Two common claims in environmental moral philosophy are that nature is worthy of respect and that we respect ourselves in respecting nature. In this paper, I articulate two modes of practical reasoning that help make sense of these claims. The first is analogical extension, which understands the respect due human life as the source of a like respect for nature. The second is analogical implication, which involves nature in human life to show us what we are like. (...) These forms of reasoning are relevant to environmental virtue ethics in that both help us conceptualize how respect for nature can be part of our sense of humanity, and not opposed to our sense of humanity. (shrink)

Extensive interpretation of legal provisions is in tension with the prohibition of reasoning by analogy in criminal law, for it is unclear what the difference is between the two. Some scholars claim that they differ from a theoretical point of view, since they do not have the same argumentative structure. On the other hand, the two come to the same result starting from the same legal materials: they justify the extension of a regulation to a case that is not (...) explicitly considered by the law. The paper deals with this issue discussing a recent Italian case and proposes an account of the distinction between the two based upon the principle of semantic tolerance and its inferential structure in legal argumentation. (shrink)

How are we individually and as a society to handle new and emerging technologies? This challenging question underlies much of the bioethical debates of modern times. To address this question we need suitable conceptions of the new technology and ways of identifying its proper management and regulation. To establish conceptions and to find ways to handle emerging technologies we tend to use analogies extensively. The aim of this article is to investigate the role that analogies play or may play in (...) the processes of understanding and managing new technology. More precisely we aim to unveil the role of analogies as analytical devices in exploring the "being" of the new technology as well the normative function of analogies in conceptualizing the characteristics and applications of new technology. Umbilical cord blood biobanking will be used as a case to investigate these roles and functions. (shrink)

In this dissertation, I provide the logical foundation for a solution to the mind-body problem, a solution which is directly based upon Wilfrid Sellars' analogical theory of thought and sensation. Chapters I-IV are devoted to an interpretation, analysis, and constructive criticism of Sellars' notions of the inner thought episode and the sensing state. My analysis is offered in support of three general contentions: I argue that the postulation of inner thought episodes and sensing states is necessary for adequate explanations (...) of agent behavior; I hope to show how the analogical theory of inner thought episodes and sensing states actually generates a legitimate problem concerning the relationship between the mental and the physical; and I demonstrate the importance of the notion of analogy in philosophical theory construction. I suggest that the role of analogy provides the key for the solution to the mind-body problem. ;Chapter One is essentially introductory in nature. I offer an interpretation and reconstruction of Sellars' illustrative story entitled "The Jonesean Myth" . The "Myth" provides a suitable representation of Sellars' overall philosophy of mind. But perhaps more importantly, the "Myth" is a paradigm example of what I shall call the analogical method of inquiry, a method employed for the introduction of the notions of inner thought episodes and sensing states. In brief, I want to show how the "Myth" provides the logical basis for a theory adequate for explanations of the mental activity of agents. ;Chapters II and III are closely related. In Chapter II, I present a theory of linguistic representation which will serve as the analogical base for the introduction and characterization of the inner thought episode. In Chapter III, I develop the notion of the inner thought episode , and I examine its nature and status as a theoretical construct. Chapters II and III are thus related by the Sellarsian thesis that the concept of mental representation is to be understood in terms which apply, primarily, to characterizations of the features of the linguistic framework presented in Chapter II. ;In Chapter IV, I argue, again following Sellars' lead, that the explication of the notion of the perceptual thought episode requires the introduction of a second distinct sort of inner episode, namely, that of the sense experience or sensing state. The argument offered in Chapter IV is designed to show that sensing states are theoretical constructs, the reference to which is essential for explanations concerning the occurrence and nature of perceptual representations. Sensing states are introduced and characterized by an analogical extension of families of predicates which are suitable for the identification and description of ordinary physical objects . ;In Chapter V, I propose a solution to the mind-body problem, as the latter is generated by the analysis given to the thought episode and the sensing state . In general terms, I argue that any purported solution to the mind-body problem must provide an explanatory basis for agent behavior, and it is for this reason that I reject "reductionistic" theories of mind of the kind represented by logical behaviorism, type-identity physicalism, and Turing Machine functionalism. My solution, instead, involves a commitment to what I shall call token physicalism, a thesis which is contingent upon the development of a theory of neurophysiology which is rich enough to capture, in an analogical sense, both the intentional features of the thought episode, and the occurrent-like qualities which are exemplified by the sensing state. (shrink)

When Johann and Daniel Bernoulli founded fluid dynamics they encountered several problems. To go beyond the vision of Newtonian particles, a new set of images was needed in order to deal with the spatial extensibility and lack of form of fluids. I point to evidence that analogy was an essential abductive strategy in the creation of this imagery. But its heuristic behavior is complex: analogy can provide an initial model or proto-model that establishes the starting point of a theoretical process, (...) but it can play other roles as well. The historical genesis analyzed here shows that the participation of analogy in physicists’ creativity is not so restricted and that its richness opens up the field for very different roles and strategies in model-based discovery processes. Analogies can crop up intermittently in the evolution of a theory; and they can cooperate with images, extreme case reasoning and thought experiments, and even activate these processes at origin. Although it may seem that the contributions of analogy are generative in the sense of helping to discover new aspects of reality, we must stress the evaluative function that sometimes is performed by analogical reasoning in order to gain confidence. The study of the Bernoulli’s genesis of the foundations of fluid dynamics generates interesting hypotheses about the multiple roles that analogy can play in scientific model-based reasoning. (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)

