In this paper I argue for the thesis that Stout's category of abstract particulars (what Husserl calls "moments') has played a role in the transition from Bradleian idealism to British analytic philosophy. That category plays this role as part of a new theory of wholes, parts and relations that Stout develops in opposition to Bradley. In Stout's theory abstract particulars are dependent parts of wholes. The critical remarks that G. E. Moore and Kevin Mulligan have made concerning Stout's (...) identification of abstract particulars and predicates are elaborated in this paper. Notwithstanding the fact that Stout mistakenly identifies abstract particulars with predicates, the category of abstract particulars may be of value in a theory of individuals, universals and truthmakers. (shrink)

In this paper we advocate the thesis that qualia are tropes (or qualitons), and not (universal) properties. The main advantage of the thesis is that we can accept both the Wittgensteinian and Sellarsian assault on the given and the claim that only subjective and private states can do justice to the qualitative character of experience. We hint that if we take qualia to be tropes, we dissolve the problem of inverted qualia. We develop an account of sensory concept acquisition that (...) takes the presence of qualia as an enabling condition for learning. We argue that qualia taken to be qualitons are part of our mechanism of sensory concept acquisition. (shrink)

In the following I take issue with the allegation that liberalism must inevitably be guilty of ‘abstract individualism’. I treat Michael Sandel’s well-known claim that there are ‘loyalties and convictions whose moral force consists partly in the fact that living by them is inseparable from understanding ourselves as the particular persons we are’ as representative of this widely held view. Specifically, I argue: (i) that Sandel’s account of the manner in which ‘constitutive’ loyalties function as reasons for action (...) presupposes the possibility of there being (what I call) ‘underivable particular obligations’, but that such obligations are, in fact, a logical impossibility; and (ii) that Sandel’s account of the self as necessarily ‘encumbered’ presupposes an account of personal identity which confuses identification with definition, and which is, therefore, fundamentally flawed. (shrink)

The present study examines the work of a group of medical scientists as they identify interpretative ‘pitfalls’ – recurrent sources of error – in the use of a new radiographic technique, formulate suggestions on how these pitfalls can be avoided and communicate their findings in the form of a scientific publication. The analysis focuses on a session in which previously diagnosed cases are discussed, and demonstrates the ways in which a certain source of diagnostic error gradually emerges as a taken-for-granted (...) in the interaction. An increased sense of recognition, recurrence and typicality is discernible in the treatment of the cases. Talk characterized by expansions and elaborations, displays of understanding in the form of reformulations, understanding checks, and so on, leave room for brief typifications and reifications of interpretative difficulties in characteristics of the imaging technique. Topical treatment of perception and interpretation, as well as embodied engagement, become decreasingly salient. It is argued that the abstracted formulations in the published text rely on the case-by-case working up of generality from particularity; from individualized accounts of why ‘I’ interpreted the image in a certain way to proffered generalizations achieved through articulated perceptions of a generalized ‘one’. If these proffers are ratified, a potential ground is established for the consensual formulation of a pitfall. The formulation of novel instructions is consequently made relevant, projecting a re-instructed diagnostic practice. (shrink)

Taking “capitalism itself as the ultimate horizon of the political situation” enables us to reframe binationalism and the Palestinian question. It helps to underscore binationalism as a universalist project, engaged in a fight against domination and exploitation. Seeking economic justice at home invariably links the Palestinian plight to other labor movements in Israel and elsewhere in the region. The solidarity of workers can effectively challenge the interests of the few, de naturalize their exploitation, and foreground binationalism as a socio-economic project, (...) not limited to its own particularist interests, but “grounded in the ‘part of no-part,’ the singular universality exemplified in those who lack a determined place in the social totality, who are ‘out of place’ in it”. If decoloniality and others fetishize the enemy, over-emphasizing his or her exceptionality, and thus always risk reifying the antagonism, binationalism, if it is to be transformative, must embrace its role as a supplement to the Palestinian/Israeli antagonism, taking the task of co-existence, of living together with each other’s neighbor, as an urgent ethico-political challenge, fully cognizant that there is no guarantee of success. And each is killing the other by the window. (shrink)

