In what follows I will address Kant’s concerns in the First Analogy and in the Refutation of Idealism. Because the two discussions have a similar trajectory, it is of interest to identify some of the differences between them. As we will see, the manifest differences are indicative of more significant underlying differences, regarding two ways of construing transcendental proofs.

Kant’s argument in the First Analogy for the permanence of substance has been cast as consisting of a simple quantifierscope mistake. Kant is portrayed as illicitly moving from a premise such as (1) at all times, there must exist some substance, to a conclusion such as (2) some particular substance must exist at all times. Examples meant to show that Kant makes this mistake feature substances coming into and out of existence, but doing so at overlapping times. I (...) argue that Kant offers an argument against this kind of example in the following passage. Kant’s claim is that, were substances to be created and destroyed as in the example, the appearances would then be related to two different times, in which existence flowed side by side, which is absurd. For there is only one time, in which all different times must not be placed simultaneously but only one after another (A188–9/B231–32). (shrink)

Henry Allison’s interpretation of Kant’s First Analogy is among the most intriguing in the literature. Its virtues are considerable, but no previous discussion has done full justice to them. Nor has any previous discussion systematically explored the most important challenges to which it seems subject. This paper does both. Early sections provide a more thorough exegesis than is otherwise available and provide stronger textual backing than does Allison himself. Later sections turn to problems, most of which have not (...) been raised by others. These problems, while serious, do not necessarily rule out the interpretation of Allison. (shrink)

This paper is concerned with a passage that has long intrigued interpreters of Kant’s First Analogy. the passage in question can be found at A188/B231 of the Critique of Pure Reason. In order to perceive that some item x comes to exist or ceases to exist, asserts Kant in this passage, you must connect the coming to exist or ceasing to exist of x to things that already exist before it takes place and continue to exist until it (...) is completed. But if you do so, he further asserts, it must be the case that x is only a determination of such things and that the coming to exist or ceasing to exist of x is a mere change in the determinations of such things. These assertions are cryptic and give rise to several questions. In what way must you perform the act described? Why must you do so in order to perceive that x comes to exist or ceases to exist? And how does this entail that x is in fact only a determination of such things and thus that its coming to exist or ceasing to exist is not in fact ex nihilo or in nihilo? The answers given in this paper serve both to clarify Kant’s argument and to identify the main issues that would have to be faced in its assessment. (shrink)

According to James Van Cleve, the principle with which Kant is concerned in the first analogy follows from the view that existence statements are properly made only with quantifiers and have to be expressible in the form ‘∃ xFx’. This thesis is extremely surprising and of great potential importance. It rests on the conviction that two more basic principles can be derived from the relevant view about existence statements. The first of these more basic principles is that (...) there can be no coming to exist ex nihilo or ceasing to exist in nihilo; the second is that there cannot be a series of modes not grounded in an ultimate subject. This paper outlines the relevant view about existence statements, traces the argument provided by Van Cleve in support of his thesis, and concludes that the argument rests on adubious assumption that ‘Everything exists’ either means or entails ‘Everything always exists’. (shrink)

Analogical counterfactuals such as “If I were you, I would do so and so...” create a puzzle for philosophical semantics. Whereas the ‘received view' in philosophical semantics has it that the first person pronoun always refers to its utterer, one may wonder whether this is still the case when the first person pronoun is embedded in analogical counterfactuals such as “If I were you, I would stay away from me”. I suggest that the intelligibility of lies in the (...) fact that the token of the expression ‘I' in the consequent of the counterfactual does not refer to its utterer. Should one then conclude, following the ‘anaphoric theory' that the second occurrence of ‘I' in does refer to its addressee? For the ‘anaphoric theory', ‘I' in ‘I would stay away from me' refers anaphorically, thanks to the linguistic context, to the referent of ‘you' in ‘If I were you'. On the basis of an analysis of the imaginative project involved in uttering a practical advise in the form of, I suggest contra the ‘anaphoric theory' that the first pronoun ‘I' in the consequent of behaves as an indexical and that its content is obtained by the application of its character to a pretend context differing from the context of its utterance. According to the so-called ‘pretence theory', the first person pronoun in its second occurrence in pretends to refer to a fictional composite of the utterer and the addressee. (shrink)