In 1498 Cajetan published a short book, On the Analogy of Names, which is often regarded as a masterly summary of Aquinas's doctrine of analogy. It opens in the very first paragraph with an attack on three views of the concept of being (ens): first, that it is a disjunction of concepts; second, that it is an ordered group of concepts; and third, that it is a single, separate concept which is unequally participated by substances and accidents. A number of (...) questions immediately spring to mind. Why are concepts being discussed when analogy is said by Cajetan to be a theory of language? What is meant by ‘concept’? Who held the views under attack and why? So far as I can tell, the extensive literature on both Aquinas and Cajetan offers no satisfactory answers to these questions. (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)

Analogical cognition, extensively researched by Dedre Gentner and her colleagues over the past thirty five years, has been described as the core of human cognition, and it characterizes our use of many words. This research provides significant insight into the nature of word meaning, but it has been ignored by linguists and philosophers of language. I discuss some of the implications of the research for our account of word meaning. In particular, I argue that the research points to, and (...) helps account for, a key explanatory role that linguistic meaning must play. The research also shows how words contribute to thought as opposed to merely being a means of conveying thought. (shrink)

This article describes the path‐mapping theory of how humans integrate analogical mapping and general problem solving. The theory posits that humans represent analogs with declarative roles, map analogs by lower‐level retrieval of analogous role paths, and coordinate mappings with higher‐level organizational knowledge. Implemented in the ACT‐R cognitive architecture, the path‐mapping theory enables models of analogical mapping behavior to incorporate and interface with other problem‐solving knowledge. Path‐mapping models thus can include task‐specific skills such as encoding analogs or generating responses, (...) and can make behavioral predictions at the level of real‐world metrics such as latency or correctness. We show that the path‐mapping theory can successfully account for the major phenomena addressed by previous theories of analogy. We also describe a path‐mapping model that can account for subjects' incremental eye‐movement and typing behavior in a story‐mapping task. We discuss extensions and implications of this work to other areas of analogy and problem‐solving research. (shrink)

This article explores Mencius’ extension of moral feelings and its potential to address a key challenge in cosmopolitan education: how to motivate students to expand their existing affection and obligations towards their family and community to the rest of the world. Rather than strong universalism, a Mencian orientation is aligned with rooted cosmopolitanism that takes into account localised and cultural contexts that underpin, determine and give value to social practices. Mencius’ approach, as argued in this essay, highlights the spontaneous (...) human reactions to ethical situations, innate human goodness, analogical reasoning, moral character and agency. A Confucian form of cosmopolitan education gives emphasis not only to the students’ moral imagination but also their instinctual responses, self-reflection and rationality. Such an education seeks to integrate emotions and reasoning through the utilisation of paradigm scenarios that identify and reinforce the natural compassionate feelings in the learner. (shrink)

We show that the maximal linear extension theorem for well partial orders is equivalent over RCA0 to ATR0. Analogously, the maximal chain theorem for well partial orders is equivalent to ATR0 over RCA0.

Analogies are partial similarities between different situations that support further inferences. Specifically, analogy is a kind of similarity in which the same system of relations holds across different objects. Analogies thus capture parallels across different situations.

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)

A genome of a living organism consists of a long string of symbols over a finite alphabet carrying critical information for the organism. This includes its ability to control post natal growth, homeostasis, adaptation to changes in the surrounding environment, or to biochemically respond at the cellular level to various specific regulatory signals. In this sense, a genome represents a symbolic encoding of a highly organized system of information whose functioning may be revealed as a natural multilayer structure in terms (...) of complexity and prominence. In this paper we use the mathematical theory of symbolic extensions as a framework to shed light onto how this multilayer organization is reflected in the symbolic coding of the genome. The distribution of data in an element of a standard symbolic extension of a dynamical system has a specific form: the symbolic sequence is divided into several subsequences (which we call layers) encoding the dynamics on various “scales”. We propose that a similar structure resides within the genomes, building our analogy on some of the most recent findings in the field of regulation of genomic DNA functioning. (shrink)

The ability to reason by analogy is particularly important because it permits the extension of knowledge of a target domain by virtue of its similarity to a base domain via a process of analogical inference. The general procedure for analogical inference involves copying structure from the base to the target in which missing information is generated, and substitutions are made for items for which analogical correspondences have already been found. A pure copying with substitution and generation (...) process is too profligate to be useful, and so constraints must be placed on what information is to be carried over. In this paper, the importance of systematicity as a constraint on inference is explored in four studies in which subjects find correspondences between domains and also make inferences. This work suggests that people prefer to make inferences of information connected to systematic correspondences between domains. A second important theme of this paper is that violations of one‐to‐one mapping can lead to inconsistent object substitutions in inference. The data reveal no such inconsistent substitutions in people's inferences, suggesting that they do respect one‐to‐one mapping in analogical inference. These findings are discussed relative to four prominent computational models of analogical mapping and inference. (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)

This article is concerned with extensions of a continuous ordering R on a set X to a subset P of the power set of X. The underlying topology will be the Hausdorff metric topology. We will see that continuous extensions of R do not require that P contain every nonempty finite subset of X. Therefore, the analysis can be applied to consumer theory and inverse choice functions. In analogy to these functions budget correspondences are established which relate alternatives x with (...) certain subsets of X, according to the extended ordering. (shrink)

The principle of sufficient reason threatens modal collapse. Some have suggested that by appealing to the indefinite extensibility of contingent truth, the threat is neutralized. This paper argues that this is not so. If the indefinite extensibility of contingent truth is developed in an analogous fashion to the most promising models of the indefinite extensibility of the concept set, plausible principles permit the derivation of modal collapse.

