Dung’s (1995) argumentation framework takes as input two abstract entities: a set of arguments and a binary relation encoding attacks between these arguments. It returns acceptable sets of arguments, called extensions, w.r.t. a given semantics. While the abstract nature of this setting is seen as a great advantage, it induces a big gap with the application that it is used to. This raises some questions about the compatibility of the setting with a logical formalism (i.e., whether it is (...) possible to instantiate it properly from a logical knowledge base), and about the significance of the various semantics in the application context. In this paper we tackle the above questions. We first propose to fill in the previous gap by extending Dung’s (1995) framework. The idea is to consider all the ingredients involved in an argumentation process. We start with the notion of an abstract monotonic logic which consists of a language (defining the formulas) and a consequence operator. We show how to build, in a systematic way, arguments from a knowledge base formalised in such a logic. We then recall some basic postulates that any instantiation should satisfy. We study how to choose an attack relation so that the instantiation satisfies the postulates. We show that symmetric attack relations are generally not suitable. However, we identify at least one ‘appropriate’ attack relation. Next, we investigate under stable, semi-stable, preferred, grounded and ideal semantics the outputs of logic-based instantiations that satisfy the postulates. For each semantics, we delimit the number of extensions an argumentation system may have, characterise the extensions in terms of subsets of the knowledge base, and finally characterise the set of conclusions that are drawn from the knowledge base. The study reveals that stable, semi-stable and preferred semantics either lead to counter-intuitive results or provide no added value w.r.t. naive semantics. Besides, naive semantics either leads to arbitrary results or generalises the coherence-based approach initially developed by Rescher and Manor (1970). Ideal and grounded semantics either coincide and generalise the free consequence relation developed by Benferhat, Dubois, and Prade (1997), or return arbitrary results. Consequently, Dung’s (1995) framework seems problematic when applied over deductive logical formalisms. (shrink)

A natural way to think of models is as abstract entities. If theories employ models to represent the world, theories traffic in abstract entities much more widely than is often assumed. This kind of thought seems to create a problem for a scientific realist approach to theories. Scientific realists claim theories should be understood literally. Do they then imply the reality of abstract entities? Or are theories simply—and incurably—false? Or has the very idea of literal understanding to (...) be abandoned? Is then fictionalism towards scientific theories inevitable? This paper argues that scientific realism can happily co-exist with models qua abstracta. (shrink)

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)

TWO OPPOSING VIEWS ABOUT THE RELATIONSHIP between concepts and the world can be found in the history of philosophy. One view—deriving from Immanuel Kant and endorsed by Karl Popper, among many others—claims that in forming and using concepts we structure the world. Concepts produce or increase order. Hence, the world, insofar as it is knowable by human beings, is necessarily a conceptually structured world. The second, still older view—represented by the Aristotelian tradition and by John Locke, for example—holds that concepts (...) are formed by abstracting from the particularities of the world. By leaving out the accidental or irrelevant features of particular entities, we abstract a concept as a general representative of a kind. (shrink)

The results in this paper are in a context of abstract elementary classes identified by Shelah and Villaveces in which the amalgamation property is not assumed. The long-term goal is to solve Shelah’s Categoricity Conjecture in this context. Here we tackle a problem of Shelah and Villaveces by proving that in their context, the uniqueness of limit models follows from categoricity under the assumption that the subclass of amalgamation bases is closed under unions of bounded, -increasing chains.

The French phenomenologist Michel Henry sees a similarity between the primordial experience of what he calls ‘Life’ and the aesthetic experience occasioned by Wassily Kandinsky’s abstract art. The triple aim of this essay is to explain and assess how Henry interprets Kandinsky’s abstract art and theory; what the consequences of his interpretation mean for the theory of the experience of abstract art; and what doubts and questions emerge from Henry’s interpretations of Kandinsky’s theory and practice. Despite its (...) containing many interesting ideas, Henry’s phenomenological approach is insufficient to describe the aesthetic experience of Kandinsky’s abstract art. For Henry, aesthetic experience is corporeal, primordial, non-intentional, and independent of knowledge and culture.By contrast, I believe that it is possible and more suitable to connect the direct, corporeal, and affective character of the aesthetic experience of abstract art with intentionality and embeddedness in culture and knowledge. (shrink)

