In this paper, I take up the conciliatory-steadfast debate occurring within social epistemology in regards to the phenomenon of peer disagreement. I will argue, because the conciliatory perspective al-lows us to understand argumentation pragmatically—as a method of problem-solving within a community rather than as a method for obtaining the truth—that in most cases, we should not simply agree to disagree.

Peter Achinstein gives in his papers [1] and [2] interesting analyses of some problems of inductive logic and of some approaches I have proposed. I shall discuss here some of these problems in order to clarify my present position. My comments will mainly concern the variety of instances, and only briefly the analogy influence, and the inductive methods for a coordinate language.

The paper explores the handling of singular analogy in quantitative inductive logics. It concentrates on two analogical patterns coextensive with the traditional argument from analogy: perfect and imperfect analogy. Each is examined within Carnap’s λ-continuum, Carnap’s and Stegmüller’s λ-η continuum, Carnap’s Basic System, Hintikka’s α-λ continuum, and Hintikka’s and Niiniluoto’s K-dimensional system. Itis argued that these logics handle perfect analogies with ease, and that imperfect analogies, while unmanageable in some logics, are quite manageable in others. The paper (...) concludes with a modification of the K-dimensional system that synthesizes independent proposals by Kuipers and Niiniluoto. (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)

The argument from analogy is examined from the point of view of Carnap's confirmation theory. It is argued that if inductive arguments are to be applicable to the real world, they must contain elementary analogical inferences. Carnap's system as originally developed (theλ -system) is not strong enough to take account of analogical arguments, but it is shown that the new system, which he has announced but not published in detail (theη -system), is capable of satisfying the conditions of inductive (...) analogy. Finally it is shown that an elementary analysis of analogical inference yields postulates of the η -system with a minimum of arbitrary assumptions. (shrink)

An important problem in inductive probability theory is the design of exchangeable analogical methods, i.e., of exchangeable inductive methods that take into account certain considerations of analogy by similarity for predictive inferences. Here a precise reformulation of the problem of predictive analogy is given and a new family of exchangeable analogical methods is introduced.Firstly, it is proved that the exchangeable analogical method introduced by Skyrms (1993) does not satisfy the best known general principles of predictive analogy. Secondly, (...) Skyrms's approach — consisting of the usage of particular hyper-Carnapian methods, i.e., mixtures of Carnapian inductive methods — is adopted in the design of a new family of exchangeable analogical methods. Lastly, it is proved that such methods satisfy an interesting general principle of predictive analogy. (shrink)

Here the author of How to Solve It explains how to become a "good guesser." Marked by G. Polya's simple, energetic prose and use of clever examples from a wide range of human activities, this two-volume work explores techniques of guessing, inductive reasoning, and reasoning by analogy, and the role they play in the most rigorous of deductive disciplines.

