We achieve several results. First, we develop a variant of the theory of absolute Galois groups in the context of many sorted structures. Second, we provide a method for coding absolute Galois groups of structures, so they can be interpreted in some monster model with an additional predicate. Third, we prove the “Weak Independence Theorem” for pseudo-algebraically closed (PAC) substructures of an ambient structure with no finite cover property (nfcp) and the property [Formula: see text]. Fourth, we describe Kim-dividing (...) in these PAC substructures and show several results related to the SOPnhierarchy. Fifth, we characterize the algebraic closure in PAC structures. (shrink)

Many of the objects that we perceive have an important characteristic: When they move, they change shape. For instance, when you watch a person walk across a room, her body constantly deforms. I suggest that we exercise a type of perceptual constancy in response to changes of this sort, which I call structure constancy. In this paper I offer an account of structure constancy. I introduce the notion of compositional structure, and propose that structure constancy involves (...) perceptually representing an object as retaining its compositional structure over time. I argue that compositional structure is represented in visual phenomenology, and I also assemble empirical evidence in support of the claim that compositional structure is recovered by the visual system. Finally, I draw out consequences of this account. I argue that structure constancy has implications for the predictive capacities of perception, and that the phenomenon places important constraints on viable accounts of both the format and reference frame of visual experience. (shrink)

Kuhn’s Structure of Scientific Revolutions has been attacked for many reasons. Key analytic terms, most importantly “paradigm,” were widely regarded as poorly defined. To many readers Structure seemed to suggest that the process of theory change is irrational, or at least non-rational. And even his characterization of normal science seemed to some readers to paint a very unflattering picture of scientists as excessively dogmatic and uncritical. More recently, Lorraine Daston has argued that the notion of “structure” that (...) figures in the title of the book, as well as in the analysis of the history of science discussed throughout the book, is “dusty and dated”. Historians of science tend to focus on the particular, in recognition that the sorts of events they study are unique. My aim in this paper is to defend Kuhn’s appeal to the notion of structure. First, I argue that Structure of Scientific Revolutions is not primarily a contribution to the history of science, despite the fact that it cites many historical sources and articles in the history of science. Consequently, it is a mistake to regard Kuhn’s appeal to the notion of structure as a case of badly written history of science. Second, I argue that insofar as the book is a contribution to philosophy, the sort of thing Kuhn means by “structure” is perfectly respectable, and is often presupposed in many philosophical studies, especially in general philosophy of science. Third, I defend Kuhn’s analysis of science, especially the enterprise of identifying the structure of scientific revolutions. (shrink)

Many contemporary proponents of hylomorphism, the view that at least some material objects are comprised of both matter and form, endorse a version of hylomorphism according to which the form of a material object is a certain complex relation or structure. In this paper, I introduce three sorts of concerns for this “structural” approach. First, I argue that, in countenancing an abundance of overlapping yet numerically distinct material objects, “structural hylomorphists” are committed to a certain sort of systematic causal (...) overdetermination. Second, I argue that, because of its relatively thin conception of form, the view risks collapsing into some already well-entrenched metaphysical account of material objects. Finally, I argue that because the view emphasizes the more static structural features of composite material objects, structural hylomorphists seem unable to explain how it is that those objects might be said to persist over time through changes in such features. (shrink)

What is the relationship between evolutionary contingency and diversity? The evolutionary contingency thesis emphasizes dependency relations and chance as the hallmarks of evolution. While contingency can be destructive of, for example, the fragile and complex dynamics in an ecosystem, I will mainly focus on the productive or causal aspect of contingency for a particular sort of diversity. There are many sorts of diversities: Gould is most famous for his diversity-to-decimation model, which includes disparate body plans distinguishing different phyla. However, structural (...) diversity construed more broadly spans scales, such as organization in and among cells, structural arrangements and biomechanics on various scales, and even the profile of ancestor-descendent relationships or community structure of interactions within ecosystems. By focusing on stochastic processes in contingent evolution, I argue that contingency causes structural diversity. Specifically, I focus on the plurality of structural types of cells, genetic codes, and phyla diversity as case studies. (shrink)

In this paper we give an axiomatisation of the concept of a computability structure with partial sequences on a many‐sorted metric partial algebra, thus extending the axiomatisation given by Pour‐El and Richards in [9] for Banach spaces. We show that every Banach‐Mazur computable partial function from an effectively separable computable metric partial Σ‐algebraAto a computable metric partial Σ‐algebraBmust be continuous, and conversely, that every effectively continuous partial function with semidecidable domain and which preserves the computability of a computably (...) enumerable dense set must be computable. Finally, as an application of these results we give an alternative proof of the first main theorem for Banach spaces first proved by Pour‐El and Richards. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim). (shrink)

Recent work by Frigg et. al. and Mayo-Wilson have called attention to a particular sort of error associated with attempts to model certain complex systems: structural modeling error. The assessment of the degree of SME in a model presupposes agreement between modelers about the best way to individuate natural systems, an agreement which can be more problematic than it appears. This problem, which we dub “the system individuation problem” arises in many of the same contexts as SME, and the two (...) often compound one another. This paper explores the common roots of the two problems in concerns about the precision of predictions generated by scientific models, and discusses how both concerns bear on the study of complex natural systems, particularly the global climate. (shrink)

Many questions about wellbeing involve metaphysical dependence. Does wellbeing depend on minds? Is wellbeing determined by distinct sorts of things? Is it determined differently for different subjects? However, we should distinguish two axes of dependence. First, there are the grounds that generate value. Second, there are the connections between the grounds and value which make it so that those grounds generate that value. Given these distinct axes of dependence, there are distinct dimensions to questions about the dependence of wellbeing. In (...) this paper, I offer a view of wellbeing that gives different answers with respect to these different dimensions. The view is subjectivist about connections but objectivist about grounds. Pluralist about grounds but monist about connections. Invariabilist about connections but variabilist about grounds. Thus, the view offers a simple account that captures the complexity of wellbeing. (shrink)

