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)

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 first obstacle that confronts the student of induction is that of defining the subject matter. One initial point is to note that much of the relevant subject matter goes under the description ‘the theory of confirmation’. The distinction is primarily that the study of induction concerns inference, i.e. cases where one takes the conclusion to be established by the evidence, whereas confirmation concerns the weight of evidence, which one may take to be something like the credibility of a hypothesis (...) in the light of the evidence. Discussions of confirmation often concern incremental confirmation, i.e. cases where the evidence is taken to increase the credibility of some hypothesis, even if not sufficiently to warrant inferring the truth of that hypothesis. However, some uses of ‘confirmation’ clearly refer to absolute confirmation, cases where the credibility of the hypothesis in the light of the evidence exceeds some (high) threshold. One may ask whether inductive inference corresponds to the case of absolute confirmation for some suitable threshold. I shall discuss inference and confirmation together, though it should be noted that some approaches eschew inference altogether. For example, the Bayesian takes scientific reasoning to be a matter of adjusting credences in propositions in the light of evidence, and says nothing about unqualified belief in a proposition. However, if we are interested in inductive knowledge then we must consider inference, since only then do we have a detached proposition that is the possible content of a mental state of knowing. A more pressing question concerns which inferences (or allegedly confirmatory relations) should be classed as inductive. A natural and straightforward approach is to define induction as encompassing any form of reasoning that extrapolates from one population to another, usually from a sample of a population to the whole population. For example, one might note that all observations of the position of some planet fall on an ellipse that has the Sun at one of its foci; from this one concludes that all the positions that planet takes fall on this ellipse (i.e.. (shrink)

The orthodox view about sensitivity and induction has it that beliefs formed via induction are insensitive. Since inductive knowledge is highly plausible, this problem is usually regarded as a reductio argument against sensitivity accounts of knowledge. Some adherents of sensitivity defend sensitivity against this objection, for example by considering backtracking interpretations of counterfactuals. All these extant views about sensitivity and induction have to be revised, since the problem of sensitivity and induction is a different one. Regardless of (...) whether we allow backtracking interpretations of counterfactuals, some instances of induction yield insensitive beliefs whereas others yield sensitive ones. These results are too heterogenous for providing a plausible sensitivity-account of inductive knowledge. Induction remains a serious problem for sensitivity accounts of knowledge. (shrink)

Inductive reasoning aims at constructing rules and models of general applicability from a restricted set of observations. Induction is a keystone in natural sciences, and it influences diverse application fields such as engineering, medicine and economics. More generally, induction plays a major role in the way humans learn and operate in their everyday life. The level of reliability that a model achieves depends on how informative the observations are relative to the flexibility of the process by which the model (...) is constructed. When the process is articulated so that the model can incorporate descriptive details and subtleties, a large set of informative observations are required to reliably tune the model, whereas models obtained from simple procedures can be tuned with fewer observations. This article introduces the concept of “dominance”, which refers to the situation in which a reduced subset of observations suffices to reconstruct the model. A mathematical framework is presented to quantify the reliability of learning procedures as a function of the size of the subset of dominant observations. Although limited in scope, we believe that our study can contribute to the understanding of some fundamental mechanisms by which knowledge is generated from observations in inductive reasoning. (shrink)

According to David Hume, the concept of causation and probability are to be understood in terms of the concepts of similarity and repetition. In this book, it is shown that they are to be understood in terms of the concept of continuity. One corollary is that there is no legitimate basis for skepticism concerning the legitimacy of inductive inference. Another is that anti-realism about theoretical entities is misconceived.