Trope theory is a leading metaphysical theory in analytic ontology. One of its classic statements is found in the work of Donald C. Williams who argued that tropes qua abstract particulars are the very alphabet of being. The concept of an abstract particular has been repeatedly attacked in the literature. Opponents and proponents of trope theory alike have levelled their criticisms at the abstractness of tropes and the associated act of abstraction. In this paper I defend the (...) concept of a trope qua abstract particular by rejecting arguments that purport to show that tropes should not be understood as abstract and by arguing that the abstractness of tropes plays an indispensable role in one of our more promising trope-theoretic analyses of universals and of concrete objects. (shrink)

Invariantists argue that the notion of concept in psychology should be reserved for knowledge that is retrieved in a context-insensitive manner. Contextualists argue that concepts are to be understood in terms of context-sensitive ad hoc constructions. I review the central empirical evidence for and against both views and show that their conclusions are based on a common mischaracterization of both theories. When the difference between contextualism and invariantism is properly understood, it becomes apparent that the way the question of stability (...) is currently investigated will not lead to a consensus. Instead of focusing directly on stability, we should turn our attention to other desiderata on a theory of concepts. In particular, I show that invariantism, but not contextualism, fails to account for compositionality and abstract concepts. (shrink)

Recent scholarship emphasizes the scaffolding role of language for cognition. Language, it is claimed, is a cognition-enhancing niche ( Clark, 2006 ), a programming tool for cognition ( Lupyan and Bergen, 2016 ), even neuroenhancement ( Dove, 2019 ) and augments cognitive functions such as memory, categorization, cognitive control, and meta-cognitive abilities (“thinking about thinking”). Yet, the notion that language enhances or augments cognition, and in particular, cognitive control does not easily fit in with embodied approaches to language processing, (...) or so we will argue. Accounts aiming to explain how language enhances various cognitive functions often employ a notion of abstract representation. Yet, embodied approaches to language processing have it that language processing crucially, according to some accounts even exclusively, involves embodied, modality-specific, i.e., non-abstract representations. In coming to understand a particular phrase or sentence, a prior experience has to be simulated or reenacted. The representation thus activated is embodied (modality-specific) as sensorimotor regions of the brain are thereby recruited. In this paper, we will first discuss the notion of representation, clarify what it takes for a representation to be embodied or abstract, and distinguish between conceptual and (other) linguistic representations. We will then put forward a characterization of cognitive control and examine its representational infrastructure. The remainder of the paper will be devoted to arguing that language augments cognitive control. To that end, we will draw on two lines of research, which investigate how language augments cognitive control: (i) research on the availability of linguistic labels and (ii) research on the active usage of a linguistic code, specifically, in inner speech. Eventually, we will argue that the cognition-enhancing capacity of language can be explained once we assume that it provides us with (a) abstract, non-embodied representations and with (b) abstract, sparse linguistic representations that may serve as easy-to-manipulate placeholders for fully embodied or otherwise more detailed representations. (shrink)

Which abstraction principles are acceptable? A variety of criteria have been proposed, in particular irenicity, stability, conservativeness, and unboundedness. This note charts their logical relations. This answers some open questions and corrects some old answers.

This article argues that abstract knowledge in the form of formally developed theory plays an increasingly important role in the economy and in financial innovation in particular.knowledge is easily reified, and this is an aspect of knowledge work that is insufficiently researched. In this article, we problematize reification of abstract knowledge in financial innovation from wisdom, ethics, and social network analysis perspectives. This article, therefore, considers the composition and structures of financial innovation networks that help avoid reification (...) by building ethicality through social practice wisdom. Finally, we discuss future directions that empirical ethics research can take. (shrink)

This paper contains a joint study of two sentential logics that combine a many-valued character, namely tetravalence, with a modal character; one of them is normal and the other one quasinormal. The method is to study their algebraic counterparts and their abstract models with the tools of Abstract Algebraic Logic, and particularly with those of Brown and Suszko's theory of abstract logics as recently developed by Font and Jansana in their "A General Algebraic Semantics for Sentential Logics". (...) The logics studied here arise from the algebraic and lattice-theoretical properties we review of Tetravalent Modal Algebras, a class of algebras studied mainly by Loureiro, and also by Figallo, Landini and Ziliani, at the suggestion of the late Antonio Monteiro. (shrink)

Proponents of mechanistic explanation all acknowledge the importance of organization. But they have also tended to emphasize specificity with respect to parts and operations in mechanisms. We argue that in understanding one important mode of organization—patterns of causal connectivity—a successful explanatory strategy abstracts from the specifics of the mechanism and invokes tools such as those of graph theory to explain how mechanisms with a particular mode of connectivity will behave. We discuss the connection between organization, abstraction, and mechanistic explanation (...) and illustrate our claims by looking at an example from recent research on so-called network motifs. (shrink)