In this article, after some thoughts on medieval logic and teaching, we present Thomas Murner’s text, Logica memorativa, showing some of his mnemonic strategies for the student to learn logic quickly. Murner offers a type of “flash cards” that illustrate much of the teaching of logic at the beginning of the sixteenth century. The first impression is visual, because the cards do not contain words that illustrate their content. Murner’s exposition rests on analogies between logic themes that are explained (...) and the visual images presented. (shrink)

Many accounts of analogy based on sentential semantics owe their continued popularity more to a lack of theoretical specificity than to their superior explicative power. I examine a recent attempt to remedy this situation.Conclusion: Once the sentential semantics account of analogy is spelled out in sufficient detail to permit its systematic application to a variety of cases, it quickly becomes apparent why it must fail, and why we should give preference to a multi-constraint theory of cognitive process instead.

Recently, I’ve championed the doctrine that fundamentally different sorts of things exist in fundamentally different ways.1 On this view, what it is for an entity to be can differ across ontological categories.2 Although historically this doctrine was very popular, and several important challenges to this doctrine have been dealt with, I suspect that contemporary metaphysicians will continue to treat this view with suspicion until it is made clearer when one is warranted in positing different modes of existence.3 I address this (...) concern here. The question of when to posit ways of being is closely related to a more general question: when should one think that some philosophically interesting expression is analogous? Accordingly, my strategy here is as follows. First, I briefly explain my interpretation of ontological pluralism, the doctrine that there are ways of being.4 Second, I introduce the notion of an analogous term, and show how, on most ways of implementing ontological pluralism, “existence” is analogous. Third, I discuss two sufficient conditions for when one is warranted in claiming that a philosophically interesting term is analogous. Fourth, I present a series of ontological schemes, each of which satisfies at least one of the sufficient conditions. The upshot is this: if you are attracted to one of these ontologies, you have reason to believe in ways of being. The careful reader will have noted the apparent modesty of my conclusion. Unfortunately, I do not believe that one could ever be rationally required to believe in ways of being. Still, in general a metaphysic is a live option to the extent that it is shown to be rationally permissible to believe. Since the apparent consensus among contemporary analytic metaphysicians is that believing that things can exist in different ways is silly or confused, establishing the rational permissibility of belief in ways of being is a non-trivial task. Let us begin. (shrink)

Since the first decade of the 14th Century, Thomas Aquinas’s disciples have struggled to explain and defend his doctrine of analogy. Analogy after Aquinas: Logical Problems, Thomistic Answers relates a history of prominent Medieval and Renaissance Thomists’ efforts to solve three distinct but interrelated problems arising from their reading both of Aquinas’s own texts on analogy, and from John Duns Scotus’s arguments against analogy and in favor of univocity in Metaphysics and Natural Theology. The (...) class='Hi'>first of these three problems concerns Aquinas’s at least apparently disparate statements on whether a name is said by analogy through a single concept or through diverse concepts. The second problem concerns the model of analogy suited for predicating names analogously across the categories of being or about God and creatures. Is “being” said analogously about God and creatures, or substance and accidents, on the model of how “healthy” is said of medicine and an animal, or on the model of how “principle” is said of a point and a line? The third problem comes from outside challenges to Aquinas’s thought, in particular Scotus’ claims that univocal names alone can mediate valid demonstrations, and any demonstration that failed to use its mediating terms univocally would fail by the fallacy of equivocation. Analogy after Aquinas makes a unique contribution to the study of philosophical theology in the tradition of Thomas Aquinas by showing the historical and philosophical connection between these three problems, as well as the variety of solutions proposed by leading representatives of this tradition. Thomists considered in the book include: Hervaeus Natalis (1250-1323), Thomas Sutton (1250-1315), John Capreolus (1380-1444), Dominic of Flanders (1425-1479), Paul Soncinas (d. 1494), Thomas dio vio Cajetan (1469-1534), Francis Silvestri of Ferrara (1474-1528), and Chrysostom Javelli (1470-1538). (shrink)