According to the sensitivity account of knowledge, if one knows that p, then (roughly) were p false, one would not believe that p. One important issue regarding sensitivity is whether or not it preserves inductive knowledge. Critics including Jonathan Vogel, Ernest Sosa, and Duncan Pritchard argue that it does not. Proponents including Kevin Wallbridge insist that it does. In this paper, I first draw attention to an often-neglected distinction between two different versions of sensitivity—a distinction that has (...) important implications for the debate regarding inductive knowledge. In particular, I distinguish between the sensitivity principle originally defended by Robert Nozick and another version that has been the focus of many recent discussions. With the distinction in place, it is shown that a sensitivity theorist cannot preserve inductive knowledge while being unscathed. For neither account can simultaneously preserve inductive knowledge while properly handling the Gettier problem. Overall, sensitivity theorists are in trouble. (shrink)

A survey of arguments and positions concerning the possibility of inductive knowledge, this piece covers: Hume's problem of induction; the underdetermination of theories by evidence; the method of hypothesis; the relationship between underdetermination and evidential holism; attempts to specify how some statements can be said to be evidentially (or justificatorily) relevant to other claims.

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)

How do humans discover causal relations when the effect is not immediately observable? Previous experiments have uniformly demonstrated detrimental effects of outcome delays on causal induction. These findings seem to conflict with everyday causal cognition, where humans can apparently identify long-term causal relations with relative ease. Three experiments investigated whether the influence of delay on adult human causal judgements is mediated by experimentally induced assumptions about the timeframe of the causal relation in question, as suggested by Einhorn and Hogarth (1986). (...) Causal judgements generally decreased when a delay separated cause and effect. This decrease was less pronounced when the thematic context of the causal relation induced participants to expect a delay. Experiment 3 ruled out an alternative explanation of the effect based on variations of cue and outcome saliencies, and showed that detrimental effects of delay are reduced even more when instructions explicitly mentioned the timeframe of the causal relation in question. Knowledge thus mediates the impact of delay on human causal judgement. Implications for contemporary theories of human causal induction are discussed. (shrink)

People are adept at inferring novel causal relations, even from only a few observations. Prior knowledge about the probability of encountering causal relations of various types and the nature of the mechanisms relating causes and effects plays a crucial role in these inferences. We test a formal account of how this knowledge can be used and acquired, based on analyzing causal induction as Bayesian inference. Five studies explored the predictions of this account with adults and 4-year-olds, using tasks (...) in which participants learned about the causal properties of a set of objects. The studies varied the two factors that our Bayesian approach predicted should be relevant to causal induction: the prior probability with which causal relations exist, and the assumption of a deterministic or a probabilistic relation between cause and effect. Adults’ judgments (Experiments 1, 2, and 4) were in close correspondence with the quantitative predictions of the model, and children’s judgments (Experiments 3 and 5) agreed qualitatively with this account. (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)

A large class of games is that of non-cooperative, extensive form games of perfect information. When the length of these games is finite, the method used to reach a solution is that of a backward induction. Working from the terminal nodes, dominated strategies are successively deleted and what remains is a unique equilibrium. Game theorists have generally assumed that the informational requirement needed to solve these games is that the players have common knowledge of rationality. This assumption, however, has (...) given rise to several problems and paradoxes. Most notably, it has been shown that the common knowledge assumption makes the theory of the game inconsistent at some information set. The present paper shows that a) no common knowledge of rationality need be assumed for the backward induction solution to hold. Rather, it is sufficient that the players have a number of levels of knowledge proportional to the length of the game, and b) it is also necessary that the number of levels of knowledge is finite and proportional to the length of the game. For a higher number of levels of knowledge, inconsistencies arise. (shrink)

