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)

Many philosophers think all abstract objects are causally inert. Here, focusing on novels, I argue that some abstracta are causally efficacious. First, I defend a straightforward argument for this view. Second, I outline an account of object causation—an account of how objects cause effects. This account further supports the view that some abstracta are causally efficacious.

This paper aims to provide hyperintensional foundations for mathematical platonism. I examine Hale and Wright's (2009) objections to the merits and need, in the defense of mathematical platonism and its epistemology, of the thesis of Necessitism. In response to Hale and Wright's objections to the role of epistemic and metaphysical modalities in providing justification for both the truth of abstraction principles and the success of mathematical predicate reference, I examine the Necessitist commitments of the abundant conception of properties endorsed by (...) Hale and Wright and examined in Hale (2013), and demonstrate how a two-dimensional approach to the epistemology of mathematics is consistent with Hale and Wright's notion of there being non-evidential epistemic entitlement rationally to trust that abstraction principles are true. A choice point that I flag is that between availing of intensional or hyperintensional semantics. The hyperintensional semantic approach that I advance is a topic-sensitive epistemic two-dimensional truthmaker semantics. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest that observational type theory can be applied to first-order abstraction principles in order to make abstraction principles recursively enumerable. Epistemic and metaphysical states and possibilities may thus be shown to play a constitutive role in vindicating the reality of mathematical objects and truth, and in providing a conceivability-based route to the truth of abstraction principles as well as other axioms and propositions in mathematics. (shrink)

Art and Art-Attempts by Christy Mag Uidhir is an excellent book about the philosophy of art.1 It is full of insight. It is brilliantly precise. Indeed, it is a model of analytic precision. This discussion will be concerned with the role of the intention of the artist in art, which is central to the book, and Mag Uidhir’s discussion of abstracta and instantiation. I shall argue that intention should be replaced with choice and that abstracta should be replaced (...) with exemplar representation to improve his account. I conclude that choice in art and focus on exemplars play a special role in aesthetic education.Here is the basic idea of the role of intention of the artist in the book:Taking intention-dependence seriously... (shrink)

La bipartition entre une dynamica abstracta et une dynamica concreta est récurrente dans la production scientifique leibnizienne en dépit des acquisitions conceptuelles qui – dès la rédaction de la Dynamica de Potentia de 1690 – permettraient de la dépasser. S’appuyant sur l’étude des manuscrits inédits réalisée en vue de la publication de la première édition critique du traité, l’article se propose : 1. d’explorer les raisons de la permanence d’une telle structure à la lumière des travaux logiques et grammaticaux (...) leibniziens sur l’abstrait et le concret – 2. d’offrir au lecteur une contextualisation et une présentation générale de l’œuvre, ainsi qu’un aperçu du nouveau matériau éditorial disponible. (shrink)

A noção de objecto abstracto desempenha um papel central em diferentes debates filosóficos contemporâneos, da metafísica à estética, passando pela filosofia da linguagem. A sua origem está contudo relacionada com a filosofia da matemática e em particular, com o trabalho de Frege nos fundamentos da aritmética. O nosso primeiro objectivo será assim o de explicar o contributo desta noção para o entendimento Fregeano da realidade matemática. Veremos também que, em virtude de certas dificuldades inerentes ao projeto Fregeano, a dada altura (...) a natureza do universo matemático passou a ser entendida nos termos da chamada teoria dos conjuntos. Com este material à nossa disposição, podemos então discutir o papel desempenhado pela noção de objecto abstracto em certos debates filosóficos contemporâneos. Em particular, procuraremos ilustrar o interesse actual da noção, discutindo a distinção abstracto/concreto. (shrink)

Of all the problems attending the sense-datum theory, arguably the deepest is that it draws a veil of appearances over the external world. Today, the sense-datum theory is widely regarded as an overreaction to the problem of hallucination. Instead of accounting for hallucination in terms of intentional relations to sense data, it is often thought that we should account for it in terms of intentional relations to properties. In this paper, however, I argue that in the versions that might address (...) the problem of hallucination, this newer account is guilty of a vice similar to sense-datum theory’s: it draws a veil of abtracta over the concrete world. (shrink)

Regarding museums as potential sites of formal learning, this article describes an innovative workshop for postgraduate researchers in philosophy and religious studies that was designed to serve as a template for other initiatives. It showcases pathways between research in the arts and humanities and museums’ collections. It is of use to scholars interested in exploring ways to use museum collections for research in arts and humanities disciplines.

