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.

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)

According to Popper and Miller [1983 and 1987], the part of a hypothesis that transcends the evidence is probablistically countersupported by the evidence. Therefore, inductive support is not probabilistic support. Their argument hinges on imposing the following necessary condition on ‘the part of a hypothesis h that goes beyond the evidence e’: that transcendent part, called k, must share no nontrivial consequences with e. I propose a new condition on k that is incompatible with Popper and Miller's condition. I (...) then show why the new condition is a viable alternative to Popper and Miller's. By doing so, I refute their argument that probabilistic support cannot be inductive. *I'd like to thank Michael Redhead. Jeremy Butterfield. and an anonymous referee for comments on earlier drafts. Thanks especially to David Miller for insightful criticisms. Adopted from work done in the Department of History and Philosophy of Science. University of Cambridge. 1989. (shrink)

Popper and Miller argued, in a 1983 paper, that there is no such thing as 'probabilistic inductive support' of hypotheses. They show how to divide a hypothesis into two "parts," where evidence only 'probabilistically supports' the "part" that the evidence 'deductively' implies, and 'probabilistically countersupports' the "rest" of the hypothesis. I argue that by distinguishing between 'support that is purely deductive in nature' and 'support of a deductively implied hypothesis', we can see that their argument fails to establish (in (...) any important way of interpreting it) their conclusion that "all probabilistic support is purely deductive." Their argument is 'not' "completely devastating to the inductive interpretation of the calculus of probability," as claimed. (shrink)

Confirmation theory is intended to codify the evidential bearing of observations on hypotheses, characterizing relations of inductive “support” and “counter­support” in full generality. The central task is to understand what it means to say that datum E confirms or supports a hypothesis H when E does not logically entail H.

In ‘Induction and Natural Kinds’, I proposed a solution to the problem of induction according to which our use of inductive inference is reliable because it is grounded in the natural kind structure of the world. When we infer that unobserved members of a kind will have the same properties as observed members of the kind, we are right because all members of the kind possess the same essential properties. The claim that the existence of natural kinds is what (...) grounds reliable use of induction is based on an inference to the best explanation of the success of our inductive practices. As such, the argument for the existence of natural kinds employs a form of ampliative inference. But induction is likewise a form of ampliative inference. Given both of these facts, my account of the reliability of induction is subject to the objection that it provides a circular justification of induction, since it employs an ampliative inference to justify an ampliative inference. In this paper, I respond to the objection of circularity by arguing that what justifies induction is not the inference to the best explanation of its reliability. The ground of induction is the natural kinds themselves. (shrink)

Inductive thinking is a universal human habit; we generalise from our experiences the best we can. The induction problem is to identify which observed regularities provide reasonable justification for inductive conclusions. In the natural sciences, we can often use strict laws in making successful inferences about unobserved states of affairs. In the social sciences, by contrast, we have no strict laws, only regularities which most often are conditioned on ceteris paribus clauses. This makes it much more difficult to (...) make reliable inferences in the social sciences. In particular, we want knowledge about general causal relations in order to be able to determine what to do in order to achieve a certain state of affairs. Knowledge about causal relations that are also valid in the future requires experiments or so called ‘natural experiments’. Only knowledge derived from such experiences enable us to draw reasonably reliable inferences about how to act in order to achieve our goals. (shrink)

How induction was understood took a substantial turn during the Renaissance. At the beginning, induction was understood as it had been throughout the medieval period, as a kind of propositional inference that is stronger the more it approximates deduction. During the Renaissance, an older understanding, one prevalent in antiquity, was rediscovered and adopted. By this understanding, induction identifies defining characteristics using a process of comparing and contrasting. Important participants in the change were Jean Buridan, humanists such as Lorenzo Valla and (...) Rudolph Agricola, Paduan Aristotelians such as Agostino Nifo, Jacopo Zabarella, and members of the medical faculty, writers on philosophy of mind such as the Englishman John Case, writers of reasoning handbooks, and Francis Bacon. (shrink)

Meta-induction, in its various forms, is an imitative prediction method, where the prediction methods and the predictions of other agents are imitated to the extent that those methods or agents have proven successful in the past. In past work, Schurz demonstrated the optimality of meta-induction as a method for predicting unknown events and quantities. However, much recent discussion, along with formal and empirical work, on the Wisdom of Crowds has extolled the virtue of diverse and independent judgment as essential to (...) maintenance of 'wise crowds'. This suggests that meta-inductive prediction methods could undermine the wisdom of the crowd inasmuch these methods recommend that agents imitate the predictions of other agents. In this article, we evaluate meta-inductive methods with a focus on the impact on a group's performance that may result from including meta-inductivists among its members. In addition to considering cases of global accessibility (i.e., cases where the judgments of all members of the group are available to all of the group's members), we consider cases where agents only have access to the judgments of other agents within their own local neighborhoods. (shrink)

