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.

Conceptual change and its connection to the development of new seien tific theories has reeently beeome an intensively discussed topic in philo sophieal literature. Even if the inductive aspects related to conceptual change have already been discussed to some extent, there has so far existed no systematic treatment of inductive change due to conceptual enrichment. This is what we attempt to accomplish in this work, al though most of our technical results are restricted to the framework of monadic (...) languages. We extend Hintikka's system of inductive logic to apply to situations in which new concepts are introduced to the original language. By interpreting them as theoretica1 concepts, it is possible to discuss a number of currently debated philosophical and methodological problems which have previously escaped systematic and exact treatment. For instance, the role which seientific theories employing theoretical con cepts may play within inductive inference can be studied within this framework. From the viewpoint of seientific realism, sueh a study gives outlines for a theory of what we call hypothetico-induetive inference. Some parts of this work which are based on Hintikka's system of in ductive logic are fairly technical. However, no previous knowledge of this system is required, but, in general, acquaintance with the basic ideas of elementary logic and probability theory is suffieient. This work is part of a project, originated by Professors Jaakko Hintikka and Raimo Tuomela, concerning the role of theoretical concepts in science. (shrink)

It is shown that many different problems have the same degree of unsolvability. Among these problems are: THE INDUCTIVE INFERENCE PROBLEM. Infer in the limit an index for a recursive function f presented as f(0), f(1), f(2),.... THE RECURSIVE INDEX PROBLEM. Decide in the limit if i is the index of a total recursive function. THE ZERO NONVARIANT PROBLEM. Decide in the limit if a recursive function f presented as f(0), f(1), f(2),... has value unequal to zero for (...) infinitely many arguments. Finally, it is shown that these unsolvable problems are strictly easier than the halting problem. (shrink)

Most standard results on structure identification in first order theories depend upon the correctness and completeness (in the limit) of the data, which are provided to the learner. These assumption are essential for the reliability of inductive methods and for their limiting success (convergence to the truth). The paper investigates inductive inference from (possibly) incorrect and incomplete data. It is shown that such methods can be reliable not in the sense of truth approximation, but in the sense (...) that the methods converge to "empirically adequate" theories, i.e. theories, which are consistent with all data (past and future) and complete with respect to a given complexity class of L-sentences. Adequate theories of bounded complexity can be inferred uniformly and effectively by polynomial-time learning algorithms. Adequate theories of unbounded complexity can be inferred pointwise by less efficient methods. (shrink)

Hilary Kornblith presents an account of inductive inference that addresses both its metaphysical and epistemological aspects. He argues that inductive knowledge is possible by virtue of the fit between our innate psychological capacities and the causal structure of the world. Kornblith begins by developing an account of natural kinds that has its origins in John Locke's work on real and nominal essences. In Kornblith's view, a natural kind is a stable cluster of properties that are bound together (...) in nature. The existence of such kinds serves as a natural ground of inductive inference. Kornblith then examines two features of human psychology that explain how knowledge of natural kinds is attained. First, our concepts are structured innately in a way that presupposes the existence of natural kinds. Second, our native inferential tendencies tend to provide us with accurate beliefs about the world when applied to environments that are populated by natural kinds. (shrink)

We advance a theory of inductive inference designed to predict the conditional probability that certain natural categories satisfy a given predicate given that others do (or do not). A key component of the theory is the similarity of the categories to one another. We measure such similarities in terms of the overlap of metabolic activity in voxels of various posterior regions of the brain in response to viewing instances of the category. The theory and similarity measure are tested (...) against averaged probability judgments elicited from a separate group of subjects. Fruit serve as categories in the present experiment; results are compared to earlier work with mammals. (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)

