Some philosophers have recently suggested that the reason mathematics is useful in science is that it expands our expressive capacities. Of these philosophers, only Stephen Yablo has put forward a detailed account of how mathematics brings this advantage. In this article, I set out Yablo’s view and argue that it is implausible. Then, I introduce a simpler account and show it is a serious rival to Yablo’s. 1 Introduction2 Yablo’s Expressionism3 Psychological Objections to Yablo’s Expressionism4 Introducing Belief Expressionism5 Objections and (...) Replies5.1 Yablo’s likely response5.2 Charity6 Conclusion. (shrink)

When painter Fritz Janschka arrived from Vienna to teach at Byrn Mawr College in October, 1949, he entered a culture seemingly as alien to his art as one can imagine. Janschka is one of the co­founders of the Vienna School of Fantastic Realism, a group of painters who studied at the Academy of Fine Arts in Vienna shortly after World War Two. The fantastic realists cultivated a precisely controlled craft informed by traditional methods and modernist sensibilities, incorporating collectively the entire (...) range of Western painting, past and present, in their attempts to come to grips with a shattered world. New York Abstract Expressionism and Viennese Fantastic Realism, two mid-twentieth century art movements, represent diametrically opposed ways of painting, yet both schools sprang out of surrealism. The Fantastic Realists were widely known in Europe and hardly known in America. Given the dominant abstractionist tendencies of post-World War Two art this is understandable. For these reasons Janschka’s openness to the techniques of the New York School in the early 1950s forms an unlikely meeting point of seemingly irreconcilable positions, one suggestive of possibilities for the meeting of abstraction and figuration, and more broadly, for addressing contemporary dehumanizing abstractionism, which I discuss in this essay. (shrink)

I offer an interpretation of the puzzle posed by Greenberg’s failure to come to terms with the explosion of postmodernist experimentation in the 1960’s. Greenberg, one of the most influential critics of the immediately preceding period and a strong supporter of New York abstract expressionism and color field painting, is indelibly associated with modernist schools of painting. His short essay, “Modernist Painting”, valorized precisely these movements and was a tour de force catapulting Greenberg into critic superstar status; it (...) is still one of the central documents in debates about modernism. Because Greenberg there makes references to Kant’s aesthetics in identifying the virtues of modernism his account is usually interpreted in terms of the formalism of the period and Kant’s analytic of the beautiful. This offers a reading of Greenberg as a formalist and as identifying modernism with a concern for the formal properties of art, the flatness of the picture frame and the formal relations between the aesthetic properties. Greenberg was also celebrated as having a legendary acuteness of aesthetic appreciation—a critical eye penetrating immediately to a work’s aesthetic depth. (shrink)

In almost all of his early works Gilles Deleuze is concerned with one and the same problem: the problem of genesis. In response to this problem, Deleuze argues for a system of heterogenesis. In this article, I argue that Deleuze’s system of heterogenesis operates on three levels: (1) the differential multiplicity of virtual Ideas; (2) the implied multiplicity of intensive dramas; (3) the extensive and qualitative diversity of actual concepts. As I hope to show, the relation between these three levels (...) can be explained in terms of the logic of expression that Deleuze develops in 'Expressionism in Philosophy: Spinoza.' In this way, I hope to gain clarity without losing nuance. The rather technical and abstract language of expression will become more concrete and understandable when it is understood in terms of intensive dramas, virtual Ideas and actual concepts. At the same time, the three levels of expression make it possible to show how these notions are interlinked. Accordingly, this article is divided in four parts. In the first part, I will explain how Deleuze takes up Kant’s discovery of the principle of difference as a reaction against the model of representation. The second part focuses on the two multiplicities (virtual Ideas and intensive dramas) that produce diversity (actual concepts). In the third part, these two multiplicities are linked to each other with the help of the logic of expression that Deleuze derives from Spinoza. The fourth, concluding part will connect the logic of expression to the complex dynamic of difference and repetition. (shrink)