The Many Gods Objection (MGO) is widely viewed as a decisive criticism of Pascal’s Wager. By introducing a plurality of hypotheses with infinite expected utility into the decision matrix, the wagerer is left without adequate grounds to decide between them. However, some have attempted to rebut this objection by employing various criteria drawn from the theological tradition. Unfortunately, such defenses do little good for an argument that is supposed to be an apologetic aimed at atheists and agnostics. The purpose of (...) this paper is to offer a defensive strategy of a different sort, one more suited to the Wager’s apologetic aim and status as a decision under ignorance. Instead of turning to criteria independent of the Wager, it will be shown that there are characteristics already built into its decision theoretic structure that can be used to block many categories of theological hypotheses including MGO’s more outrageous “cooked-up” hypotheses and “philosophers’ fictions”. -/- Please note that there are editorial errors in the published version. They have been corrected in the attached. (shrink)

Organic chemistry provides fertile ground for scholars interested in understanding the role of non-linguistic representations in scientific thinking. In this discipline, it is not plausible to regard diagrams as simply heuristic aids for expressing or applying what is essentially a linguistic theory. Instead, it is more plausible to think of linguistic representation as supplementing theories whose principal expression is diagrammatic. Among the many sorts of diagrams employed by organic chemists, structural formulas are the most important. In this paper, by examining (...) two central episodes in the development of structural formulas—Kekulé’s proposal of a structure for benzene and Ingold’s explanation of dipole moments in terms of ‘mesomerism’—I investigate how the norms for the production and interpretation of structural formulas evolve in response to experimental results and theoretical developments. I conclude that one principal way in which structural formulas embody the theory of organic chemistry is through these evolving norms. (shrink)

For a locally compact group G, we show that it is possible to present the class of continuous unitary representations of G as an elementary class of metric structures, in the sense of continuous logic. More precisely, we show how nondegenerate ∗-representations of a general ∗-algebra A (with some mild assumptions) can be viewed as an elementary class, in a many-sorted language, and use the correspondence between continuous unitary representations of G and nondegenerate ∗-representations of L1(G). We relate the notion (...) of ultraproduct of logical structures, under this presentation, with other notions of ultraproduct of representations appearing in the literature, and we characterize property (T) for G in terms of the definability of the sets of fixed points of L1 functions on G. (shrink)

A class of many-sorted polyadic set algebras is introduced. These generalise structure and model in a way that is relevant in regards to the Entscheidungsproblem and to automated reasoning.A downward Löwenheim-Skolem property is shown in that each satisfiable finite conjunction of purely relational first-order prenex sentences has a finite generalised model. This property does, together with a construction related to doubling the size of a finite structure, provide several strict generalisations of the strategy of finite model search for (...) disproving. (shrink)

Feature structures are employed in various forms in many areas of linguistics. Informally, one can picture a feature structure as a sort of tree decorated with information about constraints requiring that specific subtrees be identical (isomorphic). Here I show that this informal picture of feature structures can be used to characterize exactly the class of feature structures under their usual subsumption ordering. Furthermore, once a precise definition of tree is fixed, this characterization makes use only of standard domain-theoretic notions (...) regarding the information borne by elements in a domain, thus removing (or better, explaining) all apparentlyad hoc choices in the original definition of feature structures. In addition, I show how this characterization can be parameterized in order to yield similar characterizations of various different notions of feature structure, including acyclic structures, structures with appropriateness conditions and structures with apartness conditions (used to model path inequations). The generalizations to other notions of feature structure also emphasize that the construction given here is in fact independent of the application to feature structures. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Structure, Change, and Survival: A Response To Winthrop-youngFranco Moretti (bio)Geoffrey Winthrop-Young’s is the sort of review article one dreams of: long, intelligent, and very generous. So, first of all, thanks. And thanks also for the clarity with which disagreements are expressed. In the same spirit, here is a brief response.The first area of disagreement comes early in the article, when Winthrop-Young claims that in the Atlas, “the here (...) and now of a specific location suffers something akin to the fate of a Barthesian myth: its specificity is subordinated to a signifying function as part of an established narrative sequence. But as Moretti chooses not to address the question of how this transformation is achieved, his discussion tends to gloss over the differences between geographical, literary, and imaginary locations” [7]. Frankly, I don’t think this is true. I often do exactly what Winthrop-Young demands, using a sequence of maps to clarify the successive steps by which a geographical space ends up supporting a specific narrative strucure: see the Austen maps that open the book, or the picaresque sequence in the first chapter, or the Balzac and Dickens maps in the second chapter—where I also address the issue in conceptual terms in a section entitled “Stories of the Third.” It’s true that I don’t do so in every case (as perhaps I should), and Winthrop-Young may of course disagree with the way I chart the transformation of space into narrative, but he cannot deny that I am doing so. The fact that those maps compose sequences of increasing complexity (as is particularly clear for Austen and Our Mutual Friend) proves precisely that I am indeed mapping a “transformation” of relatively simple beginnings into a complicated final structure. Incidentally, I do something similar in Modern Epic, where I describe how Joyce’s stream of consciousness “grows” from rather slim paragraphs to the plump ones we read now, or follow the slow rise of Ulysses’s polyphony. Again: my theses may be wrong—but they are an attempt to follow the step-by-step structuration of a text (or genre). This, after all, is the basic test of critical materialism: if we cannot describe the how and the why of the various steps, we are implicitly invoking “creativity” as an explanation for literary products. Which is a bit like invoking God. But on the futility of this, Winthrop-Young and I probably agree.The second disagreement regards the tempo of literary history: does morphological change occur in brief bursts separated by long periods of stasis (as in Eldredge and Gould’s punctuated equilibria)—or is it more evenly distributed across time? Here, Winthrop-Young claims [36, fn 5] that my attempt to see Schwarz’s account of Brazilian modernism and the genesis of magic realism as a single instance of punctuated equilibria is contradicted by historical evidence. He is right. Years ago, I adopted punctuated equilibria because it proved better than any rival theory at explaining the peculiar rapidity of many literary turning points (baroque drama; the rise of the British novel; the modernist season of European literature). From this initial conviction, I was (unconsciously) led to generalize, and to treat every case of major morphological change as an instance of punctuated equilibria. This was silly, and Winthrop-Young is right in criticizing me. However, he would probably agree that a single (or even a few) contrary [End Page 41] instances do not invalidate a theory in its entirety, and that what we most need is to know more about how literary change occurs. Only after such an empirical reconnaissance will the testing of theories be on a truly sound basis. Personally, I wouldn’t be surprised if we discovered that literary change can occur in more than one way, and that we need more than one theory to account for it; still, all I know of literary history suggests that punctuated equilibria will be the theory with greatest explanatory power.The last disagreement concerns literary selection: specifically, whether my view of it is indeed Darwinian, or whether I Lamarck-like “transform the concept of selection from the traditional passive filter... (shrink)

