There are two major theories of properties that employ resemblance classes to avoid commitment to universals.1 Object-resemblance nominalism ~ORN! faces the notorious companionship and imperfect community difficulties, though some costly remedies have been proposed. Trope-resemblance nominalism ~TRN!, in contrast, is commonly supposed to avoid these difficulties altogether. My contention is that both versions of resemblance nominalism are subject to companionship and imperfect community difficulties. If I am right, ~1! trope theory loses one of its primary selling (...) points, and ~2! resemblance nominalists of either type must appeal to the troublesome remedies that I discuss below. (shrink)

This chapter is a discussion of Class and Resemblance Nominalism. According to the traditional versions of these theories, properties are classes of particulars. Thus, the property of being red is the class of red particulars, and the property of being square is the class of square particulars. Several objections have been advanced against these theories, and one of the most powerful of such objections is the so-called Coextension Difficulty, according to which Class and Resemblance (...) Nominalism have to wrongly identify distinct but coextensive properties. After discussing the nature of Class and Resemblance Nominalism, some problems of these theories and how they can be deal with, the superiority of Class and Resemblance Nominalism over other theories of properties and the superiority of Resemblance Nominalism over Class Nominalism, I concentrate on the Coextension Difficulty. With respect to this I argue that Class and Resemblance Nominalism can be developed in such a way that they admit properties without identifying them with classes, and this allows them to avoid the Coextension Difficulty, since such versions of these theories are not forced to wrongly identify distinct but coextensive properties. Thus the Coextension Difficulty is not a lethal problem for Class and Resemblance Nominalism. (shrink)

Douglas Ehring (2011) has proposed a conception of natural classes of tropes to fulfill the roles usually attributed to universals. Natural classes of tropes can avoid the difficulties that affect the classic theory of tropes – as claimed by D. C. Williams and Keith Campbell – where tropes are simple and, by themselves, are particulars and have an intrinsic nature. Natural classes of tropes are also preferable to primitive resemblance classes of tropes, because they can explain the characteristics of (...) the relation of resemblance and can also ground an internal relation of resemblance between tropes. It is contended here that the conception proposed works very differently whether tropes are conceived as modifier tropes or as module tropes. In the first case, tropes cannot be grouped directly in natural classes, because tropes have no intrinsic character. They ground the character possessed by their bearer, but they themselves have none. So, the character attributed to a trope due to its belonging to a natural class is dependent, on its turn, on the natural classes or the resemblance classes into which the objects that bear those tropes enter. In the second case, tropes do have a character. Then, they can enter ‘directly’ into natural classes. The problem in this case, though, is that tropes seem to have many different characters and seem vulnerable to the traditional problems of the ‘imperfect community’ and the ‘company’ that affect resemblance nominalism. Keywords: properties, tropes, natural classes, resemblance classes, problem of the imperfect community, problem of the company. (shrink)

Resemblance Nominalism About Perfect Naturalness is the view that perfect naturalness of classes is best defined by a conceptual primitive of resemblance between particulars. The adequacy of RNPN is defended by outlining nominalism as the strictly anti-constitutive view that the particulars’ being the fundamental ways they are is not constituted by anything further, supplying a doubly plural contrastive and graded resemblance predicate that allows for a definition of perfect naturalness on an actualist basis, and proving a representation (...) and a uniqueness theorem on the basis of a formal constraint on resemblance called “the Principle”, thereby revealing that bodies of nominalist resemblance facts are guaranteed to behave as if they were grounded in patterns of universals distributed over particulars. (shrink)

Resumen Según la tesis principal de este artículo, para articular el alcance e interés del tema wittgensteineano de los parecidos de familia se requiere ver en él, no una respuesta a la pregunta por lo que sea un concepto en general, sino una propuesta de carácter metodológico. Dos preguntas orientan la parte central del texto: (1) ¿Qué significa “conceptos de parecidos de familia”? (2) ¿Cuáles serían los conceptos en cuestión? Con respecto a (1), intento mostrar que el término no es (...) unívoco: un primer sentido dice relación con el dictum de los “parecidos que se superponen y entrecruzan” (IF 67) y se diferencia de un segundo sentido asociado al tema de los “bordes borrosos” (IF 71). Con apoyo en esta distinción ofrezco una respuesta a (2): en el primer sentido del término, no existe ningún concepto de familia, mientras que de acuerdo con el segundo todos los conceptos lo son. En la parte final propongo reinterpretar el tema en clave metodológica. Afirmar que conceptos como los de lenguaje, comprender, pensar, etc., son conceptos de familia significa que la reflexión filosófica sobre ellos no pasa fundamentalmente por buscar definiciones; que tanto o más importante es la cuidada descripción de ejemplos paradigmáticos, como “centros de variación” (EPB 190). Abstract According to the main thesis of this article, in order to articulate the scope and interest of Wittgenstein’s family resemblances topic, we should see into it not an answer to the question what concepts in general are, but a methodological proposal. Two questions guide the central part of the text: (1) What does “family-resemblances concepts” mean? (2) What concepts fall within the corresponding class? Regarding (1) I try to show that “family-resemblances concepts” is not an unequivocal term: a first sense has to do with the dictum of “similarities overlapping and criss-crossing” (IF 67) and is to be distinguished from a second sense associated with the topic of “blurred edges” (IF 71). This distinction lies behind the answer I offer to (2): in the first sense of the term, there is no family concept at all, while according to the second sense all concepts are of this kind. In the final part I propose a reinterpretation of the issue from a methodological perspective. To say that concepts like language, understanding, thinking, etc. are family concepts means that the philosophical reflection on them should not centre on the praxis of looking for definitions. As important ―maybe more important― as that it’s the careful description of paradigmatic examples, as “centers of variation” (EPB 190). (shrink)

The object of this paper is to provide a solution to Nelson Goodman’s Imperfect Community difficulty as it arises for Resemblance Nominalism, the view that properties are classes of resembling particulars. The Imperfect Community difficulty consists in that every two members of a class resembling each other is not sufficient for it to be a class such that there is some property common to all their members, even if ‘x resembles y’ is understood as ‘x and y (...) share some property’. In the paper I explain and criticise several solutions to the difficulty. Then I develop my own solution, which is not subject to the objections I make to the other solutions, and which accords completely with the basic tenets of Resemblance Nominalism. (shrink)

In this paper I argue that the analysis of natural properties as convex subsets of a metric space in which the distances are degrees of dissimilarity is incompatible with both the definition of degree of dissimilarity as number of natural properties not in common and the definition of degree of dissimilarity as proportion of natural properties not in common, since in combination with either of these definitions it entails that every property is a natural property, which is absurd. I suggest (...) it follows that we should think of the convex class analysis of natural properties as a variety of resemblance nominalism. (shrink)

Arda Denkel, in "Real Resemblances," argues for a moderate Nominalism where substances objectively have properties and relations, the latter being particulars, but dependent particulars, grouped into classes by objective relations of resemblance. This view is contrasted unfavorably with the view that properties and relations are universals instantiated by particulars. It is conceded that Denkel's scheme has much to commend it. But it is argued that the universals view has much more to be said for it than Denkel allows, and (...) that it is indeed, on balance, the superior view. (shrink)