Perhaps the question “What is philosophy?” can only be posed late in life, when old age has come, and with it the time to speak in concrete terms. It is a question one poses when one no longer has anything to ask for, but its consequences can be considerable. One was asking the question before, one never ceased asking it, but it was too artificial, too abstract; one expounded and dominated the question, more than being grabbed by it. There (...) are cases in which old age bestows not an eternal youth, but on the contrary a sovereign freedom, a pure necessity where one enjoys a moment of grace between life and death, and where all the parts of the machine combine to dispatch into the future a trait that traverses the ages: Turner, Monet, Matisse. The elderly Turner acquired or conquered the right to lead painting down a deserted path from which there was no return, and that was no longer distinguishable from a final question. In the same way, in philosophy, Kant’s Critique of Judgment is a work of old age, a wild work from which descendants will never cease to flow.We cannot lay claim to such a status. The time has simply come for us to ask what philosophy is. And we have never ceased to do this in the past, and we already had the response, which has not varied: philosophy is the art of forming, inventing, and fabricating concepts. But it was not only necessary for the response to take note of the question; it also had to determine a time, an occasion, the circumstances, the landscapes and personae, the conditions and unknowns of the question. One had to be able to pose the question “between friends” as a confidence or a trust, or else, faced with an enemy, as a challenge, and at the same time one had to reach that moment, between dog and wolf, when one mistrusts even the friend. Gilles Deleuze was professor of philosophy at the University of Paris VIII, Vincennes-St.-Denis, until his retirement in 1987. Among his books translated into English are the two-volume Capitalism and Schizophrenia , the two-volume Cinema , The Logic of Sense , and Expressionism in Philosophy: Spinoza . Daniel W. Smith is a doctoral candidate in philosophy at the University of Chicago. He is at work on a study of the philosophy of Deleuze, and is translating Deleuze’s Francis Bacon: Logique de la sensation. Arnold I. Davidson, executive editor of Critical Inquiry, teaches philosophy at the University of Chicago and is currently Marta Sutton Weeks Fellow at the Stanford Humanities Center. (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)

In this paper we describe and interpret the formal machinery of abstraction processes in which the domain of abstracta is a subset of the domain of objects from which is abstracted.

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.

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)

Philosophers have often claimed that general ideas or representations have their origin in abstraction, but it remains unclear exactly what abstraction as a psychological process consists in. We argue that the Lockean aspiration of using abstraction to explain the origins of all general representations cannot work and that at least some general representations have to be innate. We then offer an explicit framework for understanding abstraction, one that treats abstraction as a computational process that operates over an innate quality space (...) of fine-grained general representations. We argue that this framework has important philosophical implications for the nativism-empiricism dispute, for questions about the acquisition of unstructured representations, and for questions about the relation between human and animal minds. (shrink)

Theories of explanation need to account for a puzzling feature of our explanatory practices: the fact that we prefer explanations that are relatively abstract but only moderately so. Contra Franklin-Hall ([2016]), I argue that the interventionist account of explanation provides a natural and elegant explanation of this fact. By striking the right balance between specificity and generality, moderately abstract explanations optimally subserve what interventionists regard as the goal of explanation, namely identifying possible interventions that would have changed the (...) explanandum. (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.

In recent years, language has been shown to play a number of important cognitive roles over and above the communication of thoughts. One hypothesis gaining support is that language facilitates thought about abstract categories, such as democracy or prediction. To test this proposal, a novel set of semantic memory task trials, designed for assessing abstract thought non-linguistically, were normed for levels of abstractness. The trials were rated as more or less abstract to the degree that answering them (...) required the participant to abstract away from both perceptual features and common setting associations corresponding to the target image. The normed materials were then used with a population of people with aphasia to assess the relationship of abstract thought to language. While the language-impaired group with aphasia showed lower overall accuracy and longer response times than controls in general, of special note is that their response times were significantly longer as a function of a trial’s degree of abstractness. Further, the aphasia group’s response times in reporting their degree of confidence (a separate, metacognitive measure) were negatively correlated with their language production abilities, with lower language scores predicting longer metacognitive response times. These results provide some support for the hypothesis that language is an important aid to abstract thought and to metacognition about abstract thought. (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)

How can a metaphysics of abstract entities be built upon a metaphysics of time? In this paper, I address the question of how to accommodate abstract entities in a presentist world. I consider both the traditional metaontological approach of unrestricted fundamental quantification and then ontological pluralism. I argue that under the former we need to impose two constraints in the characterization of presentism in order to avoid undesired commitments to abstract entities: we have to characterize presentism as (...) a thesis only about the concrete, and we also need to avoid the widely held distinction between tensed and tenseless senses of existence. Under ontological pluralism, instead, I argue that we can naturally accommodate any view of abstract objects in a presentist world. (shrink)

