This article identifies and formalizes the logical features of analogous terms that justify their use in deduction. After a survey of doctrines in Aristotle, Aquinas, and Cajetan, the criteria of “analogy of proper proportionality” are symbolized in first-order predicate logic. A common genus justifies use of a common term, but does not provide the inferential link required for deduction. Rather, the respective differentiae foster this link through their identical proportion. A natural-language argument by analogy is formalized so as (...) to exhibit these criteria, thereby showing the validity of analogical deduction. (shrink)

a recent paper, Fábio Perin Shecaira proposes a defence of Waller’s deductivist schema for moral analogical argumentation. This defence has several flaws, the most important of them being that many good analogical arguments would be deemed bad or deficient. Additionally, Shecaira misrepresents my alternative account as something in between deductivism and non-deductivism. This paper is both an attempt at solving this misunderstanding and an analysis and criticism of Waller and Shecaira’s forms of deductivism.

Bruce Waller has defended a deductive reconstruction of the kinds of analogical arguments found in ethics, law, and metaphysics. This paper demonstrates the limits of such a reconstruction and argues for an alternative. non-deductive reconstruction. It will be shown that some analogical arguments do not fit Waller's deductive schema, and that such a schema does not allow for an adequate account of the strengths and weaknesses of an analogical argument. The similarities and differences between the account defended (...) herein and the Trudy Govier's account are discussed as well. (shrink)

This paper describes a cubic water tank equipped with a movable partition receiving various amounts of liquid used to represent joint probability distributions. This device is applied to the investigation of deductive inferences under uncertainty. The analogy is exploited to determine by qualitative reasoning the limits in probability of the conclusion of twenty basic deductive arguments (such as Modus Ponens, And-introduction, Contraposition, etc.) often used as benchmark problems by the various theoretical approaches to reasoning under uncertainty. The probability bounds imposed (...) by the premises on the conclusion are derived on the basis of a few trivial principles such as "a part of the tank cannot contain more liquid than its capacity allows", or "if a part is empty, the other part contains all the liquid". This stems from the equivalence between the physical constraints imposed by the capacity of the tank and its subdivisions on the volumes of liquid, and the axioms and rules of probability. The device materializes de Finetti's coherence approach to probability. It also suggests a physical counterpart of Dutch book arguments to assess individuals' rationality in probability judgments in the sense that individuals whose degrees of belief in a conclusion are out of the bounds of coherence intervals would commit themselves to executing physically impossible tasks. (shrink)

In this article, we address fallacious analogical reasoning and the Metaphoric Fallacy to a Deductive Inference (MFDI), recently discussed by B. Lightbody and M. Berman (2010). We claim that the authors’ proposal to introduce a new fallacy is only partly justified. We also argue that, in some relevant cases, fallacious analogical reasoning involving metaphors is only affected by the use of quaternio terminorum.

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)

Various sources in the literature claim that the deduction theorem does not hold for normal modal or epistemic logic, whereas others present versions of the deduction theorem for several normal modal systems. It is shown here that the apparent problem arises from an objectionable notion of derivability from assumptions in an axiomatic system. When a traditional Hilbert-type system of axiomatic logic is generalized into a system for derivations from assumptions, the necessitation rule has to be modified in a (...) way that restricts its use to cases in which the premiss does not depend on assumptions. This restriction is entirely analogous to the restriction of the rule of universal generalization of first-order logic. A necessitation rule with this restriction permits a proof of the deduction theorem in its usual formulation. Other suggestions presented in the literature to deal with the problem are reviewed, and the present solution is argued to be preferable to the other alternatives. A contraction-and cut-free sequent calculus equivalent to the Hubert system for basic modal logic shows the standard failure argument untenable by proving the underivability of DA from A. (shrink)

The present form of mathematical logic originated in the twenties and early thirties from the partial merging of two different traditions, the algebra of logic and the logicist tradition (see [27], [41]). This resulted in a new form of logic in which several features of the two earlier traditions coexist. Clearly neither the algebra of logic nor the logicist’s logic is identical to the present form of mathematical logic, yet some of their basic ideas can be distinctly recognized within it. (...) One of such ideas is Boole’s view that logic is the study of the laws of thought. This is not to be meant in a psychologistic way. Frege himself states that the task of logic can be represented “as the investigation of the mind; [though] of the mind, not of minds” [17, p. 369]. Moreover Frege never charges Boole with being psychologistic and in a letter to Peano even distinguishes between the followers of Boole and “the psychological logicians” [16, p. 108]. In fact for Boole the laws of thought which are the object of logic belong “to the domain of what is termed necessary truth” [2, p. 404]. For him logic does not depend on psychology, on the contrary psychology depends on logic insofar as it is only through an investigation of logical operations that we could obtain “some probable intimations concerning the nature and constitution of the human mind” [2, p. 1]. Logic is normative, not descriptive. For, the laws of thought do not “manifest their presence otherwise than by merely prescribing the conditions of formal inference” [2, p. 419]. They are, “properly speaking, the laws of right reasoning only” [2, p. 408]. So they “form but a part of the system of laws by which the actual processes of reasoning, whether right or wrong, are governed” [2, p. 409]. Boole’s idea that logic is the study of the laws of thought was taken over by Hilbert. According to him logic is “a discipline which expresses the structure of all our thought” [31, p.. (shrink)