The argument from analogy is examined from the standpoint of Carnap's confirmation theory. Carnap's own discussion of analogy in relation to his c*— function is restricted to cases where the analogues are known to be similar, but not known to be different in any respect. It has been argued by the author in a previous work,, and by P. Achinstein, that typical analogy arguments involve known differences between the analogues as well as similarities. Achinstein shows that for (...) such arguments none of Carnap's Δ— system of conflrmation functions gives satisfactory values, and it is further shown in the present paper that for these arguments the confirmation never rises above its initial value, irrespective of evidence drown from an analogue. it is argued that even if inductive arguments are to be applicable to the real world, they must in principle be capable of taking into account known differences between the instances of an inductive generalization. Hence Carnap's Δ— system is inadequate as an explication of both induction and analogy.Three conditions are stated as necessary for any confirmation theory which gives a satisfactory explication of analogical inference:I. If two individuals a and b are known to agree in certain properties and differ in others, and if in addition a has a further property, then the confirmation of the hypothesis that b also has this property is greater than its initial confirmation, at least if the weight of the similarities is sufficiently great compared with the weight of the differences.II. The confirmation‐value increases or decreases with the weight of the similarities between the analogues compared with the weight of their differences.III. The confirmation that b has a certain property is greater if a has that property than if a does not have it.The Δ— system sastisfles none of these conditions. Carnap and Stegmüller have now, however, presented a new anxiom system for confirmation functions. the — system, Which is introduced primarily to deal with languages whose primitive predicates fall into families such that each individual can only be qualified by one predicate of each family. They construct a c‐ function which, as well as dealing with a language having two families of such predicates, also depends, unlike the functions in the Δ— system, on similarities between otherwise different individuals. The system is not developed far enough in this Appendix to enable the authors to discuss the confirmation in analogy arguments satisfying conditions I — III above, but it is shown in the present paper that, with a simple generalization of the measure‐function defined by Carnap and Stegmüller, and in the simplest non‐trivial case, condition I — III are all satisfied, indeed a stronger form of condition I is satisfied, in which no known similarity of the analogues is postulated.Finally it is remarked that Carnap and Stegmüller's method of introducing their Δ— system is extremely arbitrary and ad hoc, and an alternative method of introducing is suggested. Bearing in mind the fundamental nature of the argument from analogy in all application of induction to the real world, it is suggesetd that the fundamental inductive inference needing explication is not the inference of‘P1b, from ‘P,1a, but the analogical infeence of‘P2b, from‘P1P2a.P1b,. It is posinitial confirmation of‘P2b, and the confirmation of‘P2b, given‘P2a” and that the later two confirmation‐values are equivalent to those in the Δ— system. It is then shown that Carnap and Stegmüller's new measure‐function follows from their axiom system together with these postulates. Thus some of the arbitrariness of the — system is removed by general considérations regarding inductive and analogical inference. (shrink)

Vagueness is epistemic, according to some. Vagueness is ontological, according to others. This article deploys what I take to be a compromise position. Predicates are coined in specific contexts for specific purposes, but these limited practices do not automatically fix the extensions of predicates over the domain of all objects. The linguistic community using the predicate has rarely considered, much less decided, all questions that might arise about the predicate’s extension. To this extent, the ontological view is correct. But a (...) predicate that applies in some contexts can be reasonably extended to other contexts where it is initially vague. This process of development approximates the cognitive remedy for vagueness that the epistemic view prescribes. The process is piecemeal and inductive, akin to what von Wright described as the molding of concepts. Vagueness cannot be understood apart from the backdrop of classification, for vagueness is classification gone awry. Hence these pages explore the classification of particulars, both its clear successes and vague failures. How we classify unique particulars is the theme of Sections 2 and 3, which are primarily descriptive. Section 2 identifies a way of classifying particulars that pervades discourse of all sorts, and Section 3 illustrates its use in a field notorious for vagueness: ethics. Why a certain particular should (or should not) be classified in a certain way is a normative question, however, and it occupies Sections 4 and 5. Section 4 proposes a norm for strong arguments by analogy, and Section 5 illustrates how the norm might resolve vagueness in one kind of ethical dispute. This norm, which has a strong probabilistic component, is one way of affirming that probability is a guide to life. (shrink)

This paper critiques the standard presentation of arguments from analogy in logic textbooks and offers an alternative way of understanding them which renders them both more plausible and more easily evaluated for their strength. The typical presentation presents analogies as inductive arguments in which a set of properties, known to be shared by two logical domains, supports an inference about a further property, known to belong to one domain and inferred to belong to the target domain. But framed in (...) these terms, the strength of the argument depends entirely on the relevance of the known shared properties to the inferred shared property, meaning the argument rests on an unstated assumption. Against this view, the author maintains that arguments from analogy are figurative ways of addressing properties of the target logical domain. By comparing or contrasting two logical domains, analogies articulate a general principle which illustrates something difficult to imagine or to describe literally about the target domain. Analogies can be reformulated and evaluated as deductive arguments on this view, with their chief logical import being the inquiry they incite in students as to whether the general principle is true and sufficiently general to apply to the target domain. (shrink)

