It is widely supposed that every entity falls into one of twocategories: Some are concrete; the rest abstract. The distinction issupposed to be of fundamental significance for metaphysics andepistemology. This article surveys a number of recent attempts to sayhow it should be drawn.

This volume explores the roles and uses of abstraction in scientific and artistic practice. Conceived as an interdisciplinary dialogue between experts across histories and philosophies of art and science, this collection of essays draws on the shared premise that abstraction is a rich and generative process, not reducible to the mere omission of details in a representation. When scientists attempt to make sense of complex natural phenomena, they often produce highly abstract models of them. In the history and (...) philosophy of art, there is a long tradition of debate on the function of abstraction, and - more recently - its relation with theories of depiction. Adopting a process-oriented perspective, the chapters in this volume explore the epistemic potential of a diversity of practices of abstracting. The systematic analysis of a wide range of historical cases, from early twentieth-century abstractionist painting to contemporary abstract photography, and from nineteenth-century physics to recent research in biology and neurosciences, invites the reader to reflect on the material lives of abstraction through concrete artefacts, experimental practices and theoretical and aesthetic achievements. Abstraction in Science and Art: Philosophical Perspectives will be of interest to scholars and advanced students working in aesthetics, philosophy of science, and epistemology, as well as to historians of science and art, and to practicing artists and scientists interested in exploring foundational questions at the heart of the creative practice of abstracting. (shrink)

In this paper, I explore the approaches to methodological abstraction and self-alienation developed respectively in Karl Mannheim’s early sociology of intellectuals and in Edmund Husserl’s late transcendental phenomenology. In Mannheim’s early and experimental works, the resistance to abstraction and alienation is located in a stratum of intellectuals able to meaningfully combine diverse cultural currents in a social process of cultivation (Bildung). In Husserl, to contrast, this resistance is grasped as a constant crisis in the methods of pursuing philosophical (...) truth. While these approaches seem difficult to reconcile, I suggest in closing that this difficulty can be related to their shared emphasis on a theoretical response to the practical and historical reality of self-alienation. (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, I present a class of ‘structural’ abstraction principles, and describe how they are suggested by some features of Cantor's and Dedekind's approach to abstraction. Structural abstraction is a promising source of mathematically tractable new axioms for the neo-logicist. I illustrate this by showing, first, how a theorem of Shelah gives a sufficient condition for consistency in the structural setting, solving what neo-logicists call the ‘bad company’ problem for structural abstraction. Second, I show how, (...) in the structural setting, we can measure the logical strength of abstraction principles using categories of interpretations between theories. (shrink)

The type-level abstraction is a formal way to represent molecular structures in biological practice. Graphical representations of molecular structures of biological objects are also used to identify functional processes of things. This paper will reveal that category theory is a formal mathematical language not only to visualize molecular structures of biological objects as type-level abstraction formally but also to understand how to infer biological functions from the molecular structures of biological objects. Category theory is a toolkit to understand (...) biological knowledge at the type-level formally, not individual token-level, as well as typical heuristic strategies in molecular biology. (shrink)

This paper elaborates distinctions between a core and a periphery in the ontological and the conceptual domain associated with natural language. The ontological core-periphery distinction is essential for natural language ontology and is the basis for the central thesis of my 2013 book Abstract Objects and the Semantics of Natural Language, namely that natural language permits reference to abstract objects in its periphery, but not its core.

Software is a ubiquitous artifact, yet not much has been done to understand its ontological nature. There are a few accounts offered so far about the nature of software. I argue that none of those accounts give a plausible picture of the nature of software. I draw attention to the striking similarities between software and musical works. These similarities motivate to look more closely on the discussions regarding the nature of the musical works. With the lessons drawn from the ontology (...) of musical works I offer a novel account of the nature of software. In this account, software is an abstract artifact. I elaborate the conditions under which software comes into existence; how it persists; how and on which entities its existence depends. (shrink)

The ardent antagonism between two aesthetic parties, figuration and abstraction, which for more than half a century has stamped art history in old Europe, with increasingly overlapping implications for youthful America, Japan and many other places, today tends to reduce itself to being simply the anecdotal imprint of an era: in the final analysis it seems already condemned to disappear in favor of a notion of complementarity and even synthesis.