We propose a natural deduction calculus for the modal logic S4.2. The system is designed to match as much as possible the structure and the properties of the standard system of natural deduction for first-order classical logic, exploiting the formal analogy between modalities and quantifiers. The system is proved sound and complete with respect to (w.r.t.) the standard Hilbert-style formulation of S4.2. Normalization and its consequences are obtained in a natural way, with proofs that closely follow the analogous (...) ones for first-order logic. (shrink)

Kant’s Third Analogy of Experience seeks to establish the mutual interaction of all objects of experience as a transcendental condition on the possibility of our experience of coexistence, and by extension of any cohesive or unified experience. Of Kant’s three Analogies, the Third has received both the least attention and the most criticism. I present an analysis of the Third Analogy focussing on the spatial aspect of Kant’s argument. I examine the interrelated nature of the forms of inner and outer (...) sense in the Third Analogy, linking this to their function in the Transcendental Deduction and subsequently turning to look at the problem posed by Kant’s argument regarding empty space in the Third Analogy. I present a tentative interpretation whereby the Third Analogy establishes a mutual dependence between space as a singular pure intuition, and the instantiation of the category of community in experience. (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)

Fregean predicates applied to Fregean objects are merely defined by a `timeless' deductive order of sentences. They cannot provide sufficient structure in order to explain how names can refer to objects of intuition and how predicates can express properties of substances that change in time. Therefore, the accounts of Wilson and Quine, Prior and Brandom for temporal judgments fail — and a new reconstruction of Kant's transcendental logic, especially of the analogies of experience, is needed.

This Is A New Release Of The Original 1905 Edition.

It is often taken for granted by writers who propose--and, for that matter, by writers who oppose--'justifications' of inductions, that deduction either does not need, or can readily be provided with, justification. The purpose of this paper is to argue that, contrary to this common opinion, problems analogous to those which, notoriously, arise in the attempt to justify induction, also arise in the attempt to justify deduction.

The structure of derivations in natural deduction is analyzed through isomorphism with a suitable sequent calculus, with twelve hidden convertibilities revealed in usual natural deduction. A general formulation of conjunction and implication elimination rules is given, analogous to disjunction elimination. Normalization through permutative conversions now applies in all cases. Derivations in normal form have all major premisses of elimination rules as assumptions. Conversion in any order terminates.Through the condition that in a cut-free derivation of the sequent Γ⇒C, no (...) inactive weakening or contraction formulas remain in Γ, a correspondence with the formal derivability relation of natural deduction is obtained: All formulas of Γ become open assumptions in natural deduction, through an inductively defined translation. Weakenings are interpreted as vacuous discharges, and contractions as multiple discharges. In the other direction, non-normal derivations translate into derivations with cuts having the cut formula principal either in both premisses or in the right premiss only. (shrink)

This paper addresses several issues in argumentation theory. The over-arching goal is to discuss how a theory of analogical argument schemes fits the pragma-dialectical theory of argument schemes and argument structures, and how one should properly reconstruct both single and complex argumentation by analogy. I also propose a unified model that explains how formal valid deductive argumentation relates to argument schemes in general and to analogical argument schemes in particular. The model suggests “scheme-specific-validity” i.e. that there are contrasting (...) species of validity for each type of argument scheme that derive from one generic conception of validity. (shrink)

Descartes’s most extensive discussion of the law of refraction and the shape of the anaclastic lens is contained in Rule 8 of "Rules for the Direction of the Mind". Few reconstructions of Descartes’s discovery of the law of refraction take Rule 8 as their basis. In Rule 8, Descartes denies that the law of refraction can be discovered by purely mathematical means, and he requires that the law of refraction be deduced from physical principles about natural power or force, the (...) nature of the action of light, and the behavior of light rays in a variety of transparent media. For over a century, however, there has been broad agreement that Descartes discovered the law of refraction by purely mathematical means, and that he only later provided the relevant physical rationale (via comparisons or analogies) in Dioptrics II. I execute each step in Descartes’s proposed deduction of the law of refraction and the shape of the anaclastic lens in Rule 8 and concretely show how Descartes could have discovered the law of refraction and the shape of the anaclastic by its means. Rule 8, I argue, reflects Descartes’s actual path to the discovery of the law of refraction and the shape of the anaclastic lens. (shrink)