In lieu of an abstract, here is a brief excerpt of the content: Hume's Skepticism about Inductive Inference N. SCOTT ARNOLD IT HAS BEEN A COMMONPLACE among commentators on Hume's philosophy that he was a radical skeptic about inductive inference. In addition, he is alleged to have been the first philosopher to pose the so-called problem of induction. Until recently, however, Hume's argument in this connection has not been subject to very close scrutiny. As attention has (...) become focused on this argument, a debate has been shaping up concerning just what Hume intended to establish here. The principal purpose of this article is to settle this interpretive issue as decisively as the texts permit. I should also like to locate Hume's main argument about induction in the larger context of his discussion of skepti- cism in book 1 of the Treatise. I shall suggest that arguments for the radical skepticism commonly attributed to Hume can be found only very late in book 1 of the Treatise and that the most famous argument about inductive inference establishes and is intended to establish only a relatively modest form of skepticism. The argument under consideration can found in book l, part 3, section 6 of the Treatise. It can also be found in essays 4 and 5 of the Enquiries and in the abstract of the Treatise published anonymously by Hume. I shall concen- trate on the Treatise version since it is the first and perhaps most explicit formulation of the argument and because part of my purpose is to place this argument in the larger context of book 1 of the Treatise. The received opinion concerning Hume's argument has it that Hume was highly skeptical about the mind's claims to knowledge about the future (or, more generally, about the unobserved). All beliefs arrived at via inductive I should like to thank M. G. Anderson, John Bahde, Jon Nordy, and Robert Paul Wolff, as well as David Fate Norton and a referee for the Journal of the History of Philosophy, for helpful comments on earlier drafts on this article. 32 HISTORY OF PHILOSOPHY inferences are unreasonable or unjustified. The alternative interpretation, to be defended below, is that Hume held that no such belief is or can be rendered certain relative to past experience and that such beliefs are not, upon that account, unreasonable or unjustified. Something like this inter- pretation has been defended by Tom L. Beauchamp, Thomas Mappes, and Alexander Rosenberg. ~ My view differs from theirs in that I shall argue that Hume did offer arguments for the more radical skepticism commonly attri- buted to him (though it is unclear whether he regarded them as decisive). These arguments, however, come at the end of book ~ of the Treatise and are independent of the more famous argument to be discussed below. Defenders of the received view are both numerous and distinguished. Versions of this interpretation of the main argument can be found in the writings of Karl Popper, Wesley Salmon, F. L. Will, and Norman Kemp Smith; most recently a variation on the standard interpretation has been defended by Barry Stroud. The fullest and most elaborate defense of the standard interpretation can be found in a monograph by D. C. Stove. '~ Stove's discussion is perhaps the most impressive because of his painstaking efforts to lay bare the structure of Hume's reasoning and to give a line-by- line analysis of the argument. This has the effect of bringing more clearly into focus the main grounds for the standard view. If this standard interpre- tation is correct, then Hume's position is that scientific method is epistemically no better than "superstition" and "enthusiasm." And, Hume would be among those for whom this claim, if true, would be very bad news, because one of his primary purposes in the Treatise is to construct a science of man. Thus, this argument is of considerable internal significance because, if my opponents are correct, Hume appears to have cut the ground out from under what he took to be one of his most important projects -- the construc- tion of a science of man. The other feature of this argument that makes it worthy of serious con- sideration is that it is philosophically... (shrink)

CL diagrams – the abbreviation of Cubus Logicus – are inspired by J.C. Lange’s logic machine from 1714. In recent times, Lange’s diagrams have been used for extended syllogistics, bitstring semantics, analogical reasoning and many more. The paper presents a method for testing statistical syllogisms (also called proportional syllogisms or inductive syllogisms) by using CL diagrams.

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)

The paper investigates learning functions for first order languages. Several types of convergence and identification in the limit are defined. Positive and negative results on learning problems are presented throughout the paper.

Kevin T. Kelly and Clark Glymour. Inductive Inference from Theory-Laden Data.

We are often justified in acting on the basis of evidential confirmation. I argue that such evidence supports belief in non-quantificational generic generalizations, rather than universally quantified generalizations. I show how this account supports, rather than undermines, a Bayesian account of confirmation. Induction from confirming instances of a generalization to belief in the corresponding generic is part of a reasoning instinct that is typically (but not always) correct, and allows us to approximate the predictions that formal epistemology would make.

Bayesianism and likelihoodism are two of the most important frameworks philosophers of science use to analyse scientific methodology. However, both frameworks face a serious objection: much scientific inquiry takes place in highly idealized frameworks where all the hypotheses are known to be false. Yet, both Bayesianism and likelihoodism seem to be based on the assumption that the goal of scientific inquiry is always truth rather than closeness to the truth. Here, I argue in favour of a verisimilitude framework for (...) class='Hi'>inductive inference. In the verisimilitude framework, scientific inquiry is conceived of, in part, as a process where inference methods ought to be calibrated to appropriate measures of closeness to the truth. To illustrate the verisimilitude framework, I offer a reconstruction of parsimony evaluations of scientific theories, and I give a reconstruction and extended analysis of the use of parsimony inference in phylogenetics. By recasting phylogenetic inference in the verisimilitude framework, it becomes possible to both raise and address objections to phylogenetic methods that rely on parsimony. 1Introduction2Problems with the Law of Likelihood3Introducing Verisimilitude-Based Inference4Examples of Verisimilitude-Based Inference Procedures4.1Parsimony inference over theories4.2Parsimony inference in phylogenetics5Conclusion. (shrink)