Western philosophy and science are responsible for constructing some powerful tools of investigation, aiming at discovering the truth, delivering robust explanations, verifying conjectures, showing that inferences are sound and demonstrating results conclusively. By contrast reasoning that depends on analogies has often been viewed with suspicion. Professor Lloyd first explores the origins of those Western ideals, criticises some of their excesses and redresses the balance in favour of looser, admittedly non-demonstrative analogical reasoning. For this he takes examples both from ancient (...) Greek and Chinese thought and from the materials of recent ethnography to show how different ancient and modern cultures have developed different styles of reasoning. He also develops two original but controversial ideas, that of semantic stretch and the multidimensionality of reality. (shrink)

Rodden writes, “How do stories persuade us? How do they ‘move’—and move us? The short answer: by analogies.” Rodden’s claim is a natural first view, also held by others. This chapter considers the extent to which this view is true and helpful in understanding how fictional narratives, taken as wholes, may be argumentative, comparing it to the two principal (though not necessarily exclusive) alternatives that have been proposed: understanding fictional narratives as exhibiting the structure of suppositional argument, or the (...) structure of a kind of transcendental argument. Three key aspects of understanding a fictional narrative as an argument from analogy are identified. First, the argument will be relativistic or depend in an essential way upon the circumstances or intentions of the auditor or author. Second, in view of the first aspect, the argument will be loose and subjective, and accordingly less likely to yield knowledge. Third, the argument will not exhibit a distinctive structure applicable only to fictional narratives. I find that the third, and sometimes the first and second, of these same three aspects apply to understanding fictional narratives as suppositional arguments. I present considerations that point to a way of establishing that some extended fictions exhibit the structure of a kind of transcendental argument that is neither relativistic nor subjective, is knowledge-generating, and is uniquely applicable to fictional narratives. This supports literary cognitivism—the thesis that “literary fiction can be a source of knowledge in a way that depends crucially on its being fictional.”. (shrink)

In this article I am concerned with analogical reasoning in ethics. There is no doubt that the use of analogy can be a powerful tool in our ethical reasoning. The importance of this mode of reasoning is therefore commonly accepted, but there is considerable debate concerning how its structure should be understood and how it should be assessed, both logically and epistemically. In this paper, I first explain the basic structure of arguments from analogy in ethics. I (...) then discuss the diversity of analogical arguments that can be found in ethics. I analyse their structure, assess them from a logical viewpoint, and show how they can be epistemically challenged and defended. The result of this investigation is that, contrary to a commonly held view, analogical reasoning can be a logically valid type of ethical reasoning that can provide reasons for action that are not worse than the reasons provided by any other kind of practical reasoning. (shrink)

The attention of philosophers. linguists and literary theorists has been converging on the diverse and intriguing phenomena of analogy of meaning:the different though related meanings of the same word, running from simple equivocation to paronymy, metaphor and figurative language. So far, however, their attempts at explanation have been piecemeal and inconclusive and no new and comprehensive theory of analogy has emerged. This is what James Ross offers here. In the first full treatment of the subject since the (...) fifteenth century, he argues that analogy is a systematic and universal feature of natural languages, with identifiable and law-like characteristics which explain how the meanings of words in a sentence are interdependent. Throughout he contrasts his with classical and medieval views. (shrink)