The paper provides a qualified defence of Bruce Waller’s deductivist schema for a priori analogical arguments in ethics and law. One crucial qualification is that the schema represents analogical arguments as complexes composed of one deductive inference but also of one non-deductive subargument. Another important qualification is that the schema is informed by normative assumptions regarding the conditions that an analogical argument must satisfy in order for it to count as an optimal instance of its kind. Waller’s (...) schema is defended from criticisms formulated by Trudy Govier, Marcello Guarini and Lilian Bermejo-Luque. (shrink)

This essay (a revised version of my undergraduate honors thesis at Stanford) constructs a theory of analogy as it applies to argumentation and reasoning, especially as used in fields such as philosophy and law. The word analogy has been used in different senses, which the essay defines. The theory developed herein applies to analogia rationis, or analogical reasoning. Building on the framework of situation theory, a type of logical relation called determination is defined. This determination relation solves a puzzle (...) about analogy in the context of logical argument, namely, whether an analogous situation contributes anything logically over and above what could be inferred from the application of prior knowledge to a present situation. Scholars of reasoning have often claimed that analogical arguments are never logically valid, and that they therefore lack cogency. However, when the right type of determination structure exists, it is possible to prove that projecting a conclusion inferred by analogy onto the situation about which one is reasoning is both valid and non-redundant. Various other properties and consequences of the determination relation are also proven. Some analogical arguments are based on principles such as similarity, which are not logically valid. The theory therefore provides us with a way to distinguish between legitimate and illegitimate arguments. It also provides an alternative to procedures based on the assessment of similarity for constructing analogies in artificial intelligence systems. (shrink)

RésuméEn dépit de son importance dans divers domaines, le raisonnement analogique n'a pas encore reçu de représentation formelle unifiée. Notre contribution propose un schéma d'inférence général, compatible avec différentes logiques (déductive, probabiliste, non monotone). Premièrement, un énoncé analogique définit précisément la similarité entre deux objets en fonction de leurs propriétés, de façon relative et non absolue. Deuxièmement, une inférence analogique transfère une propriété nouvelle d'un objet à un objet similaire, grâce à une hypothèse d'arrière-plan qui relie deux ensembles de propriétés. (...) Le degré de croyance dans la conclusion est alors directement relié au degré de croyance dans cette méta-hypothèse. (shrink)

We present an analytical study that puts forward a hypothesis about the role of analogy in thinking. The article presents a critique of the structural mapping hypothesis in analogy as an explanation of the analogical argument and will offer an alternative explanation — the functional hypothesis of the analogical argument. It will also be shown how such functions of thinking as recognition and memory, metaphor and syllogism, generalization and ontology, deduction and induction can be realized with the (...) help of the analogy method developed by the author. The article puts forward a hypothesis that these different functions are nothing more than different manifestations of one mechanism for the dissemination of thinking patterns through analogy.In the previous article [1] we described the results of experiments on obtaining analogs of words based on the statistics of predicates extracted from texts by a simple parser. In this article, continuing the topic of analogy, we will analyze two aspects:- how similar expressions (analogous argument) are found when solving problems and learning;- what is the role of analogy in thinking, namely, what thinking processes are realized with the help of analogy.The article critically examines the most well-known approaches to explaining and attempting to implement analogy. The authors propose another hypothesis, called functional analogy, which is distinguished by the simplicity of explaining the analogical argument, greater correspondence to examples of analogy, in the authors’ opinion, and the possibility of programmatic implementation. (shrink)