Abstract In this paper I criticise a recent account of fictional discourse proposed by Nathan Salmon. Salmon invokes abstract artifacts as the referents of fictional names in both object- and meta-fictional discourse alike. He then invokes a theory of pretence to forge the requisite connection between object-fictional sentences and meta-fictional sentences, in virtue of which the latter can be assigned appropriate truth-values. I argue that Salmon's account of pretence renders his appeal to abstract artifacts as the referents of fictional names (...) in object-fictional discourse explanatorily redundant. I further argue that his account is therefore no improvement over those he criticises, thus leaving his own account unmotivated. (shrink)

This book pursues the question of how and whether natural language allows for reference to abstract objects in a fully systematic way. By making full use of contemporary linguistic semantics, it presents a much greater range of linguistic generalizations than has previously been taken into consideration in philosophical discussions, and it argues for an ontological picture is very different from that generally taken for granted by philosophers and semanticists alike. Reference to abstract objects such as properties, numbers, propositions, and degrees (...) is considerably more marginal than generally held. (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)

Despite the importance of mathematics in our educational systems little is known about how abstract mathematical thinking emerges. Under the uniting thread of mathematical development, we hope to connect researchers from various backgrounds to provide an integrated view of abstract mathematical cognition. Much progress has been made in the last 20 years on how numeracy is acquired. Experimental psychology has brought to light the fact that numerical cognition stems from spatial cognition. The findings from neuroimaging and single cell recording experiments (...) converge to show that numerical representations take place in the intraparietal sulcus. Further research has demonstrated that supplementary neural networks might be recruited to carry out subtasks; for example, the retrieval of arithmetic facts is done by the angular gyrus. Now that the neural networks in charge of basic mathematical cognition are identified, we can move onto the stage where we seek to understand how these basics skills are used to support the acquisition and use of abstract mathematical concepts. (shrink)

Many metaphor theorists argue that our mental experience of time is grounded in our understanding of space, including motion through space. Results from recent experiments – in which people think about motion, which in turn influences their thinking about time – support this position. Still, many questions remain about the nature of the metaphorical connection between time and space. Can the mere suggestion of motion influence how people reason about time, and if so, when and how? Three experiments investigated how (...) thinking about “abstract” motion through sequences of numbers or letters would influence reasoning about time. Our results extend earlier psychological work on the link between time and space by showing that even motion in non-physical domains can influence temporal reasoning. The results provide further evidence that metaphorical understanding is grounded in our everyday physical and conceptual experience. (shrink)

In this book, Zalta attempts to lay the axiomatic foundations of metaphysics by developing and applying a (formal) theory of abstract objects. The cornerstones include a principle which presents precise conditions under which there are abstract objects and a principle which says when apparently distinct such objects are in fact identical. The principles are constructed out of a basic set of primitive notions, which are identified at the end of the Introduction, just before the theorizing begins. The main reason for (...) producing a theory which defines a logical space of abstract objects is that it may have a great deal of explanatory power. It is hoped that the data explained by means of the theory will be of interest to pure and applied metaphysicians, logicians and linguists, and pure and applied epistemologists. (shrink)

Think of a number, any number, or properties like fragility and humanity. These and other abstract entities are radically different from concrete entities like electrons and elbows. While concrete entities are located in space and time, have causes and effects, and are known through empirical means, abstract entities like meanings and possibilities are remarkably different. They seem to be immutable and imperceptible and to exist "outside" of space and time. This book provides a comprehensive critical assessment of the problems raised (...) by abstract entities and the debates about existence, truth, and knowledge that surround them. It sets out the key issues that inform the metaphysical disagreement between platonists who accept abstract entities and nominalists who deny abstract entities exist. Beginning with the essentials of the platonist–nominalist debate, it explores the key arguments and issues informing the contemporary debate over abstract reality: arguments for platonism and their connections to semantics, science, and metaphysical explanation the abstract–concrete distinction and views about the nature of abstract reality epistemological puzzles surrounding our knowledge of mathematical entities and other abstract entities. arguments for nominalism premised upon concerns about paradox, parsimony, infinite regresses, underdetermination, and causal isolation nominalist options that seek to dispense with abstract entities. Including chapter summaries, annotated further reading, and a glossary, _Entities_ is essential reading for anyone seeking a clear and authoritative introduction to the problems raised by abstract entities. (shrink)