René Descartes' Meditations on First Philosophy is his most celebrated philosophical work. The book remains one of the most significant and influential works in epistemology, metaphysics and philosophy of mind in the history of Western philosophy. In this paper I examine the relationship between the various hyperbolic doubts, the dreaming, imperfect creator, and evil demon hypotheses in Meditation I. The paper shows that the "painting analogy" occupies a central position in the First Meditation not only because it (...) effectively links together the hyperbolic doubts, but also because it lays the groundwork for the claim that although it may be impossible for us to know things outside us as our thoughts represent them to be, we can know at least the feature of our thoughts themselves. By raising the necessary doubt about our sensible experience and the corporeal world, the "painting analogy" makes the case for the primacy of the intellectual world. (shrink)

The purpose of this paper is to present two kinds of analogical representational change, both occurring early in the analogy-making process, and then, using these two kinds of change, to present a model unifying one sort of analogy-making and categorization. The proposed unification rests on three key claims: (1) a certain type of rapid representational abstraction is crucial to making the relevant analogies (this is the first kind of representational change; a computer model is presented that demonstrates (...) this kind of abstraction), (2) rapid abstractions are induced by retrieval across large psychological distances, and (3) both categorizations and analogies supply understandings of perceptual input via construing, which is a proposed type of categorization (this is the second kind of representational change). It is construing that finalizes the unification. (shrink)

The attention of philosophers. linguists and literary theorists has been converging on the diverse and intriguing phenomena of analogy of meaning:the different though related meanings of the same word, running from simple equivocation to paronymy, metaphor and figurative language. So far, however, their attempts at explanation have been piecemeal and inconclusive and no new and comprehensive theory of analogy has emerged. This is what James Ross offers here. In the first full treatment of the subject since the (...) fifteenth century, he argues that analogy is a systematic and universal feature of natural languages, with identifiable and law-like characteristics which explain how the meanings of words in a sentence are interdependent. Throughout he contrasts his with classical and medieval views. (shrink)

I present three critical points against G.E.R. Lloyd's ‘The Fortunes of Analogy’. First, I argue that Lloyd unduly criticises Aristotle's view of analogies. Second, I argue that Lloyd needs to discuss the means of limiting the semantic stretch of terms, for instance through the distinction between fiat and bona fide boundaries. Third, I point out some terminological issues in Lloyd's account, especially concerning the applicability of validity, soundness, and fallaciousness to analogies.

It is well known that Rudolf Carnap’s original system of inductive logic failed to provide an adequate account of analogical reasoning. Since this problem was identified, there has been no shortage of proposals for how to incorporate analogy into inductive inference. Most alternatives to Carnap’s system, unlike his original one, have not been derived from first principles; this makes it to some extent unclear what the epistemic situations are to which they apply. This paper derives a new analogical (...) inductive logic from a set of axioms which extend Carnap’s postulates in a natural way. The key insights come from Bruno de Finetti’s ideas about analogy. The axioms of the new system capture epistemic conditions that call for a strong kind of analogical reasoning. The new system has a number of merits, but is also subject to limitations. I shall discuss both, together with some possible ways to generalize the approach taken in this paper. (shrink)

This paper aims at integrating the work onanalogical reasoning in Cognitive Science into thelong trend of philosophical interest, in this century,in analogical reasoning as a basis for scientificmodeling. In the first part of the paper, threesimulations of analogical reasoning, proposed incognitive science, are presented: Gentner''s StructureMatching Engine, Mitchel''s and Hofstadter''s COPYCATand the Analogical Constraint Mapping Engine, proposedby Holyoak and Thagard. The differences andcontroversial points in these simulations arehighlighted in order to make explicit theirpresuppositions concerning the nature of analogicalreasoning. In (...) the last part, this debate in cognitivescience is applied to some traditional philosophicalaccounts of formal and material analogies as a basisfor scientific modeling, like Mary Hesse`s, and tomore recent ones, that already draw from the work inArtificial Intelligence, like that proposed byAronson, Harré and Way. (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)

