Structural analogies between physical laws have received considerable attention from philosospheres of science. This paper, however, focusses on structural analogies between physical systems; this type of analogy plays an important role in the physical and technological sciences. A formal, set-theoretic description of structural analogies between physical systems is presented, and it is shown that a structural analogy between systems does not require a structural analogy with regard to the laws involved, nor conversely.

Structural analogies connect Williamson’s epistemology and action theory: for example, action is the direction-of-fit mirror image of knowledge, and knowledge stands to belief as action stands to intention. These structural analogies, for Williamson, are meant to illuminate more generally how ‘mirrors’ reversing direction of fit should be understood as connecting the spectrum of our cognitive and practically oriented mental states. This paper has two central aims, one negative and the other positive. The negative aim is to (...) highlight some intractable problems with Williamson’s preferred analogical picture, which links the cognitive and the practical through the nexus of direction-of-fit mirroring. The positive aim of the paper is to propose a better alternative. In particular, we show that an achievement-theoretic proposal captures what is in common across the range of attitudes that exhibit the kind of structure that knowledge-belief, action-desire/intention do, while at the same time avoiding the problems shown to face Williamson’s proposed picture. Moreover, we draw attention to several key theoretical benefits of embracing our proposed achievement-theoretic picture, including some of the key benefits of the knowledge-first programme that Williamson’s own analogies were designed to secure. (shrink)

A theory of analogy must describe how the meaning of an analogy is derived from the meanings of its parts. In the structure‐mapping theory, the interpretation rules are characterized as implicit rules for mapping knowledge about a base domain into a target domain. Two important features of the theory are (a) the rules depend only on syntactic properties of the knowledge representation, and not on the specific content of the domains; and (b) the theoretical framework allows analogies to be (...) distinguished cleanly from literal similarity statements, applications of abstractions, and other kinds of comparisons.Two mapping principles are described: (a) Relations between objects, rather than attributes of objects, are mapped from base to target; and (b) The particular relations mapped are determined by systematicity, as defined by the existence of higher‐order relations. (shrink)

Successful accounts of analogy in law have two burdens to discharge. First, they must reflect the fact that the conclusion of an argument by analogy is a normative claim about how to decide a certain case. Second, they must not fail to accord relevance to the fact that the source case was authoritatively decided in a certain way. We argue in the first half of this paper that the common view of the structure of analogical arguments in law cannot overcome (...) these hurdles. In the second half we develop an original account that aims to succeed where others failed. (shrink)

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 or non-semantic ones, indicating possible characteristics of the referents. Such distinct types of similarity characterize different kinds of analogical arguments, all based on a similar general structure, in which a common genus 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. (shrink)

Available from UMI in association with The British Library. ;This thesis investigates the application of the theory of Conceptual Structures to an Experience Base model, which is a question-answering system for a knowledge base of pseudo-natural language statements of everyday experience. This thesis progresses to extend the fundamental principles carried from the experience base, to develop a framework for Reasoning by Analogy. Both methodologies are implemented, and uncertainty in the models is handled using the theory of Support Logic. ;Incompleteness of (...) information, uncertainty of data and the need for a definite structure to the way in which rules and data interact, are aspects which must be dealt with if the experience base is to succeed. One more aspect is the knowledge representation which dictates the ease with which processing may be performed upon it. Conceptual graphs are used to store information used by an Experience Base. Control of the reasoning is effected by plausible inference reinforced by the theory of Support Logic for handling uncertainty. The knowledge base is a set of initially completely disparate islands of knowledge, which the system automatically clusters into coherent groups in an associative network. ;The principles evolved from research into experience bases lead to the conception, development and implementation of a computational framework for Analogical Reasoning. The reasoning is performed between domains of knowledge rather than within a single domain as in case-based reasoning, and operates on pseudo-natural language statements as for the experience base. It relies on relation-based structure mapping and includes a sophisticated mechanism for translating between the new problem and the analogue. The strong connection between this work and metaphor interpretation is also investigated, together with ideas on how to negotiate with the apparent multitude of types of analogical reasoning. (shrink)