In my “Creatures of Fiction, Objects of Myth” (2014), I present and defend an argument for thinking that mythical creationism—the view that mythical objects like phlogiston and Vulcan are abstract artifacts—is false. One intriguing sort of objection to my argument has been recently put forth by Zvolenszky (2016); she claims that a crucial premise is seen to be unjustified once one considers the phenomena of inadvertently created abstracta—specifically, inadvertently created fictional characters. I argue here that even if we admit (...) inadvertently created abstracta into our ontology, my argument survives. I ultimately defend a view on which fictional characters (if real) may be countenanced as created abstracta whether purposefully created or not, yet mythical objects are best taken to be discoverable, Platonic abstracta (if real). We can see that such a hybrid ontology is justified once we take proper note of the nature of the sorts of authorial activities involved in fictional storytelling and scientific hypothesizing. (shrink)

Susan Schneider argues that physicalism must be false if abstracta are part of the physicalist's dependence base. In opposition to her view, here I set out some reasons to think that abstracta in general, including abstracta that are woven into the dependence base, are something physicalists can countenance with consistency.

I present a new argument to the effect that platonism about abstract entities undermines metaphysical naturalism and provides some support to theism. I further suggest that there are ways of extending this line of reasoning to point toward one or another more specific varieties of Christian theism.

I argue that materialism is unable to account for knowledge deriving from such abstracta as rules of inference, algorithms, and the ideals of infinity, perfection, and eternity. Both reductive and nonreductive materialism subscribe to the causal closure of the physical world, which implies that a creature’s concepts derive exclusively from the interactions of brains with the physical environment. These resources do not explain the acquisition of abstract concepts or the successful use of these concepts in gaining important knowledge about (...) the world. By contrast, if both God and souls exist, we can understand how knowledge based on abstracta is possible. (shrink)

El modelo de marcos argumentativos abstractos es actualmente la herramienta más utilizada para caracterizar la justificación de argumentos derrotables en Inteligencia Artificial. Las justificaciones se determinan en base a los ataques entre argumentos y se formalizan a través de semánticas de extensiones. Aquí sostenemos que, o bien algunos marcos argumentativos carecen de sentido bajo ciertas concepciones de ataque específicas, o bien las semánticas más usadas en la literatura, basadas en el concepto de defensa conocido como admisibilidad, no resultan adecuadas para (...) justificar, en particular, argumentos para la toma de decisiones.The abstract argumentation frameworks model is currently the most used tool for characterizing the justification of defeasible arguments in Artificial Intelligence. Justifications are determined on a given attack relation among arguments and are formalized as extension semantics. In this work we argue that, contrariwise to the assumptions in that model, either some argumentation frameworks are meaningless under certain concrete definitions of the attack relation, or some of the most used extension semantics in the literature, based on the defense notion of admissibility, are not suitable in particular for the justification of arguments for decision making. (shrink)

El modelo de marcos argumentativos abstractos es actualmente la herramienta más utilizada para caracterizar la justificación de argumentos derrotables en Inteligencia Artificial. Las justificaciones se determinan en base a los ataques entre argumentos y se formalizan a través de semánticas de extensiones. Aquí sostenemos que, o bien algunos marcos argumentativos carecen de sentido bajo ciertas concepciones de ataque específicas, o bien las semánticas más usadas en la literatura, basadas en el concepto de defensa conocido como admisibilidad, no resultan adecuadas para (...) justificar, en particular, argumentos para la toma de decisiones.The abstract argumentation frameworks model is currently the most used tool for characterizing the justification of defeasible arguments in Artificial Intelligence. Justifications are determined on a given attack relation among arguments and are formalized as extension semantics. In this work we argue that, contrariwise to the assumptions in that model, either some argumentation frameworks are meaningless under certain concrete definitions of the attack relation, or some of the most used extension semantics in the literature, based on the defense notion of admissibility, are not suitable in particular for the justification of arguments for decision making. (shrink)