Marlene van Niekerk's 1994 Triomf is a plaasroman, or farm novel, without the farm; it formally resembles a nostalgic pastoral genre initiated by the collapse of Southern African agricultural economy around the time of the Great Depression, but removes even the symbol of the farm as aesthetic compensation for material loss. In the process, van Niekerk composes a post-apartheid tragicomedy of a lumpenproletariat white supremacist family coming into long-belated class consciousness, an epiphany which, surprisingly, survives the novel's translations from (...) Afrikaans to South African English to 'international' English. Crucially, this understanding is mediated by a critical tendency to appraise Triomf in the context of Faulkner and the Southern Gothic, a generic comparison which gets a lot wrong but is ultimately very revealing, less about Triomf than about the imperial world-system through which it circulates and is consecrated. Consequently, the novel stages globally what seems at first to be a parochial question: how is one supposed to imagine democratic reconciliation and integration after apartheid, when one of the classes to be reconciled lacks historical self-consciousness and has no obvious place in either the apartheid regime or the post-apartheid dispensation? By analyzing van Niekerk's novel and the institutions which consecrate it, the paper fleshes out critiques of world-literary hermeneutics, specifically for its naive handling of genre and context, and of post-apartheid 'reconciliation' under capital. (shrink)

Realists, D. M. Armstrong among them, claim, contrary to natural class nominalists, that natural classes are analysable. Natural classes of particulars, claim the realists, can be analysed in terms of particulars having universals in common. But for the realist, there are also natural classes of universals. And if the realist's claim that natural classes are analysable is a general claim about natural classes, then the realist must also provide an analysis of natural classes of universals. For Armstrong, the unity (...) (or naturalness) of a natural class of universals is analysed in terms of universals resembling each other. I argue that Armstrong's account fails. His account fails for the same reason all other resemblance accounts of natural classes fail: some arbitrary classes satisfy the analysis for natural classes. (shrink)

I consider a class of argument implying that Hume's position on general representation is irredeemably circular in that it presupposes what it is meant to explain. Arguments of this sort (the most famous being Sellars' "myth of the given") threaten to undermine any empiricist account of general representation by showing how they depend on the naïve assumption that the relevant resemblances required for the sorting of experience into concepts for use in reasoning are simply given in experience itself. My (...) aim is to salvage Hume's account from this objection. To that end, I argue first for a "Goodmanesque" interpretation of Humean resemblance, and second for an alternative reading of Hume's account of general ideas offered at T 1.1.7 that avoids falling into "the given" trap. (shrink)

This article analyses the nature of mental imagery in metaphoric thought as envisaged by the contemporary theory of metaphor in Cognitive Linguistics (Lakoff, Cambridge University Press, 1993). Our study of metaphor in the field of marine biology draws on two crucial aspects of mental imagery, namely dynamicity and pervasiveness. Image metaphors and behaviour-based metaphors have generally been regarded as two different types of resemblance metaphor. In our view, the dynamicity of certain mental images highlights inherent similarities between these two (...) types of metaphor, and makes the differences between them more apparent than real. For this reason, we propose a more refined description of resemblance metaphors in terms of the static or dynamic nature of the mental images underlying them. Our study also underlines the fact that mental images permeate all classes of metaphor, and that the pervasiveness and dynamicity of mental images affords insights into both resemblance metaphors and non-resemblance metaphors. (shrink)

This paper investigates the semantic bases of class membership in the noun class system of Gújjolaay Eegimaa (Eegimaa henceforth), a Niger-Congo and Atlantic language of the BAK group spoken in Southern Senegal. The question of whether semantic principles underlie the overt classification of nouns in Niger-Congo languages is a controversial one. There is a common perception of Niger-Congo noun class systems as being mainly semantically arbitrary. The goal of the present paper is to show that physical properties (...) and culture-specific factors are central principles of semantic categorisation in the Eegimaa noun class system. I argue that the Eegimaa overt grammatical classification of nouns into classes is a semantic categorisation system whereby categories are structured according to prototypicality, family resemblance, metaphorical and metonymic extensions and chaining processes, as argued within the framework of Cognitive Linguistics. I show that the categorisation of entities in the Eegimaa nominal classification system productively makes use of physical properties such as shape as well as using culture-specific, less productive parameters for the semantic categorisation of entities denoted by nouns. The analysis proposed here also shows that the cases of multiple morphosyntactic classifications of nouns reflect multiple conceptual categorisation strategies. A detailed examination of the formal and semantic instances of multiple classification reveals the existence of conceptual correlations between the physical properties and the culture-specific semantic parameters of categorisation used in the Eegimaa noun class system. (shrink)

The Probably Approximately Correct (PAC) learning is a machine learning model introduced by Leslie Valiant in 1984. The PACi reducibility refers to the PAC reducibility independent of size and computation time. This reducibility in PAC learning resembles the reducibility in Turing computability. The ordering of concept classes under PAC reducibility is nonlinear, even when restricted to particular concrete examples.Due to the resemblance to Turing Reducibility, we suspected that there could be incomparable PACi and PAC degrees for the PACi and (...) PAC reducibilities as in Turing incomparable degrees. In 1957 Friedberg and in 1956 Muchnik independently solved the Post problem by constructing computably enumerable sets A and B of incomparable degrees using the priority construction method. We adapt this idea to PACi and PAC reducibilities and construct two effective concept classes C and D such that C is not reducible to D and vice versa. When considering PAC reducibility it was necessary to work on the size of an effective concept class, thus we use Kolmogorov complexity to obtain the size. The non-learnability of concept classes in the PAC learning model is explained by the existence of PAC incomparable degrees.Analogous to the Turing jump, we give a jump operation on effective concept classes for the zero jump. To define the zero jump operator for PACi degrees the join of all the effective concept classes is constructed and proved that it is a greatest element. There are many properties proven for existing degrees. Thus we can explore proving those properties to PACi and PAC degrees. But if we prove an embedding from those degrees to PACi and PAC degrees then those properties will be true for PACi and PAC degrees without explicitly proving them.Abstract prepared by Dodamgodage Gihnee M. Senadheera and taken directly from the thesisE-mail: [email protected]: https://www.proquest.com/docview/2717762461/abstract/ACD19F29A8774AF6PQ/1?accountid=13864. (shrink)

The notion of similarity plays a central role in Quine's theory of Universals and it is with the help of this notion that Quine intends to define the concept of kind which also plays a central role in the theory. But as Quine has admitted, his attempts to define kinds in terms of similarities were unsuccessful and it is mainly because of this shortcoming that Quine's theory has been ignored by several philosophers. Nominalism and realism: Universals and Scientific realism. Cambridge: (...) Cambridge University Press). In the present paper, I propose an alternative framework that accounts for the phenomena that Quine intends to explain with his resemblance theory. The framework agrees with Quine's austere ontology; in particular, it does not assume the existence of properties and of possible worlds.. Resemblance nominalism: A solution to the problem of Universals. Oxford: Clarendon Press.) Moreover, the framework is extensionalist since the abstract entities it assumes are classes and these can be individuated extensionally, for classes are identical if their members are identical. Finally, I will refute some of the objections to Quine's approach that have been raised by Armstrong and Oliver [. The metaphysics of properties. Mind, 105, 1-80.] and I will argue that, contrary to what has been claimed by Oliver in a comment on Lewis [. On the plurality of worlds. Oxford: Blackwell.], Quine is able to specify an important set of sparse properties. (shrink)