Although epistemic values have become widely accepted as part of scientific reasoning, non-epistemic values have been largely relegated to the "external" parts of science (the selection of hypotheses, restrictions on methodologies, and the use of scientific technologies). I argue that because of inductive risk, or the risk of error, non-epistemic values are required in science wherever non-epistemic consequences of error should be considered. I use examples from dioxin studies to illustrate how non-epistemic consequences of error can and should be (...) considered in the internal stages of science: choice of methodology, characterization of data, and interpretation of results. (shrink)

This chapter contains section titled: Some Context The Traditional Interpretation Disarming the Evidence for the Traditional Interpretation Evidence that Hume Considers Inductive Inference Justified The Traditional Interpretation Revisited Hume's Epistemic Options Applications to Extended Objects and Belief in God Limitations on Enumerative Induction Acknowledgments References.

The account of meta-induction (G. Schurz, Hume’s problem solved: the optimality of meta-induction, MIT Press, Cambridge, 2019) proposes a two-step solution to the problem of induction. Step 1 consists in a mathematical a priori justification of the predictive optimality of meta-induction, upon which step 2 builds a meta-inductive a posteriori justification of object-induction based on its superior track record (Sect. 1). Sterkenburg (Br J Philos Sci, forthcoming. 10.1086/717068/) challenged this account by arguing that meta-induction can only provide a (non-circular) (...) justification of inductive predictions for now and for the next future, but not a justification of inductive generalizations (Sect. 2). This paper develops a meta-inductive method that does provide an a posteriori justification of inductive generalizations, in the form of exchangeability conditions (Sect. 3). In Sect. 4, a limitation of the proposed method is worked out: while the method can justify weakly lawlike generalizations, the justification of strongly lawlike generalizations (claimed to hold for all eternity) requires epistemic principles going beyond meta-induction based on predictive success. (shrink)

In their paper on the influence of meta-induction to the wisdom of the crowd, Paul Thorn and Gerhard Schurz argue that adding meta-inductive methods to a group influences the group positively, whereas replacing independend methods of a group with meta-inductive ones may have a negative impact. The first fact is due to an improvement of average ability of a group, the second fact is due to an impairment of average diversity within a group by meta-induction. In this paper (...) some critical remarks to meta-inductive group expansion and replacement are made. In particular it is stressed that both ability and diversity are of equal importance to a group’s performance. (shrink)

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

Inductive methods can be used to estimate the accuracies of inductive methods. Call a method immodest if it estimates that it is at least as accurate as any of its rivals. It would be unreasonable to adopt any but an immodest method. Under certain assumptions, exactly one of Carnap's lambda-methods is immodest. This may seem to solve the problem of choosing among the lambda-methods; but sometimes the immodest lambda-method is λ =0, which it would not be reasonable to (...) adopt. We should therefore reconsider the assumptions that led to this conclusion: for instance, the measure of accuracy. (shrink)

In their paper on the influence of meta-induction to the wisdom of the crowd, Paul Thorn and Gerhard Schurz argue that adding meta-inductive methods to a group influences the group positively, whereas replacing independent methods of a group with meta-inductive ones may have a negative impact. The first fact is due to an improvement of average ability of a group, the second fact is due to an impairment of average diversity within a group by meta-induction. In this paper (...) some critical remarks to meta-inductive group expansion and replacement are made. In particular it is stressed that both ability and diversity are of equal importance to a group's performance. (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)

In contemporary philosophy of science, the no-miracles argument and the pessimistic induction are regarded as the strongest arguments for and against scientific realism, respectively. In this paper, I construct a new argument for scientific realism which I call the anti-induction for scientific realism. It holds that, since past theories were false, present theories are true. I provide an example from the history of science to show that anti-inductions sometimes work in science. The anti-induction for scientific realism has several advantages over (...) the no-miracles argument as a positive argument for scientific realism. (shrink)

I review prominent historical arguments against scientific realism to indicate how they display a systematic overshooting in the conclusions drawn from the historical evidence. The root of the overshooting can be located in some critical, undue presuppositions regarding realism. I will highlight these presuppositions in connection with both Laudan’s ‘Old induction’ and Stanford’s New induction, and then delineate a minimal realist view that does without the problematic presuppositions.

An account of inductive inference is presented which addresses both its epistemological and metaphysical dimensions. It is argued that inductive knowledge is possible by virtue of the fit between our innate psychological capacities and the causal structure of the world.