A comprehensive review of Grenet's book would have to approach book-length itself, for "analogy" is discovered in all the Dialogues, and the Platonic principle and method of reasoning to which Grenet gives this name, and to which he attributes absolute universality, he treats extensively in heavily documented, text-packed treatises. His book in fact is divided into four "books." I shall therefore limit myself to two general questions: What does Grenet find to be the fundamental meaning of "philosophical analogy" in Plato? (...) Is this "analogy" philosophical, and if so, in what sense and with what value? (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 idelaist 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)

Quantum interference, manifest in the two slit experiment, lies at the heart of several quantum computational speed-ups and provides a striking example of a quantum phenomenon with no classical counterpart. An intriguing feature of quantum interference arises in a variant of the standard two slit experiment, in which there are three, rather than two, slits. The interference pattern in this set-up can be written in terms of the two and one slit patterns obtained by blocking one, or more, of the (...) slits. This is in stark contrast with the standard two slit experiment, where the interference pattern cannot be written as a sum of the one slit patterns. This was first noted by Rafael Sorkin, who raised the question of why quantum theory only exhibits irreducible interference in the two slit experiment. One approach to this problem is to compare the predictions of quantum theory to those of operationally-defined ‘foil’ theories, in the hope of determining whether theories that do exhibit higher-order interference suffer from pathological—or at least undesirable—features. In this paper two proposed extensions of quantum theory are considered: the theory of Density Cubes proposed by Dakić, Paterek and Brukner, which has been shown to exhibit irreducible interference in the three slit set-up, and the Quartic Quantum Theory of Życzkowski. The theory of Density Cubes will be shown to provide an advantage over quantum theory in a certain computational task and to posses a well-defined mechanism which leads to the emergence of quantum theory—analogous to the emergence of classical physics from quantum theory via decoherence. Despite this, the axioms used to define Density Cubes will be shown to be insufficient to uniquely characterise the theory. In comparison, Quartic Quantum Theory is a well-defined theory and we demonstrate that it exhibits irreducible interference to all orders. This feature of Życzkowski’s theory is argued not to be a genuine phenomenon, but to arise from an ambiguity in the current definition of higher-order interference in operationally-defined theories. Thus, to begin to understand why quantum theory is limited to a certain kind of interference, a new definition of higher-order interference is needed that is applicable to, and makes good operational sense in, arbitrary operationally-defined theories. (shrink)

The central role played by Darwin's analogy between selection under domestication and that under nature has been adequately appreciated, but I have indicated how important the domesticated organisms also were to other elements of Darwin's theory of evolution-his recognition of “the constant principle of change,” for instance, of the imperfection of adaptation, and of the extent of variation in nature. The further development of his theory and its presentation to the public likewise hinged on frequent reference to domesticates.We have seen (...) that Darwin's reliance on the analogy between domesticated varieties and wild species was a bold and original step, in light of contemporary views on the nature of domesticates. However, as Darwin undoubtedly foresaw, his reliance on the analogy created difficulties as well as solving problems, and these began with his Malthusian codiscoverer of the principle of natural selection, Alfred Russel Wallace. Wallace's paper “On the Tendency of Varieties to Depart Indefinitely from the Original Type,” presented to the Linnean Scoiety along with the first public unveiling of Darwin's theory, states: We see, then, that no inferences as to varieties in a state of nature can be deduced from the observation of those occurring among domestic animals. The two are so much opposed to each other in every circumstance of their existence, that what applies to the one is almost sure not to apply to the other. Domestic animals are abnormal, irregular, artificial; they are subject to varieties which never occur and never can occur in a state of nature.62Much has been made of the similarity of views of Darwin and Wallace, but this quotation surely reveals how utterly different their views were on what to Darwin was an important matter. Several critics of the Origin saw Darwin's reliance on the domesticates as his Achilles heel. As Young has pointed out, Samuel Wilberforce included the following passage in his attack on the Origin: Nor must we pass over unnoticed the transference of the argument from the domesticated to the untamed animals. Assuming that man as the selector can do much in a limited time, Mr. Darwin argues that Nature, a more powerful, a more continuous power, working over vastly extended ranges of time, can do more. But why should Nature, so uniform and persistent in all her operations, tend in this instance to change? Why should she become a selector of varieties?63Another critic, Fleeming Jenkin, found the analogy a weakness in Darwin's theory because of the limited extent of variation in any one direction in domestic animals and plants.64 We have already seen that Darwin had confided a similar view to his notebook thirty years earlier, but changed his mind as a result of his profound study of domesticates. De Beer's reference to “an English country gentleman's knowledge of domestic plants and animals and their breeding”65 fails totally to recognize the originality and depth of Darwin's knowledge of domesticates.Why did Darwin, against the currents of his time, rely so heavily on mankind's experience with domesticated organisms to shape his theory about species in nature? On reason is that only with domesticates was an approach that came close to experimental verification possible. Darwin fully realized the inadequacies of the experiment, as is emphasized by his repeated contrasting of selection under nature and selection by man. Yet the extensive experience and data of plant and animal breeders offered the only reliable base against which Darwin could continually challenge his views. As he wrote in the introduction to Variation, with domestication, “man ... may be said to have been trying an experiment on a gigantic scale.”66 Given Darwin's high opinion of the quantitative work of Malthus and Quetelet (as emphasized by Schweber),67 and his unremitting efforts to secure data by which to test his theories, it was inevitable that he should attach high significance to domesticated varieties. John Tyndall, in his Belfast address of 1874, said: “The strength of the doctrine of Evolution consists, not in experimental demonstration (for the subject is hardly accessible to this mode of proof), but in its general harmony with scientific thought.”68 Darwin would have agreed with the latter thought, but I think he would have challenged the preceding one on the grounds that long experience with domesticated varieties did provide an element of experimental demonstration. It gave him confidence in his theory, and he used his vast knowledge of artificial selection boldly and creatively. (shrink)