The idea that some objects are metaphysically “cheap” has wide appeal. An influential version of the idea builds on abstractionist views in the philosophy of mathematics, on which numbers and other mathematical objects are abstracted from other phenomena. For example, Hume's Principle states that two collections have the same number just in case they are equinumerous, in the sense that they can be correlated one‐to‐one:. The principal aim of this article is to use the notion of grounding to develop this (...) sort of abstractionism. The appeal to grounding enables a unified response to the two main challenges that confront abstractionism. First, we must explicate the metaphor of metaphysical “cheapness.” Second, we must rebut the “bad company” objection, which rejects abstraction principles like (HP) as tarnished by their similarity to inconsistent principles like Frege's Basic Law V. By enforcing a simple requirement that all abstraction be properly grounded, we propose a unified solution to these two hard, and prima facie unrelated, problems. On our view, grounded abstraction simultaneously ensures “cheap” abstracta and permissible abstraction. (shrink)

In this paper, I draw jointly upon a Foucauldian ethical discourse and the example of the so-called ‘Manchester school’ of Foucauldian labour process theory (LPT) to question the political/ethical aspirations and effects of critical management studies. Specifically, I question the ethics and effects of LPT researchers’ relationships with those they/we research. I organize the discussion around four Foucauldian ethical themes or feelings. I thread these ethical themes throughout the paper to argue that, though Foucauldian LPT may be understood to abstractly (...) resonate with these themes, its contribution is seriously undermined through the authors’ lack of attention to ways of embodying this ethics in relations with the researched. By not embodying these commitments, the marriage between Foucault and LPT risks being read more as a marriage of convenience than commitment. And, further, a marriage that reproduces a politically problematic ‘modernist/positivist’ self–other separation or divorce between researcher and researched. (shrink)

According to the reading of Spinoza that Gilles Deleuze presents in Expressionism in Philosophy: Spinoza, Spinoza's philosophy should not be represented as a moment that can be simply subsumed and sublated within the dialectical progression of the history of philosophy, as it is figured by Hegel in the Science of Logic, but rather should be considered as providing an alternative point of view for the development of a philosophy that overcomes Hegelian idealism. Indeed, Deleuze demonstrates, by means of Spinoza, (...) that a more complex philosophy antedates Hegel's which cannot be supplanted by it. Spinoza therefore becomes a significant figure in Deleuze's project of tracing an alternative lineage in the history of philosophy, which, by distancing itself from Hegelian idealism, culminates in the construction of a philosophy of difference. Deleuze presents Spinoza's metaphysics as determined according to a 'logic of expression', which, insofar as it contributes to the determination of a philosophy of difference, functions as an alternative to the Hegelian dialectical logic. Deleuze's project in Expressionism in Philosophy is therefore to redeploy Spinoza in order to mobilize his philosophy of difference as an alternative to the dialectical philosophy determined by the Hegelian dialectic logic. (shrink)

In artificial intelligence, recent research has demonstrated the remarkable potential of Deep Convolutional Neural Networks (DCNNs), which seem to exceed state-of-the-art performance in new domains weekly, especially on the sorts of very difficult perceptual discrimination tasks that skeptics thought would remain beyond the reach of artificial intelligence. However, it has proven difficult to explain why DCNNs perform so well. In philosophy of mind, empiricists have long suggested that complex cognition is based on information derived from sensory experience, often appealing to (...) a faculty of abstraction. Rationalists have frequently complained, however, that empiricists never adequately explained how this faculty of abstraction actually works. In this paper, I tie these two questions together, to the mutual benefit of both disciplines. I argue that the architectural features that distinguish DCNNs from earlier neural networks allow them to implement a form of hierarchical processing that I call “transformational abstraction”. Transformational abstraction iteratively converts sensory-based representations of category exemplars into new formats that are increasingly tolerant to “nuisance variation” in input. Reflecting upon the way that DCNNs leverage a combination of linear and non-linear processing to efficiently accomplish this feat allows us to understand how the brain is capable of bi-directional travel between exemplars and abstractions, addressing longstanding problems in empiricist philosophy of mind. I end by considering the prospects for future research on DCNNs, arguing that rather than simply implementing 80s connectionism with more brute-force computation, transformational abstraction counts as a qualitatively distinct form of processing ripe with philosophical and psychological significance, because it is significantly better suited to depict the generic mechanism responsible for this important kind of psychological processing in the brain. (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)