Purpose – The purpose of this paper is to explain how abstract space of the State – universally and specifically within the context of Middle Eastern cities – aims to homogenise the city and eliminate any anomaly that threatens its power structure. Design/methodology/approach – Through a historical and discourse analysis of these policies and processes in the two case studies, this paper presents a contextualised reading of Lefebvre’s concept of abstract space and process of abstraction in relation to (...) the alienation of political public spaces. Findings – The paper proposes that regardless of these homogenising strategies being applied universally, they fail to respond to contextual particularities and therefore they – in a contradictory manner – may themselves produce a space of resistance and difference. Originality/value – This paper focusses on Iran, the case of Tehran and Turkey, the case of Taksim Square and Gezi Park in Istanbul. Recent policies and strategies have been proposed and implemented to reduce, alienate and possibly neutralise the impacts of urban and political protests in these cities and socio-political contexts. (shrink)

The need for quantitative measurement represents a unifying bond that links all the physical, biological, and social sciences. Measurements of such disparate phenomena as subatomic masses, uncertainty, information, and human values share common features whose explication is central to the achievement of foundational work in any particular mathematical science as well as for the development of a coherent philosophy of science. This book presents a theory of measurement, one that is "abstract" in that it is concerned with highly (...) general axiomatizations of empirical and qualitative settings and how these can be represented quantitatively. It was inspired by, and represents a generalization and extension of, the last major research work in this field, Foundations of Measurement Vol. I, by Krantz, Luce, Suppes, and Tversky published in 1971. (shrink)

Feminists, critical race scholars, and other social‐justice theorists sometimes object to “abstraction” in liberal normative theory. Arguing that oppression affects individual agents in powerful yet subtle ways, they contend that allegedly abstract theories often reinforce oppressive power structures. Here I critically examine and ultimately reject Onora O'Neill's “abstraction without idealization” as a solution to this problem. Because O'Neill defines abstraction as simply the “bracketing of certain predicates,” her methodology fails to guide decisions about what to bracket and what to (...) include in the theory. Moreover, it may not be possible to abstract without also relying on some particular ideals. While abstraction is unavoidable, I conclude that it must be employed with greater attention to sociopolitical hierarchies and by using ideals that do not collude with structures of oppression. I discuss the work of Susan Babbitt and Elizabeth Anderson as examples of how nonoppressive ideals might be incorporated into normative theory. (shrink)

Although Burke, Bentham, Hegel and Marx do not often agree, all criticized certain ethical theories, in particular theories of rights, for being too abstract. The complaint is still popular. It was common in Existentialist and in Wittgensteinian writing that stressed the importance of cases and examples rather than principles for the moral life; it has been prominent in recent Hegelian and Aristotelian flavoured writing, which stresses the importance of the virtues; it is reiterated in discussions that stress the (...) distinctiveness and particularity of moral vicissitudes and query the importance of ethical theory. Recent critics of abstraction are opposed not only to theories of rights, and the Kantian notions with which these are linked, but also to consequentialist ethical theories. The two ethical theories that are most influential in the English-speaking world now both stand accused of being too abstract. (shrink)

Aristotle’s philosophy of geometry is widely interpreted as a reaction against a Platonic realist conception of mathematics. Here I argue to the contrary that Aristotle is concerned primarily with the methodological question of how universal inferences are warranted by particular geometrical constructions. His answer hinges on the concept of abstraction, an operation of “taking away” certain features of material particulars that makes perspicuous universal relations among magnitudes. On my reading, abstraction is a diagrammatic procedure for Aristotle, and it is (...) through imagined variation of diagrams that one can universalize spatial inferences. In order to shift the discussion of Aristotle’s work on geometry from ontological to methodological questions, I argue in the first section that geometrical properties for Aristotle are necessary accidents of the particulars, canonically diagrams, in which they inhere. I then consider a line of research that shows how diagrams in ancient geometry are not illustrations of the textual proof but are in part constitutive of geometrical inference, an insight I claim can shed light on Aristotle’s philosophical project. Next I substantiate this assertion by giving an alternative interpretation of abstraction according to which it is a diagrammatic procedure that allows a part of a particular diagram to stand in for a universal. In the last section, I consider Aristotle’s account of mathematical cognition, arguing that there is evidence for the view that imagination is necessary both for the construction of figures, and for their presentation as abstractions subject to universal inference. (shrink)

