Analogical Reasoning as an Inference Scheme (original) (raw)
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Analogy plays an important role in science as well as in non-scientific domains such as taxonomy or learning. We make explicit the difference and complementarity between the concept of analogical statement, which merely states that two objects have a relevant similarity, and the concept of analogical inference, which relies on the former in order to draw a conclusion from some premises. For the first, we show that it is not possible to give an absolute definition of what it means for two objects to be analogous; a relative definition of analogy is introduced, only relevant from some point of view. For the second, we argue that it is necessary to introduce a background over-hypothesis relating two sets of properties; the belief strength of the conclusion is then directly related to the belief strength of the over-hypothesis. Moreover, we assert the syntactical identity between analogical inference and one case induction despite important pragmatic differences.
The logical and pragmatic structure of arguments from analogy
The reasoning process of analogy is characterized by a strict interdependence between a process of abstraction of a common feature and the transfer of an attribute of the Analogue to the Primary Subject. The first reasoning step is regarded as an abstraction of a generic characteristic that is relevant for the attribution of the predicate. The abstracted feature can be considered from a logic-semantic perspective as a functional genus, in the sense that it is contextually essential for the attribution of the predicate, i.e. that is pragmatically fundamental (i.e. relevant) for the predica-tion, or rather the achievement of the communicative intention. While the transfer of the predicate from the Analogue to the analogical genus and from the genus to the Primary Subject is guaranteed by the maxims (or rules of inference) governing the genus-species relation, the connection between the genus and the predicate can be complex, characterized by various types of reasoning patterns. The relevance relation can hide implicit arguments, such as an implicit argument from classification , an evaluation based on values, consequences or rules, a causal relation, or an argument from practical reasoning.
Analogical Reasoning and Semantic Rules of Inference.
Macagno, F., Walton, D., & Tindale, C. W. (2014). Analogical Reasoning and Semantic Rules of Inference. Revue internationale de philosophie, 270(4), 419-432.
Analogy is represented as a twofold process of abstraction and species-genus inference. This type of analysis can account for essential (i.e. intensional) and accidental similarities. In dialectical analogies, the ones analyzed in the Topics, the abstraction singles out a feature that is part of or related to the meaning of the terms and that is relevant under the respect imposed by the analogical predicate. This process can shed light on the mechanisms underlying reasoning from accidental similarity analysed in the Rhetoric.
In Defense of Analogical Reasoning
2008
I offer a defense of analogical accounts of scientific models by meeting certain logical objections to the legitimacy of analogical reasoning. I examine an argument by Joseph Agassi that purports to show that all putative cases of analogical inference succumb to the following dilemma: either (1) the reasoning remains hopelessly vague and thus establishes no conclusion, or (2) can be analyzed into a logically preferable non-analogical form. In rebuttal, I offer a class of scientific models for which (a) there is no satisfactory non-analogical analysis, and (b) we can gain sufficient clarity for the legitimacy of the inference to be assessed. This result constitutes an existence proof for a class of analogical models that escape Agassi's dilemma.
The formal structure(s) of analogical inference
Recently, Dardashti, Hartmann, Thébault, and Winsberg (2019) proposed a Bayesian model for establishing Hawking radiation by analogical inference. In this paper we investigate whether their model would work as a general model for analogical inference. We study how it performs when varying the believed degree of similarity between the source and the target system. We show that there are circumstances in which the degree of confirmation for the hypothesis about the target system obtained by collecting evidence from the source system goes down when increasing the believed degree of similarity between the two systems. We then develop an alternative model in which the direction of the variation of the degree of confirmation always coincides with the direction of the believed degree of similarity. Finally, we argue that the two models capture different types of analogical inference. Citation information: Gebharter, A., & Osimani, B. (forthcoming). The formal structure(s) of analogical inference. Erkenntnis.