The goal of this dissertation is to show that cognitive science, while dealing with the special subject of the mind, can nonetheless fit into the same general model that Bas van Fraassen provides for the natural sciences. The dissertation focuses specifically on the nature of explanation in the cognitive sciences. ;Chapter One makes clear what I take cognitive science to be in the work. The two central cases here are Noam Chomsky's theory of generative syntax, and David Marr's computational theory (...) of vision. The bulk of this chapter is devoted to setting out the structure of the two theories, in order to provide concrete case studies in the sorts of explanations they give. ;Chapter Two sets out the model of explanation employed by considering the relative virtues of several recent approaches--Hempel's classic D-N model, Salmon's statistical relevance model, and Stalnaker and Lewis' counterfactual approach--and concluding with van Fraassen's pragmatics-oriented model. Like many accounts, van Fraassen's takes explanations to be answers to "Why?" questions, and emphasizes the pragmatic machinery at work in question-asking. ;Chapter Three considers two influential views of explanation in cognitive science. Such explanations are often said to be functional or dispositional. I look at proposals of each sort and argue that none of the explanatory strategies singled out can count as the central one in cognitive scientific explanation, because cognitive science has no central explanatory strategy. ;In Chapter Four I hold instead that cognitive science uses all the relevance relations found in natural science. The odd features of cognitive scientific explanation turn instead around the sorts of objects and processes that get posited in its theories--abstract, multiply-instantiable objects that can act as representations, and abstract processes of transformation on these objects. I do not, then, deny that we get new sorts of explanation in cognitive science--only that the source of this novelty has been properly located. (shrink)

We explore a notion of pseudofinite dimension, introduced by Hrushovski and Wagner, on an infinite ultraproduct of finite structures. Certain conditions on pseudofinite dimension are identified that guarantee simplicity or supersimplicity of the underlying theory, and that a drop in pseudofinite dimension is equivalent to forking. Under a suitable assumption, a measure-theoretic condition is shown to be equivalent to local stability. Many examples are explored, including vector spaces over finite fields viewed as 2-sorted finite structures, and homocyclic groups. Connections are (...) made to products of sets in finite groups, in particular to word maps, and a generalization of Tao's Algebraic Regularity Lemma is noted. (shrink)

In many contemporary philosophical writings, what is most surprising to me is not the things asserted, nor those denied, but those not even mentioned . Several of these slighted topics are summed up in the title of this essay. At the age of twenty, when I was not reading any technical philosophers, nor any author who held an essentially social view of experience, I attempted to persuade myself of the adequacy of a non-social view, expressed partly in a self-interest theory (...) of motivation, and partly in an idea of perception as experience of things not themselves constituted by any sort of experiences. So far from succeeding in this attempt, I began to find reasons for regarding both motivation and perception as manifestations of a single principle, that of the overlapping or inter-individual unity of minds, not simply of human minds, but of mind on various levels of, nature, including inorganic nature. This overlapping I thought I found in experience itself, and not merely through speculation or postulation. Subsequent reading in philosophy has not shown me a basic error in Hhis early philosophizing, but only a vagueness and blurring of dis; Jinctions which, when taken into account, strengthen rather than weaken the case. (shrink)

The first book of the Aristotelian Physics may be considered as a sort of general introduction to the whole work. In particular, chapters 2 and 3 result very interesting for the foundation of the science of nature according to Aristotle; indeed, in these two chapters, the Stagirite criticizes the position of the Eleates Parmenides and Melissus. These two philosophers are considered as those who claim that change does not exist because the existence of the not-being is impossible to suppose. For (...) this reason, since the Eleates deny that motion and change really exist, the refutation of their thesis results essential for the logical and ontological foundation of the Aristotelian science of nature. This paper wants to make light on the argumentations that Aristotle uses against Parmenides and Melissus. Indeed, since the Stagirite makes often use of his philosophical categories, it seems that his critics sound a little bit anachronistic. In many passages of the text is seems that Aristotle “simply” replace the presupposition of the Eleatic philosophy with the thesis of the evidence of moving and plurality, in general. The aim of this contribution is to reflect on the critics present in Ph. I 2–3 in order to underline the importance of the Eleatic philosophy for the Aristotelian science of nature. (shrink)