Theorem 0.1LetK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {K}$$\end{document}be an abstract elementary class with amalgamation and no maximal models. Letλ>LS\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda > {LS}$$\end{document}. IfK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {K}$$\end{document}is categorical inλ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}, then the model of cardinalityλ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}is Galois-saturated.This answers a question asked independently by Baldwin (...) and Shelah. We deduce several corollaries: K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {K}$$\end{document} has a unique limit model in each cardinal below λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}, K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {K}$$\end{document} is weakly tame below λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}, and the thresholds of several existing categoricity transfers can be improved.We also prove a downward transfer of solvability :Corollary 0.2LetK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {K}$$\end{document}be an AEC with amalgamation and no maximal models. Letλ>μ>LS\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda> \mu > {LS}$$\end{document}. IfK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {K}$$\end{document}is solvable inλ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}, thenK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {K}$$\end{document}is solvable inμ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document}. (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)

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)

As a version of creationism—which claims that fictional charac- ters are created by authors who write characters into existence by penning their names in their works—abstract creationism claims that fictional objects are abstract entities. However, I want to modify the conception of what constitutes a fictional object. In short, I am going to give a defense of abstract creationism that offers answers to the questions, as outlined by Stuart Brock, of ontology, identity, and plenitude by developing a (...) claim that—except for rigidly referring proper names—fictional terms and nonfictional terms are all abstract objects.Working off the debates surrounding abstract creationism, and with a nod to D. M. Armstrong's... (shrink)

This work introduces the Attack-Support Argumentation Framework (ASAF), an approach to abstract argumentation that allows for the representation and combination of attack and support relations. This framework extends the argumentation Framework with Recursive Attacks (AFRA) in two ways. Firstly, it adds a support relation enabling to express support for arguments; this support can also be given to attacks, and to the support relation itself. Secondly, it extends AFRA’s attack relation by allowing attacks to the aforementioned support relation. Moreover, since (...) the support relation of the ASAF has a necessity interpretation, the ASAF also extends the Argumentation Framework with Necessities (AFN). Thus, the ASAF provides a unified framework for representing attack and support for arguments, as well as attack and support for the attack and support relations at any level. (shrink)

The notion of politicization has been often assimilated to that of partisanship, especially in political and social sciences. However, these accounts underestimate more fine-grained, and yet pivotal, aspects at stake in processes of politicization. In addition, they overlook cognitive mechanisms underlying politicizing practices. Here, we propose an integrated approach to politicization relying on recent insights from both social and political sciences, as well as cognitive science. We outline two key facets of politicization, that we call partial indetermination and contestability, and (...) we show how these can be accounted for by appealing to recent literature in cognitive science concerned with abstract conceptual knowledge. We suggest that politicizing a concept often implies making its more abstract components more salient, hence legitimating its contestable character. Finally, we provide preliminary suggestions to test our proposal, using the concept of gender as case study. (shrink)

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)

A new case of Shelah's eventual categoricity conjecture is established: Let be an abstract elementary class with amalgamation. Write and. Assume that is H2‐tame and has primes over sets of the form. If is categorical in some, then is categorical in all. The result had previously been established when the stronger locality assumptions of full tameness and shortness are also required. An application of the method of proof of the mentioned result is that Shelah's categoricity conjecture holds in the (...) context of homogeneous model theory (this was known, but our proof gives new cases): If D be a homogeneous diagram in a first‐order theory T and D is categorical in a, then D is categorical in all. (shrink)

This is a version of a paper delivered at the Beckett centenary conference held at University College Cork, May 26-27, 2006. It was subsequently published under the title ‘Stellar Separation orMachine? Badiou and Deleuze and Guattari on Beckett’ in Beckett Re-Membered: After the Centenary, edited by James Carney,Mi chael O’Sullivan, Leonard Madden and Karl White, pp. 92-107, ISBN 1443835005. This is a pre-publication version of the paper as it appeared in the latter publication. OPENING PARAGRAPH: In the most important study (...) to date of the respective use of Beckett’s writings in the work of Deleuze and Badiou, Jean-Jacques Lecercle concludes by surmising that “Perhaps the close proximity, in the French edition, of Deleuze’s essay, ‘The Exhausted’, to Beckett’s own text, is indeed more than a fortunate coincidence: perhaps it is a symptom”.1 For, Lecercle, despite his long-term support for Deleuze and indeed despite his misgivings concerning Badiou’s characteristically strong reading of Beckett, decides that there may be, after all, something more compelling in the Badiou than in the less consistent Deleuze. This may also be, he suggests, attributable to Deleuze’s own modernism as a writer, which, though it gives him greater access to, and understanding of, the materiality of Beckett’s writing, also in the final analysis, renders his reading of Beckett somewhat orthodox. By contrast, the defiantly declarative and unhesitatingly dogmatic reading advanced by Badiou, is able to disclose strikingly original insights, not least because of the co-implication and reversibility of the readings of Badiou-Beckett and Beckett-Badiou. This essay seeks to examine the symptomatology of one text in particular as it operates and produces or is indicative of symptoms in the work of Badiou and Deleuze respectively. (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)