A general theory of logical oppositions is proposed by abstracting these from the Aristotelian background of quantified sentences. Opposition is a relation that goes beyond incompatibility (not being true together), and a question-answer semantics is devised to investigate the features of oppositions and opposites within a functional calculus. Finally, several theoretical problems about its applicability are considered.

objects are standardly taken to be causally inert, but this claim is rarely explicitly argued for. In the context of his platonism about musical works, in order for musical works to be audible, Julian Dodd argues that abstracta are causally efficacious in virtue of their concrete tokens participating in events. I attempt to provide a principled argument for the causal inertness of abstracta by first rejecting Dodd’s arguments from events, and then extending and generalizing the causal exclusion argument to the (...) abstract/concrete distinction. For reasons of parsimony, if concrete tokens or instantiations of abstract objects account for all causal work, then there is no reason to attribute causal efficacy to abstracta, and thus reason to maintain their causal inertness. I then consider how one of the main arguments against causal exclusion, namely Stephen Yablo’s notion of “proportionality”, could be modified to support the causal efficacy of abstracta. I argue that from a few simple premises Yablo’s account in fact supports their causal inertness. Having a principled reason for the causal inertness of abstracta appears to entail that the musical platonist must admit that we never literally hear the musical work, but only its performances. I sketch a solution to this problem available to Dodd, so that the musical platonist can maintain that musical works are abstract objects and are causally inert while retaining their audibility. (shrink)

This paper develops a novel theory of abstraction—what we call collective abstraction. The theory solves a notorious problem for noneliminative structuralism. The noneliminative structuralist holds that in addition to various isomorphic systems there is a pure structure that can be abstracted from each of these systems; but existing accounts of abstraction fail for nonrigid systems like the complex numbers. The problem with the existing accounts is that they attempt to define a unique abstraction operation. The theory of collective abstraction instead (...) simultaneously defines a collection of distinct abstraction operations, each of which maps a system to its corresponding pure structure. The theory is precisely formulated in an essentialist language. This allows us to throw new light on the question to what extent structuralists are committed to symmetric dependence. Finally, we apply the theory of collective abstraction to solve a problem about converse relations. (shrink)

Beach's Gaelic Symphony is plausibly an abstract object that Beach created. The view that people create some abstract objects is called abstract creationism. There are abstract creationists about many kinds of objects, including musical works, fictional characters, arguments, words, internet memes, installation artworks, bitcoins, and restaurants. Alternative theories include materialism and Platonism. This paper discusses some of the most serious objections against abstract creationism. Arguably, these objections have ramifications for questions in metaphysics pertaining to the (...) abstract/concrete distinction, time, causation, vague existence, vague identity, and inadvertent creation. (shrink)

We present an abstract model of rationality that focuses on structural properties of attitudes. Rationality requires coherence between your attitudes, such as your beliefs, values, and intentions. We define three 'logical' conditions on attitudes: consistency, completeness, and closedness. They parallel the familiar logical conditions on beliefs, but contrast with standard rationality conditions like preference transitivity. We establish a formal correspondence between our logical conditions and standard rationality conditions. Addressing John Broome's programme 'rationality through reasoning', we formally characterize how you (...) can (not) become more logical by reasoning. Our analysis connects rationality with logic, and enables logical talk about multi-attitude psychology. (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)

This study investigated the rhetorical move structure of the dental sciences research article abstract (RAA) genre using Swales’ (2004) model of move analysis, CARS (Create a Research Space), to find the frequency of rhetorical moves and steps in RAAs of the selected journals and also to examine the association between the frequency of moves and steps in the RAAs. To this end, 251 abstracts from articles published in 2018, 2019, and 2020 in four Iranian PubMed-indexed dentistry journals were selected (...) and examined. The frequencies were counted and compared using the Chi Square statistic. The findings revealed that all of the abstracts included M3S4 and M3S5, and all but only one, included M3S1. Yet, M3S2 and M3S7 had not been used in the abstracts whatsoever, and M1S3 had been employed only once. It was also found that the RAAs in the Journal of Dentistry and the Dental Research Journal used the steps considerably more frequently than the RAAs in the Journal of Dental Research and Frontiers in Dentistry. The findings of this study can provide EAP instructors with practical insights into the needs and wants of dental students, and also serve as a complement to the guidelines for academic writing for dental researchers to produce more received RAAs. (shrink)

Neo-Fregeans such as Bob Hale and Crispin Wright seek a foundation of mathematics based on abstraction principles. These are sentences involving a relation called the abstraction relation. It is usually assumed that abstraction relations must be equivalence relations, so reflexive, symmetric and transitive. In this article I argue that abstraction relations need not be reflexive. I furthermore give an application of non-reflexive abstraction relations to restricted abstraction principles.