One of the important problems that have to be dealt with in the Philosophy of Science is to account for the high reliability of a very large part of our inductive inferences. This reliability is noteworthy because not only were many of these inferences made by ordinary people, even by children, but they were very often based on the observation of just a few positive instances. In the present paper, I deal with this problem by treating it as a (...) normal empirical problem. This approach enables us to make an important step towards an explanation of the phenomenon and, consequently, towards the formulation of a general theory of scientific inquiry. (shrink)

In many areas of scientific inquiry, the phenomena under investigation are viewed as functions on the real numbers. Since observational precision is limited, it makes sense to view these phenomena as bounded functions on the rationals. One may translate the basic notions of recursion theory into this framework by first interpreting a partial recursive function as a function on Q. The standard notions of inductive inference carry over as well, with no change in the theory. When considering the (...) class of computable functions on Q, there are a number of natural ways in which to define the distance between two functions. We utilize standard metrics to explore notions of approximate inference — our inference machines will attempt to guess values which converge to the correct answer in these metrics. We show that the new inference notions, NV∞, EX∞, and BC∞, infer more classes of functions than their standard counterparts, NV, EX, and BC. Furthermore, we give precise inclusions between the new inference notions and those in the standard inference hierarchy. We also explore weaker notions of approximate inference, leading to inference hierarchies analogous to the EXn and BCn hierarchies. Oracle inductive inference is also considered, and we give sufficient conditions under which approximate inference from a generic oracle G is equivalent to approximate inference with only finitely many queries to G. (shrink)

Results in recursion-theoretic inductive inference have been criticized as depending on unrealistic self-referential examples. J. M. Bārzdiņš proposed a way of ruling out such examples, and conjectured that one of the earliest results of inductive inference theory would fall if his method were used. In this paper we refute Bārzdiņš' conjecture. We propose a new line of research examining robust separations; these are defined using a strengthening of Bārzdiņš' original idea. The preliminary results of the new (...) line of research are presented, and the most important open problem is stated as a conjecture. Finally, we discuss the extension of this work from function learning to formal language learning. (shrink)

Freivalds defined an acceptable programming system independent criterion for learning programs for functions in which the final programs were required to be both correct and "nearly" minimal size, i.e., within a computable function of being purely minimal size. Kinber showed that this parsimony requirement on final programs limits learning power. However, in scientific inference, parsimony is considered highly desirable. A lim-computablefunction is (by definition) one calculable by a total procedure allowed to change its mind finitely many times about its (...) output. Investigated is the possibility of assuaging somewhat the limitation on learning power resulting from requiring parsimonious final programs by use of criteria which require the final, correct programs to be "not-so-nearly" minimal size, e.g., to be within a lim-computable function of actual minimal size. It is shown that some parsimony in the final program is thereby retained, yet learning power strictly increases. Considered, then, are lim-computable functions as above but for which notations for constructive ordinals are used to bound the number of mind changes allowed regarding the output. This is a variant of an idea introduced by Freivalds and Smith. For this ordinal notation complexity bounded version of lim-computability, the power of the resultant learning criteria form finely graded, infinitely ramifying, infinite hierarchies intermediate between the computable and the lim-computable cases. Some of these hierarchies, for the natural notations determining them, are shown to be optimally tight. (shrink)

Bayesian inference is limited in scope because it cannot be applied in idealized contexts where none of the hypotheses under consideration is true and because it is committed to always using the likelihood as a measure of evidential favouring, even when that is inappropriate. The purpose of this article is to study inductive inference in a very general setting where finding the truth is not necessarily the goal and where the measure of evidential favouring is not necessarily (...) the likelihood. I use an accuracy argument to argue for probabilism and I develop a new kind of argument to argue for two general updating rules, both of which are reasonable in different contexts. One of the updating rules has standard Bayesian updating, Bissiri et al.’s general Bayesian updating, Douven’s IBE-based updating, and Vassend’s ]) quasi-Bayesian updating as special cases. The other updating rule is novel. (shrink)