What mechanisms underlie children’s language production? Structural priming—the repetition of sentence structure across utterances—is an important measure of the developing production system. We propose its mechanism in children is the same as may underlie analogical reasoning: structure-mapping. Under this view, structural priming is the result of making an analogy between utterances, such that children map semantic and syntactic structure from previous to future utterances. Because the ability to map relationally complex structures develops with age, younger children are less (...) successful than older children at mapping both semantic and syntactic relations. Consistent with this account, 4-year-old children showed priming only of semantic relations when surface similarity across utterances was limited, whereas 5-year-olds showed priming of both semantic and syntactic structure regardless of shared surface similarity. The priming of semantic structure without syntactic structure is uniquely predicted by the structure-mapping account because others have interpreted structural priming as a reflection of developing syntactic knowledge. (shrink)

In this paper we present Drama, a distributed model of analogical mapping that integrates semantic and structural constraints on constructing analogies. Specifically, Drama uses holographic reduced representations (Plate, 1994), a distributed representation scheme, to model the effects of structure and meaning on human performance of analogical mapping. Drama is compared to three symbolic models of analogy (SME, Copycat, and ACME) and one partially distributed model (LISA). We describe Drama's performance on a number of example analogies and assess (...) the model in terms of neurological and psychological plausibility. We argue that Drama's successes are due largely to integrating structural and semantic constraints throughout the mapping process. We also claim that Drama is an existence proof of using distributed representations to model high‐level cognitive phenomena. (shrink)

Casuistry, which involves analogical reasoning, is a popular methodological approach in bioethics. The method has its advantages and challenges, which are widely acknowledged. Meta-philosophical reflection on exactly how bioethical casuistry works and how the challenges can be addressed is limited. In this paper we propose a framework for structuring casuistry and analogical reasoning in bioethics. The framework is developed by incorporating theories and insights from the philosophy of science: Mary Hesse’s ideas on horizontal and vertical relations in analogical reasoning in (...) the sciences, Paul Bartha’s articulation model of analogical reasoning and Daniel Steel’s insights on mechanism-based extrapolation in biomedical research. Adopting our framework results in two practical benefits: it sets methodological standards for analogical reasoning and enables us to compare and evaluate diverging lines of analogical reasoning in a systematic way. Adopting the framework also has theoretical benefits: it helps to understand how analogical reasoning can have moral normativity; it pinpoints exactly where moral principles or theories enter analogical reasoning; and it helps to understand why casuistry is an attractive method in bioethics and in applied ethics more generally. (shrink)

Theories of analogical reasoning have viewed relational structure as the dominant determinant of analogical mapping and inference, while assigning lesser importance to similarity between individual objects. An experiment is reported in which these two sources of constraints on analogy are placed in competition under conditions of high relational complexity. Results demonstrate equal importance for relational structure and object similarity, both in analogical mapping and in inference generation. The human data were successfully simulated using a computational analogy model (LISA) that treats (...) both relational correspondences and object similarity as soft constraints that operate within a limited-capacity working memory; but not with a model (SME) that treats relational structure as pre-eminent. (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)

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. (shrink)

The present article aims to expose some aspects of the specific features of classical Chinese analogisms. First, it exposes the supposition that this type of analogism did not focus exclusively on forms without considering their content, that is, that it was linguistically and semantically determined. Second, it also aims to show that classical Chinese analogies are based on structural relations between the objects in question, which constitute the similarity of two types of things that share certain attributes. This (...) article additionally sheds light on the question of how and why the structure underlying these relations represents a semantic and axiological referential framework that functions as the... (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)

The writings of John Paul II are rich in meanings and analogies that enrich our understanding of human person and God. According to the tradition, what is specific to human person is reason, which means the ability to assume responsibility. Nevertheless, such responsibility is paradoxical, because it is only realized in relationship with events that depend on circumstances - which are manifested especially in relationships with others, specifically through love. Now, it is properly the paradox of such personal responsibility (...) that can give an analogical understanding of the mystery of God, one and triune. (shrink)