Analogies have been traditionally recognized as a proper part of inductive procedures, akin to generalizations. Seldom, however, have they been presented as superior to generalizations, in the attainability of a higher degree of certitude for their conclusions or in other respects. Though Bacon definitely preferred analogy to generalization1, the tradition seems to me to go the other way-until the recent publication of works by Mary B. Hesse ([2], pp.21-28 and passim) and, perhaps, R. Harr6 ([1], pp.23-28 and passim). The (...) aim of the present note is to argue the following two points. First, generalizations proper are preferable to predictions from past observations to a single future observation, since the latter are ad hoc. Second, analogies are either generalizations proper-perhaps higher-level ones-or ad hoc. In any case, they are not more certain than generalizations, but they are still equally legitimate. (shrink)

How surprising is the insight, that being equals I in the 15th lecture of the Doctrine of Science 1804/II? It might have been indeed an unexpected turn for his contemporaries in Berlin listening to Fichte for the first time, but should it be surprising for us, having at least since 2012 (the year the last volume of [Gesamtausgabe] appeared) access to all his published and unpublished works? I want to propose a way of reading Fichte, which bypasses two popular (...) and contradictory interpretations of his philosophy in the post-Jena period: (a) the Absolute is the new first principle (hence the I is just a shadow of the much higher being) and (b) his system basically remains unchanged (hence the being is nothing more than the I). At first, I analyze the functions of later Fichte’s improved version of the Kantian and Reinholdian abstract subject-object-symbolism and assign specific content to it. This will shed light on the structure and the first principle of the Doctrine of Science 1804/II. In the second section I give reasons why Fichte calls both God and I “absolute” and “pure being” and explain their relation to each other referring to a thought experiment sometimes used by Kant—an analogy between the divine and human (pure) reason. The analogical thinking of this kind remains within the borders of transcendental philosophy as long as it is used only for certain didactic purposes. (shrink)

In this paper I address Descartes’ use of analogy in physics. First, I introduce Descartes’ hypothetical reasoning, distinguishing between analogy and hypothesis. Second, I examine in detail Descartes’ use of analogy to both discover causes and add plausibility to his hypotheses—even though not always explicitly stated, Descartes’ practice assumes a unified view of the subject matter of physics as the extension of bodies in terms of their size, shape and the motion of their parts. Third, I (...) present Descartes’ unique “philosophy of analogy”, where the absence of analogy serves as a criterion for falsifying proposed explanations in physics. I conclude by defending Descartes’ philosophy of analogy by appeal to the value scientists assign to simplicity in their explanations. (shrink)

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)

This paper investigates a famous argument, first introduced by Richard Taylor, that attempts to establish a radical similarity in the concepts of space and time. The argument contends that the spatial and temporal aspects of material bodies are much more alike, or analogous, than has been hitherto acknowledged. As will be demonstrated, most of the previous investigations of Taylor and company have failed to pinpoint the weakest link in their complex of analogies. By concentrating on their most fundamental cases, (...) however, a substantial difference, or disanalogy, can be brought to light that undermines this purported equivalence of space and time. (shrink)

Human cognition is striking in its brilliance and its adaptability. How do we get that way? How do we move from the nearly helpless state of infants to the cognitive proficiency that characterizes adults? In this paper I argue, first, that analogical ability is the key factor in our prodigious capacity, and, second, that possession of a symbol system is crucial to the full expression of analogical ability.

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)

Analogy making from examples is a central task in intelligent system behavior. A lot of real world problems involve analogy making and generalization. Research investigates these questions by building computer models of human thinking concepts. These concepts can be divided into high level approaches as used in cognitive science and low level models as used in neural networks. Applications range over the spectrum of recognition, categorization and analogy reasoning. A major part of legal reasoning could be formally (...) interpreted as an analogy making process. Because it is not the same as reasoning in mathematics or the physical sciences, it is necessary to use a method, which incorporates first the ability to specify likelihood and second the opportunity of including known court decisions. We use for modelling the analogy making process in legal reasoning neural networks and fuzzy systems. In the first part of the paper a neural network is described to identify precedents of immaterial damages. The second application presents a fuzzy system for determining the required waiting period after traffic accidents. Both examples demonstrate how to model reasoning in legal applications analogous to recent decisions: first, by learning a system with court decisions, and second, by analyzing, modelling and testing the decision making with a fuzzy system. (shrink)