Domain constraint, the requirement that analogues be selected from "the same category," inheres in the popular saying "you can't compare apples and oranges" and the textbook principle "the greater the number of shared properties, the stronger the argument from analogy." I identify roles of domains in biological, linguistic, and legal analogy, supporting the account of law with a computer word search of judicial decisions. I argue that the category treatments within these disciplines cannot be exported to general informal (...) logic, where the relevance of properties, not their number, must be the logically prior criterion for evaluating analogical arguments. (shrink)

Alvin plantinga and michael slote, Following ayer, Have attempted to formulate the argument from analogy for the existence of other minds as an enumerative induction. Their way of avoiding the 'generalizing from a single case' objection is shown to be fallacious.

An important debate in the reasoning literature concerns the extent to which inference processes are domain-free or domain-specific. Typically, evidence in support of the domain-specific position comprises the facilitation observed when abstract reasoning tasks are set in realistic context. Three experiments are reported here in which the sources of facilitation were investigated for contextualised versions of Raven's Progressive Matrices (Richardson, 1991) and non-verbal analogies from the AH4 test (Richardson & Webster, 1996). Experiment 1 confirmed that the facilitation observed for the (...) contextualised matrices was in part due to extraneous aspects of commentaries originally intended to activate domainspecific processes. Experiments 2 and 3 indicated that the remainder of the facilitation for the matrices, and all of the facilitation for the analogies, could be explained by visual salience: Converting the item elements into realistic objects had enabled them and their transitions to be identified more easily. Hence, performance at simplified abstract items was as good as, or better than, at contextualised items. It is concluded that facilitation effects cannot be interpreted as showing that domain-specific processes constitute a self-contained system separate from domain-free processes. In turn, this means that domain-free processes cannot be dismissed as being unimportant for reasoning. (shrink)

Gustav Theodor Fechner was one of the main proponents of inductive metaphysics in the 19th century. The idea of inductive metaphysics is to use empirical sources and inductive forms of inference in metaphysics. Although this sounds like a research program which might well appeal to scientifically minded philosophers, some of Fechner’s metaphysical conclusions look very suspicious from a scientific viewpoint. For example, Fechner famously argues that the planets and stars are animated by a soul and that the same holds for (...) the whole universe. In the present article it is shown that Fechner’s mystical cosmological views are based on a principle of analogy which is too permissive and that as a result of that his central argument to the conclusion that the earth is animated by a soul is not correct. As the article argues, the principle Fechner bases his inference on has to be supplemented by a causal condition along the lines of Mary Hesse’s account of analogical inferences, a condition Fechner at least implicitly recognizes but fails to meet. (shrink)

This Is A New Release Of The Original 1905 Edition.

The λ-continuum of inductive methods was derived from an assumption, called λ-condition, which says that the probability of finding an individual having property $x_{j}$ depends only on the number of observed individuals having property $x_{j}$ and on the total number of observed individuals. So, according to that assumption, all individuals with properties which are different from $x_{j}$ have equal weight with respect to that probability and, in particular, it does not matter whether any individual was observed having some property similar (...) to $x_{j}$ (the most complete proof of this result is presented in Carnap, 1980). The problem thus remained open to find some general condition, weaker than the λ-condition, which would allow for the derivation of probability functions which might be sensitive to similarity. Carnap himself suggested a weakening of the λ-condition which might allow for similarity sensitive probability functions (Carnap, 1980, p. 45) but he did not find the family of probability functions derivable from that principle. The aim of this paper is to present the family of probability functions derivable from Carnap's suggestion and to show how it is derived. In Section 1 the general problem of analogy by similarity in inductive logic is presented, Section 2 outlines the notation and the conceptual background involved in the proof, Section 3 gives the proof, Section 4 discusses Carnap's principle and the result, Section 5 is a brief review of the solutions which have previously been proposed. (shrink)

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

We propose an Analogy Principle in the context of Unary Inductive Logic and characterize the probability functions which satisfy it. In particular in the case of a language with just two predicates the probability functions satisfying this principle correspond to solutions of Skyrmsʼ ‘Wheel of Fortune’.