We prove two embedding and extension theorems in the context of the constructive theory of metric spaces. The first states that Cantor space embeds in any inhabited complete separable metric space (CSM) without isolated points, X, in such a way that every sequentially continuous function from Cantor space to ℤ extends to a sequentially continuous function from X to ℝ. The second asserts an analogous property for Baire space relative to any inhabited locally non‐compact CSM. Both results rely on (...) having careful constructive formulations of the concepts involved.As a first application, we derive new relationships between “continuity principles” asserting that all functions between specified metric spaces are pointwise continuous. In particular, we give conditions that imply the failure of the continuity principle “all functions from X to ℝ are continuous”, when X is an inhabited CSM without isolated points, and when X is an inhabited locally non‐compact CSM. One situation in which the latter case applies is in models based on “domain realizability”, in which the failure of the continuity principle for any inhabited locally non‐compact CSM, X, generalizes a result previously obtained by Escardó and Streicher in the special case X = C[0, 1].As a second application, we show that, when the notion of inhabited complete separable metric space without isolated points is interpreted in a recursion‐theoretic setting, then, for any such space X, there exists a Banach‐Mazur computable function from X to the computable real numbers that is not Markov computable. This generalizes a result obtained by Hertling in the special case that X is the space of computable real numbers. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim). (shrink)

One major facilitator of analogical reasoning is conceptual metaphor: cross-domain mappings that preserve relations and thereby motivate the extension of linguistic terms from the source to the target domain. Their conscious and explicit use in analogical reasoning has been helpful and productive in disciplines ranging from physics to psychology, and philosophy. At the same time, students of metaphor have suggested that partially unwitting use of conceptual metaphors led to unsound but intuitive conceptions of the mind, in philosophy (...) and psychology. This paper develops an explanation of some highly influential intuitions from the philosophy of mind, which helps answer the resulting question: When and why does the frequently helpful use of metaphors in analogical reasoning turn pernicious? In response, the paper brings together two hitherto largely distinct strands of research from cognitive psychology, in a case-study on the philosophy of mind: The paper uses structure-mapping theory to explain how simple analogical reasoning generates conceptual metaphors that facilitate more complex analogical reasoning, which is often non-intentional. Second, the paper examines how such reasoning interacts with partial-matching effects in memory-based processing. Drawing on Budiu and Anderson’s model of “information-based processing”, the paper shows that this interaction leads to predictable fallacies. It brings out the relevance of such fallacies by showing that they shaped introspective conceptions of the mind that dominated philosophical discourse throughout early modernity and retain some cultural influence to this day. On this basis, the paper delineates when and where those fallacies are liable to occur. (shrink)

In spite of extensive criticisms, war metaphors are still widespread in medical discourse. In the domain of public health analogies between war and infectious diseases are rooted in the similar impacts they can have on political institutions and communities. This similarity has been emphasized by the recent trend of addressing infectious disease from the point of view of national security. Nevertheless, it is here argued that the analogy cannot be used to model normative principles for treating carriers of contagious diseases (...) after the principles of ius in bello . Yet, the analogy may provide some useful practical and theoretical insights in tackling the growing problem of limiting the spread of drug-resistant pathogens: an issue that generates increasing worries and raises difficult ethical and political questions of rights, responsibilities and obligations. It is suggested that if anti-microbials and antibiotics are seen as strategic information, their misuse can be usefully compared to careless talk in times of war. (shrink)

I defend what I take to be a genuinely Kantian view on temporal extension: time is not an object but a human horizon of concrete particulars. As such, time depends on the existence of embodied human subjects. It does not, however, depend on those subjects determined as spatial objects. Starting with a realist notion of “apperception” as applied to indexical space, I proceed with the need for external criteria of temporal duration. In accordance with Kant’s Second Analogy of Experience, (...) these criteria are found in concepts and laws of motion and change. I then see what follows from this for a reasonable notion of transcendental idealism. Finally, in support of my Kantian conclusions, I argue for the transcendentally subjective nature of particular temporal extension. (shrink)

The object of this paper is to study the analogy, drawn both positively and negatively, between mathematics and fiction. The analogy is more subtle and interesting than fictionalism, which was discussed in part I. Because analogy is not common coin among philosophers, this particular analogy has been discussed or mentioned for the most part just in terms of specific similarities that writers have noticed and thought worth mentioning without much attention's being paid to the larger picture. I intend with this (...) analogy (looking at others' comparisons) to shed a little light on what is going on in mathematics, how one can understand it a bit other than experientially. This intention is philosophical and the way that I am attempting to accomplish it is also philosophical. I shall conclude my attempt to explain how it is possible and even natural for mathematics and fiction to have the analogy they have, taking it for granted, as argued in part I, that they are not to be identified. To this end I shall discuss philosophers' comparisons, mainly those of Hodes, Resnik, Tharp, and Wagner, who are the writers that seem to me to have written most thoughtfully and sufficiently extensively about fiction in making the comparison and of Körner, whose comparison is different. Whether either of these comparisons or the more general analogy is of permanent philosophical interest will have to be decided by philosophers now that they have had a fuller examination. I shall mention some other writers' reference to fiction, but not all; indeed, I am sure that I have not even found all the comparisons that there are. (shrink)