Reification is to abstraction as disease is to health. Whereas abstraction is singling out, symbolizing, and systematizing, reification is neglecting abstractive context, especially functional, historical, and analytical-level context. William James and John Dewey provide similar and nuanced arguments regarding the perils and promises of abstraction. They share an abstraction-reification account. The stages of abstraction and the concepts of “vicious abstractionism,” “/the/ psychologist’s fallacy,” and “the philosophic fallacy” in the works of these pragmatists are here analyzed in detail. For instance, in (...) 1896 Dewey exposes various fallacies associated with reifying dualistic reflex arc theory. The conclusion prescribes treatments (pluralism and assumption archaeology) for de-reifying ill models (i.e., universalized, narrowed, and ontologized models) in contemporary scientific fields such as cognitive science and biology. (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)

Hume’s critique of traditional abstraction entails a result that undercuts his account of the idea of identity. To save his account of identity, Hume would have to accept abstraction as well. What links these two discussions is (1) Hume’s widely shared assumption that traditional abstraction is separating in the mind what are inseparable in reality, (2) his principle that what are different are mentally separable, and (3) his principle that we cannot conceive of the impossible. Given these, it will turn (...) out that abstraction is mentally separating something from itself, which will entail that abstraction is conceiving of something as distinct from itself. But it is impossible for something to be distinct from itself, and so it is inconceivable. Therefore abstraction is impossible. Yet consider Hume’s account of the idea of identity. On that account, to conceive of an identity is to conceive of something as one single thing viewed one way and as two distinct things viewed another. How we can take these opposing views of the same thing is a problem that I’ve termed Hume’s Difficulty concerning Identity. It will turn out that we can take the opposing views only if we can conceive of the single thing viewed one way as somehow distinct from itself when viewed the other way. That is, we must be able to conceive of something as distinct from itself. However, if we cannot conceive of something as distinct from itself when abstracting, then we cannot do it when conceiving of an identity. So traditional abstraction and Hume’s account of the idea of identity stand or fall together. (shrink)

> Context • The alleged dichotomy between mind and matter is pervasive. Therefore, the attempt to explain mat- ter in terms of mind (idealism) is often considered a mirror image of that of explaining mind in terms of mat- ter (mainstream physicalism), in the sense of being structurally equivalent despite being reversely arranged. > Problem • I argue that this is an error arising from language artifacts, for dichotomies must reside in the same level of abstraction. > Method • I (...) show that, because matter outside mind is not an empirical observation but rather an explanatory model, the epistemic symmetry between the two is broken. Consequently, matter and mind cannot reside in the same level of abstraction. > Results • It then becomes clear that attempting to explain mind in terms of matter is epistemically more costly than attempting to explain matter in terms of mind. > Implications • The qualities of experience are suggested to be not only epistemically, but also ontologically primary. > Constructivist content • I high- light the primacy of perceptual constructs over explanatory abstraction on both epistemic and ontic levels. > Key words • Idealism, physicalism, pancomputationalism, anti-realism, hard problem of consciousness, epistemic symmetry, explanatory abstraction, levels of abstraction. (shrink)

The following abstracts were selected by AJOB-Neuroscience judges as the best submitted to the International Neuroethics Society 2024 Annual Meeting based on merit, novelty, relevance, and contribution to the field of neuroethics. The scores were tallied and the top abstracts appear in alphabetical order by first author surname.