This book seeks to offer original answers to all the major open questions in epistemology—as indicated by the book’s title. These questions and answers arise organically in the course of a validation of the entire corpus of human knowledge. The book explains how we know what we know, and how well we know it. The author presents a positive theory, motivated and directed at every step not by a need to reply to skeptics or subjectivists, but by the need (...) of a rational individual to know the world. -/- The author draws heavily from Ayn Rand’s theory of concepts as presented in her book, Introduction to Objectivist Epistemology, but departs from her epistemology—especially as explicated by leading exponents of her philosophy—in important ways. Areas of departure include the perception of entities and the role of probability theory in epistemology. -/- A main idea in the book is to begin the validation of the law of causality by identifying that existence causes our consciousness of it. Another key idea is this: The very fact that we perceive entities is the most basic and most extensive evidence that causal forces and causal interactions are regular. -/- Applying Ayn Rand’s principle that characteristics are ranges of measurement, the book offers a philosophical validation of “nonparametric predictive inference,” in turn providing an objective basis for prior probabilities in Bayesian analysis. -/- This book is primarily for a specialized readership—familiar with epistemological ideas and with Ayn Rand’s theory of concepts in particular. The last third of the book uses probability theory and mathematics somewhat beyond basic calculus, but less mathematical explanations are also included to make the general ideas accessible to lay readers. (shrink)

There are many disputes about induction in the logic and philosophy of science. One of the problem is that we often use the term „induction“ in different meanings. This is precisely the point of Aristotle, the first thinker who analyzed induction systematically. The aim of the paper is to show that we are confronted with at least four different meanings of induction in Aristotleś writings, to analyze them and to show the role of induction in acquiring scientific knowing and the (...) consequences for the structure and characteristics of Aristotleś system of scientific knowledge. (shrink)

This essay defends the view that inductive reasoning involves following inductive rules against objections that inductive rules are undesirable because they ignore background knowledge and unnecessary because Bayesianism is not an inductive rule. I propose that inductive rules be understood as sets of functions from data to hypotheses that are intended as solutions to inductive problems. According to this proposal, background knowledge is important in the application of inductive rules and Bayesianism (...) qualifies as an inductive rule. Finally, I consider a Bayesian formulation of inductive skepticism suggested by Lange. I argue that while there is no good Bayesian reason for judging this inductive skeptic irrational, the approach I advocate indicates a straightforward reason not to be an inductive skeptic. (shrink)

Robert Aumann argues that common knowledge of rationality implies backward induction in finite games of perfect information. I have argued that it does not. A literature now exists in which various formal arguments are offered in support of both positions. This paper argues that Aumann's claim can be justified if knowledge is suitably reinterpreted.

This paper naturalizes inductive inference by showing how scientific knowledge of real mechanisms provides large benefits to it. I show how knowledge about mechanisms contributes to generalization, inference to the best explanation, causal inference, and reasoning with probabilities. Generalization from some A are B to all A are B is more plausible when a mechanism connects A to B. Inference to the best explanation is strengthened when the explanations are mechanistic and when explanatory hypotheses are themselves mechanistically (...) explained. Causal inference in medical explanation, counterfactual reasoning, and analogy also benefit from mechanistic connections. Mechanisms also help with problems concerning the interpretation, availability, and computation of probabilities. (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)

This work is a departure from traditional investigations of induction. Rather than consider issues related to the justification or construction of a scientific inductive logic, Professor Will exposes, evaluates, and rejects the epistemological framework within which work in the philosophy of induction is usually conducted. He argues that the frustrating difficulties faced in the philosophy of induction are endemic to that theory of knowledge which "resulted from the empiricist criticism and revision of the basic Cartesian view that (...) class='Hi'>knowledge is a kind of vision or intuition, that there are certain first intuitions, and that further knowledge consists of consequent intuitions elicited from or founded upon these." According to this view of knowledge, a knowledge claim can be justified in the face of the challenge of philosophical skepticism only if it is either itself indubitable or rests on some foundation that is indubitable. The burden of Will’s work is to show that this foundation or "justification" picture of knowledge is seriously mistaken and must be replaced with a more adequate and more realistic view. Human knowledge, he stresses, is best seen as analogous to a constitution. As human knowledge differs from area to area these constitutions differ, "just as history differs from horticulture and architecture from aviation." However, "collectively they form a huge sprawling entity that represents what may be thought of as the constitution for the institutionalized activity of human knowledge.". (shrink)