Hirsch’s revision results from his attempt to think through the difficult question that underlies the whole essay: How does the movement of time and circumstance affect the stability of meaning? The first part of his answer is that the relation between original meaning and subsequent understanding or applications of that meaning is analogous to the relation between a concept and its extension. For example, if he reads Shakespeare’s sonnet 55 and applies it to his beloved, and one of us (...) reads it and applies it to his beloved, “that does not make the meaning of the sonnet different for us, assuming that we both understand that the text’s meaning is not limited to any particular exemplification but rather embraces many, many exemplifications” . That is, the sonnet has a status analogous to that of the concept “bicycle,” and the two applications have a status analogous to that of a three-speed and a ten-speed bicycle. Whereas Hirsch formerly considered such exemplifications part of a text’s significance, he now considers them part of its meaning. This revision indicates that for Hirsch meaning is not the product of a consciousness producing an intrinsic genre but of a consciousness communicating something broader and more general than an intrinsic genre—an intention-concept that can have numerous extensions or exemplifications, including many that the originating consciousness could not have anticipated. Formerly, Hirsch used intrinsic genre to describe that sense of the whole which governed the horizon of developing meaning and which, when the work was completed—when all the blanks were filled in—gave the work its specific determinate meaning. That is, determinacy of meaning was in large part a function of narrowing the class of implications; when the work was completed, the class of implications was restricted to those synonymous with expressed meaning. In short, in the old theory, meaning-intention is a “narrow,” not a broad “concept.” James L. Battersby, professor of English at Ohio State University, is the author of Rational Praise and Natural Lamentation: Johnson, Lycidas, and Principles of Criticism and Elder Olson: An Annotated Bibliography. He is currently at work on a study of the relationship between “thought” and structure in various genres. James Phelan is associate professor English at Ohio State University and the author of Worlds from Words: A Theory of language in Fiction. His work in progress concerns character and narrative progression. (shrink)

In this philosophical paper, we explore computational and biological analogies to address the fine-tuning problem in cosmology. We first clarify what it means for physical constants or initial conditions to be fine-tuned. We review important distinctions such as the dimensionless and dimensional physical constants, and the classification of constants proposed by Lévy-Leblond. Then we explore how two great analogies, computational and biological, can give new insights into our problem. This paper includes a preliminary study to examine the two analogies. Importantly, (...) analogies are both useful and fundamental cognitive tools, but can also be misused or misinterpreted. The idea that our universe might be modelled as a computational entity is analysed, and we discuss the distinction between physical laws and initial conditions using algorithmic information theory. Smolin introduced the theory of "cosmological natural selection" with a biological analogy in mind. We examine an extension of. (shrink)

Offered here is an interpretation of the ancient Confucian philosopher Mengzi's (372–289 B.C.E.) method of cultivating moral feelings, which he calls "extension." It is argued that this method is both psychologically plausible and an important, but often overlooked, part of moral life. In this interpretation, extending our moral feelings is not a project in logical consistency, analogical reasoning, or emotional intuition. Rather, Mengzi's method of extension is a project in realigning the human heart that harnesses our rational, (...) reflective, and emotional capacities in order to extend the feelings we already have to the appropriate objects for these feelings. It is argued that there are three main features of Mengzi's account that make it an attractive explanation of the cultivation of moral feelings. The first is the way Mengzi sees reasoning and philosophical reflection as an aid to, rather than the foundation for, moral development. The second is Mengzi's precision regarding the relationship between the basic moral feelings we start with (the "sprouts") and their corresponding virtues. The method of extension acts as a well-designed bridge between feelings and virtues. Third, Mengzi's account, unlike that of the Mohist Yi Zhi, whom he criticizes, pays special attention to the complexities and limitations of human psychology. In conclusion it is shown how a Mengzian understanding of the relationship between feelings and morality can answer some traditional challenges, especially Kantian ones, regarding the proper role of emotion in moral life. (shrink)

Let me discuss first the principal points raised in the extensive commentaries from the three invited respondents. I shall next turn to the other shorter comments in the second part of this respons...