This paper looks at the history of the problem of individuation from Plato to Whitehead. Part I takes as its point of departure Reiner Wiehl’s interpretation of the different meanings of “abstract” in the metaphysics of Alfred North Whitehead and arrives at a corresponding taxonomy of different ways things can be called concrete. Part II compares the way philosophers in different periods understand the relation between thought and intuition. The view mostly associated with ancient philosophy is that thought and (...) sense-perception target different kinds of objects. The view mostly associated with modern philosophy (although it was introduced by the Stoics) is that thought and sense-perception are different ways of targeting the same objects. These differences have specific consequences for theories of individuation, which are assessed historically in Part III and then applied to Whitehead’s difficult texts in part IV. (shrink)

The existence of mereological sums can be derived from an abstraction principle in a way analogous to numbers. I draw lessons for the thesis that “composition is innocent” from neo-Fregeanism in the philosophy of mathematics.

Structuralism has recently moved center stage in philosophy of mathematics. One of the issues discussed is the underlying logic of mathematical structuralism. In this paper, I want to look at the dual question, namely the underlying structures of logic. Indeed, from a mathematical structuralist standpoint, it makes perfect sense to try to identify the abstract structures underlying logic. We claim that one answer to this question is provided by categorical logic. In fact, we claim that the latter can be (...) seen—and probably should be seen—as being a structuralist approach to logic and it is from this angle that categorical logic is best understood. (shrink)

This is my main contribution to P. Gould (ed.) Beyond the Control of God?: Six Views on the Problem of God and Abstract Objects Bloomsbury. (The other contibutors to this work are: Keith Yandell; Paul Gould and Rich Davis; Greg Welty; William Lane Craig; and Scott Shalkowski.) I argue that, when it comes to a comparative assessment of the merits of theism and atheism, it makes no difference whether one opts for realism or fictionalism concerning abstract objects.

Some tools introduced by Linnebo to show that mathematical entities are thin objects can also be applied to non-mathematical entities, which have been thought to be thin as well for a variety of reasons. In this paper, I discuss some difficulties and opportunities concerning the application of abstraction and interpretational modalities to mereological sums. In particular, I show that on one hand some prima facie attractive candidates for the role of an explanatory plural abstraction principle for mereological sums (in terms (...) of pluralities of summed entities) are not really explanatory; on the other hand, singular abstraction principles (in terms of single summed entities) are materially inadequate. Nonetheless, explanatory criteria of identity and conditions of existence for mereological sums are provided by classical extensional mereology independent of abstraction principles. Thus, given classical extensional mereology, the reasons why, according to Linnebo, mathematical abstracted entities are thin also hold for mereological sums. Finally, I contend that interpretational modalities can be used to characterise the process by which a subject adds sums of previously admitted entities to the domain of quantification. (shrink)

The way we understand the environment is analogous to the way we draw a map. Drawing insights from this analogy, this paper shows how the abstraction that occurs in ecological explanation can lead to damaging distortion. It is mistaken, therefore, to assume that by abstraction we can easily determine the correct variables for controlling a given ecosystem as if it were ideally closed. Recent work shows that the environment is a global composite with a very high degree of internal dependence (...) between its parts, a kind of dependence that makes it more holistic than a machine and perhaps even as holistic as an organism. This paper was presented at the 6th European Meeting of Jesuits in Science on “Science and Culture”, Frankfurt a. M., Germany (8th - 12th September 1999). (shrink)

Abstract objects are standardly taken to be causally inert, however principled arguments for this claim are rarely given. As a result, a number of recent authors have claimed that abstract objects are causally efficacious. These authors take abstracta to be temporally located in order to enter into causal relations but lack a spatial location. In this paper, I argue that such a position is untenable by showing first that causation requires its relata to have a temporal location, but (...) second, that if an entity is temporally located then it is spatiotemporally located since this follows from the theory of Relativity. Since abstract objects lack a spatiotemporal location, then if something is causally efficacious, it is not abstract. (shrink)

This article aims to provide a reassessment of the relationship between God and abstract objects. This reassessment will provide a new conceptualisation of this important relationship and will be formulated, first, within the theoretical framework of ‘Theistic Aspectivalism’, which is grounded on the notion of an aspect, proposed by Donald L.M. Baxter, which provides a means to ward off the ‘Bootstrapping Problem’. Second, within the theoretical framework of ‘Theistic Essentialism’, which is based on the notion of essence and essential (...) dependence, as proposed by Kit Fine, Jonathan Lowe, and Katherin Koslicki, which provides a metaphysical basis for the relationship between God and abstract objects to be further elucidated and for the position of 'Platonic Theism' to be free from the primary issues that are often raised against it. (shrink)