Abstract In this article, a critical assessment is carried out of the two available forms of nominalism with respect to the ontological constitution of material objects: resemblance nominalism and trope theory. It is argued that these two nominalistic ontologies naturally converge towards each other when the problems they have to face are identified and plausible solutions to these problems are sought. This suggests a synthesis between the two perspectives along lines first proposed by Sellars, whereby, at least at the (...) level of the simplest, truly fundamental constituents of reality, every particular is literally both an object and a particularized property (or, alternatively put, the distinction between objects and properties dissolves). Some potential problems and open issues for such an approach to nominalism in ontology are identified and discussed, with particular emphasis on the sort of fundamentalism that seems to crucially underlie the proposed ontology. Content Type Journal Article Pages 1-14 DOI 10.1007/s12136-011-0145-x Authors Matteo Morganti, Department of Philosophy, University of Rome ‘RomaTRE’, Via Ostiense, 234, 00144 Rome, Italy Journal Acta Analytica Online ISSN 1874-6349 Print ISSN 0353-5150. (shrink)

Kant’s subject as source of universality and necessity in human understanding is Modern Philosophy's solution to the old problem of the universals, a solution which appeared to supersede once and for all the Aristotelian theory of abstraction. The present paper intends to show how Aquinas's Aristotelian doctrine on abstraction may stand the Kantian challenge and resolve the old problem when three principles are brought into play: 1) the same perfection can subsist in two different modes of being, and thus the (...) universal content of knowledge can be present in the particular reality (Summa, I, 84, 1); 2) things which are really distinct between themselves can be known in their distinction, even when they cannot exist separately (metaphysical distinction justifies gnoseological separation); 3) as Cornelio Fabro suggests, it is artificial to separate in the object of experience the object’s different levels of objectivity (quality, configuration and meaning) and, as a result, human experience could be considered the source not only of sensible content but also of intelligible content. This “defense” of Thomistic abstraction intends to offer an account of knowledge which reunites again epistemology with common sense experience, so that philosophy may no longer be a Platonic abstraction but a meaningful explanation of life. (shrink)

The main thesis of this book is that abstraction, far from being confined to higher forms of cognition, language and logical reasoning, has actually been a major driving force throughout the evolution of creatures with brains. It is manifest in emotive as well as rational thought. Wending its way through the various facets of abstraction, the book attempts to clarify - and relate - the often confusing meanings of the word 'abstract' that one may encounter even within the same (...) discipline. The unusual synoptic approach, which draws upon research in psychology, neural network theory, child language acquisition, philosophy and consciousness studies, as well as a variety of linguistic disciplines, cannot be compared directly to other books on the market that touch upon just one particular aspect of abstraction. It is aimed at a wide readership - anyone interested in the nature of abstraction and the cognitive processing and purpose behind it. (shrink)

In this paper we study abstract elementary classes with Löwenheim-Skolem number $\kappa$ , where $\kappa$ is cofinal with $\omega$ , which have finite character. We generalize results obtained by Kueker for $\kappa=\omega$ . In particular, we show that $\mathbb{K}$ is closed under $L_{\infty,\kappa}$ -elementary equivalence and obtain sufficient conditions for $\mathbb{K}$ to be $L_{\infty,\kappa}$ -axiomatizable. In addition, we provide an example to illustrate that if $\kappa$ is uncountable regular then $\mathbb{K}$ is not closed under $L_{\infty,\kappa}$ -elementary equivalence.

This essay introduces the concept of deictic abstraction , taking as a point of departure Husserl’s prototypical but insufficient description of the act of ideation in which a shade of color comes to givenness as an ideal object, i.e., a non-individual or abstract object, on the basis of a perceived individual object. This concept comprises not only color-ideation and ideations of universalities of the sensuous sphere , but all acts founded in perceptions in which ideal objects are directly referred (...) to by means of demonstrative expressions . This allows various types of deictic ideations or abstractions, corresponding to the degree of universality and the kind of ideal object concerned, to be brought to light through the analysis of particular cases of everyday acts of deictic abstraction, including deictic abstractions of predicative universals of the lowest level of universality ; deictic abstractions of non-predicative universals, especially of universal ways of doing something ; and deictic abstractions of individual styles of doing something . Deictic abstractions not only turn out to be constitutive for the formation of perceptual concepts of the lower and lowest levels, but also prove to be foundational for all kinds of learning in which schemata of actions are acquired from a model. (shrink)