In lieu of an abstract, here is a brief excerpt of the content:The Simile of the Fugitive Homicide, Iliad 24.480–84:Analogy, Foiling, and AllusionBruce HeidenHomer elaborates "the most dramatic moment in the whole of the Iliad"1 with a unique, disturbing, and pathetic simile. Only in the scene of Priam's unheralded arrival in Achilles' lodging does the predicament of a murderer seeking refuge in a strange land ever provide the material for a Homeric illustration.(Il. 24.477–86)The simile explicitly compares only the wonder experienced (...) by the fugitive's host in the simile and by Achilles in the main narrative as each gazes upon his unexpected visitor. But since the narrator withholds this [End Page 1] link until the end of the simile, the implicit analogy between Priam and the murderer, both suppliants in a stranger's dwelling, seems at least equally prominent. Yet the tenor and the vehicle of this comparison are more notable for their dissimilarity than their resemblance: Priam is not a murderer,2 he is not in a foreign land but in his own, the man he supplicates is an enemy.3 According to MacLeod, "The simile heightens the moment by contrasting a more usual situation with this one."4 Mark W. Edwards writes of the "shock effect" produced by the reversal of roles between Priam and Achilles.5 While these authors see dissimilarity as a functional element of the simile, they do not explore the effects, or potential effects, of an emotional intensification achieved through the particular contrasts presented by this simile alone.6Upon close examination, the simile of the fugitive homicide reveals a multitude of internal and external associations that suggest mysterious, even uncanny interpretive density. It is hardly to be imagined that these associations could have been accurately recognized, much less interpreted, on a single hearing. Indeed, less acute listeners might not even have been troubled by the simile, while the more acute would have registered different disturbing subtleties and pondered them differently. Discussion here, therefore, does not aim at reproducing a single ideal reading of the passage, or at imputing to the poet techniques for eliciting such a reading. Instead it exposes a range of provocations which the simile offers to its audiences and suggests a range of interpretive responses. [End Page 2]The concept of foiling seems promising for the interpretation of sharp contrasts such as those in the simile of the fugitive homicide. In foiling, one or both contrasted qualities are emphasized through their juxtaposition. We find this technique constantly employed in the priamel, a structure that Homer could combine with similes.7 Fränkel perceived that "an interplay of polar (absolute or extreme) opposites is a basic constituent of early Greek (especially archaic) thought and feeling.... as a consequence thought constantly operated with contrasting foils."8 But he scarcely applied this insight to Homeric similes, despite his extensive study of them.9 Porter has convincingly argued that in the numerous similes in the Iliad in which the carnage of the battlefield is compared to scenes of peace, "the grimness and bloodiness of the battlefield are inevitably rendered darker and more tragic by the constant brief glimpses we get in the similes of a world where milk flows, etc.... Conversely, these momentary glimpses of the world of peace are made more idyllic and poignant by the panorama of violence and destruction which surrounds them."10The simile of the fugitive homicide is a bit more complicated than most of the juxtapositions discussed by Porter. Rather than comparing a scene of war to one of peace, this simile compares a scene comprising two elements, one violent, the other not (Achilles, Priam), to another scene of two elements, one violent the other nonviolent (the suppliant homicide and his host). Thus the comparison of violent and nonviolent is doubled. But Porter's basic principle of the mutual emphasis of peace and war through contrastive juxtaposition still applies. The comparison of Priam to a murderer seems to serve as a foil that emphasizes the harmlessness, indeed victimhood, of the elderly Trojan king. Priam's juxtaposition with the violent man he is supplicating would have the same effect: never could he be more powerless than when prostrate before the... (shrink)

There exist two known types of ultrafilter extensions of first-order models, both in a certain sense canonical. One of them comes from modal logic and universal algebra, and in fact goes back to Jónsson and Tarski :891–939, 1951; 74:127–162, 1952). Another one The infinity project proceeding, Barcelona, 2012) comes from model theory and algebra of ultrafilters, with ultrafilter extensions of semigroups as its main precursor. By a classical fact of general topology, the space of ultrafilters over a discrete space is (...) its largest compactification. The main result of Saveliev The infinity project proceeding, Barcelona, 2012), which confirms a canonicity of this extension, generalizes this fact to discrete spaces endowed with an arbitrary first-order structure. An analogous result for the former type of ultrafilter extensions was obtained in Saveliev. Results of such kind are referred to as extension theorems. After a brief introduction, we offer a uniform approach to both types of extensions based on the idea to extend the extension procedure itself. We propose a generalization of the standard concept of first-order interpretations in which functional and relational symbols are interpreted rather by ultrafilters over sets of functions and relations than by functions and relations themselves, and define ultrafilter models with an appropriate semantics for them. We provide two specific operations which turn ultrafilter models into ordinary models, establish necessary and sufficient conditions under which the latter are the two canonical ultrafilter extensions of some ordinary models, and obtain a topological characterization of ultrafilter models. We generalize a restricted version of the extension theorem to ultrafilter models. To formulate the full version, we propose a wider concept of ultrafilter models with their semantics based on limits of ultrafilters, and show that the former concept can be identified, in a certain way, with a particular case of the latter; moreover, the new concept absorbs the ordinary concept of models. We provide two more specific operations which turn ultrafilter models in the narrow sense into ones in the wide sense, and establish necessary and sufficient conditions under which ultrafilter models in the wide sense are the images of ones in the narrow sense under these operations, and also are two canonical ultrafilter extensions of some ordinary models. Finally, we establish three full versions of the extension theorem for ultrafilter models in the wide sense. The results of the first three sections of this paper were partially announced in Poliakov and Saveliev On two concepts of ultrafilter extensions of first-order models and their generalizations, Springer, Berlin, 2017). (shrink)

This paper is a full version of the author’s talk at “Procedural Logic and Philosophy of Consciousness”, a discussion dedicated to A.V. Smirnov’s book “The Logic of Mean­ing as a Philosophy of Consciousness: An Invitation to Reflection” (2021). The proposed content can be viewed as a co-reflection on the key concepts of the logical-semantic con­cept of consciousness: coherence, integrity, constriction, extension as the foundations and methods of conceptualization in their existential perspective. It is stressed that the logi­cal-semantic approach of (...) A.V. Smirnov reveals new facets in the understanding of philo­sophical rationality, personal and cultural subjectivity, experience, consciousness and their formation. To demonstrate the general philosophical, methodological status of the system of concepts introduced by the author, analogies are drawn with the understanding of exis­tential experience as a constriction of meaning-forming experiences that are unfolded by the subject in communication, creativity, self-understanding. The concepts that have re­ceived a conceptual justification in the works of A.V. Smirnov bring the origins of experi­ence to another level of comprehension, in accordance with which the spectrum of under­standing of human reflexive capabilities also changes. If we “start with integrity”, as the author advises us, then the idea of recursiveness of experience as a pulsating process of comprehension and self-reflection in the process of human interaction with the world or his “flickering” being-in-the-world is strengthened and acquires new angles. Of partic­ular importance here is the very style of author’s reflection, which is associated with the revision of established philosophical categories and their interpretations, the departure from the usual interpretations to discover one’s own philosophical language: one’s own – both in terms of the individual author’s approach and in aspects of the formation of the modern domestic philosophical tradition. (shrink)