With his 1951 publication of “Two Dogmas of Empiricism”, W.V.O. Quine launched a series of arguments against the idea that analyticity – “truth in virtue of meaning alone” – could be a philosophically explanatory notion. While his rejection represents a significant philosophical stride in its own right, to which many in the contemporary philosophical scene pay verbal respects, the revolutionary consequences of this insight often go ignored today. Much of current professional philosophy in virtually every sub-discipline carries on as though (...) analyticity were a viable notion, because much of it aims at conceptual analysis – the “discovery” of the meanings of philosophical concepts, such as ‘mind’, ‘truth’, ‘meaning’, ‘person’, and ‘right’. Rejecting analyticity as a viable philosophical notion undermines such efforts insofar as they aim at conceptual analysis. If philosophers give up the notion of analyticity, as they should, they are left with the questions of what goals and methods are viable for the analysis of concepts. One option is to concentrate effort on explication of familiar concepts; explication is an alternative to conceptual analysis in that it does not aim to dig out analytic truths about given concepts. Rather, it identifies what is interesting about a certain vague concept, and generates a new, more rigorous and precise concept to replace the old one. The justification for the replacement, in the most appealing cases, is in the possibilities for understanding that are introduced by the new explication. Examples of explication in my sense are the replacement of ordinary grammatical terms by the operators of first order logic, replacement of ‘game’ with a decision theoretic notion of games in game theory, and replacement of ‘true’ with ‘true-in-L’ in Tarskian semantics. Advances of this sort depart consciously in some ways from ordinary usage of the terms they focus on, but in so departing, they develop new possibilities and perspectives for rigorously understanding the world. In the dissertation that follows, I not only recommend explication as a method, I also put it into practice. I develop an explication of the sameness and difference relations that relies solely on the relation of denotation between a predicate and objects of which it is true. Two things are the same with respect to R just in case there is at least one R-predicate that denotes them in common. I used this explication to develop related explications of similarity and analogy. These latter explications, I use to critique the current fashion of research on similarity and analogy in cognitive psychology. These studies have produced an immense body of interesting and promising work in the past several decades; however, much of the research design and data interpretation harbors philosophical errors and so often imports unjustified prejudices from the researchers themselves. My explication offers alternative formulations of the most salient aspects of these research traditions, formulations that avoid the errors of past research and, more importantly, suggest new research questions and possibilities that would not occur under the previous, philosophically muddled paradigm. The project closes with an application of my explication of analogy to a discussion and critique of the philosophical literature on analogical arguments. While philosophers and logicians have developed workable theories for deductive and inductive reasoning, very little work of promise has been done on analogical arguments. My explication of analogy is used to diagnose the problems of past attempts by philosophers to develop logics for analogical arguments and suggest, in light of the psychological research on analogy and the use of analogies in scientific thought, that philosophers should focus on analogical arguments as creative, heuristic devices, rather than as truth-preserving inference structures. (shrink)

Accounts of analogical inference are usually categorized into four broad groups: abductive, deductive, inductive and sui generis. The purpose of this paper is to defend a sui generis model of analogical inference. It focuses on the sui generis account, as developed by Juthe [2005, 2009, 2015, 2016] and Botting’s [2017] criticism of it. This paper uses the pragmadialectical theory of argumentation as the methodological framework for analyzing and reconstructing argumentation. The paper has two main points. First, that Juthe’s (...) arguments against a deductive interpretation of prima facie analogy argumentation remain unaffected by Botting’s criticism, which means that many of the reasons against deductive reformulation of analogy argumentation still stand. The additional argument, which Botting himself brings up, that a deductive interpretation cannot account for the cumulative effect of analogies, just provides further reason to reject deductivism. The second main point of this paper is that an inductive interpretation of analogical inference also fails. There are constitutional differences between inductive and analogical inference that cannot be bridged. The result is a firm defense of the sui generis view of analogical inference. (shrink)

ABSTRACT: In this essay I characterize arguments by analogy, which have an impor- tant role both in philosophical and everyday reasoning. Arguments by analogy are dif- ferent from ordinary inductive or deductive arguments and have their own distinct features. I try to characterize the structure and function of these arguments. It is further discussed that some arguments, which are not explicit arguments by analogy, nevertheless should be interpreted as such and not as inductive or deductive arguments. The result is that (...) a presumed outcome of a philosophical dispute will have to be reconsidered. (shrink)

T. Govier's description of ‘conductive argument’ and 'A priori analogy' is taken as a start to investigate non-deductive argumentation. It is here argued, that the nature of those types can be better understood when taking up a dynamic view (in addition to the usual structural view). The concepts of ‘frame’ and ‘position’ are constructed in order to establish such a twofold approach.