Abstract: According to certain dispositional accounts of meaning, an agent's meaning is determined by the dispositions that an idealized version of this agent has in optimal conditions. We argue that such attempts cannot properly fix meaning. For even if there is a way to determine which features of an agent should be idealized without appealing to what the agent means, there is no non-circular way to determine how those features should be idealized. We sketch an alternative dispositional account that (...) avoids this problem, according to which an agent's meaning is determined by the dispositions that an abstract version of this agent has in optimal conditions. (shrink)

Fundamental to Computer Science is the distinction between abstractions and implementations. When that distinction is applied to various philosophical questions it yields the following conclusions. -/- • EMERGENCE. It isn’t as mysterious as it’s made out to be; the possibility of strong emergence is not a threat to science. -/- • INTERACTIONS BETWEEN HIGHER-LEVEL ENTITIES. Physical interaction among higher-level entities is illusory. Abstract interactions are the source of emergence, new domains of knowledge, and complex systems. -/- • PHYSICS and (...) the SPECIAL SCIENCES. The new domains of knowledge derived from abstract interactions are the basis of the autonomy of the special sciences. -/- • DOWNWARD CAUSATION. It’s a zombie idea that should have a stake put through its heart and be replaced by downward entailment. (shrink)

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)

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)

I reconcile the spatiotemporal location of repeatable artworks and impure sets with the non-location of natural numbers despite all three being varieties of abstract objects. This is possible because, while the identity conditions for all three can be given by abstraction principles, in the former two cases spatiotemporal location is a congruence for the equivalence relation featuring in the relevant principle, whereas in the latter it is not. I then generalize this to other ‘physical’ properties like shape, mass, and (...) causal powers. (shrink)

An important lesson that philosophy can learn from the Turing Test and computer science more generally concerns the careful use of the method of Levels of Abstraction (LoA). In this paper, the method is first briefly summarised. The constituents of the method are “observables”, collected together and moderated by predicates restraining their “behaviour”. The resulting collection of sets of observables is called a “gradient of abstractions” and it formalises the minimum consistency conditions that the chosen abstractions must satisfy. Two useful (...) kinds of gradient of abstraction – disjoint and nested – are identified. It is then argued that in any discrete (as distinct from analogue) domain of discourse, a complex phenomenon may be explicated in terms of simple approximations organised together in a gradient of abstractions. Thus, the method replaces, for discrete disciplines, the differential and integral calculus, which form the basis for understanding the complex analogue phenomena of science and engineering. The result formalises an approach that is rather common in computer science but has hitherto found little application in philosophy. So the philosophical value of the method is demonstrated by showing how making the LoA of discourse explicit can be fruitful for phenomenological and conceptual analysis. To this end, the method is applied to the Turing Test, the concept of agenthood, the definition of emergence, the notion of artificial life, quantum observation and decidable observation. It is hoped that this treatment will promote the use of the method in certain areas of the humanities and especially in philosophy. (shrink)

This article reconstructs and defends Theodor Adorno’s social theory by motivating the central role of abstract domination within it. Whereas critics such as Axel Honneth have charged Adorno with adhering to a reductive model of personal domination, I argue that the latter rather understands domination as a structural and de-individualized feature of capitalist society. If Adorno’s social theory is to be explanatory, however, it must account for the source of the abstractions that dominate modern individuals and, in particular, that (...) of value. While such an account remains undeveloped in Adorno, Marx provides resources for its development, in positing the constitution of value neither in production nor exchange alone, but in the social totality. This article argues that Marx’s account is compatible with Adorno’s, and that it may be used to render Adorno’s theory of domination more credible on explanatory grounds. (shrink)

In this paper, I explore a line of argument against one form of realism about fictional characters : abstract artifact theory, the view according to which fictional characters like Harry Potter are part of our reality, but, they are abstract objects created by humans, akin to the institution of marriage and the game of soccer. I will defend artifactualism against an objection that Mark Sainsbury considers decisive against it: the category-mistake objection. The objection has it that artifactualism attributes (...) to people who produce and process sentences and thoughts about Harry Potter massive error, indeed, a category mistake about what kind of thing Harry Potter is; for an abstract object isn’t the sort of thing that can wear glasses, ride a double-decker bus, attend school. Given problems with this objection, artifactualism, I shall conclude, remains a tenable contender. (shrink)