This chapter presents a new semantics for inductive empirical knowledge. The epistemic agent is represented concretely as a learner who processes new inputs through time and who forms new beliefs from those inputs by means of a concrete, computable learning program. The agent’s belief state is represented hyper-intensionally as a set of time-indexed sentences. Knowledge is interpreted as avoidance of error in the limit and as having converged to true belief from the present time onward. Familiar topics (...) are re-examined within the semantics, such as inductive skepticism, the logic of discovery, Duhem’s problem, the articulation of theories by auxiliary hypotheses, the role of serendipity in scientific knowledge, Fitch’s paradox, deductive closure of knowability, whether one can know inductively that one knows inductively, whether one can know inductively that one does not know inductively, and whether expert instruction can spread common inductive knowledge—as opposed to mere, true belief—through a community of gullible pupils. (shrink)

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.

Sosa, Pritchard, and Vogel have all argued that there are cases in which one knows something inductively but does not believe it sensitively, and that sensitivity therefore cannot be necessary for knowledge. I defend sensitivity by showing that inductive knowledge is sensitive.

Depending on whether we are somewhat tolerant of nearby error-possibilities or not, the safety condition on knowledge is open to a strong reading and a weak reading. In this paper, it is argued that induction and conjunction introduction constitute two horns of a dilemma for the safety account of knowledge. If we opt for the strong reading, then the safety account fails to account for inductive knowledge. In contrast, if we opt for the weak reading, then (...) the safety account fails to accommodate knowledge obtained via the method of conjunction introduction. (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)

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.

Drawing the complex terrain of the theories of induction and of the various ways to ground inductive knowledge in the middle ages is the aim of this paper. There have already been two excellent attempts to draw this terrain. The first is by Julius R. Weinberg and the second by E. P. Bos. My attempt differs from theirs in two major respects. The first is that it is more detailed in the examination of the various theories and their (...) relations. The second is that I focus on the role of natural necessities in induction. In particular, I try to place the various conceptions of induction within a network of issues that relate to the problem of universals, natural necessities and a power-based approach to activity in nature. Here is the road map. Section 2 explains Aristotle’s views of induction, as this were mainly developed in Posterior Analytics Book II.19 and states what I take it to be the main dilemma of induction, as this was described by Sextus Empiricus: induction is either perfect and impossible or imperfect and unjustified. In section 3, I move to Thomas Aquinas and his own attempt to justify induction and the actuality of general and necessary principles based on experience by an appeal to the natural light of reason. In section 4 I discuss John Duns Scotus’s reliance on a self-evident maxim to bridge the gap between imperfect and perfect induction. Section 5 moves to William of Ockham ’s peculiar attempt to justify single-instance inductions. Then, section 6 offers a detailed account of Jean Buridan’s ground-breaking re-conceptualisation of induction and the role of intellect in it. Section 7 discusses the critique of induction by Nicolaus of Autrecourt. Finally, section 8 offers a brief account of Pseudo-Scotus’s move from knowledge to opinion. (shrink)

A computational theory of induction must be able to identify the projectible predicates, that is to distinguish between which predicates can be used in inductive inferences and which cannot. The problems of projectibility are introduced by reviewing some of the stumbling blocks for the theory of induction that was developed by the logical empiricists. My diagnosis of these problems is that the traditional theory of induction, which started from a given (observational) language in relation to which all inductive (...) rules are formulated, does not go deep enough in representing the kind of information used in inductive inferences. As an interlude, I argue that the problem of induction, like so many other problems within AI, is a problem of knowledge representation. To the extent that AI-systems are based on linguistic representations of knowledge, these systems will face basically the same problems as did the logical empiricists over induction. In a more constructive mode, I then outline a non-linguistic knowledge representation based on conceptual spaces. The fundamental units of these spaces are "quality dimensions". In relation to such a representation it is possible to define "natural" properties which can be used for inductive projections. I argue that this approach evades most of the traditional problems. (shrink)