Ken Pledger devised a one-sorted approach to the incidence relation of plane geometries, using structures that also support models of propositional modal logic. He introduced a modal system 12g that is valid in one-sorted projective planes, proved that it has finitely many non-equivalent modalities, and identified all possible modality patterns of its extensions. One of these extensions 8f is valid in elliptic planes. These results were presented in his 1980 doctoral dissertation, which is reprinted in this issue of the Australasian (...) Journal of Logic. Here we show that 12g and 8f are strongly complete for validity in their intended one-sorted geometrical interpretations, and have the finite model property. The proofs apply standard technology of modal logic together with a step-by-step procedure introduced by Yde Venema for constructing two-sorted projective planes. (shrink)

What place does consciousness have in the natural world? If we reject materialism, could there be a credible alternative? In one classic example, philosophers ask whether we can ever know what is it is like for bats to sense the world using sonar. It seems obvious to many that any amount of information about a bat's physical structure and information processing leaves us guessing about the central questions concerning the character of its experience. A Place for Consciousness begins with (...) reflections on the existence of this gap. Is it just a psychological shortcoming in our merely human understanding of the physical world? Is it a trivial consequence of the simple fact that we just cannot be bats? Or does it mean there really are facts about consciousness over and above the physical facts? If so, what does consciousness do? Why does it exist? Rosenberg sorts out these problems, especially those centering on the causal role of consciousness. He introduces a new paradigm called Liberal Naturalism for thinking about what causation is, about the natural world, and about how to create a detailed model to go along with the new paradigm. Arguing that experience is part of the categorical foundations of causality, he shows that within this new paradigm there is a place for something essentially like consciousness in all its traditional mysterious respects. A striking feature of Liberal Naturalism is that its central tenets are motivated independently of the mind-body problem, by analyzing causation itself. Because of this approach, when consciousness shows up in the picture it is not introduced in an ad hoc way, and its most puzzling features can be explained from first principles. Ultimately, Rosenberg's final solution gives consciousness a causally important role without supposing either that it is physical or that it interacts with the physical. (shrink)

Many areas of frontier physics are confronted with the crisis of a lack of accessible, direct evidence. As a result, direct model building has failed to lead to any new empirical discoveries. In this paper I argue that these areas of frontier physics have developed common methods for turning precision measurements of known quantities into potential evidence for anomalies hinting at new physics. This method of framework generalization has arisen as a sort of model-independent method for generalizing beyond known physics (...) and organizing experimental searches. I argue that this method is well-justified given the current epistemic landscape, and that theory construction in general is much broader than simply building new dynamical models. (shrink)

The type II phosphatidylinositol 4-kinases produce the lipid phosphatidylinositol 4-phosphate and participate in a confusing variety of membrane trafficking and signaling roles. This review argues that both historical and contemporary evidence supports the function of the PI4KIIs in numerous trafficking pathways, and that the key to understanding the enzymatic regulation is through membrane interaction and the intrinsic membrane environment. By summarizing new research and examining the trafficking roles of the PI4KIIs in the context of recently solved molecular structures, I highlight (...) how mechanisms of PI4KII function and regulation are providing insights into the development of cancer and in neurological disease. I present an integrated view connecting the cell biology, molecular regulation, and roles in whole animal systems of these increasingly important proteins. The type II phosphatidylinositol 4-kinases are versatile mediators of membrane trafficking, controlling pathways that impact on disease. Recent advances suggest that the membrane lipid environment regulates enzyme activity and that the complexity of trafficking routes can be explained by the ability of these kinases to promote membrane trafficking in different directions. (shrink)

When did historians begin to put quotation marks around the wordreal? There are many examples of this habit and some of them will be set forth as evidence in what follows. But before doing so we might ask a preliminary question: What are the quotation marksthemselvessupposed to mean? Today we find them so familiar they hardly need to be written and they are more frequently consigned to the everyday repertoire of silent gesture: two fingers on either hand clutch at the (...) air as if they meant to tickle the flanks of the invisible beast between them. The popular term is “scare-quotes,” a pun on the word “scarecrow.” Its etymology is revealing: just as a mere representation of a body in a field may scare off birds, so too scare-quotes permit someone to deploy a word without sincere commitment to what it normally means. But further reflection tells us that the effects are not so similar after all: To use a term without sincerity robs it of its original meaning and holds up its lifeless corpse to ridicule. The more knowing sort of crow can settle on the shoulder of the figure on the pole precisely because it recognizes that such a sorry excuse for a man can in fact harm no one. Similarly when one putsrealityin quotation marks we are put in mind of the living concept but we are immediately alerted to the fact that, for the user at least, the new term enjoys no metaphysical prestige. How did this happen? When and why did the single most privileged word in the entire lexicon of metaphysics begin to lose its authority such that in certain spheres of intellectual sophistication its sincere use would only seem an embarrassment and a sign of naïveté? (shrink)

The computer is one of the most complex artifacts ever built. Given its complexity, it can be described from many different points of view. The aim of this paper is to investigate the representational structure and multifunctionality of a particular subset of computers, namely personal devices from a user-centred perspective. The paper also discusses the concept of “cognitive task”, as recently employed in some definitions of cognitive artifacts, and investigates the metaphysical properties of such artifacts. From a representational point (...) of view, the article introduces the concepts of artifactual meta-representation and of semi-transparency, two features that personal devices share with some cognitive and non-cognitive artifacts. Recognising the meta-representational nature of personal devices and of other cognitive artifacts, thus overcoming semi-transparency, is important for the understanding of why different artifacts offer us different cognitive affordances as well as different cognitive advantages. In this sense, it is not simply a theoretical achievement, but has some important practical consequences. In our highly technological world we can use different kinds of computers and artifacts for solving the same tasks, and we need to understand why some artifacts are better suited for some tasks than others. The ultimate characterisation of personal devices that emerges from this work is that of a sort of super-artifact. This special status is given to personal devices because of their distinctive features. They are in fact intrinsically multifunctional and meta-representational artifacts, with extremely variable structures. As super-artifacts, personal devices are characterised by macro-functionality and can be easily used as both cognitive artifacts and tools for other functions, depending on the kind of representations they instantiate. (shrink)