In this paper, I try to accomplish two goals. The first is to provide a general characterization of a method of proofs called — in mathematics — the diagonal argument. The second is to establish that analogical thinking plays an important role also in mathematical creativity. Namely, mathematical research make use of analogies regarding general strategies of proof. Some of mathematicians, for example George Polya, argued that deductions is impotent without analogy. What I want to show is that there (...) exists a direct line leading from Cantor’s diagonal argument to constructions that underlies of the proofs of several important theorems of the mathematical logic (in particular, Church’s theorem concerning the undecidability of formal arithmetic, Gödel’s theorem concerning the incopleteness of formal arithmetic, Tarski’s theorem concerning truth, and Turing’s theorem concerning the Halting Problem), and that the line could be described as an analogical mapping. In other words, Cantor’s diagonal argument and the proofs of the limitative theorems are structurally the same. Hence they can be represented as instances (or special cases) of the same general scheme. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Plato's Political Analogy: Fallacy or Analogy? ROBERT W. HALL THE INTERPRETATIONOf the familiar political analogy between the state and the soul is crucial to a proper understanding of Plato's conception of the individual and his relation to the polls. Interpretations which, consciously or not, tend to identify the justice of the individual with that of the state result either in a subordination of justice of the individual to that (...) of the state, or in endowing the ordinary citizen with an inferior justice. These interpretations of the political analogy have beert adequately dealt with? Recently, Vlastos has stressed what he considers to be the logical or deductive character of the analogy." He finds defects or fallacies in Plato's logic, which, while not necessarily fatal to the significance of the analogy, seriously impair its cogency. What is of particular interest is Vlastos' claim that the primary goal of the analogy is a demonstration, unknown to most scholars, albeit an unsuccessful one, that the justice of the individual necessarily instantiates or entails ordinary acts of justice,a Vlastos has thus raised the question of what kind of approach is most fruitful in unlocking the meaning of the political analogy. My own conviction is that the political analogy can best be understood through a careful examination or observation of the two wholes, the state and the individual, and the character of their relationship. A consideration of the essentials of Vlastos' outlook on the analogy will be a useful introduction to what may be termed a "phenomenological" approach. Such a perspective may provide a better understanding of what Plato is attempting to establish in the analogy, and of how he goes about it. Vlastos' interpretation of the political analogy is strongly colored by his assessment of the central concern of the Republic, the proof that justice "pays." By this Vlastos means that what he terms "psychological justice," the correct, hierarchical arrangement of the three parts or aspects of the soul, must be proven to result in acts of external justice. It is this relationship between psychological justice and ordinary or social justice which sets the problem of logical consistency in Vlastos' account of the political analogy. As the definition of justice of the individual or psychological justice, Vlastos offers Socrates' statement, "In the case of each one of us, whoever is such that each of the three [psychic elements] in him does its own, he is a just man." The social description of justice is: What we laid down at the start as a general requirement when we were founding the polls this, or some form of it, is justice. We did lay down, and often stated, if you recall, that every single person ought to engage in the social function.., for which his own nature is I For exponents of these positions and their critics, cf. my "Plato's Theory of Justice in the Republic," Bucknell Review, XV, 2 (May, 1967), 60, n. I. G. Vlastos, "Justice and Psychic Harmony in the Republic," The 1ournal of Philosophy, LXVI, 16 (August 21, 1969), 505-521. All further references to this article will be by page number. s 506, 515. [419] 420 HISTORY OF PHILOSOPHY best fitted.uWe did say this.--And indeed that to do one's own and not to be meddlesome is justice, this we have often heard from many others, and have often said ourselves.-Wc have said it.--This, then, my friend, if taken in a certain way, appears to be justice: to do one's own. (433A-B) 4 Vlastos admits that this social description is not really a definition of the justice of the individual, "that 'doing one's own' was not meant to constitute a definition of the justice of an individual person.''~ Nonetheless, this social description functions for him as a definition of the individual's justice, and plays a prominent role in the supposed fallacy of equivocation in the meaning of justice. Vlastos argues for this social description on the grounds that "/or Plato every just man must have the disposition named by the 'doing one's own' formula.''e The basis for this claim is Socrates' declaration that "the same (moral) characters... (shrink)

This study was concerned with Wason's THOG task, a hypothetico-deductive reasoning problem for which performance is typically very poor ( < 20% correct). Recently, however, Needham and Amado (1995) and Koenig and Griggs (2004) have observed both facilitation and spontaneous analogical transfer effects for the Pythagoras version of this task. Based on their findings, Koenig and Griggs concluded that in addition to the separation of the data (the properties of the designated THOG) from the hypotheses that need to be (...) generated (the possible combinations of properties written down), an explicit request to generate these hypotheses is necessary to obtain significant analogical transfer. In the present study we extended the generalisability of this conclusion in three experiments with 214 undergraduate participants using O'Brien et al.'s (1990) Blackboard version of the task. We discuss the relationship of the results to dual process theories of reasoning and propose that analogical transfer may be a better criterion than task facilitation for judging participants' task understanding. (shrink)

Given a π -institution I , a hierarchy of π -institutions I is constructed, for n ≥ 1. We call I the n-th order counterpart of I . The second-order counterpart of a deductive π -institution is a Gentzen π -institution, i.e. a π -institution associated with a structural Gentzen system in a canonical way. So, by analogy, the second order counterpart I of I is also called the “Gentzenization” of I . In the main result of the paper, it (...) is shown that I is strongly Gentzen , i.e. it is deductively equivalent to its Gentzenization via a special deductive equivalence, if and only if it has the deduction-detachment property. (shrink)