The view that abstracta cannot exert causal power is pretty common in metaphysics. According to Friedell (2020), however, this view is mistaken. In a recent paper in this journal, he has argued that at least some abstracta are causally efficacious. My goal in what follows is to demonstrate that, given certain plausible methodological assumptions, Friedell 2020’s argument is not as strong as it might at first seem.

Much attention has been given to the question of ontic vagueness, and the issues usually center around whether certain paradigmatically concrete entities – cats, clouds, mountains, etc. – are vague in the sense of having indeterminate spatial boundaries. In this paper, however, I wish to focus on a way in which some abstracta seem to be locationally vague. To begin, I will briefly cover some territory already covered regarding certain types of “traditional” abstracta and the ways they are (...) currently alleged to be vague. I then wish to discuss two types of “nontraditional” abstracta and the sense in which I think some of these objects are locationally vague. I will next reexamine some of the traditional abstracta and discuss whether any of these objects are locationally vague in the novel way suggested for the nontraditional sorts. I’ll finish by discussing objections, and conclude with some remarks about characterizing the abstract/concrete distinction. (shrink)

En este artículo me propongo abordar el problema del tiempo en las sociedades contemporáneas desde un diálogo entre las construcciones teóricas de Moishe Postone y Hartmut Rosa y el trabajo de Michel Foucault. Los dos primeros se han centrado en explicar cómo la temporalidad se ha convertido en un tipo de dominación abstracta, impersonal y cuasiobjetiva a partir de conceptos como la densificación temporal, la aceleración o la hibridación. Foucault, en cambio, concibe el tiempo bajo el prisma de la (...) racionalidad política neoliberal, por la cual el tiempo pasa a ser un recurso que debe gestionarse por los sujetos en términos empresariales y que termina por configurar una ética neoliberal de la administración del tiempo. Este diálogo ejemplifica de manera privilegiada la tensión entre la coacción o la presión temporal y la administración estratégica del tiempo propia de las sociedades contemporáneas. (shrink)

Many mathematicians are platonists: they believe that the axioms of mathematics are true because they express the structure of a nonspatiotemporal, mind independent, realm. But platonism is plagued by a philosophical worry: it is unclear how we could have knowledge of an abstract, realm, unclear how nonspatiotemporal objects could causally affect our spatiotemporal cognitive faculties. Here I aim to make room in our metaphysical picture of the world for the causal relevance of abstracta.

I argue that thoughts and concepts are mental representations rather than abstracta. I propose that the most important difference between the two views is that the mentalist believes that there are concept and thought tokens as well as types; this reveals that the dispute is not terminological but ontological. I proceed to offer an argument for mentalism. The key step is to establish that concepts and thoughts have lexical as well as semantic properties. I then show that this entails (...) that concepts and thoughts are susceptible to the type/token distinction. I finish by considering some objections to the argument. (shrink)

I argue that thoughts and concepts are mental representations rather than abstracta. I propose that the most important difference between the two views is that the mentalist believes that there are concept and thought tokens as well as types; this reveals that the dispute is not terminological but ontological. I proceed to offer an argument for mentalism. The key step is to establish that concepts and thoughts have lexical as well as semantic properties. I then show that this entails (...) that concepts and thoughts are susceptible to the type/token distinction. I finish by considering some objections to the argument. (shrink)