The naive theory of properties states that for every condition there is a property instantiated by exactly the things which satisfy that condition. The naive theory of properties is inconsistent in classical logic, but there are many ways to obtain consistent naive theories of properties in nonclassical logics. The naive theory of classes adds to the naive theory of properties an extensionality rule or axiom, which states roughly that if two classes have exactly the same members, they are identical. In (...) this paper we examine the prospects for obtaining a satisfactory naive theory of classes. We start from a result by Ross Brady, which demonstrates the consistency of something resembling a naive theory of classes. We generalize Brady’s result somewhat and extend it to a recent system developed by Andrew Bacon. All of the theories we prove consistent contain an extensionality rule or axiom. But we argue that given the background logics, the relevant extensionality principles are too weak. For example, in some of these theories, there are universal classes which are not declared coextensive. We elucidate some very modest demands on extensionality, designed to rule out this kind of pathology. But we close by proving that even these modest demands cannot be jointly satisfied. In light of this new impossibility result, the prospects for a naive theory of classes are bleak. (shrink)

Following independence in 1948, the Hebrew University of Jerusalem founded a law faculty and modeled it on the European example. Today, the Israeli law faculty is much more similar to the U.S. law school than to institutions of legal education in Europe. This Article traces the history of the changes in Israeli legal education. It argues that the shift began after 1967, faced resistance in the 1980s, and gained momentum in the 1990s. Presently we may be witnessing the beginning of (...) a shift away from U.S. influence and back to Continental Europe or even Asia. The Article discusses three major educational components, which together signaled the shift to U.S. influence: a student-run law review, curricular reform, and open and lively class discussion. The Article then offers several factors to explain the shift: judicial opinions that began to rely on American decisional law, the adoption of the U.S. model of practice by the legal profession, the privatization of law schools, globalization, and Americanization and foreign affairs. Finally, the Article considers the contribution to Americanization made by active U.S. attempts to export American law to other legal systems. (shrink)

Tropes are particular features of concrete objects. Properties—the extensions of predicates—are primitive resemblance classes of tropes. Friends of tropes have been criticized for failing to answer three questions. First, are there fundamental items other than tropes? Second, what criteria determine whether some tropes are all and only the features of some one object? Third, can trope classes be formed adequately using only primitive resemblance? Trading on the spatiotemporal status of tropes, this essay offers new responses to each of (...) these questions. The novel thesis is that there is a sui generis property called ‘markedness’, whose tropes “mark” certain locations in an ontologically basic way. The spatiotemporal distribution of markedness tropes fixes the distribution of familiar characterizing tropes like mass and charge, and characterizing tropes are bundled by being co-contained in the location of a maximally connected markedness trope. This novel theory of trope bundling is defended by appeal to theoretical utility: it is ontologically parsimonious and solves outstanding problems involving co-location and resemblance class construction. (shrink)

Has the theory of direct reference for general terms ontological consequences or requirements? It has normally been said that general terms should be conceived as rigid designators of “natural classes”, but this is a very vague expression. What is a “natural class” here? Is it a universal? Is it a class of resembling objects or tropes? It is argued that the theory of direct reference functions better in connection with an ontology of universals. The semantic model actually requires (...) certain type of successful cognitive relation with the referent and it is difficult to explain how such a successful connection could be obtained if there are no universal properties, but only perfect resemblance classes of objects or tropes. (shrink)

There are a number of different versions of Reductive Nominalism, versions distinguished by the way in which each accounts for facts about having and sharing properties. This chapter discusses three broad varieties of Reductive Nominalism: Predicate Nominalism, Class Nominalism, and Resemblance Nominalism. Class Nominalism identifies properties with classes or sets. Resemblance Nominalists come in two sub‐varieties, depending on whether they take the resemblance relation to hold between particular properties (called 'tropes') or particular things that have (...) properties (ordinary particulars). Trope Theory comes in two varieties depending on whether one plumps for universals. It should not be difficult to see that Extreme Resemblance Nominalism is faced with Class Nominalism's extensionality problems, both the problem of contingent predication and the co‐extensive property problem. Resemblance Nominalists can reply by insisting on a distinction between a priori or conceptual equivalence and metaphysical equivalence. The chapter focuses on the extensionality problems for Class Nominalism. (shrink)

Analytic theology is a thriving research program at the intersection of theology and analytic philosophy. Prior to Oliver Crisp and Michael Rea’s launch of “analytic theology” in 2009, the discipline functioned under the moniker “philosophical theology.” Considerable ink has been spilled on what is analytic theology in the past decade, and most recently by William Wood (2021). Some theologians (e.g., Abraham 2009) have argued that it is systematic theology while others (e.g., Coakley 2013) have been content to remain in a (...) family resemblance class rooted in philosophical theology. At the same time, analytic theology has welcomed Christian philosophers (e.g., Beall 2021) who have migrated into Christian doctrine via philosophy of religion. These philosophers are not systematic theologians, but, rather, philosophical theologians. This essay analyzes the relation between analytic theology, philosophical theology, and philosophy by examining their starting points and how they perceive and access truth, and then proposes a spectrum to graph their overlapping zones of research. I conclude that philosophical theology stands at the heart of the disciplines and thus remains an appropriate term for analytic theologians and Christian philosophers working somewhere in the vicinity of Jerusalem. (shrink)

The concern of this paper is a version of Resemblance Nominalism according to which resemblance classes, i.e. classes of resembling things, are determined by paradigms. I show that the theory is false, since paradigms do not generally determine resemblance classes. Although I concentrate upon the version of the theory which was delineated by H. H. Price, my results apply to any other theory constructing resemblance classes out of paradigms.

The Reply to Dr. Rolfs essay makes the following main points: (1) The logic of inexactness has the same syntax as Kleene's three-valued logic. Its semantics is different in that the third truth-value can by choice be correctly turned into either truth or falsehood. (2) The definition of resemblance classes includes, but is not exhausted by, ostensive rules. (3) The application of classical mathematics to sense-experience consists in the limited identification of non-isomorphic structures. (4) There are exact perceptual and (...) vague mathematical concepts. (5) The distinction between my categorial framework, a categorial framework and the true categorial framework, if any, is neither relativistic nor absolutistic. (shrink)

Universals are a class of mind independent entities, usually contrasted with individuals, postulated to ground and explain relations of qualitative identity and resemblance among individuals. Individuals are said to be similar in virtue of sharing universals. An apple and a ruby are both red, for example, and their common redness results from sharing a universal. If they are both red at the same time, the universal, red, must be in two places at once. This makes universals quite different (...) from individuals, and controversial. (shrink)

속성 이론들 중 하나인 개체 유명론은 굿맨의 두 난점들에 직면한다는 점에서 성공적이지 않은 입장으로 평가된다. 반면, 트롭주의는 닮음의 관계항들이 복합적 개체들이 아니라 단순한 트롭들이라는 점 덕분에 굿맨의 난점들을 피할 수 있는 것으로 간주된다. 이에 맨리는 그의 논문(2002)에서 트롭주의 역시 개체 유명론과 마찬가지로 성공적이지 않다고 주장한다. 그에 따르면 트롭주의는 변형된 버전의 굿맨의 난점들에 직면하게 되는데, 이를 피하기 위한 어떤 전략들도 트롭주의자에게 유효하지 않다. 그러나 트롭들로부터 속성을 구성하려 할 적에 변형된 굿맨의 난점에 직면하게 된다는 그의 주장은 의심스럽다. 이 논문에서는 맨리가 제시하는 변형된 (...) 굿맨의 난점이 트롭주의 관점에서 충분히 방어할 수 있기에, 이 경우 여전히 트롭주의는 적어도 개체 유명론에 비해 우세한 입장일 수 있음을 보일 것이다. (shrink)