This article argues that the analogical argument employed by Augustine in De Trinitate (the soul-God analogy) is formally identical to the analogical argument employed by Plato in the Republic (the city-soul analogy). The similarities between these two analogies, however, have received insufficient attention in the secondary literature. My goal is to fill this lacuna. I first provide a summary of the analogical methodology of these two works, and I then proceed to translate these two analogies into one (...) analogical argument form, showing that they are formally equivalent. I then differentiate these two analogies from other analogical arguments by focusing on their exploratory and programmatic character. This differentiation helps to capture the uniqueness of these two analogies, to understand their function, and, ultimately, to appreciate more fully the consonance between Augustine’s methodology and Plato’s. (shrink)

The goal of the paper is to reply to David Duarte’s critique of the partial reducibility thesis―a claim I defended in one of my books that analogy is partly reducible to the balancing of legal principles. In the first part of the paper I sketch the framework against which the thesis was formulated, i.e. Robert Alexy’s theory of legal reasoning. In the second part I attempt to rebut Duarte’s objections, pointing out that they do not take into account (...) the Alexian background of my considerations. Finally, I suggest that some aspects of my theory of analogical reasoning are independent of its theoretical background and may be of value for any conceptualization of analogy in the law. (shrink)

Gauge symmetries provide one of the most puzzling examples of the applicability of mathematics in physics. The presented work focuses on the role of analogical reasoning in the gauge argument, motivated by Mark Steiner’s claim that the application of the gauge principle relies on a Pythagorean analogy whose success undermines naturalist philosophy. In this paper, we present two different views concerning the analogy between gravity, electromagnetism, and nuclear interactions, each providing a different philosophical response to the problem of (...) the applicability of mathematics in the natural sciences. The first is based on an account of Weyl’s original work, which first gave rise to the gauge principle. Drawing on his later philosophical writings, we develop an idealist reading of the mathematical analogies in the gauge argument. On this view, mathematical analogies serve to ensure a conceptual harmony in our scientific account of nature. We further discuss the construction of Yang and Mills’s gauge theory in light of this idealist reading. The second account presents a naturalist alternative, formulated in terms of John Norton’s account of a material analogy, according to which the analogy succeeds in virtue of a physical similarity between the different interactions. This account is based on the methodological equivalence principle, a simple conceptual extension of the gauge principle that allows us to understand the relation between coordinate transformations and gravity as a manifestation of the same method. The physical similarity between the different cases is based on attributing the success of this method to the dependence of the coupling on relational physical quantities. We conclude by reflecting on the advantages and limits of the idealist, naturalist, and anthropocentric Pythagorean views, as three alternative ways to understand the puzzling relation between mathematics and physics. (shrink)

There is deep ambivalence about analogy, both as an object of philosophical fascination and in contexts of practice, like archaeology, where it plays a seemingly central role. In archaeology there has been continuous vacillation between outright rejection of analogical inference as overtly speculative, even systematically misleading, and, when this proves un-tenable, various stock strategies for putting it 'on a firmer foundation'. Frequently these last are accomplished by assimilating analogy to more tractible (better warranted, more readily controllable) forms of (...) inference, salvaging respectability but at the expense, ironically, of reverting to a strategy of elimination. I have been struck by the parallels between this pattern of response and that typical of philosophy; the central question raised in both contexts is that of whether, or in what sense, there is any distinctively analogical form of inference and what sort of warrant (formal, methodological) accrues to it. In what follows I will assess two recent philosophical positions on this question, first in their own terms and then in consideration of archaeological uses of analogy. In this I hope to put the projects of justification themselves on a firmer footing. (shrink)