Regular polysemes are sets of ambiguous words that all share the same relationship between their meanings, such as CHICKEN and LOBSTER both referring to an animal or its meat. To probe how a distributional semantic model, here exemplified by bidirectional encoder representations from transformers (BERT), represents regular polysemy, we analyzed whether its embeddings support answering sense analogy questions similar to “is the mapping between CHICKEN (as an animal) and CHICKEN (as a meat) similar to that which maps between LOBSTER (as (...) an animal) to LOBSTER (as a meat)?” We did so using the LRcos model, which combines a logistic regression classifier of different categories (e.g., animal vs. meat) with a measure of cosine similarity. We found that (a) the model was sensitive to the shared structure within a given regular relationship; (b) the shared structure varies across different regular relationships (e.g., animal/meat vs. location/organization), potentially reflective of a “regularity continuum;” (c) some high-order latent structure is shared across different regular relationships, suggestive of a similar latent structure across different types of relationships; and (d) there is a lack of evidence for the aforementioned effects being explained by meaning overlap. Lastly, we found that both components of the LRcos model made important contributions to accurate responding and that a variation of this method could yield an accuracy boost of 10% in answering sense analogy questions. These findings enrich previous theoretical work on regular polysemy with a computationally explicit theory and methods, and provide evidence for an important organizational principle for the mental lexicon and the broader conceptual knowledge system. (shrink)

We propose and investigate an Analogy Principle in the context of Unary Inductive Logic based on a notion of support by structural similarity which is often employed to motivate scientific conjectures.

Recently, Barbara Renzi argued that Kuhn's account of scientific change is undermined by mismatches in the analogy that Kuhn supposedly draws between scientific change and biological evolution. We argue that Renzi's criticism is inadequate to Kuhn's account of scientific change, as Kuhn does not draw any precise analogy between the mechanisms of scientific change and biological evolution nor aims to argue that the mechanisms of scientific change and biological evolution are similar in any important respects. Therefore, pointing to mismatches between (...) the central concepts that feature in the descriptions of the two phenomena simply misses the point of Kuhn's analogy. *Received January 2010; revised January 2010. †To contact the authors, please write to: Thomas A. C. Reydon, Leibniz Universität Hannover, Im Moore 21, D‐30167 Hannover, Germany; e‐mail: [email protected]‐hannover.de. (shrink)

A model of analogical mapping is proposed that uses five principles to generate consistent and conflicting hypotheses regarding assignments of elements of a source domain to analogous elements of a target domain. The principles follow the fine conceptual structure of the domains. The principles are: (1) the principle of proportional analogy; (2) the principle of mereological analogy, (3) the principle of chain reinforcement; (4) the principle of transitive reinforcement; and (5) the principle of mutual inconsistency. A constraint-satisfaction network is used (...) to find the set of assignments that preserves the greatest relational structure of the source. In contrast to the model proposed here, most models of analogical mapping use only the principle of proportional analogy. The use of many principles is shown to be superior in that it permits smoother integration of pragmatic factors and results in a more efficient mapping process. (shrink)

The thesis we develop in this essay is that all humans are endowed with a moral faculty. The moral faculty enables us to produce moral judgments on the basis of the causes and consequences of actions. As an empirical research program, we follow the framework of modern linguistics.1 The spirit of the argument dates back at least to the economist Adam Smith (1759/1976) who argued for something akin to a moral grammar, and more recently, to the political philosopher John Rawls (...) (1971). The logic of the argument, however, comes from Noam Chomsky’s thinking on language specifically and the nature of knowledge more generally (Chomsky, 1986, 1988, 2000; Saporta, 1978). If the nature of moral knowledge is comparable in some way to the nature of linguistic knowledge, as defended recently by Harman (1977), Dwyer (1999, 2004), and Mikhail (2000; in press), then what should we expect to find when we look at the anatomy of our moral faculty? Is there a grammar, and if so, how can the moral grammarian uncover its structure? Are we aware of our moral grammar, its method of operation, and its moment-to-moment functioning in our judgments? Is there a universal moral grammar that allows each child to build a particular moral grammar? Once acquired, are different moral grammars mutually incomprehensible in the same way that a native Chinese speaker finds a native Italian speaker incomprehensible? How does the child acquire a particular moral grammar, especially if her experiences are impoverished relative to the moral judgments she makes? Are there certain forms of brain damage that disrupt moral competence but leave other forms of reasoning intact? And how did this machinery evolve, and for what particular adaptive function? We will have more to say about many of these questions later on, and Hauser (2006) develops others. However, in order to flesh out the key ideas and particular empirical research paths, let us turn to some of the central questions in the study of our language faculty.. (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)