We trace self-reference phenomena to the possibility of naming functions by names that belong to the domain over which the functions are defined. A naming system is a structure of the form ,{ }), where D is a non-empty set; for every a∈ D, which is a name of a k-ary function, {a}: Dk → D is the function named by a, and type is the type of a, which tells us if a is a name and, if it (...) is, the arity of the named function. Under quite general conditions we get a fixed point theorem, whose special cases include the fixed point theorem underlying Gödel's proof, Kleene's recursion theorem and many other theorems of this nature, including the solution to simultaneous fixed point equations. Partial functions are accommodated by including “undefined” values; we investigate different systems arising out of different ways of dealing with them. Many-sorted naming systems are suggested as a natural approach to general computatability with many data types over arbitrary structures. The first part of the paper is a historical reconstruction of the way Gödel probably derived his proof from Cantor's diagonalization, through the semantic version of Richard. The incompleteness proof–including the fixed point construction–result from a natural line of thought, thereby dispelling the appearance of a “magic trick”. The analysis goes on to show how Kleene's recursion theorem is obtained along the same lines. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:On the Historical Significance and Structure of Monroe Beardsley's AestheticsAn AppreciationNoël Carroll (bio)IntroductionMonroe C. Beardsley's Aesthetics: Problems in the Philosophy of Criticism, published in 1958 by Harcourt, Brace and World Inc.,1 was a watershed event in the history of analytic aesthetics—a climax of sorts with respect to what preceded it and, at the same time, the opening of a new, more intricately developed and defended research program in (...) aesthetics than what had been previously on offer. Beardsley's Aesthetics, and developments therefrom,2 consolidated and crystallized a tendency in aesthetics that had begun to emerge at least by the time of the publication of Francis Hutcheson's An Inquiry Concerning Beauty, Order, Harmony, Design,3 which tendency, following Beardsley, we can call the aesthetic theory of art. Assembled out of parts and suggestions from Hutcheson, Kant, Schopenhauer, and Bell, among others, the aesthetic theory of art—of which Beardsley's version is one of the most accomplished, if not the most accomplished—has shown remarkable resilience, continuing to command allegiance from many distinguished, contemporary proponents, including Nick Zangwill, Gary Iseminger, and, with certain important modifications, Alan Goldman and Malcolm Budd.Part of what I would like to do in this essay is not only to trace the evolution of the aesthetic theory of art from its origins through to Beardsley's Aesthetics (and his subsequent tinkering with this masterwork) but also to show how the structure of the aesthetic theory of art, as crafted by Beardsley, is simultaneously so elegant, comprehensive, and systematic that it is understandable that Beardsley preferred constantly to repair it after each attack rather than to abandon it for the kinds of alternatives being proffered by Goodman, Danto, Wollheim, Dickie, Wolterstorff, and then Walton. In other words, Beardsley's reluctance to give up was genuinely motivated. [End Page 2] For, if only the kinks could have been smoothed out of it, the aesthetic theory of art, of the sort initiated in Aesthetics and elaborated subsequently by Beardsley, was itself a thing of beauty: exceedingly economical in its foundational principles and powerful in its reach. Thus, whereas typically I address the shortcomings of the aesthetic theory of art, in this essay I would like to talk about its strengths, strengths that I believe encouraged Monroe Beardsley to stick with it through thick and thin—that is, through a thick swarm of often thin counterexamples.In the next part of this essay, I will try to place Aesthetics historically in the course of Western aesthetics. Then in the final section, I shall attempt to explain how the structure of the sort of aesthetic theory of art incipient in Beardsley's Aesthetics and pursued by him in later works is so almost irresistibly attractive that virtually no number of anomalies can shake its friends out of the faith that such problems can be ultimately controlled, if not entirely overcome.On the Historical Significance of Beardsley's AestheticsBeardsley's Aesthetics is the culmination of certain tendencies that had been coalescing in various ways in Western aesthetics since the eighteenth century. One of Beardsley's most significant and influential twentieth-century predecessors was Clive Bell, who in his book Art, as is well known, defined art as that which possessed significant form. Significant form, in turn, was characterized as that which caused an aesthetic emotion. Bell's notion of an aesthetic emotion, I conjecture, derived from Schopenhauer's claim that what an artwork does is to lift us out of our everyday concerns—out of the world of striving. The aesthetic emotion, according to Bell, is a matter of being carried "out of life into ecstasy."4 The aesthetic experience, according to the Schopenhauer-Bell line of thought, involves the release of the individual from the pressures of life—from the pursuit of an endless process of desiring in Schopenhauer's lingo.This notion of aesthetic experience as detachment owes something to Kant's hypothesis that an authentic aesthetic judgment is disinterested, which, of course, itself is descended historically from Hutcheson's contention that beauty amounts to an experience of disinterested pleasure. However, whereas for Hutcheson and Kant disinterestedness is a... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:THREE NOTIONS OF RESOLUTIO AND THE STRUCTURE OF REASONING IN AQUINAS 1 EILEEN c. SWEENEY Boston College Chestnut Hill, Massachusetts RESOLUTIO, better known by the English transliteration of its Greek counterpart, "analysis," has been touted as " the conceptual model for some of the most important ideas in the history of philosophy, including the history of the methodology and philosophy of science." 2 But while resolution /analysis may (...) be important in the histories of philosophy and science, its own history is, to say the least, confused. A Renaissance commentator, Jeremias Triverius gives some sense of this when, after giving a list of four methods of dialectic (division, definition, demonstration, and resolution),3 he writes, 1 I have used the following abbreviations for works by Thomas Aquinas. All translations of Aquinas are my own. Commentum in Quatuor Libros Sententiarum (ed. Busa): In Sent; Compendium Theologiae (ed. Busa): Comp Theo!; E:rpositio Super Librum Boethii De Trinitate (ed. Decker): Exp de Trin; In Aristotelis Libros Posterium Analyticorum (ed. Marietti) : In Anal Post; In Duodecem Libros Metaphysicorum Aristotelis E:rpositio (ed. Marietti): In Meta; In Librum Beati Dionysii De Divinis Nominibus E:rpositio (ed. Marietti): In Div Nom; Sententia Libri Ethicorum Aristotelis ad Nichomachum: In Ethic; Sententia Libri Politicormn Aristotelis (ed. Leonine): In Pol; De Substantiis Separatis (ed. Busa): De Sub Sep; Summa Contra Gentiles (ed. Leonine): SCG; Summa Theologiae (ed. Leonine): ST; Questiones Disputatae de Veritate: QDV. 2 Jaakko Hintikka and Unto Remes, The Method of Analysis (Boston: D. Reidel, 1974), p. 1. s These four methods of dialectic are also given by a number of ancient commentators, for example, Ammonius (In Porphyrii Isagogen, in Commentaria in Aristotelem Graeca [hereafter, CAG], ed. Maximilian Wallies [Berlin, 1891], vol. IV, pt. 6, p. 34, 11. 19-20) and a later commentator, David (Davidis Prolegomena et in Porphyrii Isagogen Commentarium, CAG, ed. Adolf Busse [Berlin, 1904], vol. 18, p. 88, 11. 6-10). 197 198 EILEEN C. SWEENEY Now anyone who has some knowledge of dialectical matters knows what Definition, Division, and Demonstration are. There is no general agreement, however, so far as I can see, on Resolution. Some identify it with Division. Others regard it as contrary [to Divi- • ] 4 S!On, ••• Triverius, like many modern commentators, adds to, rather than sorts out, the confusion, continuing, " And since each one is entitled to his opinion, I am now maintaining that Resolution is contrary to Demonstration...." 5 Many centuries before Triverius we find a similar ambiguity in Greek commentators on Aristotle, who outline several types of analysis. Unlike Triverius, however, most seem untroubled by the multiple types; Ammonius and David, without puzzlement, explain carefully that analysis is the opposite of each of the other three methods.6 The lack of 4 Jeremias Triverius, In texnhn [sic] Galeni clarissimi commentarii (Lyon, 1547), p. 14; cited and translated in Nea! Gilbert, Renaissance Concepts of Method (New York: Columbia University Press, 1960), p. 106. Galen's opening remarks of the Ars medica, giving three methods of teaching (analysis, synthesis, and definition) is a common locus for the discussion of resolution/ analysis in the Middle Ages and Renaissance. Galen's contribution, at least for Aquinas, seems to have been completely mediated by Medieval Arabic commentators. Galen's own discussions are either incomplete, as in the opening passage to the Ars medica (in Claudii Galeni Opera Omnia, ed. C. G. Kiihn, [Repr. Hildesheim: Georg Olms, 1965], vol. I, pp. 305-306), which merely mentions the word, or are unclear accounts of analysis (Cf. Galen's discussion of analysis in De Peccatorum, in Opera Omnia, vol. 5, ch. 5, pp. 80-81). On two of the Arabic commentaries' descriptions of analysis to accompany medieval translations of Galen, see below, nn. 80 & 83. On Galen's supposed contribution to the notion of resolution and method in the development of experimental science, see A. C. Crombie, Robert Grosseteste and the Origins of Experimental Science (Oxford: Clarendon Press, 1953), especially pp. 7680, and Gilbert, Renaissance Method, pp, 13-27, 44-46. 5 Triverius, In texnhn, p. 14; Gilbert, p. 106. 6 For analysis as the opposite of division, definition, and demonstration, see Ammonius, In Aristotelis Analyticorum Priorum Librum I Commentarium, CAG, ed. Maximilian Wallies, (Berlin, 1891... (shrink)