This is a global comparative analysis of the social, political and economic experiences, effects and consequences of the COVID-19 pandemic. Part of it was written during an early stage of the pandemic and captures some of the initial reactions of competitive international panic. It demonstrates the new class structuration resulting from the management of the viral onslaught. It distinguishes coping and failing states of the pandemic world, and discusses the reasons for them. It highlights the widespread and rapid abandonment (...) of neoliberal economic policies, a change spearheaded by the former vanguard of neoliberalism, the USA and the UK. The end of neoliberalism is also related to the change of the political economy of the world, from capitalist globalization to imperial and national geopolitics. The decisive reason for the turn was the realization by the US elite in the 2010s that China was winning the game of competitive market globalization. In the new game of geopolitics state interests, state security and state power are paramount. This process had started earlier but was accentuated during the pandemic, and accelerated with the Ukraine war, which also has clarified that the new geopolitical era may be the beginning of the endgame of the semi-millennial western domination of the world. The western powers draw closer together, after the early pandemic free-for-all, while the rest of world increasingly asserts its independence. The article ends with a discussion of the post-pandemic near future in terms of historical post-crisis parallels from European history. Finding ‘1945’ and ‘1932’ inappropriate, in contrast to early hopes and assessments, the conclusion is that the current world of the North most resembles a before- rather than an after-moment, the summer of 1914, when the world ‘sleepwalked’ into the mass slaughter of the First World War. (shrink)

What determines qualitative sameness and difference? This book explores four principal accounts of the ontological basis of properties, including universals, trope theory, resemblance nominalism, and class nominalism, considering the assumptions and ontolological commitments which are required to make each into a plausible account of properties. -/- The latter half of the book investigates the applications of property theory and the different conceptions of properties which might be adopted with these in mind: first, the possibility and desirability of individuating (...) properties, and the distinction between sparse and abundant conceptions of properties; second, the distinction between intrinsic and extrinsic properties; third, the relationship between properties and their causal powers, and whether this is necessary or contingent; fourth, the relationship between properties and causation, modality, and laws of nature; finally, whether properties exist objectively, and if they do, what our epistemic position is with respect to such entities. (shrink)

Halldén completeness closely resembles the relevance property. To prove Halldén completeness in terms of Kripke-style semantics, the van Benthem–Humberstone theorem is often used. In relevant modal logics, the Halldén completeness of Meyer–Fuhrmann logics has been obtained using the van Benthem–Humberstone theorem. However, there remain a number of Halldén-incomplete relevant modal logics. This paper discusses the Halldén completeness of a wider class of relevant modal logics, namely, those with some Sahlqvist axioms.

If representation is resemblance, how we do we think of groups or classes of things? According to a tradition Berkeley opposed—a tradition represented by Locke—we do so by forming abstract or incomplete ideas. I show that Berkeley's opposition does not depend on his own personal failure to form abstract images, but on what he took to be the impersonal or objective impossibility of abstract objects. Berkeley himself accounts for general thinking not in terms of abstract or incomplete ideas, but (...) in terms of our selective attention to ideas both concrete and determinate. Contentful thought about the natural world is impossible without ideas as objects, Berkeley believes, but ideas do not, in his view, completely fix the content of our thought. (shrink)

Dynamic algebras combine the classes of Boolean (B 0) and regular (R ; *) algebras into a single finitely axiomatized variety (B R ) resembling an R-module with scalar multiplication . The basic result is that * is reflexive transitive closure, contrary to the intuition that this concept should require quantifiers for its definition. Using this result we give several examples of dynamic algebras arising naturally in connection with additive functions, binary relations, state trajectories, languages, and flowcharts. The main result (...) is that free dynamic algebras are residually finite (i.e. factor as a subdirect product of finite dynamic algebras), important because finite separable dynamic algebras are isomorphic to Kripke structures. Applications include a new completeness proof for the Segerberg axiomatization of prepositional dynamic logic, and yet another notion of regular algebra. (shrink)

For several terms at Cambridge in 1939, Ludwig Wittgenstein lectured on the philosophical foundations of mathematics. A lecture class taught by Wittgenstein, however, hardly resembled a lecture. He sat on a chair in the middle of the room, with some of the class sitting in chairs, some on the floor. He never used notes. He paused frequently, sometimes for several minutes, while he puzzled out a problem. He often asked his listeners questions and reacted to their replies. Many (...) meetings were largely conversation. These lectures were attended by, among others, D. A. T. Gasking, J. N. Findlay, Stephen Toulmin, Alan Turing, G. H. von Wright, R. G. Bosanquet, Norman Malcolm, Rush Rhees, and Yorick Smythies. Notes taken by these last four are the basis for the thirty-one lectures in this book. The lectures covered such topics as the nature of mathematics, the distinctions between mathematical and everyday languages, the truth of mathematical propositions, consistency and contradiction in formal systems, the logicism of Frege and Russell, Platonism, identity, negation, and necessary truth. The mathematical examples used are nearly always elementary. (shrink)

This is surely a bit of Socrates' famous irony. He draws the analogy to explain how his friends should regard poetry as they regretfully banish it from the ideal state. But lovers were no more sensible then than they are now. The advice to banish poetry, undermined already by Plato's own delight and skill in drama, is perhaps undermined still further by this evocation of a 'sensible' lover who counts love so well lost. Yet Socrates' image is one of avowed (...) rationality and prudence. The sensible lover imitates the older literary example of Ulysses' tying himself to the mast. (The example belongs therefore to the class of problems treated in Elster (1979)). Both this lover and Ulysses foresee that under certain possible future conditions, their opinions, values and preferences will or would differ from what they are now, in a very definite fashion. To what extent is such foresight possible? Correspondingly (when we do not claim foreknowledge) to what extent is such opinion reasonable, rational, coherent, or consistent in some suitably broad sense? It is not easy to understand exactly what is possible or even logically permissible in this respect. In an earlier paper, "Belief and the Will", I argued for a principle ("Reflection") to govern such deliberation. Here I will both generalize the treatment of opinion in "Belief and the Will" and respond to criticism. Critical examples mainly resembled the story of Ulysses who foresaw a period of dysfunction (at the sound 2 of the sirens) in his epistemic and/or doxastic future. Other criticism focused on the model of opinion used (precise numerical subjective probability) and on the merits of Dutch Book arguments. The present argument will not rely on Dutch Book arguments and strategies, and the Reflection principle will be formulated so as to apply also to vague opinion. (shrink)

An interesting feature of some sets of representations is that their structure mirrors the structure of the items they represent. Founding an account of representational content on isomorphism, homomorphism or structural resemblance has proven elusive, however, largely because these relations are too liberal when the candidate structure over representational vehicles is unconstrained. Furthermore, in many cases where there is a clear isomorphism, it is not relied on in the way the representations are used. That points to a potential resolution: (...) that an isomorphism must be used, hence usable, if it is to be an ingredient in a theory of content. This paper argues that the class of exploitable isomorphisms can indeed play a content-constituting role. (shrink)