Analogical cognition refers to the ability to detect, process, and learn from relational similarities. The study of analogical and similarity cognition is widely considered one of the ‘success stories’ of cognitive science, exhibiting convergence across many disciplines on foundational questions. Given the centrality of analogy to mind and knowledge, it would benefit philosophers investigating topics in epistemology and the philosophies of mind and language to become familiar with empirical models of analogical cognition. The goal of this essay is to describe (...) recent empirical work on analogical cognition as well as model applications to philosophical topics. Topics to be discussed include the epistemological distinction between implicit knowledge and explicit knowledge, the debate between empiricists and nativists, the frame problem, expertise, creativity and autism, cognitive architecture, and relational knowledge. Particular attention is given to Dedre Gentner and colleague’s structure-mapping theory – the most developed and widely accepted model of analogical cognition. (shrink)

A Christian bioethic needs to place the medical approach to sickness, suffering, and death within the context of redemption and the renewal of humanity in the image of God. This can be done by accounting for the way in which the disruptions of the human life-world that attend the illness experience manifest the structure of the problem of evil and point toward an answer that transcends the individual and the medical community. Further, the disease-oriented approach to medicine, when understood in (...) the context of the analogia entis, can be taken as an analogy for a deeper spiritual healing, and can thus become a vehicle through which one can minister to the disruptions of a patient's life-world. An appreciation of the analogical structure of healing provides the basis for a Christian ethic of care. (shrink)

(2013). Two facets of cognitive control in analogical mapping: The role of semantic interference resolution andgoal-driven structure selection. Thinking & Reasoning. ???aop.label???

We argue that analogical reasoning, particularly Gentner's structure-mapping theory, provides an integrative theoretical framework through which we can better understand the development of symbol use. Analogical reasoning can contribute both to the understanding of others’ intentions and the establishment of correspondences between symbols and their referents, two crucial components of symbolic understanding. We review relevant research on the development of symbolic representations, intentionality, comparison, and similarity, and demonstrate how structure-mapping theory can shed light on several ostensibly disparate findings in the (...) literature. Focusing on visual symbols, we argue that analogy underlies and supports the understanding of both intention and correspondence, which may enter into a reciprocal bootstrapping process that leads children to gain the prodigious human capacity of symbol use. (shrink)

In this paper I argue that Aquinas’ account of analogy provides resources for resolving the prima facie conflict between his claims that (1) the divine relations constituting the persons are “one and the same” with the divine essence; (2) the divine persons are really distinct, (3) the divine essence is absolutely simple. Specifically, I argue that Aquinas adopts an analogical understanding of the concepts of being and unity, and that these concepts are implicit in his formulation of claims about substance (...) and relation in the Trinity. I then show how Aquinas appeals to key structural features of analogical concepts, notably, the simpliciter/secundum quid characterization, to resolve apparent conflicts between the unity of substance and distinction of relations in the Trinity. (shrink)

Recent accounts of scientific method suggest that a model, or analogy, for an axiomatized theory is another theory, or postulate set, with an identical calculus. The present paper examines five central theses underlying this position. In the light of examples from physical science it seems necessary to distinguish between models and analogies and to recognize the need for important revisions in the position under study, especially in claims involving an emphasis on logical structure and similarity in form between theory (...) and analogy. While formal considerations are often relevant in the employment of an analogy they are neither as extensive as proponents of this viewpoint suggest, nor are they in most cases sufficient for allowing analogies to fulfill the roles imputed to them. Of major importance, and what these authors generally fail to consider, are physical similarities between analogue and theoretical object. Such similarities, which are characteristic in varying degrees of most analogies actually employed, play an important role in affording a better understanding of concepts in the theory and also in the development of the theoretical assumptions. (shrink)

A multiple analogy is a structured comparison in which several sources are likened to a target. In "Multiple analogies in science and philosophy," Shelley provides a thorough account of the cognitive representations and processes that participate in multiple analogy formation. Through analysis of real examples taken from the fields of evolutionary biology, archaeology, and Plato's "Republic," Shelley argues that multiple analogies are not simply concatenated single analogies but are instead the general form of analogical inference, of which (...) single analogies are a special case. The result is a truly general cognitive model of analogical inference.Shelley also shows how a cognitive account of multiple analogies addresses important philosophical issues such as the confidence that one may have in an analogical explanation, and the role of analogy in science and philosophy.This book lucidly demonstrates that important questions regarding analogical inference cannot be answered adequately by consideration of single analogies alone. (shrink)