Views which deny that there are necessary connections between distinct existences have often been criticized for leading to inductive skepticism. If there is no glue holding the world together then there seems to be no basis on which to infer from past to future. However, deniers of necessary connections have typically been unconcerned. After all, they say, everyone has a problem with induction. But, if we look at the connection between induction and explanation, we can develop the problem of (...) induction in a way that hits deniers of necessary connections, but not their opponents. The denier of necessary connections faces an `internal' problem with induction -- skepticism about important inductive inferences naturally flows from their position in a way that it doesn't for those who accept necessary connections. This is a major problem, perhaps a fatal one, for the denial of necessary connections. (shrink)

In recent years, the argument from inductive risk against value free science has enjoyed a revival. This paper investigates and clarifies this argument through means of a case-study: neonicitinoid research. Sect. 1 argues that the argument from inductive risk is best conceptualised as a claim about scientists’ communicative obligations. Sect. 2 then shows why this argument is inapplicable to “public communication”. Sect. 3 outlines non-epistemic reasons why non-epistemic values should not play a role in public communicative contexts. Sect. (...) 4 analyses the implications of these arguments both for the specific case of neonicitinoid research and for understanding the limits of the argument from inductive risk. Sect. 5 sketches the broader implications of my claims for understanding the “Value Free Ideal” for science. (shrink)

Is it possible to combine different logics into a coherent system with the goal of applying it to specific problems so that it sheds some light on foundational aspects of those logics? These are two of the most basic issues of combining logics. Paranormal modal logic is a combination of paraconsistent logic and modal logic. In this paper, I propose two further combinatory developments, focusing on each one of these two issues. On the foundational side, I combine paranormal modal logic (...) with normal modal logic, resulting into a paraconsistent and paracomplete multimodal logic dealing with the notions of plausibility and certainty. On the application side, I combine this logic with Reiter’s default logic, resulting into an inductive and consequently nonmonotonic paraconsistent and paracomplete logic able to represent some key inductive principles. (shrink)

Safety accounts of knowledge claim, roughly, that knowledge that p requires that one's belief that p could not have easily been false. Such accounts have been very popular in recent epistemology. However, one serious problem safety accounts have to confront is to explain why certain lottery‐related beliefs are not knowledge, without excluding obvious instances of inductive knowledge. We argue that the significance of this objection has hitherto been underappreciated by proponents of safety. We discuss Duncan Pritchard's recent solution to (...) the problem and argue that it fails. More importantly, the problem reaches deeper and poses a threat to any current safety accounts that require a belief's modal stability in close possibilities (as well as safety accounts that appeal to ‘normality’). We end by arguing that ways out of the problem require substantial reconstruction for a safety‐based account of knowledge. (shrink)

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

In a recent work, Popper claims to have solved the problem of induction. In this paper I argue that Popper fails both to solve the problem, and to formulate the problem properly. I argue, however, that there are aspects of Popper's approach which, when strengthened and developed, do provide a solution to at least an important part of the problem of induction, along somewhat Popperian lines. This proposed solution requires, and leads to, a new theory of the role of simplicity (...) in science, which may have helpful implications for science itself, thus actually stimulating scientific progress. (shrink)

The pessimistic induction plays an important role in the contemporary realism/anti-realism debate in philosophy of science. But there is some disagreement about the structure and aim of the argument. And a number of scholars have noted that there is more than one type of PI in the philosophical literature. I review four different versions of the PI. I aim to show that PIs have been appealed to by philosophers of science for a variety of reasons. Even some realists have appealed (...) to a PI. My goal is to advance our understanding of what the various PIs can teach us about science and the threat posed by PIs to scientific realism. (shrink)

Originally published in 1969. This book explains what is wrong with the traditional methodology of "inductive" reasoning and shows that the alternative scheme of reasoning associated with Whewell, Pierce and Popper can give the scientist a useful insight into the way he thinks.

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)

This paper formulates some paradoxes of inductive knowledge. Two responses in particular are explored: According to the first sort of theory, one is able to know in advance that certain observations will not be made unless a law exists. According to the other, this sort of knowledge is not available until after the observations have been made. Certain natural assumptions, such as the idea that the observations are just as informative as each other, the idea that they are independent, (...) and that they increase your knowledge monotonically (among others) are given precise formulations. Some surprising consequences of these assumptions are drawn, and their ramifications for the two theories examined. Finally, a simple model of inductive knowledge is offered, and independently derived from other principles concerning the interaction of knowledge and counterfactuals. (shrink)