In Asian countries, there is a tradition that a rabbit, known as the Moon rabbit, lives on the Moon. Typically, two reasons are mentioned for the origin of this tradition. The first reason is that the color pattern of the lunar surface resembles the shape of a rabbit. The second reason is that both the Moon and rabbits are symbols of fertility, as the Moon appears and disappears (i.e., waxing and waning) cyclically and rabbits are known for their high fertility. (...) Considering the latter reason, is the color pattern of the lunar surface not similar to a rabbit? Here, the similarity between rabbit and the lunar surface pattern was evaluated using seven AI architectures. In the test conducted with Contrastive Language-Image Pre-Training (CLIP), which can classify images based on given words, it was assumed that people frequently observe the Moon in the early evening. Under this condition, the lunar surface pattern was found to be more similar to a rabbit than a face in low-latitude regions, while it could also be classified as a face as the latitude increases. This result is consistent with that the oldest literatures about the Moon rabbit were written in India and that a tradition of seeing a human face in the Moon exists in Europe. In a 1000-class test using seven AI architectures, ConvNeXt and CLIP sometimes classified the lunar surface pattern as a rabbit with relatively high probabilities. Cultures are generated by our attitude to the environment. Both dynamic and static similarities may be essential to induce our imagination. (shrink)

Writing this article was motivated by the wave of protests in 2013 in Bulgaria. The long and massive protest in the summer of 2013 combined three important features: 1) young people and middle class as the main driver of the events, 2) political action for non-economic value and 3) denial of partisanship and political representation, and support for participatory democracy. These features of the protest relate well to the Inglehart’s framework and describe the profile of “postmaterialists”: people with self-expression (...) values. A question I ask is: how, in a “materialistic democracy” like Bulgaria, with only 2% of postmaterialists, was it possible to take place a large-scale protest for a non-economic value like “moral in politics”, which at the same time resembles other protests that have taken place around the world? The protests were closely connected with the usage of the Internet and social networks and in my article I discuss how the Internet can facilitate behavior consistent with higher-order, postmaterial values. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 37.4 (2003) 73-84 [Access article in PDF] Music-Picture:One Form of Synthetic Art Education"Music-picture (a picture drawn through musical perception)" has been widely accepted by art educators in Japan. The purpose of this essay is to propose the making of music-pictures as art education and to put it on afirm theoretical base. I first investigate three gestalt rules: adjacency, continuance, and resemblance, all of (...) which are applicable to the senses of both seeing and hearing. Next I present research on color hearing as one version ofsynaesthesia, which is the comprehensive faculty that binds the five senses in various ways. The well-organized music-picture program by Kaoru Sasaki 1 is introduced as an example. 2 The synthetic art-educational value of music-picture will become clearer through these examinations. The Interrelations between Visual Arts and Music It is exciting that the visual arts meet music in an art class, even if these subjects are entirely different in regard to media, expressive form, the category of perception, and mastery of techniques. Put simply, Picasso's works are visible, whereas Stravinsky's pieces are invisible. Nevertheless, both powerfully convey imaginative and often narrative messages. Relying on intuition alone, I firmly believe both are interchangeable.My research on common methods of organizing both recorded music and painting was my first observation of the mutual relationship between music and visual arts. 3 But what I considered then would not be applied to art class directly because the research was based on my practical experience. It did not have any educational goals. Now I recognize that instructive approaches are necessary to lay the foundation for art classes dealing with interaction between two distinct modalities.In Japan, the Ministry of Education and Science provides the government curriculum guidelines nearly every ten years. It contains descriptions on two subjects: The visual arts and music taught in these classes are at an elementary school level and a junior high school level, both located within a compulsory education system. The new version has been in force since April 2002 (the new school term starts in April in Japan). Objectives in the two educational fields are similar and ideas of what art and music education ought to be are almost the same. The aim common to both in the government curriculum guidelines: "Through expression and appreciation, we [End Page 73] cultivate students' sentiments" invites the linking of music and the visual arts across the curriculum.Many art educators in Japan are interested in this sort of idea and have actually put it into practice. 4 They are engaged in interrelating or even unifying music and the visual arts. Additionally I know other teachers who have designed and proposed many ideas toward this crossover. Listed below are general ideas that seek to combine visual arts with music in an art class.1) Music-picture: to make a pictorial description of impressions received from music.2) Sound map: to make a map of sounds heard at a given location. Each sound is visualized by simple marks like - - -, <<<, ~~~, ooo, and xxx.3) Graphic notation: to write a score which directs the details, whole form, and progression of music by graphics instead of staff notation. Using onomatopoeias or instructions by words are common. It can be improvised, based on intuitively translating visual impacts into sounds.4) Sound toy: to make an original musical instrument of familiar easil obtained materials. For instance, a corrugated cardboard ukulele whose strings are rubber bands, a pair of maracas made of empty cans and soybeans, and so forth.5) Sound sculpture: to make sculpture producing interesting sounds (sometimes noises like creak or clatter). Extensive genres: wood sculpture, metal construction, assemblage (junk arts), kinetic arts, and so on.6) Sound installation: to make a place where participants experience sounds generated by objects or equipment.7) Multimedia: in the broad sense, to mix visuals with music; noises like jingle, tap, and bang! in daily life, or natural environmental sounds like a pit-a-pat of falling rain, a whisper of leaves, or... (shrink)

