repeated for each of the five examined purely inductive negative dependence relations. Chapter 12 closes with a brief recapitulation and critical discussion of the main results. (shrink)

The fact that simplicity has been linked with induction by many philosophers of science, some of whom have proposed or supported criteria of “inductive simplicity,” means that the problem must be given some serious attention. I take “inductive simplicity” as a title, however, only by way of concession to these historical treatments, since it is precisely the burden of my paper to show that there is no such thing. So much for the conclusion. I shall spend the remainder (...) of my time arguing for it. (shrink)

Within analytic philosophy, induction has been seen as a problem concerning inferences that have been analysed as relations between sentences. In this article, we argue that induction does not primarily concern relations between sentences, but between properties and categories. We outline a new approach to induction that is based on two theses. The first thesis is epistemological. We submit that there is not only knowledge-how and knowledge-that, but also knowledge-what. Knowledge-what concerns relations between properties and categories and we argue that (...) it cannot be reduced to knowledge-that. We support the partition of knowledge by mapping it onto the long-term memory systems: procedural, semantic and episodic memory. The second thesis is that the role of inductive reasoning is to generate knowledge-what. We use conceptual spaces to model knowledge-what and the relations between properties and categories involved in induction. (shrink)

Within analytic philosophy, induction has been seen as a problem concerning inferences that have been analysed as relations between sentences. In this article, we argue that induction does not primarily concern relations between sentences, but between properties and categories. We outline a new approach to induction that is based on two theses. The first thesis is epistemological. We submit that there is not only knowledge-how and knowledge-that, but also knowledge-what. Knowledge-what concerns relations between properties and categories and we argue that (...) it cannot be reduced to knowledge-that. We support the partition of knowledge by mapping it onto the long-term memory systems: procedural, semantic and episodic memory. The second thesis is that the role of inductive reasoning is to generate knowledge-what. We use conceptual spaces to model knowledge-what and the relations between properties and categories involved in induction. (shrink)

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...) preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Marc Lange has criticized my assertion that relative to a Bayesian conception of inductive reasoning, Hume's argument for inductive scepticism cannot be run. I reply that the way in which Lange suggests one should run the Humean argument in a Bayesian framework ignores the fact that in Bayesian models of learning from experience, the domain of an agent's probability measure is exogenously determined. I also show that Lange is incorrect to equate probability distributions which 'support inductive (...) inferences' with probability distributions which assign probability to contingent propositions/events. (shrink)

Marc Lange argues that proofs by mathematical induction are generally not explanatory because inductive explanation is irreparably circular. He supports this circularity claim by presenting two putative inductive explanantia that are one another’s explananda. On pain of circularity, at most one of this pair may be a true explanation. But because there are no relevant differences between the two explanantia on offer, neither has the explanatory high ground. Thus, neither is an explanation. I argue that there is no (...) important asymmetry between the two cases because they are two presentations of the same explanation. The circularity argument requires a problematic notion of identity of proofs. I argue for a criterion of proof individuation that identifies the two proofs Lange offers. This criterion can be expressed in two equivalent ways: one uses the language of homotopy type theory, and the second assigns algebraic representatives to proofs. Though I will concentrate on one example, a criterion of proof identity has much broader consequences: any investigation into mathematical practice must make use of some proof-individuation principle. (shrink)

The papers collected in this volume were originally presented at a sym posium held at the University of Pennsylvania in December of 1968. Each of the papers has been revised in light of the discussions that took place during this symposium. None of the papers has appeared in print previously. The extensive bibliography that appears at the end of the volume was originally distributed during the symposium and was revised on the basis of many helpful suggestions made by those who (...) participated. The symposium was made possible by a grant from The National Science Foundation and funds contributed by the Philosophy Depart ment of the University of Pennsylvania. On behalf of the contributors to this volume, I would like to express my thanks to these organizations for their generous support. In addition, I would like to express my gratitude to the members of the Graduate Philosophy Students Organization at the University of Penn sylvania for the considerable assistance they gave me during the sym posium. My thanks, also, to Judith Sofranko and Lynn Luckett for their very responsible efforts in the preparation of the manuscript. Finally, I would like to thank Professor James Cornman for his invaluable advice and encouragement. (shrink)