By Parallel Reasoning: The Construction and Evaluation of Analogical Arguments
The Philosophical Review, 2012
To the extent that the worth of scientific or philosophical efforts can be assessed by the number of productive research avenues they open up, this is definitely an important book. It deserves careful consideration by scientists, mathematicians, psychologists, and philosophers. Since it does not fit neatly into any usual category but rather stands athwart many research areas, its reception may depend on precisely who attends to its bold claims. This book aims to answer two questions: "What criteria should we use to evaluate analogical arguments used in science?" and "How can we provide a philosophical justification for those criteria?" (ix). Paul Bartha recognizes that analogies are widely used in all areas of human action-but claims: "We have no substantive normative theory of analogical arguments" (3). He persuasively argues that none of the theoretical approaches to analogical argumentation that previously have been developed is generally applicable. But he holds that the uses of analogies in science and mathematics are "key or 'leading' special cases that provide an excellent basis for a general normative theory" of analogical reasoning (3). This book proposes a systematic theoretical treatment, and a set of evaluation criteria, that (Bartha claims) apply to all varieties of analogical reasoning-both in science and elsewhere. This assertion is not modest, but careful arguments support it well. The claim seems quite plausible. Analogical arguments involve "source" (S) and "target" (T) domains that are similar to each other in certain respects. Positive analogies occur when property P and relation R pertain to domain S , and corresponding property P * and relation R * pertain to T. If the target domain T has feature A * but the source domain S lacks that feature (so that , A applies to S), this constitutes a negative analogy. The question at issue is: Under what conditions (and with what degree of confidence) would it be correct to infer that if S has a feature Q , then T has a corresponding feature Q * ? In favorable cases deductive reasoning may lead to conclusions that are considered correct with a high degree of certainty. In contrast, analogical reasoning at its best leads to results that are 'plausible'-that is "they have some degree of support" (15). Plausibility can be interpreted probabilistically, so that plausible statements are understood to have a rather high probability of being true, and additional relevant evidence may increase that probability. In
Demonstrative and non-demonstrative reasoning by analogy
2008
Analogy and analogical reasoning have more and more become an important subject of inquiry in logic and philosophy of science, especially in virtue of its fruitfulness and variety: in fact analogy «may occur in many contexts, serve many purposes, and take on many forms» 1 . Moreover, analogy compels us to consider material aspects and dependent-on-domain kinds of reasoning that are at the basis of the lack of wellestablished and accepted theory of analogy: a standard theory of analogy, in the sense of a theory as classical logic, is therefore an impossible target. However, a detailed discussion of these aspects is not the aim of this paper and I will focus only on a small set of questions related to analogy and analogical reasoning, namely:
Varieties of Analogical Reasoning
Motivation -The purpose of this article is to reinvigorate debate concerning the nature of analogy and broaden the scope of current conceptions of analogy. Research approach -An analysis of the history of the concept of analogy, case studies on the use of analogy in problemsolving, cognitive research on analogy comprehension, and a naturalistic inquiry into the various functions of analogy. Findings and Implications -Psychological theories and computational models have generally relied on: (a) A single set of ontological concepts (a property called "similarity" and a structuralist categorization of types of semantic relations) (b) A single form category (i.e., the classic four-term analogy), and (c) A single set of morphological distinctions (e.g., verbal versus pictorial analogies). The taxonomy presented here distinguishes functional kinds of analogy, each of which presents an opportunity for research on aspects of reasoning that have been largely unrecognized. Originality/Value -The various functional kinds of analogy will each require their own treatment in macrocognitive theories and computational models. Take away message -The naturalistic investigation of the functions of analogy suggests that analogy is a macrocognitive phenomenon derivative of number of supporting processes, including the apperception of resemblances and distinctions, metaphor, and the balancing of semantic flexibility and inference constraint.
Analogical Arguments: Inferential Structures and Defeasibility Conditions
The purpose of this paper is to analyze the structure and the defeasibility conditions of argument from analogy, addressing the issues of determining the nature of the comparison underlying the analogy and the types of inferences justifying the conclusion. In the dialectical tradition, different forms of similarity were distinguished and related to the possible inferences that can be drawn from them. The kinds of similarity can be divided into four categories, depending on whether they represent fundamental semantic features of the terms of the comparison (essential similarities) or non-semantic ones, indicating possible characteristics of the referents (accidental similarities). Such distinct types of similarity characterize different kinds of analogical arguments, all based on a similar general structure, in which a common genus (or rather a generic feature) is abstracted. Depending on the nature of the abstracted common feature, different rules of inference will apply, guaranteeing the attribution of the analogical predicate to the genus and to the primary subject. This analysis of similarity and the relationship thereof with the rules of inference allows a deeper investigation of the defeasibility conditions.
Reasoning by Analogy and by Difference
The article presents a novel and extended analysis of reasoning by analogy. It delves deeper into the concept of 'domain,' derived from Wittgenstein's idea of categories, which serves as a fundamental aspect in defining relative analogies. Building upon this foundation, it closely examines what the literature refers to as 'determination rules,' and specifies their probabilistic and non-monotonic forms. A detailed exploration of the range of specific cases that can be encountered, introducing new concepts such as separation rules, counter-determination rules, and counter-separation rules, is proposed. Subsequently, we illustrate how this set of rules enables a unified set of inference schemes of analogical reasoning. This leads to address examples typically treated as independent and specific instances in the literature, often relying on vague epistemic recommendations. The article suggests that reasoning by analogy is a particular case within a broader framework of reasoning by analogy and by difference, shedding light on various analogical debates.