To understand and begin to answer the question of this article, I compare Heidegger's position to Hegel's, since the two appear structurally similar and Heidegger is explicitly indebted to Hegel's aesthetics. On the basis of this comparison, I argue that abstract art has the potential to play an important role on Heideggerian grounds. I conclude that modernist art should be understood not as a supplement to the project of self-realization that characterizes Hegelian freedom but rather as a disruptive event (...) that could potentially challenge the constraining technological mindset that is characteristic of our time. (shrink)

This paper is addressed to recent theoretical discussions of the Anthropocene, in particular Bernard Stiegler’s Neganthropocene (Open Universities Press, 2018), which argues: “As we drift past tipping points that put future biota at risk, while a post-truth regime institutes the denial of ‘climate change’ (as fake news), and as Silicon Valley assistants snatch decision and memory, and as gene-editing and a financially-engineered bifurcation advances over the rising hum of extinction events and the innumerable toxins and conceptual opiates that Anthropocene Talk (...) fascinated itself with—in short, as ‘the Anthropocene’ discloses itself as a dead-end trap…”. The objective of this paper is therefore twofold: (1) to discuss how the Anthropocene is appropriated to certain ideological discourses (paradoxically) to maintain the hegemony of precisely those systems of production that have most accelerated climate change etc.; (2) to consider how the factography of the Anthropocene is exploited in this process to mask the ideological character of industry-aligned “technocratic” environmental management. The paper is not concerned with specific case studies in terms of government and industry policy, or climate science, but rather with the ways in which the discourse of the Anthropocene has been inflected within the humanities and the broader cultural field—that is to say, ideologically, as a system or logic of meaning. How the Anthropocene “means” is, in this respect, a question of some importance. This paper does not attempt to address all the facets of this question, but focuses upon a central “apocalyptic” strain in the discourse of the Anthropocene drawn particularly from Francis Fukuyama’s millennial posthumanism and centred in the question of “sustainability” as catastrophe management—with the risk that real environmental degradation will become an alibi for a revived neoliberalism. In other words, that the critical Earth system transformations that characterise the Anthropocene are themselves commodities, and that the project of their amelioration is in process of defining a future (opportunistic) “crisis” rhetoric with a global political franchise. The ideological import of the Anthropocene stems precisely from the fact that it is planetary and, while catalysed by human agency, independent in its specific behaviour from it. The Anthropocene objectively presents as the contemporary counterpart of the Cold War doctrine of Mutually Assured Destruction and the most compelling argument for a new kind of technological “arms race.” But it also presents as the condition of an emerging ideological discourse which will determine how this race is run. From the discourse on “energy security” to the widespread “security crackdown” on environmental activists across the so-called developed & developing world, the Anthropocene has come to represent the co-option of a scientific factography for the thinly disguised resurgence of “ideological science” of the Fukuyamaesque variety (post-history, post-human). For Fukuyama, the true meaning of “posthuman” is thus the accomplishment of humanity’s historical mission. As the “End of History” designates an end of ideological struggle, so too the dénouement of the Anthropocene and the “ends of man” represent the accomplished purpose of species warfare: dominion, not simply over the world, but over all possible worlds. According to this narrative, science—like technology—must be uniquely at the service of the maintenance of the global order, organised around a universal appeal to “crisis management.” It is precisely for this reason that what calls itself post-human masks the return of an ever-more-apocalyptic Humanism. (shrink)