The cognitive unbinding paradigm suggests that the synthesis of neural information is attenuated by general anesthesia. Here, we analyzed the functional organization of brain activities in the conscious and anesthetized states, based on functional segregation and integration. Electroencephalography recordings were obtained from 14 subjects undergoing induction of general anesthesia with propofol. We quantified changes in mean information integration capacity in each band of the EEG. After induction with propofol, mean information integration capacity was reduced most prominently in the γ band (...) of the EEG . Furthermore, we demonstrate that loss of consciousness is reflected by the breakdown of the spatiotemporal organization of γ waves. We conclude that induction of general anesthesia with propofol reduces the capacity for information integration in the brain. These data directly support the information integration theory of consciousness and the cognitive unbinding paradigm of general anesthesia. (shrink)

A two-fold challenge faces any account of inductive inference. It must provide means to discern which are the good inductive inferences or which relations capture correctly the strength of inductive support. It must show us that those means are the right ones. Formal theories of inductive inference provide the means through universally applicable formal schema. They have failed, I argue, to meet either part of the challenge. In their place, I urge that background facts in (...) each domain determine which are the good inductive inferences; and we can see that they are good in virtue of the meaning of the pertinent background facts. This material theory of induction is used to assess the competing inductive inferences in the debate in 1972 between John N. Bahcall and Halton Arp over the import of the redshift of light from the galaxies. (shrink)

First I employ Bayes's Theorem to give some precision to the atheologian's thesis that it is improbable that God exists given the amount of evil in the world (E). Two arguments result from this: (1) E disconfirms God's existence, and (2) E tends to disconfirm God's existence. Secondly, I evaluate these inductive arguments, suggesting against (1) that the atheologian has abstracted from and hence failed to consider the total evidence, and against (2) that the atheologian's evidence adduced to (...) class='Hi'>support his thesis regarding the relevant probabilities is inadequate. (shrink)

Indicators of the reliability of informants are essential for social learning in a society that is initially dominated by ignorance or superstition. Such reliability indicators should be based on meta-induction over records of truth-success. This is the major claim of this paper, and it is supported in two steps. One needs a non-circular justification of the method of meta-induction, as compared to other learning methods. An approach to this problem has been developed in earlier papers and is reported in section (...) 2. It is based on the predictive optimality of meta-inductive learning, under the assumption that objective success records are globally available. The rest of the paper develops an extension of this approach, so-called local meta-induction. Here individuals can access only success records of individuals in their immediate epistemic neighborhood. It is shown that local meta-inductive learning can spread reliable information over the entire population, and has clear advantages compared to success-independent social learning methods such as peer-imitation and authority-imitation.Send article to KindleTo send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.META-INDUCTION IN EPISTEMIC NETWORKS AND THE SOCIAL SPREAD OF KNOWLEDGEVolume 9, Issue 2Gerhard SchurzDOI: https://doi.org/10.1017/epi.2012.6Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. META-INDUCTION IN EPISTEMIC NETWORKS AND THE SOCIAL SPREAD OF KNOWLEDGEVolume 9, Issue 2Gerhard SchurzDOI: https://doi.org/10.1017/epi.2012.6Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. META-INDUCTION IN EPISTEMIC NETWORKS AND THE SOCIAL SPREAD OF KNOWLEDGEVolume 9, Issue 2Gerhard SchurzDOI: https://doi.org/10.1017/epi.2012.6Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation Request permission. (shrink)

1. Thesis: My contention is that critics can give inductive reasons in support of their evaluative judgments of art, even though making such judgments is neither the only nor the major function of a critic, even though not all evaluations which are made are such that they can be supported inductively, and even though those judgments which can be supported inductively can be understood as inductively supportable only from a philosophic perspective often rejected by the very critics who (...) make the judgments. I further argue that this rejection of inductive reasoning in criticism—and the subsequent search for new ‘logics’ of imperatives, performatives, and attitudes—is due primarily to a fundamental failure to examine the metaphysical presuppositions of judgment; more specifically, it can be shown that from the common rejection by most contemporary Anglo-American philosophers of certain metaphysical propositions, it is possible to deduce a model which displays the grounds for an inductive interpretation of critical reasoning. (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)