In this paper it is shown that there is a natural way of dealing with analogy by similarity in inductive systems by extending intuitive ways of introduction of systems without analogy. This procedure leads to Carnap-like systems, with zero probability for contingent generalizations, satisfying a general principle of so-called virtual analogy. This new principle is different from, but compatible with, Carnap's principle. It will be shown that the latter principle is satisfied, and should only be satisfied, if (...) the underlying distance function is such that all predicates have the same "predicate-environment". Finally, the claim that the new systems have the property of order indifference only with respect to the past will be defended. (shrink)

Analogies come in several forms that serve distinct functions. Inductive analogy is a common type of analogical argument, but critical thinking texts sometimes treat all analogies as inductive. Such an analysis ignores figurative analogies, which may elucidate but do not argue; and also neglects a priori arguments by analogy, a type of analogical argument prominent in law and ethics. A priori arguments by analogy are distinctive, but--contrary to the claims of Govier and Sunstein-they are best understood as (...) deductive, rather than a special form of non deductive reasoning. (shrink)

The purpose of the work reported here was to investigate the role of problem comparison and, specifically, analogical comparison in the induction of problem categories. This work was motivated by two factors. First, it is well-documented that experts and novices represent problems in very different ways and that solution success often depends on producing expert-like problem representations (DeGroot, 1965; Duncker, 1945; Chi, Feltovich, & Glaser, 1981; Hardiman, Dufresne, & Mestre, 1989; Novick, 1988; Schoenfeld & Herrmann, 1982; Silver, 1979, 1981). (...) Second, the problem representations produced by experts and novices appear to reflect differences in the way the two groups organize their knowledge bases. Although both groups appear to represent their problem-solving knowledge in terms of problem classes, or categories, expert categories tend to be defined in terms of deep structural features, whereas novice categories tend to be defined in terms of surface features (Adelson, 1981; Chase & Simon, 1973; Chi et al., 1981; Schoenfeld &. Herrmann, 1982; Silver, 1979, 1981). Because of this differential organization, experts are more likely than novices to retrieve solution-relevant information from their categories when constructing problem representations. (shrink)

This article examines the development and critique of analogical arguments in the kalām tradition. There are two basic positions on analogical arguments: one holds that if analogical arguments yield certainty, then they are analyzable as deductive inferences, rendering the analogy itself redundant. Proponents of this view thus hold that if the analogy is useful at all, it will never yield the certainty demanded in the rational sciences; another holds that the analogy remains useful even when the argument (...) is deductively sound, either because the universal premise is epistemically dependent on the source case, or, because the source case is useful in dialectical contexts. The exploration of these themes will center around Juwaynī’s formalization and subsequent critique of analogical arguments in the kalām tradition. (shrink)

In section I the notions of logical and inductive probability will be discussed as well as two explicanda, viz. degree of confirmation, the base for inductive probability, and degree of evidential support, Popper's favourite explicandum. In section II it will be argued that Popper's paradox of ideal evidence is no paradox at all; however, it will also be shown that Popper's way out has its own merits.

This paper defines the form of prior knowledge that is required for sound inferences by analogy and single-instance generalizations, in both logical and probabilistic reasoning. In the logical case, the first order determination rule defined in Davies (1985) is shown to solve both the justification and non-redundancy problems for analogical inference. The statistical analogue of determination that is put forward is termed 'uniformity'. Based on the semantics of determination and uniformity, a third notion of "relevance" is defined, both logically (...) and probabilistically. The statistical relevance of one function in determining another is put forward as a way of defining the value of information: The statistical relevance of a function F to a function G is the absolute value of the change in one's information about the value of G afforded by specifying the value of F. This theory provides normative justifications for conclusions projected by analogy from one case to another, and for generalization from an instance to a rule. The soundness of such conclusions, in either the logical or the probabilistic case, can be identified with the extent to which the corresponding criteria (determination and uniformity) actually hold for the features being related. (shrink)