I examine the abstraction/representation theory of computation put forward by Horsman et al., connecting it to the broader notion of modeling, and in particular, model-based explanation, as considered by Rosen. I argue that the ‘representational entities’ it depends on cannot themselves be computational, and that, in particular, their representational capacities cannot be realized by computational means, and must remain explanatorily opaque to them. I then propose that representation might be realized by subjective experience (qualia), through being the bearer (...) of the structure of abstract objects that are represented. (shrink)

We present a new model of skilled performance in geometry proof problem solving called the Diagram Configuration model (DC). While previous models plan proofs in a step‐by‐step fashion, we observed that experts plan at a more abstract level: They focus on the key steps and skip the less important ones. DC models this abstract planning behavior by parsing geometry problem diagrams into perceptual chunks, called diagram configurations, which cue relevant schematic knowledge. We provide verbal protocol evidence that DC's (...) schemas correspond with the step‐skipping inferences experts make in their initial planning. We compare DC with other models of geometry expertise and then, in the final section, we discuss more general implications of our research. DC's reasoning has important similarities with Larkin's (1988) display‐based reasoning approach and Johnson‐Laird's (1983) mental model approach. DC's perceptually based schemas are a step towards a unified explanation of (1) experts' superior problem‐solving effectiveness, (2) experts' superior problem‐state memory, and (3) experts' ability, in certain domains, to solve relatively simple problems by pure forward inferencing. We also argue that the particular and efficient knowledge organization of DC challenges current theories of skill acquisition as it presents an end‐state of learning that is difficult to explain within such theories. Finally, we discuss the implications of DC for geometry instruction. (shrink)

Frege suggests that criteria of identity should play a central role in the explanation of reference, especially to abstract objects. This paper develops a precise model of how we can come to refer to a particular kind of abstract object, namely, abstract letter types. It is argued that the resulting abstract referents are ‘metaphysically lightweight’.

A great deal of the criticism directed at Locke's theory of abstract ideas assumes that a Lockean abstract idea is a special kind of idea which by its very nature either represents many diverse particulars or represents separately things that cannot exist in separation. This interpretation of Locke has been challenged by scholars such as Kenneth Winkler and Michael Ayers who regard it as uncharitable in light of the obvious problems faced by this theory of abstraction. Winkler and (...) Ayers argue that Locke instead held that to have an abstract idea is to attend selectively to some portion of the content of a particular idea. On this view, to have an abstract idea is not to have a special kind of idea but to have an ordinary idea in a special way. Ayers argues that Locke inherited this theory from Arnauld. I argue that the case made by Ayers for the attribution of the extrinsic theory to Locke rests on a misinterpretation of Arnauld. In fact, both Locke and Arnauld regard selective attention as part of a process whereby a new kind of idea is constructed. (shrink)

In this paper we explore the thesis that the role of argumentation in practical reasoning in general and legal reasoning in particular is to justify the use of defeasible rules to derive a conclusion in preference to the use of other defeasible rules to derive a conflicting conclusion. The defeasibility of rules is expressed by means of non-provability claims as additional conditions of the rules.We outline an abstract approach to defeasible reasoning and argumentation which includes many existing formalisms, (...) including default logic, extended logic programming, non-monotonic modal logic and auto-epistemic logic, as special cases. We show, in particular, that the admissibility semantics for all these formalisms has a natural argumentation-theoretic interpretation and proof procedure, which seem to correspond well with informal argumentation. (shrink)

In this paper, we try to establish that some mathematical theories, like K-theory, homology, cohomology, homotopy theories, spectral sequences, modern Galois theory (in its various applications), representation theory and character theory, etc., should be thought of as (abstract) machines in the same way that there are (concrete) machines in the natural sciences. If this is correct, then many epistemological and ontological issues in the philosophy of mathematics are seen in a different light. We concentrate on one problem which immediately (...) follows the recognition of the particular status of these theories: the demarcation problem between ‘natural kinds’ and ‘artefacts’. (shrink)

Several difficulties, concerning the individuation and the variation of tropes, beset the initial classic version of trope theory. K. Campbell (Abstract particulars, Oxford, Basil Blackwell, 1990) presented a modified version that aims to avoid those difficulties. Unfortunately, the revised theory cannot make the case that one of the fundamental tropes, space-time, is a genuine particular.