In this paper, I present a polar concept argument for the existence of abstract objects. After recalling the fundamentals concerning the debate about the existence of abstracta, I present in a detailed way the argument for the existence of abstracta. I offer two different variations of the argument: one, deductive and the other, inductive. The argument rests primarily on the fact that our universe is well-balanced. This well-balanced property results from the fact that all instantiable polar dualities are (...) instantiated. Hence, the abstract pole of the abstract/concrete duality must also be exemplified. Lastly, I review several objections that can be raised against this latter argument. (shrink)

Hierarchical structures are rapidly and flexibly built up in the domains of human language and music. These domains require a tree-building capacity – “dendrophilia” – to dynamically infer hierarchical structures from sensory input, based on subunits stored in a lexicon. This dynamic process involves a crucial class of abstracta overlooked in the target article.

Benjamin Callard has recently suggested that causation between Platonic objects—standardly understood as atemporal and non-spatial—and spatio-temporal objects is not ‘a priori’ unintelligible. He considers the reasons some have given for its purported unintelligibility: apparent impossibility of energy transference, absence of physical contact, etc. He suggests that these considerations fail to rule out a priori Platonic-object causation. However, he has overlooked one important issue. Platonic objects must causally affect different objects differently, and different Platonic objects must causally affect the same objects (...) differently. How are Platonic objects—ones outside space and time—supposed to do that? CiteULike Connotea Del.icio.us What's this? (shrink)

One common attitude toward abstract objects is a kind of platonism: a view on which those objects are mind-independent and causally inert. But there's an epistemological problem here: given any naturalistically respectable understanding of how our minds work, we can't be in any sort of contact with mind-independent, causally inert objects. So platonists, in order to avoid skepticism, tend to endorse epistemological theories on which knowledge is easy, in the sense that it requires no such contact—appeals to Boghossian’s notion of (...) epistemic analyticity are particularly common here, as are appeals to some broadly pragmatic account of the good standing of basic beliefs. I argue, though, that these appeals are hopeless: an argument adapted from the Benacerraf–Field challenge shows that, even if some such theory can deliver the verdict that our beliefs about abstract objects have some prima facie good standing, this good standing will inevitably be defeated. (shrink)

La critique du nihilisme par Lowe est soumise à une évaluation. Le nihilisme semble impliquer un engagement à l'existence d'entités abstraites et Lowe utilise le principe de dépendance (PD) — les abstraits dépendent des concrets — pour bloquer la référence à des entités abstraites : les nombres sont dits dépendre de concrets. On défendra l'idée que cette forme de fictionnalisme n'est pas innocente et que nous devons sérieusement envisager l'alternative que constitue le platonisme. On défendra une forme de platonisme, le (...) platonisme particularisé. En conclusion on proposera de renoncer au PD. (shrink)

La critique du nihilisme par Lowe est soumise à une évaluation. Le nihilisme semble impliquer un engagement à l'existence d'entités abstraites et Lowe utilise le principe de dépendance (PD) — les abstraits dépendent des concrets — pour bloquer la référence à des entités abstraites : les nombres sont dits dépendre de concrets. On défendra l'idée que cette forme de fictionnalisme n'est pas innocente et que nous devons sérieusement envisager l'alternative que constitue le platonisme. On défendra une forme de platonisme, le (...) platonisme particularisé. En conclusion on proposera de renoncer au PD. (shrink)

This paper takes a fresh look at Kant’s transcendental idealism with a new reading of negative noumena as abstract entities. It shows that the three criteria for abstractness, i.e., non-spatiotemporality, causal inefficacy, and non-indiscernibility, are true of Kant’s negative noumena. Phenomena, by contrast, are concrete entities in space and time, which can be understood as spatiotemporally instantiated noumena. Kant’s distinction between noumena in the positive and negative sense will be reinterpreted as a distinction between non-spatiotemporally instantiated concrete entities and uninstantiated (...) abstract entities. It argues that noumenal ignorance is confined to positive noumena, which can be identified with things in themselves. (shrink)

ABSTRACTAccording to Yablo, in uttering sentences that imply the existence of abstract objects, we do not assert their literal content. Instead, we only make a weaker conditional claim that does not have the controversial implication. In this commentary I argue that the conditional claims Yablo suggests we are making are true only if abstract objects exist and, thus, also carry the controversial implication.