John Baconthorpe (c.1290-1345/8) was the best-known of the Carmelite scholastics in the Middle Ages. This article is a brief study of his solution to the philosophical problem of how the soul may be wholly present in the human body and present whole and undivided in each part. Baconthorpe’s account is of great interest for a number of reasons. He takes issue with one of his fellow Carmelite masters, alerting us to diversity of opinion within that ‘school’. Furthermore, in using terminology (...) and illustrative analogies drawn from terminist logic and the mathematical sciences, Baconthorpe is an important witness to what has been described as the ‘mathematization’ of philosophy and theology in late medieval England. Finally, study of Baconthorpe’s texts provides further evidence of the emergence of the theme of extension in fourteenth-century thought in which we can discern the roots of modern philosophical debate. (shrink)

In relevant logics, necessary truths need not imply each other. In justification logic, necessary truths need not all be justified by the same reason. There is an affinity to these two approaches that suggests their pairing will provide good logics for tracking reasons in a fine-grained way. In this paper, I will show how to extend relevant logics with some of the basic operators of justification logic in order to track justifications or reasons. I will define and study three kinds (...) of frames for these logics. For the first kind of frame, I show soundness and highlight a difficulty in proving completeness. This motivates two alternative kinds of frames, with respect to which completeness results are obtained. Axioms to strengthen the justification logic portions of these logics are considered. I close by developing an analogy between the dot operator of justification logic and theory fusion in relevant logics. (shrink)

It seems that Whitehead's original problem, as evidenced in his earlier works, was epistemological and metaphysical dualism. His method of extensive abstraction is an attempt to bring the factual world and the abstract world of thought together. So far as his books on nature are concerned, then, Whitehead denied the ultimate reality of a static world and accepted the reality of dynamic relations analogous to the relations found in a biological organism.

We prove two embedding and extension theorems in the context of the constructive theory of metric spaces. The first states that Cantor space embeds in any inhabited complete separable metric space (CSM) without isolated points, X, in such a way that every sequentially continuous function from Cantor space to ℤ extends to a sequentially continuous function from X to ℝ. The second asserts an analogous property for Baire space relative to any inhabited locally non‐compact CSM. Both results rely on (...) having careful constructive formulations of the concepts involved.As a first application, we derive new relationships between “continuity principles” asserting that all functions between specified metric spaces are pointwise continuous. In particular, we give conditions that imply the failure of the continuity principle “all functions from X to ℝ are continuous”, when X is an inhabited CSM without isolated points, and when X is an inhabited locally non‐compact CSM. One situation in which the latter case applies is in models based on “domain realizability”, in which the failure of the continuity principle for any inhabited locally non‐compact CSM, X, generalizes a result previously obtained by Escardó and Streicher in the special case X = C[0, 1].As a second application, we show that, when the notion of inhabited complete separable metric space without isolated points is interpreted in a recursion‐theoretic setting, then, for any such space X, there exists a Banach‐Mazur computable function from X to the computable real numbers that is not Markov computable. This generalizes a result obtained by Hertling in the special case that X is the space of computable real numbers. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim). (shrink)

In his famous article “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” Eugen Wigner argues for a unique tie between mathematics and physics, invoking even religious language: “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve”. The possible existence of such a unique match between mathematics and physics has been extensively discussed by philosophers and historians of mathematics. Whatever the merits (...) of this claim are, a further question can be posed with regard to mathematization in science more generally: What happens when we leave the area of theories and laws of physics and move over to the realm of mathematical modeling in interdisciplinary contexts? Namely, in modeling the phenomena specific to biology or economics, for instance, scientists often use methods that have their origin in physics. How is this kind of mathematical modeling justified? (shrink)

The claim that skeptical theism induces moral paralysis or aporia (known as the moral paralysis objection) has been extensively discussed. In this context, Stephen Maitzen has introduced the Alien Doctor Analogy, an intriguing case that he employs to advance the moral paralysis objection. Michael Rea, however, has criticized the analogy for portraying the skeptical theist uncharitably. In this essay, I argue that Maitzen and Rea are both incorrect: the Alien Doctor Analogy is flawed indeed, but because it portrays the skeptical (...) theist too charitably. I modify the analogy to remedy this flaw. I then use the analogy to advance an original version of the moral paralysis objection. Specifically, I contend that skeptical theists, whenever they encounter apparently gratuitous evil that they could prevent, should be convinced by what I call the “God-Knows-Best Argument,” which always concludes that they should refrain from intervening. Thus, skeptical theism does induce moral paralysis. (shrink)

Socially inspired robotics involves drawing on the observation and study of human social interactions to apply them to the design of sociable robots. As there is increasing expectation that robots may participate in social care and provide some relief for the increasing shortage of human care workers, social interaction with robots becomes of increasing importance. This paper demonstrates the potential of socially inspired robotics through the exploration of a case study of the interaction of a partially sighted social worker with (...) a support worker. This is framed within the capability approach in which the interaction of a human and a sociable robot is understood as resulting in a collaborative capability which is grounded the relationship between the human and the robot rather than the autonomous capabilities of the robot. The implications of applying the case study as an analogy for human–robot interaction are expressed through a discussion of capabilities and social practice and policy. The study is attenuated by a discussion of the technical limits of robots and the extensive complexity of the social context in which it is envisaged sociable robots may be employed. (shrink)