She has always existed and is more than a citizen of multiverses,‭ ‬most likely the ground of all.‭ ‬In the West she was introduced around C.570‭ ‬and since then many individuals have searched for her,‭ ‬tried to become familiar with her and created all sorts of,‭ ‬frequently ridiculous,‭ ‬things in her name. Once someone has a passion for her it cannot be extinguished but increases.‭ ‬Objectively this need for her is referred to as‭ ‘‬love of wisdom‭’‬,‭ ‬the need for wisdom,‭ (...) ‬while personally it is a need of some individuals. -/- This passion and need has become institutionalized and it has developed a discourse and became a socio-cultural practice of its own.‭ ‬Fairly recently it has even become a discipline at,‭ ‬mostly higher,‭ ‬institutions of learning.‭ ‬Previously those searching for and attempting to interact with her came from many walks of life and all kinds of professions,‭ ‬while in the last century or so many people began to live off her as they are remunerated for talking about,‭ ‬about the history of searching for and investigating her and saying all sorts of things about her. -/- Many things are done in her name and all sorts of neologisms are fabricated to label them,‭ ‬such as analytic,‭ ‬continental,‭ ‬idealism,‭ ‬rationalism,‭ ‬empiricism,‭ ‬and all these labels are again specified and specified ad infinitum with terms such as materialism,‭ ‬physicalism,‭ ‬weak naturalism,‭ ‬speculative and new realism,‭ ‬etc. -/- Individuals from many other disciplines and areas of life,‭ ‬such as sociology,‭ ‬the arts,‭ ‬humanities,‭ ‬cognitive sciences,‭ ‬sport,‭ ‬etc got on the bandwagon so that we now have a philosophy or love of wisdom,‭ ‬epistemologies,‭ ‬ontologies etc of everything under the sun.‭ ‬Even if you were to write some theses or do some study you will stipulate your epistemology,‭ ‬ontology,‭ ‬methodology,‭ ‬etc.‭ ‬Just as those who live off philosophy become involved in every area of humanity and all its socio-cultural practices produce so-called peer reviewed publications,‭ ‬articles,‭ ‬essays and books on philosophy of art,‭ ‬sport,‭ ‬humanities,‭ ‬cognitive sciences,‭ ‬religion,‭ ‬gods,‭ ‬sex,‭ ‬rock‭ ‘‬n roll,‭ ‬language,‭ ‬words,‭ ‬ideas,‭ ‬how words and ideas and concepts do their thing,‭ ‬etc,‭ ‬etc.‭ -/- The way these subject-matter are treated will usually consists of some form of reasoning,‭ ‬the use of arguments or argumentation and some kind of logic and a process that resembles the features,‭ ‬steps,‭ ‬stages and processes of theorizing,‭ ‬the construction and development of models,‭ ‬short term,‭ ‬medium or large theories.‭ ‬The latter is often presented in the form of entire‭ ‘‬metaphysical‭’ ‬and speculative systems such as those of Plato,‭ ‬Aristotle,‭ ‬Kant,‭ ‬Hegel,‭ ‬Marx,‭ ‬Husserl,‭ ‬Habermas et al.‭ ‬While Socrates and to some extent the later Wittgenstein attempted to be more authentic to the original principles of trying to follow and developed the ideal of identifying,‭ ‬capturing by verbal interaction‭ (‬be it discourse,‭ ‬or dialogue‭) ‬and becoming one‭ (‬like mystics of all religions who are passionate about‭ ‘‬the one‭’‬,‭ ‬the Beloved,‭ ‬the one Real Self,‭ ‬etc and attempt to become one,‭ ‬united with or‭ ‘‬oned‭’ ‬with their object or subject of desire‭) ‬with Sophos‭ – ‬by exploring and investigating or applying and executing practical use of language,‭ ‬and thereby to uncover and capture her. -/- The effects of the institutionalization of the discipline are far-reaching and the professionalization of the role of philosopher as a‭ ‘‬profession‭’‬,‭ ‬an employee of an institution and a representative of the status quo are discussed in a number of articles being cited. -/- The methods of the philosophical discourse vary,‭ ‬first of all between the so-called Continental and Anglophone Analytic philosophies,‭ ‬its movements,‭ ‬schools and institutions,‭ ‬such as research universities,‭ ‬journals,‭ ‬communities and book publishers.‭ ‬It seems as if increasingly philosophizing employs some of the stages and steps of the processes of theorizing.‭ ‬Other aspects of her methods are heuristic devices,‭ ‬the use of metaphors and analogies,‭ ‬philosophical logic,‭ ‬informal and other types of logic,‭ ‬arguments and argumentation.‭ ‬This involves the creation of fallacies in thinking and reasoning and the causing of all sorts of fallacies or crooked thinking. -/- The nature and changes of philosophical subject-matter are discussed as the socio-cultural practice lost most of its traditional‭ ‘‬objects‭’ ‬with the social and cultural differentiation of other,‭ ‬specialized disciplines.‭ ‬In turn the discourse attempts to fabricate other subject-matter,‭ ‬for example the development of so-called Experimental Philosophy,‭ ‬inter-disciplinary studies such as cognitive sciences and philosophies or meta-level explorations of and speculations about other disciplines,‭ ‬professions and domains‭ (‬for example normative,‭ ‬instrumental and subjective aesthetic‭ – ‬this the terminology and distinctions according to the working class obsessive Critical Theory of the so-called Frankfurt Schule.‭ ‬One always wonders what degree of personal experience their educated,‭ ‬middle class academics have of‭ ‘‬the working class‭’‬,‭ ‬whatever that is meant to be‭?)) ‬of human activity.‭ ‬Such as philosophy of medicine,‭ ‬sport,‭ ‬art,‭ ‬religion,‭ ‬just name it and it is bound to exist.‭ -/- Another‭ ‘‬extension‭’ ‬of or interest in‭ ‘‬philosophy‭’ ‬is that of certain individuals,‭ ‬schools or movements in other disciplines,‭ ‬for example social‭ ‘‬sciences‭’ ‬such as sociology and supporters of the above mentioned‭ ‘‬Schule‭’‬.‭ ‬They frequently use philosophical words such as ontology,‭ ‬epistemology,‭ ‬multi-dimensional,‭ ‬many-levels,‭ ‬contexts assumptions,‭ ‬pre-suppositions,‭ ‬immanent,‭ ‬transcendent,‭ ‬etc.‭ ‬Is this intended to be an extension of philosophy and the doing of philosophizing or merely cognitive bias of the form‭ ‘‬authority bias‭’‬.‭ ‬In this case the authority being‭ ‘‬the discipline of philosophy‭’‬,‭ ‬as well as the‭ ’‬use of the word philosophy‭ ‬and terms from the philosophical discourse‭’‬.‭. 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Recent feminist research suggests that individual women find menopause an inconsequential or positive experience overall. While recent aging scholarship also documents that contemporary individuals often define aging neutrally or positively, menopause may not resemble other aging processes in meaning and experience. The author argues that menopause, or reproductive aging, may be unique because of its reproductive and aging contexts. Data in this article are based on interviews with 45 middle-class, heterosexual, menopausal women in a midwestern state in 2001. Interviewees (...) propose that, upon menopause, they do not feel old. They explain these feelings by describing their widespread use of contraceptive technologies, greater enjoyment of sexual activity upon menopause, and parallels between menopause and menarche. As women in this sample place menopause within the context of previous reproductive experiences and compare it to other aging processes, they suggest that reproductive aging represents a “good old.”. (shrink)

: "Work on aspect has long focussed on classifications of linguistic expressions into aspectual types, or Vendler-classes. Typical Vendler-classes include states, processes, and events. Such classifications miss the important generalization about aspectual interpretationthat it is a compositional process. It has been noted in the literature that terms can switch Vendler-classes; this has been called the category-switch problem. In our analysis, it is proposed that meanings and not expressions fall into aspectual classes, and that the aspectual type of a meaning is (...) derived by a process of aspectual composition. This process operates on underlying generalized activities that are similar to the nuclei proposed by Moens & Steedman, which in turn resemble plans.The interplay between semantic selection for a certain aspectual type and the application of type-changing operators to the meanings of verbphrases and sentences that occurs during aspectual composition constitutes weak aspectual type coercion. Our approach is illustrated with a unification-based grammar fragment that accounts for aspectual composition with certain adverbials, such as in a day or for an hour.". (shrink)

A semantics of pictorial representation should provide an account of how pictorial signs are associated with the contents they express. Unlike the familiar semantics of spoken languages, this problem has a distinctively spatial cast for depiction. Pictures themselves are two-dimensional artifacts, and their contents take the form of pictorial spaces, perspectival arrangements of objects and properties in three dimensions. A basic challenge is to explain how pictures are associated with the particular pictorial spaces they express. Inspiration here comes from recent (...) proposals that analyze depiction in terms of geometrical projection. In this essay, I will argue that, for a central class of pictures, the projection-based theory of depiction provides the best explanation for how pictures express pictorial spaces, while rival perceptual and resemblance theories fall short. Since the composition of pictorial space is itself the basis for all other aspects of pictorial content, the proposal provides a natural foundation for further pictorial semantics. (shrink)

Group-structured populations, of the kind prominent in discussions of multilevel selection, are contrasted with ‘neighbor-structured’ populations. I argue that it is a necessary condition on multilevel description of a selection process that there should be a nonarbitrary division of the population into equivalence classes (or an approximation to this situation). The discussion is focused via comparisons between two famous problem cases involving group structure (altruism and heterozygote advantage) and two neighbor-structured cases that resemble them. Conclusions are also drawn about the (...) role of correlated interaction in the evolution of altruism. 1 Introduction 2 Two Kinds of Population Structure 3 Objections and Replies 4 Particles on a Line 5 Conclusion Appendix: Neighborhoods and Selection CiteULike Connotea Del.icio.us What's this? (shrink)