According to decision theory, the rational initial action in a sequential decision-problem may be found by backward induction or folding back. But the reasoning which underwrites this claim appeals to the agent's beliefs about what she will later believe, about what she will later believe she will still later believe, and so forth. There are limits to the depth of people's beliefs. Do these limits pose a threat to the standard theory of rational sequential choice? It is argued, first, (...) that the traditional solutions of certain games depend on knowledge which exceeds depth limits, and that these solutions therefore cannot be shown rational in the usual sense. Then, for that related reason even folding back solutions of one-person problems cannot be! A revision of our notion of rational choice is proposed, analogous to the reliabilist account of knowledge of Goldman and others, by which this paradox is resolved. (shrink)

The analogical position, as traditionally understood, is the claim that a person can inductively infer the existence of other minds from what he knows about his own mind and about physical objects. Of course this body of knowledge must not include such propositions about physical objects as "that human body over there is animated by a human mind," or "this automobile was designed by a human mind"; nor could my evidence for the existence of other minds be that I have (...) it on the authority of some of the best minds in the country. The body of knowledge in question must not entail that there are any other minds. In "Induction and Other Minds" I used the term "total evidence" to refer to this body of knowledge, defining that term as follows. (shrink)

But here a preliminary difficulty must be dealt with: can't we sometimes see that a man is in pain? Can't we sometimes see that someone is thinking, depressed, or exuberant? And if anything would be "determining by observation" that another is in pain, surely seeing that he is would be: so why is a tenuous analogical inference necessary?

In "Induction and Other Minds," Plantinga casts the Argument from Analogy in the form of an inductive argument in the following way.

It is the aim of this paper to find a systematic approach to the study of induction by integrating the ideas of several disciplines to have a successful instrument for analyzing processes of inference, learning and discovery. On the way to generalities which enable sensible forecasts the social and economic sciences use empirical work and nowadays we are encouraged to use more and more experimental access to investigate analogous situations. Induction is used as a fundamental concept and experimental (...) work has brought some lights behind learning and inference. (shrink)

It is the aim of this paper to find a systematic approach to the study of induction by integrating the ideas of several disciplines to have a successful instrument for analyzing processes of inference, learning and discovery. On the way to generalities which enable sensible forecasts the social and economic sciences use empirical work and nowadays we are encouraged to use more and more experimental access to investigate analogous situations. Induction is used as a fundamental concept and experimental (...) work has brought some lights behind learning and inference. (shrink)

It is the aim of this paper to find a systematic approach to the study of induction by integrating the ideas of several disciplines to have a successful instrument for analyzing processes of inference, learning and discovery. On the way to generalities which enable sensible forecasts the social and economic sciences use empirical work and nowadays we are encouraged to use more and more experimental access to investigate analogous situations. Induction is used as a fundamental concept and experimental (...) work has brought some lights behind learning and inference. (shrink)

The paper contains an axiomatic treatment of the intuitionistic theory of hereditarily finite sets, based on an induction axiom-schema and a finite set of single axioms. The main feature of the principle of induction used (due to Givant and Tarski) is that it incorporates Foundation. On the analogy of what is done in Arithmetic, in the axiomatic system selected the transitive closure of the membership relation is taken as a primitive notion, so as to permit an immediate (...) adaptation of the theory to cases of restricted induction (in particular primitive recursive induction). At the end of the paper several different forms of induction, which play an important role in the development of the theory, are compared. An alternative axiomatization of the theory, which is of intrinsic interest, is also discussed. (shrink)

Many believe that Goodman’s new riddle of induction proves the impossibility of a purely syntactical theory of confirmation. After discussing and rejecting Jackson’s solution to Goodman’s paradox, I formulate the “new riddle of deduction,” in analogy to the new riddle of induction. Since it is generally agreed that deductive validity can be defined syntactically, the new riddle of induction equally does not show that inductive validity cannot be defined syntactically. I further rely on the analogy (...) between induction and deduction in order to explain why some predicates, such as “grue,” are unprojectible. (shrink)