Studies on so-called Change Blindness and Inattentional Blindness have been taken to establish the claim that conscious perception of a stimulus requires the attentional processing of that stimulus. One might contend, against this claim, that the evidence only shows attention to be necessary for the subject to have access to the contents of conscious perception and not for conscious perception itself. This “Methodological Argument” is gaining ground among philosophers who work on attention and consciousness, such as Christopher Mole. I find (...) that, without the supporting evidence of inaccessible consciousness, this argument collapses into an indefensible form of inductive parsimony. The Methodological Argument is thus shown to be unsuccessful when used against the claim that attention is required for conscious perception, though I suggest that it may be successful against the more ambitious claim that attention is necessary for all conscious experience. (shrink)

Background: Flow states are considered a positive, subjective experience during an optimal balance between skills and task demands. Previously, experimentally induced flow experiences have relied solely on adaptive tasks. Objective: To investigate whether cathodal transcranial direct current stimulation (tDCS) over the left dorsolateral prefrontal cortex (DLPFC) area and anodal tDCS over the right parietal cortex area during video game play will promote an increased experience of flow states. Methods: Two studies had participants play Tetris or first-person shooter (FPS) video games (...) while receiving either real tDCS or sham stimulation. Tetris recruited nineteen untrained players who infrequently played video games while the ten FPS participants played FPS frequently. Flow experience was assessed before and after stimulation. Results: Compared to sham stimulation, real stimulation increased flow experience for both untrained Tetris and trained FPS players. No ceiling effects were noticed between trained and untrained groups. Conclusion: Cathodal and anodal tDCS over the left DLPFC and right parietal areas respectively may encourage flow experiences in complex real-life motor tasks that occur during sports, games and everyday life. (shrink)

Backward induction has been the standard method of solving finite extensive-form games with perfect information, notwithstanding the fact that this procedure leads to counter-intuitive results in various games. However, beginning in the late eighties, the method of backward induction became an object of criticism. It is claimed that the assumptions needed for its defence are quite implausible, if not incoherent. It is therefore natural to ask for the justification of backward induction: Can one show that rational players who know the (...) structure of the game, have trust in each other's practical rationality and reason correctly, will act in accordance in backward induction? Several researchers have tried a justification of this kind, but the argument presented in Robert Aumann's paper from 1995 is perhaps the most well-known and influential attempt to provide such a justification. Clausing provides a sustained discussion of the justification problem for backward induction. It is an excellent work and the criticism I will present below does not detract from this evaluation: the issues discussed by the author are complex and it is difficult to get everything right. Furthermore, I hope that the criticism to be presented may be instructive; Even though it has not been Clausing's intention, his logical reconstruction of Aumann's defence of backward induction allows us to see very clearly what is wrong with that argument. It also provides us with * This paper was presented at workshops in Lund and in Uppsala, in the Fall of 1999. I am indebted to the participants for their useful comments. The work on the paper was supported by a generous research grant from The Bank of Sweden Tercentenary Foundation. (shrink)

There are two important traditions in the philosophy of induction. According to one tradition, which has dominated for the last couple of centuries, inductive arguments are warranted by rules. Bayesianism is the most popular view within this tradition. Rules of induction provide functional accounts of inductive support, but no rule is universal; hence, no rule is by itself an accurate model of inductive support. According to another tradition, inductive arguments are not warranted by rules (...) but by matters of fact. Norton’s material theory of induction (MTI) is an influential view within this tradition. Norton’s MTI fails to provide an account of inductive support, but it provides a good account of inductive warrant that can help us define the domain of validity of each rule of induction. Despite their limitations, both approaches to induction are illuminating important aspects of how relations of inductive support work. In this article I present a hybrid theory of induction (HTI), in which I acknowledge and articulate the role of both rules and matters of fact in our understanding of inductive support. According to the HTI, rules of induction accurately describe relations of inductive support when they are warranted, and a rule of induction is warranted if the right facts about the matter of the induction obtain. Crucially, the HTI allows us to address the main challenges that each tradition faces while retaining their strengths, thus obtaining a functional and accurate account of inductive support. The HTI also provides a useful general framework to examine and understand induction, to make sense of how different rules of induction can coexist and to tackle some problems in epistemology. Moreover, the HTI allows us to clarify and resolve some current debates on induction, like the apparent divide between Norton and rule-based theorists. (shrink)