According to the deliberative view of democracy, the legitimacy of democratic politics is closely tied to whether the use of political power is accompanied by a process of rational deliberation among the citizenry and their representatives. Critics have questioned whether this level of deliberative capacity is even possible among modern citizenries--due to limitations of time, energy, and differential backgrounds--which therefore calls into question the very possibility of this type of democracy. In my dissertation, I counter this line of criticism, arguing (...) that deliberative democrats and their critics have both idealized the wrong kind of citizen deliberation. Citizen deliberation should not be concerned with the indeterminate project of "translating" abstract democratic principles and values into everyday cases of political problem-solving. Instead, deliberation should take the form of analogy, just as we already find it in everyday politics and affairs. When ordinary citizens use analogies, they do not derive decisions from general principles or values, but they still reason nonetheless. Seen from this analogical perspective, deliberative democracy is already a practical reality to a large degree. When an election is on the horizon, a campaign season arises in which debates, forums, and "barstool" dialogues exponentially increase the amount of citizen deliberation. In these settings, citizens can readily be seen to be mapping analogous past candidates, elections, issues, and problems onto those currently on the ballot so as to reason about them. Consequently, analogical reasoning allows citizens to treat the majority rule mechanisms that proliferate in real politics as "deliberative outlets," which is to say, as catalysts of deliberation akin to the "creative outlets" that catalyze self-expression in the arts. While citizens may recognize majority rule mechanisms as catalysts of deliberation, many democratic theorists will hesitate to embrace this vision of the practical reality of deliberative politics. Isn't analogical reasoning too low in rigor to be placed at the heart of the deliberative ideal? I develop two arguments to explain the foundational role analogy plays in deliberation and to counter such critics. First, I draw on the explosion of research on analogical reasoning over the past two decades to show that it is far more rigorous and systematic than many suppose. Second, I argue that to the extent that citizen deliberation is concerned with rational planning, rather than just reasoning in general, analogical reasoning is logically superior. When we reason about what to do, we make plans that incorporate predictions about what is likely to ensue when a given course of action is selected. However, as soon as predictions enter into deliberation, its underlying logic changes as well. The reason for this change in logic is that as our probabilistic reasoning expands, the probability of its conclusions degenerates. Therefore, when assessing probabilities, we no longer should seek decisions derived from long, elegant chains of reasoning that connect our various options to generalities like values and principles. Instead, what we need is "short and sweet," or terse, humble lines of reasoning, which are more congruent with this form of deliberation. Thus, to the extent that democratic deliberation is involved in rational planning, it calls not for the elegant, deductive kind of reasoning idealized by proponents and critics of deliberative democracy alike. Instead, democratic deliberation calls for the "short and sweet," analogical kind of decision-making we associate with ordinary citizens already. After all, as research has shown, analogies are a much preferred and rigorous way by which even experts engage in probabilistic reasoning. By focusing on analogical reasoning, I therefore conclude that the practical reality of deliberative democracy should be recognized in ways that might ordinarily be dismissed. (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 (...) class='Hi'>deduction in order to explain why some predicates, such as “grue,” are unprojectible. (shrink)

In a priori analogies, the analogue is constructed in imagination, sharing certain properties with the primary subject. The analogue has some further property clearly consequent on those shared properties. Ceteris paribus the primary subject has that property also. The warrant involves non-empirical, e.g., moral intuition but is also defeasible. The argument is thus neither deductive nor inductive, but an additional type. In an inductive analogy, the analogues back the warrant from below. Distinguishing these two types of arguments by analogy gives (...) epistemic evaluative factors primacy over resemblance factors in classifying arguments—a prescient insight on Govier’s part. (shrink)

This article is an effort to improve understanding between Moist and Aristotelian logics on analogy. I argue that Chinese logic can neither fit in Aristotelian deductive framework, nor completely fit in Aristotelian inductive framework. One of the major reasoning skills that ancient Chinese logicians applied is analogical reasoning. Having examined thirteen Moist analogical propositions in a Moist text, the Da Qu 〈大取〉from the perspective of finding rationales (li 理) among things, I conclude that if the rationales can be (...) found in a changing world, then Chinese logicians seek for the “beauty of creative thinking” in the process of argumentation. (shrink)

The Logic of Metaphor uses techniques from possible worlds semantics to provide formal truth-conditions for many grammatical classes of metaphors. It gives logically precise and practically useful syntactic and semantic rules for generating and interpreting metaphors. These rules are implemented in a working computer program. The book treats the lexicon as a conceptual network with semantics provided by an intensional predicate calculus. It gives rules for finding analogies in such networks. It shows how to syntactically and semantically analyze texts containing (...) metaphors and how to use structural similarities between parts of possible worlds to provide truth-conditions for metaphors. Meanings for metaphors are linked to the modal logics of identity and indiscernibility. The book shows how to extend deductive and abductive inference systems to handle metaphors. It shows how to handle novel metaphorical word-senses. The Logic of Metaphor will be useful to philosophers, logicians, linguists, and computer scientists. (shrink)

In this paper I will argue that most objections to deductive analyses of a priori analogies are incorrect, often involve basic misinterpretations of what the deductive reconstruction of those arguments are saying, and sometimes also betray a confusion about what part of the reasoning corresponds to the analogical inference. In particular, I will be focusing on a raft of objections made by Juthe in [2015] and subject his alternative views to criticism. -/- I will then argue that Juthe does (...) implicitly have a good argument against deductivism: adding further analogues seems to have a cumulative force that they would not have on a deductivist analysis. This is so not only in ordinary analogical arguments but, perhaps surprisingly, with a priori analogical arguments. I will then argue that this does not favor a sui generis view of the analogical argument over inductivist views, and attempt to show that a confirmation-theoretic approach to analogical inference makes the best sense of our intuitions about the strength of analogical arguments. (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)