A number of philosophers have recently suggested that some abstract, plausibly non-causal and/or mathematical, explanations explain in a way that is radically dif- ferent from the way causal explanation explain. Namely, while causal explanations explain by providing information about causal dependence, allegedly some abstract explanations explain in a way tied to the independence of the explanandum from the microdetails, or causal laws, for example. We oppose this recent trend to regard abstractions as explanatory in some sui generis way, and argue (...) that a prominent ac- count of causal explanation can be naturally extended to capture explanations that radically abstract away from microphysical and causal-nomological details. To this end, we distinguish di erent senses in which an explanation can be more or less abstract, and analyse the connection between explanations’ abstractness and their explanatory power. According to our analysis abstract explanations have much in common with counterfactual causal explanations. (shrink)

Paolo Mancosu provides an original investigation of historical and systematic aspects of the notions of abstraction and infinity and their interaction. A familiar way of introducing concepts in mathematics rests on so-called definitions by abstraction. An example of this is Hume's Principle, which introduces the concept of number by stating that two concepts have the same number if and only if the objects falling under each one of them can be put in one-one correspondence. This principle is at (...) the core of neo-logicism. In the first two chapters of the book, Mancosu provides a historical analysis of the mathematical uses and foundational discussion of definitions by abstraction up to Frege, Peano, and Russell. Chapter one shows that abstraction principles were quite widespread in the mathematical practice that preceded Frege's discussion of them and the second chapter provides the first contextual analysis of Frege's discussion of abstraction principles in section 64 of the Grundlagen. In the second part of the book, Mancosu discusses a novel approach to measuring the size of infinite sets known as the theory of numerosities and shows how this new development leads to deep mathematical, historical, and philosophical problems. The final chapter of the book explore how this theory of numerosities can be exploited to provide surprisingly novel perspectives on neo-logicism. (shrink)

This chapter contains sections titled: Introduction Computer Science as the Master of Its Domain The Concept of Law in Computer Science Computer Science Laws as Invariants The Interplay of Freedom and Constraint Conclusion References.

An abstract framework for structured arguments is presented, which instantiates Dung's ('On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming, and n- Person Games', Artificial Intelligence , 77, 321-357) abstract argumentation frameworks. Arguments are defined as inference trees formed by applying two kinds of inference rules: strict and defeasible rules. This naturally leads to three ways of attacking an argument: attacking a premise, attacking a conclusion and attacking an inference. To resolve such attacks, preferences may (...) be used, which leads to three corresponding kinds of defeat: undermining, rebutting and undercutting defeats. The nature of the inference rules, the structure of the logical language on which they operate and the origin of the preferences are, apart from some basic assumptions, left unspecified. The resulting framework integrates work of Pollock, Vreeswijk and others on the structure of arguments and the nature of defeat and extends it in several respects. Various rationality postulates are proved to be satisfied by the framework, and several existing approaches are proved to be a special case of the framework, including assumption-based argumentation and DefLog. (shrink)

In the recent literature on causal and non-causal scientific explanations, there is an intuitive assumption according to which an explanation is non-causal by virtue of being abstract. In this context, to be ‘abstract’ means that the explanans in question leaves out many or almost all causal microphysical details of the target system. After motivating this assumption, we argue that the abstractness assumption, in placing the abstract and the causal character of an explanation in tension, is misguided in ways that are (...) independent of which view of causation or causal explanation one takes to be most accurate. On major accounts of causation, as well as on major accounts of causal explanation, the abstractness of an explanation is not sufficient for it being non-causal. That is, explanations are not non-causal by dint of being abstract. (shrink)

Abstract creationism about fictional characters is the view that fictional characters are abstract objects that authors create. I defend this view against criticisms from Stuart Brock that hitherto have not been adequately countered. The discussion sheds light on how the number of fictional characters depends on authorial intention. I conclude also that we should change how we think intentions are connected to artifacts more generally, both abstract and concrete.