Wright claims that “the epistemology of good abstraction principles should be assimilated to that of basic principles of logical inference”. In this paper I follow Wright’s recommendation, but I consider a different epistemology of logic, namely anti-exceptionalism. Anti-exceptionalism’s main contention is that logic is not a priori, and that the choice between rival logics should be based on abductive criteria such as simplicity, adequacy to the data, strength, fruitfulness, and consistency. This paper’s goal is to lay down the foundations for (...) an application of the anti-exceptionalist methodology to abstraction principles. In Sect. 1 I outline my strategy. I show that anti-exceptionalism has a bearing on the so-called Bad Company problem (Sect. 2), and explore some versions of anti-exceptionalism about abstraction (Sect. 3). I then consider new criteria for choosing between rival abstraction principles, and, in particular, between consistent revisions of Frege’s Basic Law V (Sect. 4). I finally consider how the abstractionist can compare between competing criteria (Sect. 5), and argue that anti-exceptionalists should be pluralists about abstraction (Sect. 6). (shrink)

What sorts of things are there in the world? Clearly enough, there are concrete, material things; but are there other things too, perhaps nonconcrete or non-material things? Some people believe that there are such things, which are often called abstract ; purported examples of such objects include numbers, properties, possible but non-actual states of affairs, propositions, and sets. Following a long-standing tradition, I shall describe persons who believe that there are abstract objects as ‘platonists’. In this paper, I (...) shall not directly address the plausibility of platonism, as compared with its rivals; instead, I shall confine my attention to one way in which some people have tried to combine platonism and theism. More specifically, I shall concentrate upon the claim that abstract objects depend upon God ontologically ; I shall argue that platonistic theists should reject DEP in favour of the claim that abstract objects exist independently of God . In order to evaluate the relative merits of DEP versus IND, it will be helpful to examine in some detail a particular articulation of DEP. When it comes to recent work on DEP, we can do no better in this regard than to examine the recent work of Thomas V. Morris and Christopher H. Menzel. According Morris and Menzel, there is a sense in which God literally creates such abstracta through engaging in intellective activities. (shrink)

We propose the notion of a quasiminimal abstract elementary class. This is an AEC satisfying four semantic conditions: countable Löwenheim–Skolem–Tarski number, existence of a prime model, closure under intersections, and uniqueness of the generic orbital type over every countable model. We exhibit a correspondence between Zilber’s quasiminimal pregeometry classes and quasiminimal AECs: any quasiminimal pregeometry class induces a quasiminimal AEC, and for any quasiminimal AEC there is a natural functorial expansion that induces a quasiminimal pregeometry class. We show in (...) particular that the exchange axiom is redundant in Zilber’s definition of a quasiminimal pregeometry class. (shrink)

Berkeley and Hume object to Locke's account of abstraction. Abstraction is separating in the mind what cannot be separated in reality. Their objection is that if a is inseparable in reality from b, then the idea of a is inseparable from the idea of b. The former inseparability is the reason for the latter. In most interpretations, however, commentators leave the former unexplained in explaining the latter. This article assumes that Berkeley and Hume present a unified front against Locke. Hume (...) supplements Berkeley's argument just where there are gaps. In particular, Hume makes explicit something Berkeley leaves implicit: The argument against Locke depends on the principle that things are inseparable if and only if they are identical. Abstraction is thinking of one of an inseparable pair while not thinking of the other. But doing so entails thinking of something while not thinking of it. This is the fundamental objection. (shrink)

Can we feel emotions about abstract objects, assuming that abstract objects exist? I argue that at least some emotions can have abstract objects as their intentional objects and discuss why this conclusion is not just trivially true. Through critical engagement with the work of Dacher Keltner and Jonathan Haidt, I devote special attention to awe, an emotion that is particularly well suited to show that some emotions can be about either concrete or abstract objects. In responding (...) to a possible objection, according to which we can only feel emotions about things that we take to matter to our flourishing, and thus cannot feel emotions about causally inefficacious abstract objects, I explore how abstract objects can be relevant to human flourishing and discuss someemotions other than awe that can be about abstract objects. I finish by explaining somereasons why my conclusion matters, including the fact that it presents a challenge to perceptual theories of emotion and causal theories of intentionality. (shrink)