Analogical reasoning is often employed in problem-solving and metaphor interpretation. This paper submits that, as a default, analogical reasoning addressing these different tasks employs different mapping strategies: In problem-solving, it employs analogy-maximising strategies (like structure mapping, Gentner & Markman 1997); in metaphor interpretation, analogy-minimising strategies (like ATT-Meta, Barnden 2015). The two strategies interact in analogical reasoning with conceptual metaphors. This interaction leads to predictable fallacies. The paper supports these hypotheses through case-studies on ‘mind’-metaphors from ordinary discourse, and abstract problem-solving in (...) the philosophy of mind, respectively: It shows that (1) default metaphorical interpretations for vision- and space-cognition metaphors can be derived with a variant of the analogy-minimising ATT-Meta approach, (2) philosophically influential introspective conceptions of the mind can be derived with conceptual metaphors only through an analogy-maximising strategy, and (3) the interaction of these strategies leads to hitherto unrecognised fallacies in analogical reasoning with metaphors. This yields a debunking explanation of introspective conceptions. (shrink)

In their exhaustive study of the cognitive operation of analogy, Hofstadter and Sander arrive at a paradox: the creative and inexhaustible production of analogies in our thought must derive from a “reminding” operation based upon the availability of the detailed totality of our experience. Yet the authors see no way that our experience can be stored in the brain in such detail nor do they see how such detail could be accessed or retrieved such that the innumerable analogical remindings (...) we experience can occur. Analogy creation, then, should not be possible. The intent here is to sharpen and deepen our understanding of the paradox, emphasizing its criticality. It will be shown that the retrieval problem has its origins in the failure of memory theory to recognize the actual dynamic structure of events. This structure is comprised of invariance laws as per J. J. Gibson, and this event “invariance structure” is exactly what supports Hofstadter and Sander’s missing mechanism for analogical reminding. Yet these structures of invariants, existing only over optical flows, auditory flows, haptic flows, etc., are equally difficult to imagine being stored in a static memory, and thus only exacerbate the problem of the storage of experience in the brain. A possible route to the solution of this dilemma, based in the radical model of Bergson, is also sketched. (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)

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

The argument by analogy for other minds is customarily rejected as a weak inference because the argument is based on a single instance. The current paper argues that this objection fundamentally misunderstands the inferential structure of analogies and so misrepresents the role analogy plays in the justifycation of belief in other minds. Arguments by be uniquely suited to draw inferences from single instances. This defense does not remove all difficulties faced by the argument by analogy for other minds.

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.

Analogy belongs to the class of concepts notorious for a variety of definitions generating continuing disputes about their preferred understanding. Analogy is typically defined by or at least associated with similarity, but as long as similarity remains undefined this association does not eliminate ambiguity. In this paper, analogy is considered synonymous with a slightly generalized mathematical concept of similarity which under the name of tolerance relation has been the subject of extensive studies over several decades. In this approach, analogy can (...) be mathematically formalized in terms of the sequence of binary relations of increased generality, from the identity, equivalence, tolerance, to weak tolerance relations. Each of these relations has cryptomorphic presentations relevant to the study of analogy. The formalism requires only two assumptions which are satisfied in all of the earlier attempts to formulate adequate definitions which met expectations of the intuitive use of the word analogy in general contexts. The mathematical formalism presented here permits theoretical analysis of analogy in the contrasting comparison with abstraction, showing its higher level of complexity, providing a precise methodology for its study and informing philosophical reflection. Also, arguments are presented for the legitimate expectation that better understanding of analogy can help mathematics in establishing a unified and universal concept of a structure. (shrink)

This paper proposes an account of natural analogy in scientific theorizing via Mary Hesse’s original understanding of analogical reasoning. Starting with discussing Hesse’s examples and her symbolic scheme, I argue that the traditional distinction between the type of formal analogy and the type of material analogy should be abandoned. All analogies in theorizing, that are both formal and material, contain a set of pretheoretic associations and a theoretic structure between two analogues. I thus provide a new interpretation of Hesse’s (...) symbolic scheme to reveal the pretheoretical and the structural dimensions of analogy and further illustrate the account of natural analogy by applying it to the history of the construction of Coulomb’s law, which is traditionally seen as a typical case of formal analogy, arguing that pretheoretic associations as well as a theoretic structure play a necessary role in this case. In the final part of this paper, I argue that the account of natural analogy is preferable to Dedre Gentner’s structural mapping theory. (shrink)