Carl G. Hempel has often stated that inductive-statistical explanations, as he conceives them, are inductive arguments. This discussion note raises the question of whether such arguments are to be understood as (1) arguments of the traditional sort, containing premises and conclusions, governed by some sort of inductive "acceptance rules," or (2) something more closely akin to Carnap's degree of confirmation statements which occur in an inductive logic which entirely eschews inductive "acceptance rules." Hempel's writings do (...) not seem unequivocal on this issue. It is suggested that adoption of construal (2) would remove the need for Hempel's high probability requirement on I-S explanations. (shrink)

This paper aims to be a friendly introduction to formal learning theory. I introduce key concepts at a slow pace, comparing and contrasting with other approaches to inductive inference such as con…rmation theory. A number of examples are discussed, some in detail, such as Goodman’s Riddle of Induction. I outline some important results of formal learning theory that are of philosophical interest. Finally, I discuss recent developments in this approach to inductive inference.

An argument, different from the Newman objection, against the view that the cognitive content of a theory is exhausted by its Ramsey sentence is reviewed. The crux of the argument is that Ramsification may ruin inductive systematization between theory and observation. The argument also has some implications concerning the issue of underdetermination.

A complete calculus of inductive inference captures the totality of facts about inductive support within some domain of propositions as relations or theorems within the calculus. It is demonstrated that there can be no complete, non-trivial calculus of inductive inference.

An inductive logic is a system of inference that describes the relation between propositions on data, and propositions that extend beyond the data, such as predictions over future data, and general conclusions on all possible data. Statistics, on the other hand, is a mathematical discipline that describes procedures for deriving results about a population from sample data. These results include predictions on future samples, decisions on rejecting or accepting a hypothesis about the population, the determination of probability assignments (...) over such hypotheses, the selection of a statistical model for studying the population, and so on. Both inductive logic and statistics are calculi for getting from the given data to propositions or results that transcend the data. (shrink)

Inductive reasoning requires exploiting links between evidence and hypotheses. This can be done focusing either on the posterior probability of the hypothesis when updated on the new evidence or on the impact of the new evidence on the credibility of the hypothesis. But are these two cognitive representations equally reliable? This study investigates this question by comparing probability and impact judgments on the same experimental materials. The results indicate that impact judgments are more consistent in time and more accurate (...) than probability judgments. Impact judgments also predict the direction of errors in probability judgments. These findings suggest that human inductive reasoning relies more on estimating evidential impact than on posterior probability. (shrink)

Non-trivial calculi of inductive inference are incomplete. This result is demonstrated formally elsewhere. Here the significance and background to the result is described. This note explains what is meant by incompleteness, why it is desirable, if only it could be secured, and it gives some indication of the arguments needed to establish its failure. The discussion will be informal, using illustrative examples rather than general results. Technical details and general proofs are presented in Norton.

This article develops an axiomatic theory of induction that speaks to the recent debate on Bayesian orgulity. It shows the exact principles associated with the belief that data can corroborate universal laws. We identify two types of disbelief about induction: skepticism that the existence of universal laws of nature can be determined empirically, and skepticism that the true law of nature, if it exists, can be successfully identified. We formalize and characterize these two dispositions toward induction by introducing novel axioms (...) for subjective probabilities. We also relate these dispositions to the axiom of σ-additivity. (shrink)

In this classic work of philosophy, Thilly provides a comprehensive overview of inductive reasoning and its role in scientific inquiry. With clear examples and lucid prose, Thilly's text remains an essential resource for anyone seeking to understand the nature of knowledge and the scientific method. 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. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Some birds can migrate over great distances with remarkable accuracy. To explain this ability, we must find the right sort of connection between some structured feature of the environment and some feature of the birds’ cognitive economy. For example, it has been suggested that some birds have organs sensitive to the orientation of the earth’s magnetic field. It may thus be possible to explain avian navigation in terms of the relation between the magnetic field of the earth and the compasses (...) in the birds. (shrink)

This book by one of the world's foremost philosophers in the fields of epistemology and logic offers an account of suppositional reasoning relevant to practical deliberation, explanation, prediction and hypothesis testing. Suppositions made 'for the sake of argument' sometimes conflict with our beliefs, and when they do, some beliefs are rejected and others retained. Thanks to such belief contravention, adding content to a supposition can undermine conclusions reached without it. Subversion can also arise because suppositional reasoning is ampliative. These two (...) types of nonmonotonic logic are the focus of this book. A detailed comparison of nonmonotonicity appropriate to both belief contravening and ampliative suppositional reasoning reveals important differences that have been overlooked. (shrink)