We revisit the notion of initial sets by Xu and Cayrol 2016), i. e., non-empty minimal admissible sets in abstract argumentation frameworks. Initial sets are a simple concept for analysing conflicts in an abstract argumentation framework and to explain why certain arguments can be accepted. We contribute with new insights on the structure of initial sets and devise a simple non-deterministic construction principle for any admissible set, based on iterative selection of initial sets of the original framework and (...) its induced reducts. In particular, we characterise many existing admissibility-based semantics via this construction principle, thus providing a constructive explanation on the structure of extensions. We also investigate certain problems related to initial sets with respect to their computational complexity. (shrink)

In Die Grundlagen der Arithmetik, Frege attempted to introduce cardinalnumbers as logical objects by means of a second-order abstraction principlewhich is now widely known as ``Hume's Principle'' (HP): The number of Fsis identical with the number of Gs if and only if F and G are equinumerous.The attempt miscarried, because in its role as a contextual definition HP fails tofix uniquely the reference of the cardinality operator ``the number of Fs''. Thisproblem of referential indeterminacy is usually called ``the Julius Caesar (...) problem''.In this paper, Frege's treatment of the problem in Grundlagen is critically assessed. In particular, I try to shed new light on it by paying special attention to the framework of his logicism in which it appears embedded. I argue, among other things, that the Caesar problem, which is supposed to stem from Frege's tentative inductive definition of the natural numbers, is only spurious, not genuine; that the genuine Caesar problem deriving from HP is a purely semantic one and that the prospects of removing it by explicitly defining cardinal numbers as objects which are not classes are presumably poor for Frege. I conclude by rejecting two closely connected theses concerning Caesar put forward by Richard Heck: (i) that Frege could not abandon Axiom V because he could not solve the Julius Caesar problem without it; (ii) that (by his own lights) his logicist programme in Grundgesetze der Arithmetik failed because he could not overcome that problem. (shrink)

In this paper we study an alternative approach to the concept of abstract logic and to connectives in abstract logics. The notion of abstract logic was introduced by Brown and Suszko —nevertheless, similar concepts have been investigated by various authors. Considering abstract logics as intersection structures we extend several notions to their κ -versions, introduce a hierarchy of κ -prime theories, which is important for our treatment of infinite connectives, and study different concepts of κ -compactness. (...) We are particularly interested in non-topped intersection structures viewed as semi-lattices with a minimal meet-dense subset, i.e., with a minimal generator set. We study a chain condition which is sufficient for a minimal generator set, implies compactness of the logic, and in regular logics is equivalent to compactness of the consequence relation together with the existence of a inconsistent set, where κ is the cofinality of the cardinality of the logic. Some of these results are known in a similar form in the context of closure spaces, we give extensions to intersection structures and to big cardinals presenting new proofs based on set-theoretical tools. The existence of a minimal generator set is crucial for our way to define connectives. Although our method can be extended to further non-classical connectives we concentrate here on intuitionistic and infinite ones. Our approach leads us to the concept of the set of complete theories which is stable under all considered connectives and gives rise to the definition of the topological space of the logic. Topological representations of abstract logics by means of this space remain to be further investigated. (shrink)

What can philosophy bring to the reading of Beckett? Combining intertextual analysis with a ‘schizoanalytic genealogy’ derived from the authors of L’Anti-Œdipe, Garin Dowd’s Abstract Machines: Samuel Beckett and Philosophy after Deleuze and Guattari offers an innovative response to this much debated question. The author focuses on zones of encounter and thresholds of engagement between Beckett’s writing and a range of philosophers (among them Spinoza, Leibniz and Kant) and philosophical concepts. Beckett’s writing impacts in a variety of ways on (...) Deleuze and Guattari’s thought, and, in particular, resonates with Deleuze’s contributions to the history of philosophy (in books such as Le Pli: Leibniz et le baroque), and his ‘critical and clinical’ approach to literature. Furthermore, the books co-written with Guattari, concerned as they are with the ‘molecularization’ of the discipline of philosophy in the name of ‘thinking otherwise’, reveal themselves in a new light when explored in conjunction with Beckett’s œuvre. With its arresting perspectives on a wide range of Beckett’s works, Abstract Machines will appeal to academics and postgraduate students interested in the philosophical aspects of his writing. Its engagement with alternative contributions to the question of Beckett and philosophy, including that of Alain Badiou, renders it a timely and provocative intervention in contemporary debates on the relationship between literature and philosophy, both within the field of Beckett studies and beyond. (shrink)