According to a number of researchers in linguistics and artificial intelligence, the key to the meanings of expressions such as in other words, that is, and for example/for instance lies in the particular coherence relations they express in discourse. It is argued that these relations are sub-types of the relation of Elaboration and hence are ideational or semantic relations which express some experience of the world about us and within our imagination. In this paper I argue that the notion of (...) Elaboration does not provide an adequate theoretical basis for the analysis of these expressions. I show, first, that their analysis in terms of ideational relations cannot capture the way in which utterances that contain them are understood, and, second, that the phenomena which are said to fall under the relation of Elaboration do not in fact constitute a single class. I show that Sperber and Wilson's relevance theoretic pragmatics provides a better explanatory framework for the analysis of these expressions, arguing that while their notion of interpretive resemblance plays a central role in the analysis of some utterances, there are other cases which must be analysed in terms of inferential relations between propositions. In all cases, the question of how the utterance is to be understood does not depend on the classification of the coherence relation it exhibits but on how it achieves relevance. (shrink)

We study randomness beyond${\rm{\Pi }}_1^1$-randomness and its Martin-Löf type variant, which was introduced in [16] and further studied in [3]. Here we focus on a class strictly between${\rm{\Pi }}_1^1$and${\rm{\Sigma }}_2^1$that is given by the infinite time Turing machines introduced by Hamkins and Kidder. The main results show that the randomness notions associated with this class have several desirable properties, which resemble those of classical random notions such as Martin-Löf randomness and randomness notions defined via effective descriptive set theory (...) such as${\rm{\Pi }}_1^1$-randomness. For instance, mutual randoms do not share information and a version of van Lambalgen’s theorem holds.Towards these results, we prove the following analogue to a theorem of Sacks. If a real is infinite time Turing computable relative to all reals in some given set of reals with positive Lebesgue measure, then it is already infinite time Turing computable. As a technical tool towards this result, we prove facts of independent interest about random forcing over increasing unions of admissible sets, which allow efficient proofs of some classical results about hyperarithmetic sets. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Investment, Profit, and Tenancy: The Jurists and the Roman Agrarian EconomyDaniel J. GargolaDennis P. Kehoe. Investment, Profit, and Tenancy: The Jurists and the Roman Agrarian Economy. Ann Arbor: University of Michigan Press, 1997. xiv 1 269 pp. Cloth, $42.50, £29.95 (UK, Europe).This book is more than an investigation into an aspect of Roman law and legal thought. At the very beginning, Dennis Kehoe clearly identifies his goal: “My (...) purpose in this study is to clarify the basic relationships characterizing the agrarian economy of the early Roman Empire by analyzing the economic mentality that guided upper-class Romans in managing their wealth. My conviction is that the type of agrarian planning based on upper-class conceptions of investment and profit played a fundamental role in shaping the Roman economy as a whole.... In this study, I propose to address this problem by analyzing the assumptions that the Roman jurists in the Digest of Justinian and in other classical sources made about investment and profit in agriculture as they addressed legal issues involving private property. I base my analysis on the legal sources because, as I shall demonstrate, they offer a more comprehensive picture of the economic interests of upper-class Romans than we can gain from other types of evidence, including literary evidence, documentary papyri, and inscriptions” (vii).The author’s awareness of the problems in using legal evidence to shed light on larger issues and his openness about his own assumptions and about the limitations of the methods and the sources he has chosen to employ are among the work’s great strengths. In marked contrast with some other investigations of such matters, Kehoe does not assume that laws provide a simple, straightforward, and transparent entry into the structure and organization of economy and society. The work opens with an examination of the legal sources as evidence. Their condition offers one problem. The writings of the late Republican and early Imperial jurists are preserved largely in relatively brief citations included in the great collections of the sixth-century a.d.: Justinian’s Digest and Code. As Kehoe notes, this presents a major problem for investigators: to what extent do these passages represent the original—that is, was obsolete material removed systematically, and were the passages adjusted to fit the compilers’ concerns? Following authorities such as M. Kaser and F. Wieacker, the author takes an optimistic view of the matter, suggesting that “contemporary scholarship is justified in moving away from the suspicion that the Digest is so thoroughly interpolated that the opinions of the classical jurists can only be recovered after exhaustive reconstruction of the texts” (9). While accepting the possibility of interpolation in individual cases, he has based his study on the “belief that the existing collections of legal texts do allow us to trace the thinking, in particular the economic thinking, of the classical Roman legal authorities” (10).Having declared his intention to regard the citations as reasonably accurate reflections of their originals, Kehoe then turns to a more central question: the extent to which juristic writings reflect actual conditions. One school of [End Page 323] thought, represented by scholars such as Alan Watson (The Spirit of Roman Law [Athens, Ga., 1995]), suggests that Roman jurists operated within a system of traditional representations, maintained as if fossilized long after the conditions that had given rise to them had changed, and that legal writers largely wrote about internal problems in interpretation that had arisen within this system. The jurists, then, did not address problems of their own day, nor were they interested in adapting the law to new circumstances, and their opinions need bear little resemblance to actual arrangements in their own time and place. Others, however, are more convinced of the timeliness of Roman legal writing. Scholars such as B. W. Frier (Landlords and Tenants in Imperial Rome [Princeton 1980]) and S. D. Martin (The Roman Jurists and the Organization of Private Building in the Late Republic and Early Empire [Brussels 1989]) maintain that Roman jurists consciously and directly addressed in their writings the social and economic concerns of their contemporaries in the governing elite.Once again, Kehoe takes care to situate... (shrink)

Our aim in this essay is to take a look at cartoons under philosophical light. What are some of the similarities between philosophy and the art of cartooning? In what ways can cartoons be helpful to philosophy? What are some of the problems cartoons pose for philosophy? Perhaps the most basic philosophical question concerning cartoons is, “What is a cartoon?”. We argue that it is not easy to pin down necessary and sufficient conditions for something being a cartoon. We defend (...) the view that cartoons form a class whose members are interconnected with the Wittgensteinian “family resemblance” relations. We then look into the problems involved in finding a connectionist parallel-processing correlate of the Wittgensteinian notion in the context of cartoons. (shrink)

A grafted frame is a new kind of frame which combines a modal frame and some relevance frames. A grafted model consists of a grafted frame and a truth-value assignment. In this paper, the grafted frame and the grafted model are constructed and used to show the completeness of S1. The implications of S1-completeness are discussed. A grafted frame does not combine two kinds of frames simply by putting relations defined in the components together. That is, the resulting grafted frame (...) is not in the form of $\langle W, R, R'\rangle$ , or more generally, in the form of $\langle W, R, R', R'',...\rangle$ , which consists of a non-empty set with several relations defined on it. Rather, it resembles the construction of fibering proposed by D. M. Gabbay and M. Finger (see [4] and [3]). On a grafted frame, some modal worlds, which belong to the initial modal frame, are attached by some relevance frames. However, these two semantics have important differences. Consider the combined semantics involving semantics of relevance logic and modal logic. A fibred model and a grafted model proposed in this paper differ in the following respects. First, a fibred model is constructed from a class of modal models and a class of relevance models. A grafted model consists of a grafted frame and a truth-value assignment, where the grafted frame is constructed from a modal frame and some relevance frames, and the assignment is a union of a modal truth-value assignment V M and some relevance truth-value assignments V R . V M (V R ) defined in this paper is not the same as the assignment contained in a modal (relevance) model. Second, in a fibred model each relevance world is associated (or fibred) with a modal model and each modal world with a relevance model. To be the grafted frame on which a grafted model is based, it is enough to have some modal worlds attached by some relevance frames. Moreover, no relevance world is associated with a modal frame in the grafted frame. Third, fibred models are intended to provide an appropriate semantics to combined logics. Grafted frames and grafted models are inspired to characterize S1, which, containing only one modality □, is not a combined logic. It is shown in this paper that S1 is sort of a meta-logic of the intersection of S0.4 and F, where S0.4, a new system proposed in this paper, is in turn a meta-logic of the relevance logic. (shrink)