Kant's response to ‘Hume's problem’ in his analysis of the a priori structure of causality as law-governed succession in the Second Analogy of Experience has unquestionably overshadowed the account of simultaneity (Zugleichsein), which follows in the Third Analogy. The analysis of simultaneity in the first Critique relies entirely upon that of succession and is ultimately no more than a more complicated variant of the causal dependence of substances: two objects are experienced as simultaneous only when each of those objects grounds (...) some determination of the other, that is when they are reciprocally determined in dynamic community. By investigating Kant's remark in the third Critique that the experience of the sublime “makes simultaneity intuitable” this paper develops a Kantian analysis of simultaneity that is irreducible to the more prominent analysis of causal succession. This more robust account of simultaneity is then seen to play an essential role in the constitution of the objects of perception (and not only the regulation of their relations) as thematized in the Axioms of Intuition in the Critique of Pure Reason. (shrink)

Some philosophers have argued that, owing to our humble evolutionary origins, some mysteries of the universe will forever remain beyond our ken. But what exactly does it mean to say that humans are ‘cognitively closed’ to some parts of the universe, or that some problems will forever remain ‘mysteries’? First, we distinguish between representational access and imaginative understanding, as well as between different modalities of cognitive limitation. Next, we look at tried-and-tested strategies for overcoming our innate cognitive limitations. In particular, (...) we consider how metaphors and analogies can extend the reach of the human mind, by allowing us to make sense of bizarre and counterintuitive things in terms of more familiar things. Finally, we argue that this collection of mind-extension devices is combinatorial and open-ended, and that therefore pronouncements about cognitive closure and about the limits of human inquiry are premature. (shrink)

According to the Cambridge Platonist Henry More, individual spirits--the souls of humans and non-human animals--are extended but cannot be physically divided. His contemporaries and recent commentators have charged that More has never given an explication of the grounds on which the indivisibility of spirits is based. In this article, I suggest that exploring the usage that More makes of the analogy between spirits and light could go some way towards providing such an explication. More compares the relation between spirit and (...) matter to the relation that, according to Aristotelian theories of light, holds between ?intentional species? and matter. I will argue that the purpose of his comparison is to highlight that both intentional species and spirits are existentially independent from matter. The existential independence of intentional species from matter expresses itself in the fact that light is not moved through the motion of the illuminated body. The existential independence of spirits from matter expresses itself in the fact that when a body that is coextensive with a spirit is divided, the spirit is not thereby divided but rather contracts into the remaining living organism. (shrink)

Al-Shāfi’ī has been unreservedly credited as one of the designers, if not the “master architect,” of uṣūl al-fiqh. His most important scholarly work, Al-Risālah, clearly demonstrates his cognitive creativity in this field. One of the methodologies for the decision of cases under Islamic law that Al-Shāfi’ī championed is qiyās, which he equated with ijtihād. His balanced approach invites further enquiry into the extensive use of qiyās in general and in criminal law in particular. The extent to which qiyās can be (...) applied to Islamic criminal law depends upon the degree or typology of qiyās being used, taking into account the Islamic theory of criminology. This article will analyse the position of al-Shāfi’ī in this regard. It will critically examine al-Shāfi’ī’s complex views on the use of qiyās as a method for establishing culpability under Islamic criminal law. It will then explore how his position corresponds to the human rights paradigm in the contemporary age. This article concludes that, while the use of qiyās in criminal law, especially in law of retaliation and predetermined punishments in accordance with al-Shāfi’ī’s approach is tantamount to incriminating a person based on less than certainty, it also represents the most promising way of protecting the right of victim. (shrink)

How does an audience receive a work of art? Does the experience only affect the viewer or does it have an effect and thus influence his or her actions? It is the cultural philosopher Ernst Cassirer and his successors in philosophy and developmental psychology as well as in neuroscience to this day who postulate that perception in general and perception of art in particular are not neutral in their origins but alive and thus meaningful. They assume that both are based (...) on analogous principles: in the perception of moving forms and spatial forms in the world and rhythms of forms, colors, light and shadow in art. In practice, this means that perception and its felt effects have an effect on the feelings of the viewer and thus help him to inform himself directly and intensively about the world through art. In contrast to this general epistemological aesthetic theory, which philosophers in particular accept, it is to be shown that this assumption must be redefined not with reference to the world, but with reference to art and design. For the latter, the approach will be extended to a semiotic theory. The background is that in contrast to the world, the designed forms and thus the designed intentions of the artist and designer or his client in relation to the chosen theme have an impact on the viewer and thus on culture and its communicative dynamics. (shrink)

Motivated by the search for a logic for polynomial time, we study rank logic which extends fixed-point logic with counting by operators that determine the rank of matrices over finite fields. WhileFPRcan express most of the known queries that separateFPCfromPtime, almost nothing was known about the limitations of its expressive power.In our first main result we show that the extensions ofFPCby rank operators over different prime fields are incomparable. This solves an open question posed by Dawar and Holm and also (...) implies that rank logic, in its original definition with a distinct rank operator for every field, fails to capture polynomial time. In particular we show that the variant of rank logic${\text{FPR}}^{\text{*}}$with an operator that uniformly expresses the matrix rank over finite fields is more expressive thanFPR.One important step in our proof is to consider solvability logicFPSwhich is the analogous extension ofFPCby quantifiers which express the solvability problem for linear equation systems over finite fields. Solvability logic can easily be embedded into rank logic, but it is open whether it is a strict fragment. In our second main result we give a partial answer to this question: in the absence of counting, rank operators are strictly more expressive than solvability quantifiers. (shrink)