The argument from inductive risk is considered to be one of the strongest challenges for value-free science. A great part of its appeal lies in the idea that even an ideal epistemic agent—the “perfect scientist” or “scientist qua scientist”—cannot escape inductive risk. In this paper, I scrutinize this ambition by stipulating an idealized Bayesian decision setting. I argue that inductive risk does not show that the “perfect scientist” must, descriptively speaking, make non-epistemic value-judgements, at least not in (...) a way that undermines the value-free ideal. However, the argument is more successful in showing that there are cases where the “perfect scientist” should, normatively speaking, use non-epistemic values. I also show that this is possible without creating problems of illegitimate prescription and wishful thinking. Thus, while inductive risk does not refute value-freedom completely, it still represents a powerful critique of value-free science. (shrink)

In this three-part paper, my concern is to expound and defend a conception of science, close to Einstein's, which I call aim-oriented empiricism. I argue that aim-oriented empiricsim has the following virtues. (i) It solve the problem of induction; (ii) it provides decisive reasons for rejecting van Fraassen's brilliantly defended but intuitively implausible constructive empiricism; (iii) it solves the problem of verisimilitude, the problem of explicating what it can mean to speak of scientific progress given that science advances from one (...) false theory to another; (iv) it enables us to hold that appropriate scientific theories, even though false, can nevertheless legitimately be interpreted realistically, as providing us with genuine , even if only approximate, knowledge of unobservable physical entities; (v) it provies science with a rational, even though fallible and non-mechanical, method for the discovery of fundamental new theories in physics. In the third part of the paper I show that Einstein made essential use of aim-oriented empiricism in scientific practice in developing special and general relativity. I conclude by considering to what extent Einstein came explicitly to advocate aim-oriented empiricism in his later years. (shrink)

I want to examine a possible solution to the problem of induction-one which, as far as I know, has not been discussed elsewhere. The solution makes crucial use of the notion of objective natural necessity. For the purposes of this discussion, I shall assume that this notion is coherent. I am aware that this assumption is controversial, but I do not have space to examine the issue here.

John Foster; VI*—Induction, Explanation and Natural Necessity, Proceedings of the Aristotelian Society, Volume 83, Issue 1, 1 June 1983, Pages 87–102, https://d.

Pure Inductive Logic is the study of rational probability treated as a branch of mathematical logic. This monograph, the first devoted to this approach, brings together the key results from the past seventy years, plus the main contributions of the authors and their collaborators over the last decade, to present a comprehensive account of the discipline within a single unified context.

The standard backward-induction reasoning in a game like the centipede assumes that the players maintain a common belief in rationality throughout the game. But that is a dubious assumption. Suppose the first player X didn't terminate the game in the first round; what would the second player Y think then? Since the backwards-induction argument says X should terminate the game, and it is supposed to be a sound argument, Y might be entitled to doubt X's rationality. Alternatively, Y might doubt (...) that X believes Y is rational, or that X believes Y believes X is rational, or Y might have some higher-order doubt. X’s deviant first move might cause a breakdown in common belief in rationality, therefore. Once that goes, the entire argument fails. The argument also assumes that the players act rationally at each stage of the game, even if this stage could not be reached by rational play. But it is also dubious to assume that past irrationality never exerts a corrupting influence on present play. However, the backwards-induction argument can be reconstructed for the centipede game on a more secure basis.1 It may be implausible to assume a common belief in rationality throughout the game, however the game might go, but the argument requires less than this. The standard idealisations in game theory certainly allow us to assume a common belief in rationality at the beginning of the game. They also allow us to assume this common belief persists so long as no one makes an irrational move. That is enough for the argument to go through. (shrink)

This book brings together eleven case studies of inductive risk-the chance that scientific inference is incorrect-that range over a wide variety of scientific contexts and fields. The chapters are designed to illustrate the pervasiveness of inductive risk, assist scientists and policymakers in responding to it, and productively move theoretical discussions of the topic forward.

Applying good inductive rules inside the scope of suppositions leads to implausible results. I argue it is a mistake to think that inductive rules of inference behave anything like 'inference rules' in natural deduction systems. And this implies that it isn't always true that good arguments can be run 'off-line' to gain a priori knowledge of conditional conclusions.

John Stuart Mill’s System of Logic (1843) is often considered to be a work that defends an inductivist epistemology. In this article, I propose to question this status by examining the definition of induction set out in Mill’s book, and the consequences that can be deduced from it. I show that Mill’s inductivism implies a methodology of scientific research in which deductive reasoning is just as important, if not more important, than inductive methods, so that the classical opposition between (...) induction and deduction is transformed into a complementarity. I then show how the concepts of natural law and causality emerge from these discussions, and examine how well the methods proposed by Mill are able to account for subsequent scientific discoveries. (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 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.