Socrates’ expert-analogies is frequent both in Plato’s dialogues and in the Socratic writings of Xenophon, and is also ascribed to Socrates by Aristotle and Aeschines. Socrates makes an analogy from a non-controversial expert (or an expertise) like the cobbler or ship-captain, to another (often controversial) expert (or expertise) like the statesman. This paper defends an interpretation of the expert-analogy as valid deductions. It infers from one type of expert (such as the ship-captain) to another type of expert (such as the (...) statesman), and the attribute inferred (for instance ‘should not be selected by lot’) belongs to these types of experts because they are experts. The general logical form, which makes no mention of the expert and which is valid in virtue of its form, infers from one or more species to another species of the same genus, and the attribute inferred is presupposed to belong as such to the genus and only accidentally to the species. (shrink)

Following a Toulmian account of argument analysis and evaluation, I offer a general unitary schema for, so called, deductive and inductive types of analogical arguments. This schema is able to explain why certain analogical arguments can be said to be deductive, and yet, also defeasible.

This essay partly builds on and partly criticizes a striking idea of Dieter Henrich. Henrich argues that Kant's distinction in the first Critique between the question of fact (quid facti) and the question of law (quid juris) provides clues to the argumentative structure of a philosophical "Deduction". Henrich suggests that the unity of apperception plays a role analogous to a legal factum. By contrast, I argue, first, that the question of fact in the first Critique is settled by the (...) Metaphysical Deduction, which establishes the purity of origin of the Categories, and, second, that in the second Critique, the relevant factum is the Fact of Reason, which amounts to the fact that the Moral Law is pure in origin. (shrink)

In a central variant, moral fictionalism is the view that we should replace moral belief with make-believe, that is, be disposed to accept some moral propositions in everyday contexts and to reject all such propositions in more critical circumstances. It is said by its opponents to face three significant problems: in contrast with a real morality, a fictional morality would not allow for deductive inferences; moral make-believe would lack the motivational force that is typical of moral belief; and moral make-believers (...) could not genuinely disagree with one another about ethical matters nor, consequently, articulate their practical conflicts in moral terms. This chapter argues that all three objections rest on a misconception of the kind of attitudes recommended by fictionalism. Once misleading analogies are dismissed and the nature of moral make-believe is clarified, it becomes clear that a fictional morality would preserve deductive inference, moral motivation, and ethical disagreement. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Kant's Transcendental Deduction by Alison LaywineKatherine DunlopAlison Laywine. Kant's Transcendental Deduction. Oxford: Oxford University Press, 2020. Pp. iv + 318. Hardback, $80.00.Alison Laywine's contribution to the rich literature on Kant's "Transcendental Deduction of the Categories" stands out for the novelty of its approach and conclusions. Laywine's declared "strategy" is "to compare and contrast" the Deduction with the Duisburg Nachlaß, an important set of manuscript (...) jottings from the 1770s (10). But her approach is also deeply informed by Kant's writings on metaphysics from the 1750s and 1760s; moreover, she gives attention to ancient Greek geometry and its importance for Kant's thought.I believe Laywine's most important interpretative claim is that the Transcendental Deduction's "final step" addresses "the question of how nature is possible" (210). Here, 'nature' is understood in what Kant calls the "formal sense," as "the totality of rules under which appearances must stand if they are to be thought as joined in one experience" (Prolegomena, §36; cf. B 165). This constitutes a novel answer to the problem posed in Dieter Henrich's landmark 1969 paper "The Proof Structure of the Transcendental Deduction" (Review of Metaphysics 22 [1969]: 640–59): how to understand §§21–26 of the (B-edition) Deduction as proving more than the thesis already stated in §20 (that the manifold in an intuition necessarily stands under the categories).Crucial support for Laywine's interpretation comes from §26 of the Deduction, which claims the possibility of cognizing objects "a priori through categories... as far as the laws of their combination are concerned, thus the possibility of as it were prescribing the law to nature and even making [nature] possible," is now "to be explained" (B 159). Kant does not use the term 'world' in this passage (as he does in Prolegomena §36). But Laywine contends that here the word 'nature' "has unmistakable, deliberate, cosmological connotations," and in fact "means 'world' in the sense of Kant's early cosmology": roughly, a whole unified by means of laws (12–13).The "cosmological" language of §26 does not recur in the following, officially concluding, section of the Deduction. So, we might ask whether Kant's explanation of how the understanding prescribes laws to nature is integral to the Deduction; Henry Allison, for instance, describes this explanation as an "appendix" (Kant's Transcendental Deduction: An Analytical-Historical Commentary [Oxford: Oxford University Press, 2015], 9). The question of whether it belongs integrally has bite because, as Laywine makes clear in her "Conclusion," the universal laws at issue are just the Analogies of Experience. Thus, the passage could be read as the "promissory note with a forward-looking reference to the System of Principles" that she finds missing from the Deduction (289). Laywine meets such worries by arguing that "the reappropriation [from the pre-Critical period] of the general cosmology is actually [End Page 162] doing... a lot of hard work" in the Deduction (13). This sustained argument comes to a head in chapter 4, which contends that each of the two steps into which Laywine divides the first half of the (B-edition) Deduction, treated in chapters 2 and 3 (respectively), relies on cosmological presuppositions.Chapter 2 analyzes the conception of knowledge as relation to an object that is asserted (in §17) to rely on the synthetic unity of apperception. Laywine traces this conception to the Duisburg Nachlaß's account of "exposition," which relates concepts a priori to appearances, in something like the way that geometrical construction relates them to pure intuition. (Laywine further connects the Latin term expositio to the Greek ekthesis, which expositio translates in the context of geometrical proof. She thereby gives the notion of ekthesis broader importance than does Jaakko Hintikka, who noted its relevance to Kant's philosophy of mathematics in "Kant on the Mathematical Method" [Monist 51 (1967): 352–75]. Laywine claims that Borelli's edition of Euclid could have been Kant's source for the term, but I doubt it was known to Kant and his contemporaries, since it is not among the editions cited by Christian Wolff; Commandino seems likelier to me. Chapter 2 is concerned to articulate the notion of... (shrink)