Basically, the connection of two many-sorted theories is obtained by taking their disjoint union, and then connecting the two parts through connection functions that must behave like homomorphisms on the shared signature. We determine conditions under which decidability of the validity of universal formulae in the component theories transfers to their connection. In addition, we consider variants of the basic connection scheme. Our results can be seen as a generalization of the so-called E-connection approach for combining modal logics to an (...) algebraic setting. (shrink)

We show that the spectrum of a sentence ϕ in Counting Monadic Second Order Logic (CMSOL) using one binary relation symbol and finitely many unary relation symbols, is ultimately periodic, provided all the models of ϕ are of clique width at most k, for some fixed k. We prove a similar statement for arbitrary finite relational vocabularies τ and a variant of clique width for τ-structures. This includes the cases where the models of ϕ are of tree width at most (...) k. For the case of bounded tree-width, the ultimate periodicity is even proved for Guarded Second Order Logic GSOL. We also generalize this result to many-sorted spectra, which can be viewed as an analogue of Parikh's Theorem on context-free languages, and its analogues for context-free graph grammars due to Habel and Courcelle. Our work was inspired by Gurevich and Shelah (2003), who showed ultimate periodicity of the spectrum for sentences of Monadic Second Order Logic where only finitely many unary predicates and one unary function are allowed. This restriction implies that the models are all of tree width at most 2, and hence it follows from our result. (shrink)

We consider question-answer dialogues between participants who may disagree with each other. The main problems are: (a) How different speech-acts affect the information in the dialogue; and (b) How to represent what was said in a dialogue, so that we can summarize it even when it involves disagreements (i.e., inconsistencies).We use a fully-typed many-sorted language L with a possible-worlds semantics. L contains nominals representing short answers. The speech-acts are uniformly represented in a dialogue language DL by focus structures, consisting of (...) a mood operator, a topic component and a focus component. Each stage of the dialogue is associated with a set of information functions (g-functions), which are partial functions taking a topic component (representing a question raised) to a set of propositions determined by the corresponding focus component (to the set of answers given to it). (shrink)