Dedekind used to refer to Riemann as his main model concerning mathematical methodology, particularly regarding the use of abstract notions as a basis for mathematical theories. So, in passages written in 1876 and 1895 he compared his approach to ideal theory with Riemann’s theory of complex functions. In this paper, I try to make sense of those declarations, showing the role of abstract notions in Riemann’s function theory, its influence on Dedekind, and the importance of the methodological principle of avoiding (...) ‘forms of representation’ in shaping ideal theory. In order to emphasize the abstract viewpoint of Riemann and Dedekind, I compare their work with that of their great german contemporaries, Weierstrass and Kronecker; so, an influential ‘Göttingen group’ is confronted with the ‘Berlin school’ of mathematics. Some light is also thrown on the relation between Riemann and Dedekind, particularly with respect to Dedekind’s interest on Riemann’s ideas --in function theory, geometry and topology--, beginning in the 1850s and through later works. The abstract approach of the ‘Göttingen group’ was determinant for the turn to abstract mathematics in our century, and the direct influence of Riemann on Dedekind shows how this approach developed. (shrink)

This work aims to reveal as an ungrounded prejudice the widespread notion according to which Max Horkheimer has a purely negative and pessimistic view regarding technical progress. We will show that Horkheimer conceives the birth of modern technique as inseparable from the bourgeois emancipation process. Horkheimer understands that the technique loses its emancipatory potential, becoming an instrument for the perpetuation of an oppressive system once the bourgeoisie stablishes itself as a ruling class. However, that same instrument allows Horkheimer to glimpse (...) a true possibility of social transformation. (shrink)

El presente trabajo investiga las tesis sobre el poder civil de Alonso de la Veracruz que buscan incorporar en la comunidad política española a los habitantes autóctonos del Nuevo Mundo, tesis que suelen relacionarse con F. de Vitoria y el tomismo español, y que últimamente son consideradas parte del republicanismo novohispano elaborado desde la periferia americana. Se busca demostrar que su propósito era aplicar una teoría de derechos naturales, sin que ello implique participación política de los indios americanos. Se analiza (...) la postura del fraile frente a la diversidad cultural y la guerra contra los indios. The paper explores Alonso de la Veracruz's theses on civil power, which sought to integrate the native inhabitants of the New World into the Spanish political community. These theses, which have usually been associated with F. de Vitoria and Spanish Thomism, have recently come to be considered part of a Novohispanic republicanism developed in the American periphery. The article seeks to show that the purpose of such theses was to apply a theory of natural rights that did not entail the political participation of the indigenous population, as well as to analyze Veracruz's position regarding cultural diversity and the war against the indigenous peoples. (shrink)

In this reply I defend Kripke’s creationist thesis for mythical objects against Jeffrey Goodman’s counter-argument to the thesis, 35–40, 2014). I argue that Goodman has mistaken the basis for when mythical abstracta are created. Contrary to Goodman I show that, as well as how, Kripke’s theory consistently retains the analogy between creation of mythical objects and creation of fictional objects, while also explaining in what way they differ.

ABSTRACT This essay has three goals. The first is to introduce the notion of fundamentality and to argue that physicalism can usefully be conceived of as a thesis about fundamentality. The second is to argue for the advantages of fundamentality physicalism over modal formulations and that fundamentality physicalism is what many who endorse modal formulations of physicalism had in mind all along. Third, I describe what I take to be the main obstacle for a fundamentality-oriented formulation of physicalism: ‘the problem (...) of abstracta’, which asks how physical can accommodate phenomena such as mathematics and universals, and which modal formulations do not face. I canvas three solutions: the inapt for ground solution, the concrete restriction, and the contingency restriction. (shrink)