Inductive reasoning, initially identified with enumerative induction is nowadays commonly understood more widely as any reasoning based on only partial support that the premises give to the conclusion. This is a tad too sweeping, for this includes any inconclusive reasoning. A more moderate and perhaps more adequate characterization requires that inductive reasoning not only includes generalizations, but also any predictions or explanations obtained in absence of suitable deductive premises. Inductive logic is meant to provide guidance in (...) choosing the most supported from a given assembly of conjectures. (shrink)

In his essay on 'Broad on Induction and Probability' (first published in 1959, reprinted in this volume), Professor G. H. von Wright writes: "If Broad's writings on induction have remained less known than some of his other contributions to philosophy . . . , one reason for this is that Broad never has published a book on the subject. It is very much to be hoped that, for the benefit of future students, Broad's chief papers on induction and probability will (...) be collected in a single volume . . . . " The present volume attempts to perform this service to future students of induction and probability. The suggestion of publishing a volume of this kind in Synthese Library was first made by Professor Donald Davidson, one of the editors of the Library, and was partly prompted by Professor von Wright's statement. In carrying out this suggestion, the editors of Synthese Library have had the generous support of Professor Broad who has among other things supplied a new Addendum to 'The Principles of Problematic Induction' and corrected a number of misprints found in the first printings of this paper. The editors gratefully acknow ledge Professor Broad's help and encouragement. A bibliography of Professor Broad's writings (up to 1959) has been compiled by Dr. C. Lewy and has appeared in P. A. Schilpp, editor, The Philosophy of C. D. Broad (The Library of Living Philosophers), pp. 833-852. (shrink)

The Problem of Old Evidence is a perennial issue for Bayesian confirmation theory. Garber famously argues that the problem can be solved by conditionalizing on the proposition that a hypothesis deductively implies the existence of the old evidence. In recent work, Hartmann and Fitelson :712–717, 2015) and Sprenger :383–401, 2015) aim for similar, but more general, solutions to the Problem of Old Evidence. These solutions are more general because they allow the explanatory relationship between a new hypothesis and old evidence (...) to be inductive, rather than deductive. In this paper, I argue that these solutions are either unsound or under-motivated, depending on the case of inductive explanation that we have in mind. This lends support to the broader claim that Garber–Style Bayesian confirmation cannot capture the sense in which new hypotheses that do not deductively imply old evidence nevertheless seem to be confirmed via old evidence. (shrink)

The Problem of Old Evidence is a perennial issue for Bayesian confirmation theory. Garber (Test Sci Theor 10:99–131, 1983) famously argues that the problem can be solved by conditionalizing on the proposition that a hypothesis deductively implies the existence of the old evidence. In recent work, Hartmann and Fitelson (Philos Sci 82(4):712–717, 2015) and Sprenger (Philos Sci 82(3):383–401, 2015) aim for similar, but more general, solutions to the Problem of Old Evidence. These solutions are more general because they allow the (...) explanatory relationship between a new hypothesis and old evidence to be inductive, rather than deductive. In this paper, I argue that these solutions are either unsound or under-motivated, depending on the case of inductive explanation that we have in mind. This lends support to the broader claim that Garber–Style Bayesian confirmation cannot capture the sense in which new hypotheses that do not deductively imply old evidence nevertheless seem to be confirmed via old evidence. (shrink)

We provide eductive foundations for the concept of forward induction, in the class of games with an outside option. The formulation presented tries to capture in a static notion the rest point of an introspective process, achievable from some restricted preliminary beliefs. The former requisite is met by requiring the rest point to be a Nash equilibrium that yields a higher payoff than the outside option. With respect to the beliefs, we propose the Incentive Dominance Criterion. Players should consider one (...) action more likely than another whenever the former is better than getting the outside option for more conjectures over his rival's actions. We apply this model to the case where the subgame is a coordination game with a conflict between payoff dominance and risk dominance. Our results provide support for dominance solvability, but not for Van Damme's notion of forward induction. We show how the forward induction logic helps to select the Pareto dominant equilibrium. This is the case whenever player 1's act of giving up the outside option reverses the incentive dominance relations among 1's pure actions in the subgame. (shrink)