The usual completeness theorem for first-order logic is extended in order to allow for a natural incorporation of real analysis. Essentially, this is achieved by building in the set of real numbers into the structures for the language, and by adjusting other semantical notions accordingly. We use many-sorted languages so that the resulting formal systems are general enough for axiomatic treatments of empirical theories without recourse to elements of set theory which are difficult to interprete empirically. Thus we provide a (...) way of applying model theory to empirical theories without tricky detours. Our frame is applied to axiomatizations of three empirical theories: classical mechanics, phenomenological thermodynamics, and exchange economics. (shrink)

A linear space is a system of points and lines such that any two distinct points determine a unique line; a Steiner k-system is a linear space such that each line has size exactly k. Clearly, as a two-sorted structure, no linear space can be strongly minimal. We formulate linear spaces in a vocabulary $\tau $ with a single ternary relation R. We prove that for every integer k there exist $2^{\aleph _0}$ -many integer valued functions $\mu $ such (...) that each $\mu $ determines a distinct strongly minimal Steiner k-system $\mathcal {G}_\mu $, whose algebraic closure geometry has all the properties of the ab initio Hrushovski construction. Thus each is a counterexample to the Zilber Trichotomy Conjecture. (shrink)

A Theory of Freedom and Government has provided a systematic basis for republican theory in the idea of freedom as non-domination. Can a pure republican view, which confines itself to the normative resources thus afforded, adequately address the full range of issues of social justice? This article argues that while there are many sorts of structural injustice with which a pure republican view can well cope, unfair disparities in political influence, of the kind that Rawls labeled failures of the ‘fair (...) value’ of the equal political liberties, cannot be well addressed by a pure republican view. In arguing the point, the article assesses the reach not only of the core ideal of freedom as non-domination itself, but also of three further layers in Pettit’s republican theory: its suggestion that domination is to be minimized, its account of a set of institutions needed to restrict domination, and its requirement that, to prevent governments from having the power to act arbitrarily and so to dominate, they be made responsive to the common good. Some of these further conceptual resources are shown to be of no help in addressing unfair disparities in political influence, while the ones that are promising are so only because they rely on distinctively liberal ideals, and so depart from a pure republican basis. Key Words: republicanism • liberalism • justice • common good • non-domination • fair value • Philip Pettit • John Rawls. (shrink)

Quine often argued for a simple, untyped system of logic rather than the typed systems that were championed by Russell and Carnap, among others. He claimed that nothing important would be lost by eliminating sorts, and the result would be additional simplicity and elegance. In support of this claim, Quine conjectured that every many-sorted theory is equivalent to a single-sorted theory. We make this conjecture precise, and prove that it is true, at least according to one reasonable notion of theoretical (...) equivalence. Our clarification of Quine’s conjecture, however, exposes the shortcomings of his argument against many-sorted logic. (shrink)

In this compact volume the author gives a sprightly introduction to modern symbolic logic, at no time side-stepping philosophical problems concerning the nature of formal logic. The first chapter is a brief comparison of traditional syllogistic logic and modern "logistic"; the next three chapters deal with the nature of logic as illustrated through various elementary logical systems: logic as ontology, logic as theory of language, logic as methodology of deductive sciences. Hasenjaeger then examines richer systems—many-sorted, those with definite descriptors, etc.—and (...) then the paradoxes. A chapter follows concerning logic developed in a combinatory style and its connections with the idea of a generative theory of formal structures—structures as calculi of concepts. The last chapter discusses formal logic as a branch of probability theory and inductive logic. This well-presented book would serve well in a study of the philosophy of mathematics and logic.—P. J. M. (shrink)

The three volumes of Capital form an immensely complex work, including a variety of quite different sorts of texts. Marx’s systematic ordering of the essential determinations of capital, beginning in Volume I with relatively simple and abstract social forms and then proceeding step by step to ever more complex and concrete determinations provides a unifying thread. Many fundamental structures of the capitalist mode of production remained to be considered at the point where Marx left off in Volume III. At one (...) point, at least, Marx planned to conclude his project with volumes on the state, foreign trade, and the world market and crisis (Marx 1973, 227, 264). This paper is devoted to two questions. Why exactly did Marx place the category of the world market at the very culmination of his systematic ordering? And what are the essential features of the social form referred to by this category? Before addressing these issues some further methodological remarks are in order. (shrink)

Many philosophers have claimed that “belief aims at the truth”. But is there any interpretation of this claim on which it counts as true? According to some philosophers, the best interpretation of the claim takes it as the normative thesis that belief is subject to a truth-norm. The goal of this essay is to clarify this normative interpretation of the claim. First, the claim can be developed so that it applies to partial beliefs as well as to flat-out full beliefs. (...) Secondly, an answer is given to the objection that has been raised against the claim that belief is subject to a truth-norm of this sort by Krister Bykvist and Anandi Hattiangadi; responding to this objection will involve careful reflection on the structure of normative concepts, and of how these normative concepts apply to belief. (shrink)

Prominent experts present papers which discuss problems regarding this subject. Coverage includes case studies in the translation of logics for second-order and propositional dynamic logic; many-sorted algebras and equational logic; logical foundations of artificial intelligence along with a variety of methods that exist to encode information; program verification techniques such as Floyd-Hoare, intermittent assertion and temporal logic of programs.