To achieve more cost-effective deterrence of unreasonable risktaking through civil liability, I propose and demonstrate previously unrecognized benefits of using simple random sampling to resolve multiple claims against a business or government defendant in the aggregate. I show that counter to intuition and prevailing assumptions and practice, simple sampling will enhance, not compromise, deterrent results regardless of the number of claims and the variety and significance of differences among them. Indeed, it can be used to resolve multiple claims that bear (...) no resemblance to one another except for targeting the same defendant. The proposal can thus be employed to increase the efficiency of resolving relatively similar claims in class and consolidated actions and, by extending the application of such collectivizing processes, lower the cost of resolving all other claims that would be adjudicated as separate actions. I close by sketching a design for a reformed civil liability system that fully integrates and exploits the law enforcement benefits of sampling to better achieve the primary social objectives of accident risk deterrence and insurance. (shrink)

This thesis divides naturally into two parts, each concerned with the extent to which the theory of $L$ can be changed by forcing.The first part focuses primarily on applying generic-absoluteness principles to how that definable sets of reals enjoy regularity properties. The work in Part I is joint with Itay Neeman and is adapted from our paper Happy and mad families in $L$, JSL, 2018. The project was motivated by questions about mad families, maximal families of infinite subsets of $\omega (...) $ of which any two have only finitely many members in common. We begin, in the spirit of Mathias, by establishing a strong Ramsey property for sets of reals in the Solovay model, giving a new proof of Törnquist’s theorem that there are no infinite mad families in the Solovay model.In Chapter 3 we stray from the main line of inquiry to briefly study a game-theoretic characterization of filters with the Baire Property.Neeman and Zapletal showed, assuming roughly the existence of a proper class of Woodin cardinals, that the boldface theory of $L$ cannot be changed by proper forcing. They call their result the Embedding Theorem, because they conclude that in fact there is an elementary embedding from the $L$ of the ground model to that of the proper forcing extension. With a view toward analyzing mad families under $\mathsf {AD}^+$ and in $L$ under large-cardinal hypotheses, in Chapter 4 we establish triangular versions of the Embedding Theorem. These are enough for us to use Mathias’s methods to show that there are no infinite mad families in $L$ under large cardinals and that $\mathsf {AD}^+$ implies that there are no infinite mad families. These are again corollaries of theorems about strong Ramsey properties under large-cardinal assumptions and $\mathsf {AD}^+$, respectively. Our first theorem improves the large-cardinal assumption under which Todorcevic established the nonexistence of infinite mad families in $L$. Part I concludes with Chapter 5, a short list of open questions.In the second part of the thesis, we undertake a finer analysis of the Embedding Theorem and its consistency strength. Schindler found that the the Embedding Theorem is consistent relative to much weaker assumptions than the existence of Woodin cardinals. He defined remarkable cardinals, which can exist even in L, and showed that the Embedding Theorem is equiconsistent with the existence of a remarkable cardinal. His theorem resembles a theorem of Harrington–Shelah and Kunen from the 1980s: the absoluteness of the theory of $L$ to ccc forcing extensions is equiconsistent with a weakly compact cardinal. Joint with Itay Neeman, we improve Schindler’s theorem by showing that absoluteness for $\sigma $ -closed $\ast $ ccc posets—instead of the larger class of proper posets—implies the remarkability of $\aleph _1^V$ in L. This requires a fundamental change in the proof, since Schindler’s lower-bound argument uses Jensen’s reshaping forcing, which, though proper, need not be $\sigma $ -closed $\ast $ ccc in that context. Our proof bears more resemblance to that of Harrington–Shelah than to Schindler’s.The proof of Theorem 6.2 splits naturally into two arguments. In Chapter 7 we extend the Harrington–Shelah method of coding reals into a specializing function to allow for trees with uncountable levels that may not belong to L. This culminates in Theorem 7.4, which asserts that if there are $X\subseteq \omega _1$ and a tree $T\subseteq \omega _1$ of height $\omega _1$ such that X is codable along T, then $L$ -absoluteness for ccc posets must fail.We complete the argument in Chapter 8, where we show that if in any $\sigma $ -closed extension of V there is no $X\subseteq \omega _1$ codable along a tree T, then $\aleph _1^V$ must be remarkable in L.In Chapter 9 we review Schindler’s proof of generic absoluteness from a remarkable cardinal to show that the argument gives a level-by-level upper bound: a strongly $\lambda ^+$ -remarkable cardinal is enough to get $L$ -absoluteness for $\lambda $ -linked proper posets.Chapter 10 is devoted to partially reversing the level-by-level upper bound of Chapter 9. Adapting the methods of Neeman, Hierarchies of forcing axioms II, we are able to show that $L$ -absoluteness for $\left |\mathbf {R}\right |\cdot \left |\lambda \right |$ -linked posets implies that the interval $[\aleph _1^V,\lambda ]$ is $\Sigma ^2_1$ -remarkable in L.prepared by Zach Norwood.E-mail: [email protected]. (shrink)

In an enumerative induction we project a property found in all the examined members of a class to a hitherto unexamined member of that class. I consider an unresolved disagreement between Stephen Thomas and John Nolt about how likely the conclusion of one example of such reasoning is, given the premisses. Reflection on their controversy, and on the example, indicates that many textbook commonplaces about enumerative inductions are false. In particular, uniformity of the examined members of a (...) class='Hi'>class does not necessarily make it highly likely that the next member will have the target property; this proposition may still be unlikely, or on the other hand be quite definite, depending on our background knowledge. Also, enumerative induction need not rely on any general assumption about the uniformity of nature or the resemblance of the future to the past. (shrink)

Humans have only finite discriminatory capacities. This simple fact seems to be incompatible with the existence of appearances. As many authors have noted, the hypothesis that appearances exist seems to be refuted by reductio: Let A, B, C be three uniformly coloured surfaces presented to a subject in optimal viewing conditions, such that A, B, and C resemble one another perfectly except with respect to their colours. Their colours differ slightly in the following way: the difference between A and B (...) and the difference between B and C are below the discrimination threshold, but the difference between A and C is above this threshold. According to an intuitive construal of what an appearance is, given that A and B appear (to the subject) identical in colour, A and B have the same (colour1) appearance P1; likewise, B and C have the same appearance P2. B's appearance is both P1 and P2. This seems to imply that P1=P2. But then, A and C also have the same appearance, which contradicts the hypothesis that A and C are discriminable. If A and C are discriminable with respect to their colour, they do not have the same appearance with respect to colour. The paradox arising from such a series of judgments of sameness or difference between pairs of coloured surfaces seems to belong to the class of sorites paradoxes. I will show that there is a way to construe colours and their appearances in a way that does not fall prey to the reduction just sketched. (shrink)