Awareness is a two-place determinable relation some determinates of which are seeing, hearing, etc. Abstract objects are items such as universals and functions, which contrast with concrete objects such as solids and liquids. It is uncontroversial that we are sometimes aware of concrete objects. In this paper I explore the more controversial topic of awareness of abstract objects. I distinguish two questions. First, the Existence Question: are there any experiences that make their subjects aware of abstract objects? (...) Second, the Grounding Question: if an experience makes its subject aware of an abstract object, in virtue of what does it do so? I defend the view that intuitions, specifically mathematical intuitions, sometimes make their subjects aware of abstract objects. In defending this view, I develop an account of the ground of intuitive awareness. (shrink)

In recent discussions concerning the definition of argument, it has been maintained that the word ‘argument’ exhibits the process-product ambiguity, or an act/object ambi-guity. Drawing on literature on lexical ambiguity we argue that ‘argument’ is not ambiguous. The term ‘argument’ refers to an object, not to a speech act. We also examine some of the important implications of our argument by considering the question: what sort of abstract objects are arguments?

If mathematics is the purest form of knowledge, the perfect foundation of all the hard sciences, and a uniquely precise discipline, then how can the human brain, an imperfect and imprecise organ, process mathematical ideas? Is mathematics made up of eternal, universal truths? Or, as some have claimed, could mathematics simply be a human invention, a kind of tool or metaphor? These questions are among the greatest enigmas of science and epistemology, discussed at length by mathematicians, physicians, and philosophers. But, (...) curiously enough, neuroscientists have been absent in the debate, even though it is precisely the field of neuroscience—which studies the brain’s mechanisms for thinking and reasoning—that ought to be at the very center of these discussions. How our Emotions and Bodies are Vital for Abstract Thought explores the unique mechanisms of cooperation between the body, emotions, and the cortex, based on fundamental physical principles. It is these mechanisms that help us to overcome the limitations of our physiology and allow our imperfect, human brains to make transcendent mathematical discoveries. This book is written for anyone who is interested in the nature of abstract thought, including mathematicians, physicists, computer scientists, psychologists, and psychiatrists. (shrink)

The stability theory of first order theories was initiated by Saharon Shelah in 1969. The classification of abstract elementary classes was initiated by Shelah, too. In several papers, he introduced non-forking relations. Later, Shelah [17, II] introduced the good non-forking frame, an axiomatization of the non-forking notion.We improve results of Shelah on good non-forking frames, mainly by weakening the stability hypothesis in several important theorems, replacing it by the almost λ-stability hypothesis: The number of types over a model of (...) cardinality λ is at most λ+.We present conditions on Kλ, that imply the existence of a model in Kλ+n for all n. We do this by providing sufficiently strong conditions on Kλ, that they are inherited by a properly chosen subclass of Kλ+. What are these conditions? We assume that there is a ‘non-forking’ relation which satisfies the properties of the non-forking relation on superstable first order theories. Note that here we deal with models of a fixed cardinality, λ.While in Shelah [17, II] we assume stability in λ, so we can use brimmed models, here we assume almost stability only, but we add an assumption: The conjugation property.In the context of elementary classes, the superstability assumption gives the existence of types with well-defined dimension and the ω-stability assumption gives the existence and uniqueness of models prime over sets. In our context, the local character assumption is an analog to superstability and the density of the class of uniqueness triples with respect to the relation ≼bs is the analog to ω-stability. (shrink)

Studies of reasoning have often invoked a distinction between a natural or ordinary consideration of the premises, in which they are interpreted, and even distorted, in the light of empirical knowledge, and an analytic or logical consideration of the premises, in which they are analysed in a literal fashion for their logical implications. Two or three years of schooling have been seen as critical for the spontaneous use of analytic reasoning. In two experiments, however, 4-year-olds who were given brief instructions (...) that prompted use of an analytic approach continued to adopt this approach one week later. Thus, when given syllogistic problems in which the major premise was incongruent with their empirical knowledge (e.g. "All snow is black"), instructed children reasoned more accurately from that premise both immediately and a week later as compared to children given only a basic introduction. A third experiment showed that instructions also improved 4-year-olds' performance on hard-to-imagine, abstract material (e.g."All mib is white"). Similarities between the effects of brief instruction and of schooling are discussed. (shrink)

This is Francesco Orilia's book review of Edward N. Zalta's 1983 book, Abstract Objects: An Introduction to Axiomatic Metaphysics.

Let be an abstract elementary class with amalgamation, and Lowenheim Skolem number LS. We prove that for a suitable Hanf number gc0 if χ0 < λ0 λ1, and is categorical inλ1+ then it is categorical in λ0.