his paper is an excerpt from a larger project that aims to open a new pathway into Spinoza's Ethics by formally reconstructing an initial fragment of this text. The semantic backbone of the project is a custom-made Spinozian model theory that lays out some of the formal prerequisites for more ne-grained investigations into Spinoza's fundamental ontology and modal metaphysics. We implement Spinoza's theory of attributes using many-sorted models with a rich system of identity that allows us to clarify the puzzling (...) status of such logical principles as the Substitution of Identicals and Transitivity of Identity in Spinoza's thought. The intensional structure of our Spinozian models also captures his proposal that states of a airs can be necessitated or excluded by the essences of particular things, an essence-relative modality that should be of interest to philosophers who have sought to rehabilitate the concept of essence in contemporary analytic metaphysics. (shrink)

A study of the elementary theory of quotients of symmetric groups is carried out in a similar spirit to Shelah . Apart from the trivial and alternating subgroups, the normal subgroups of the full symmetric group S on an infinite cardinal μ are all of the form Sκ = the subgroup consisting of elements whose support has cardinality 20, cƒ 20 < κ, 0 < κ < 20, and κ = 0, we make a further analysis of the first order (...) theory of Sλ/Sκ. introducing many-sorted second order structures , all of whose sorts have cardinality at most 20, and in terms of which we can completely characterize the elementary theory of the groups Sλ/Sκ. (shrink)

Many discussions of the moral dimensions of borders emphasize how those borders foster and sustain a national community. In this paper, I discuss three distinct sorts of goods that might be best preserved in the presence of state borders. The first of these is decolonization; I argue that undermining colonial structures might require political institutions with the right to refuse unwanted outsiders. The second of these is social solidarity; we might find that the inability to exclude outsiders could reduce the (...) willingness of insiders to voluntarily comply with political institutions. The final of these is risk and insurance; the border sustains the ability of a political society to internalize the costs and benefits of political decisions about social welfare. All three of these, I suggest, are important additions to our collective discussions about migration, since none of these goods depend upon our attaching any ethical value to nationality itself. (shrink)

As noted in 1962 by Timothy Smiley, if Aristotle’s logic is faithfully translated into modern symbolic logic, the fit is exact. If categorical sentences are translated into many-sorted logic MSL according to Smiley’s method or the two other methods presented here, an argument with arbitrarily many premises is valid according to Aristotle’s system if and only if its translation is valid according to modern standard many-sorted logic. As William Parry observed in 1973, this result can be proved using my 1972 (...) proof of the completeness of Aristotle’s syllogistic. (shrink)

Any sort of cognition, perception, and action is necessarily shaped by (re)activation of “schemata.” Any interpretation is schema (re)activation. Schemata are epistemologically speaking “structural” activation patterns which are psychologically and neurologically speaking accommodated, adapted, “learned” by co- and re-activating neuronal assemblies. Six levels of interpretative schema activations (schema interpretations) are outlined from invariable primary “interpretations” through conventional, classificatory, and justificatory, as well as meta-interpretations. Constitutive schema interpretations are unavoidable. Many philosophical problems will have to be reformulated or reinterpreted along these (...) lines, e.g., a sort of moderated pragmatic (interpretational) realism in epistemology. (shrink)

Many philosophers have shown great interest in the recent anti-realist turn in Hilary Putnam's thought, whereby he rejects "meta-physical realism" in favor of "internal realism". However, many have also found it difficult to gain an exact understanding, and hence a correct assessment of Putnam's ideas. This work strives for some progress on both of these accounts. ;Part one explicates what Putnam understands by "metaphysical realism" and considers to what extent Putnam himself formerly adhered to it. It reconstructs Putnam's arguments for (...) the indeterminacy of reference and for the rejection of reference and of truth as correspondence, and it shows how such arguments hinge both on considerations in the theory of reference and in metaphysics. It suggests that commentators have often missed the actual structure of Putnam's argumentation, e.g. by simply identifying it with the so called "model-theoretic" argument. Finally, Part One examines Putnam's "internal realism", stressing its ties to such authors as Kant, Goodman and Dummett, and explaining in what senses it is really a strong kind of anti-realism. Basically, Putnam does not deny that a mind-independent world exists, but he denies that we may refer to it, and claims that the world we know is thoroughly mind-dependent. ;Part two criticizes Putnam's arguments for indeterminacy along with some similar indeterminacy arguments such as Goodman's argument on confirmation, and the Kripke-Wittgenstein argument on rules. This is done by vindicating the notion of objective similarity, and by relying on it to fix reference. Putnam's claim that we have no theory showing how reference could possibly be determinate is countered by sketching a possible account of reference--distinctly owing to functionalism--which might answer such question. Putnam's notorious "brains in the vat" argument is also discussed and criticized. ;Putnam's metaphysical picture, by which the mind-independent world is not sorted out into objects or properties, is granted. But it is argued that nonetheless we may refer to the mind-independent world, and have beliefs which are true of it. (shrink)

Many commentators have attempted to say, more clearly than Wittgenstein did in his Tractatus logico-philosophicus, what sort of things the ‘simple objects’ spoken of in that book are. A minority approach, but in my view the correct one, is to reject all such attempts as misplaced. The Tractarian notion of an object is categorially indeterminate: in contrast with both Frege's and Russell's practice, it is not the logician's task to give a specific categorial account of the internal structure of (...) elementary propositions or atomic facts, nor, correlatively, to give an account of the forms of simple objects. The few commentators who have hitherto maintained this view have mainly devoted themselves to establishing that this was Wittgenstein's intention, and do not much address the question why Wittgenstein held that it is not the logician's business to say what the objects are. The present paper means to fill this lacuna by placing this view in the context of the Tractatus's treatment of logic generally, and in particular by connecting it with Wittgenstein's treatment of generality and with his reaction to Russell's approach to logical form. (shrink)

Topic of this paper is the way in which the structure of events features in discourse. We focus on the structure as introduced by verbs that express some sense of progress. First it is shown by means of examples that this structure is anaphorically available in discourse. Then we go on to discuss the different ways in which the same event may be structured within one discourse situation. We give formal representations of the crucial examples in many-sorted (...) dynamic logic. (shrink)