Our article identifies and describes the metaphoric fallacy to a deductive inference (MFDI) that is an example of incorrect reasoning along the lines of the false analogy fallacy. The MFDI proceeds from informal semantical (metaphorical) claims to a supposedly formally deductive and necessary inference. We charge that such an inference is invalid. We provide three examples of the MFDI to demonstrate the structure of this invalid form of reasoning. Our goal is to contribute to the set of known informal fallacies.

Seldom does human reasoning fit the standards of deduction. Yet logicians have tended to use the strict standards of deductive validity for assessing all inferences. _Within Reason_ develops instead a way of assessing arguments and inferences that is directly appropriate to the non-deductive forms people regularly use. It uses analogy, and argument from analogy, to provide a thread that unites various forms: raising objections, inductions of various sorts, arguments to explanation, and arguments to action. The discussion is developed progressively, (...) at each stage building on the skills learned previously. And at each stage the book suggetss ways of assessing the strength of reasoning. Most of the examples are taken from the great texts of the Western tradition. In the exercises that form an integral part of each chapter an even broader range of writing is presented, offering instructors an extraordinary variety of texts at various levels ot assign to their students. The thesis implicit in the book is that induction, arguments to explanation and arguments to action are all sophisticated forms of arguments from analogy. Burbidge is concerned not simply to warn against the misuse of non-deductive reasoning but also to develop a more positive theory that allows us both to better udnerstand the workings of non-deductive reasoning, and to better employ it. (shrink)

Seldom does human reasoning fit the standards of deduction. Yet logicians have tended to use the strict standards of deductive validity for assessing all inferences. _Within Reason_ develops instead a way of assessing arguments and inferences that is directly appropriate to the non-deductive forms people regularly use. It uses analogy, and argument from analogy, to provide a thread that unites various forms: raising objections, inductions of various sorts, arguments to explanation, and arguments to action. The discussion is developed progressively, (...) at each stage building on the skills learned previously. And at each stage the book suggetss ways of assessing the strength of reasoning. Most of the examples are taken from the great texts of the Western tradition. In the exercises that form an integral part of each chapter an even broader range of writing is presented, offering instructors an extraordinary variety of texts at various levels ot assign to their students. The thesis implicit in the book is that induction, arguments to explanation and arguments to action are all sophisticated forms of arguments from analogy. Burbidge is concerned not simply to warn against the misuse of non-deductive reasoning but also to develop a more positive theory that allows us both to better udnerstand the workings of non-deductive reasoning, and to better employ it. (shrink)

ABSTRACTThis article, which summarises some of the main arguments of Analogical Investigations [Lloyd 2015], undertakes a comparative cross-cultural critique of the dominant Western view that downgrades analogy especially when that is contrasted unfavourably with a notion of axiomatic-deductive demonstration aiming to secure incontrovertible conclusions. It draws on materials from ancient Greece, ancient China and modern social anthropology and philosophy of science to explore the problems of translation and mutual intelligibility. It develops the idea of semantic stretch to qualify the (...) literal/metaphorical dichotomy and the notion of the multidimensionality of reality to clarify aspects of the controversy between realism and relativism. (shrink)