Recent work on mood choice considers fine-grained semantic differences among desire predicates (notably, ‘want’ and ‘hope’) and their consequences for the distribution of indicative and subjunctive complement clauses. In that vein, this paper takes a close look at ‘intend’. I show that cross-linguistically, ‘intend’ accepts nonfinite and subjunctive complements and rejects indicative complements. This fact poses difficulties for recent approaches to mood choice. Toward a solution, a broad aim of this paper is to argue that—while ‘intend’ is loosely in the (...) family of desire predicates—it differs from ‘want’ and ‘hope’ in that it has a causative component, and this is relevant to its mood choice behavior, given that causative predicates also systematically reject indicative complements. More concretely, my analysis has three ingredients: (i) following related proposals in philosophy, intention reports have causally self-referential content; (ii) encoding causal self-reference requires abstraction over the complement clause’s eventuality argument; and (iii) nonfinite and subjunctive clauses enable such abstraction but indicative clauses do not. Aside from causative predicates, independent support for the proposal comes from the syntax of belief-/intention-hybrid attitude predicates like ‘decide’ and ‘convince’, anankastic conditional antecedents, aspectual predicates, and memory and perception reports. Synthesizing this result with that of previous literature, the emergent generalization is that subjunctive mood occurs in attitude reports that involve either comparison or eventuality abstraction. Toward a unified theory of mood choice, I suggest that both comparison and eventuality abstraction represent departures from the clausal semantics of unembedded assertions and consequently that subjunctive mood signals such a departure. (shrink)

concepts typically are defined in terms of lacking physical or perceptual referents. We argue instead that they are not devoid of perceptual information because knowledge of real-world situations is an important component of learning and using many abstract concepts. Although the relationship between perceptual information and abstract concepts is less straightforward than for concrete concepts, situation-based perceptual knowledge is part of many abstract concepts. In Experiment 1, participants made lexical decisions to abstract words that were preceded by related and unrelated (...) pictures of situations. For example, share was preceded by a picture of two girls sharing a cob of corn. When pictures were presented for 500 ms, latencies did not differ. However, when pictures were presented for 1,000 ms, decision latencies were significantly shorter for abstract words preceded by related versus unrelated pictures. Because the abstract concepts corresponded to the pictured situation as a whole, rather than a single concrete object or entity, the necessary relational processing takes time. In Experiment 2, on each trial, an abstract word was presented for 250 ms, immediately followed by a picture. Participants indicated whether or not the picture showed a normal situation. Decision latencies were significantly shorter for pictures preceded by related versus unrelated abstract words. Our experiments provide evidence that knowledge of events and situations is important for learning and using at least some types of abstract concepts. That is, abstract concepts are grounded in situations, but in a more complex manner than for concrete concepts. Although people's understanding of abstract concepts certainly includes knowledge gained from language describing situations and events for which those concepts are relevant, sensory and motor information experienced during real-life events is important as well. (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)

Presents a new framework for the complexity of algorithms, for all readers interested in the theory of computation.

This book offers an historically-informed critical assessment of Dummett's account of abstract objects, examining in detail some of the Fregean presuppositions whilst also engaging with recent work on the problem of abstract entities.

L'idealisme radical de Jean-Michel Le Lannou conteste l'identification de la pensee et de la representation. Loin de soumettre a la vacuite et la mort, l'abstraction manifeste ses puissances d'exces. Plus rien ne nous oblige a persister dans notre amour du fini. Pourtant, la philosophie s'est longtemps meprise sur elle-meme. D'ou provient une telle mesentente sur le desir du penser? Montrer comment la pensee a pu ainsi se fourvoyer sur elle-meme doit permettre d'entreprendre sa liberation definitive. Les etudes reunies ici (...) s'attachent avec ambition a eclairer ce mouvement insurrectionnel d'une pensee qui refuse de se laisser retenir par la particularite et qui, dans son detachement meme, rejoint l'affirmation substantielle la plus intense. (shrink)