A Belief Expressionist Explanation of Divine Conceptualist Mathematics

Metaphysica ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
David M. Freeman

Abstract Many have pointed out that the utility of mathematical objects is somewhat disconnected from their ontological status. For example, one might argue that arithmetic is useful whether or not numbers exist. We explore this phenomenon in the context of Divine Conceptualism (DC), which claims that mathematical objects exist as thoughts in the divine mind. While not arguing against DC claims, we argue that DC claims can lead to epistemological uncertainty regarding the ontological status of mathematical objects. This weakens DC attempts to explain the utility of mathematical objects on the basis of their existence. To address this weakness, we propose an appeal to Liggins’ theory of Belief Expressionism (BE). Indeed, we point out that BE is amenable to the ontological claims of DC while also explaining the utility of mathematical objects apart from reliance upon their existence. We illustrate these themes via a case study of Peano Arithmetic.

Vivarium ◽  
2016 ◽  
Vol 54 (2-3) ◽  
pp. 204-249
Author(s):  
Helen Hattab

René Descartes is neither a Conceptualist nor a Platonist when it comes to the ontological status of the eternal truths and essences of mathematics but articulates a view derived from Proclus. There are several advantages to interpreting Descartes’ texts in light of Proclus’ view of universals and philosophy of mathematics. Key passages that, on standard readings, are in conflict are reconciled if we read Descartes as appropriating Proclus’ threefold distinction among universals. Specifically, passages that appear to commit Descartes to a Platonist view of mathematical objects and the truths that follow from them are no longer in tension with the Conceptualist view of universals implied by his treatment of the eternal truths in the Principles of Philosophy. This interpretation also fits the historical evidence and explains why Descartes ends up with seemingly inconsistent commitments to divine simplicity and God’s efficient creation of truths that are not merely conceptually distinct from the divine essence.


Author(s):  
Mirco Sambrotta

The aim of this paper is to explore the possibility that, at least, some metaphysical debates are ‘metalinguistic negotiations’ (to employ a recent term coined by David Plunkett and Timothy Sundell). I will take the dispute between the dominant approaches of realism and the anti-realism ones (especially Fictionalism) about the ontological status of scientific models as a case-study. I will argue that such a debate may be better understood as a disagreement, at bottom normatively, motivated, insofar as a normative and non-factual question may be involved in it: how the relevant piece of language ought to be used. Even though I will generally assess the prospects for a broadly deflationist approach, I shall outline a sense in which the dispute can be recast as ‘minimally substantive’. 


Author(s):  
Anna Wiehl

The hypothesis underlying this article is that new documentary practices potentially enable new forms of mediation allowing all interactors to experience complexity and deal with contingency in a world of polyvocality through multilayered configurations. An exploration of the Korsakow documentary Racing Home (Marianne McMahon and Phil Hoffman, 2014) brings into focus the epistemological and ontological status of these assemblages. A central issue is the question of how significantly specific modes of editing in Korsakow affect the overall experience for both the authoring instances and for the user-interactor: not only the authorship is shared between the interrelated agents, but also the heterogeneity of materials from various sources adds to the complexity of the assemblages. Central research questions include the role that polyvocality and algorithmic editing play in Korsakow, its specific embracement of contingency and its probing of nonlinear narratives. The answers provided through the analysis of the case study lead to the conclusion that Korsakow is more than just a tool to promote a special purpose and/or a platform to distribute material. Rather, Korsakow is best seen as a methodology to approach complex matters and provide multiple affective and cognitive ways to respond to them.


Author(s):  
John J. Cleary

I examine one aspect of the central role which mathematics plays in Proclus's ontology and epistemology, with particular reference to his Elements of Theology. I focus on his peculiar views about the ontological status of mathematical objects and the special faculties of the soul that are involved in understanding them. If they are merely abstract objects that are "stripped away" from sensible things, then they are unlikely to reorient the mind towards the intelligible realm, as envisioned by Plato in the Republic. Thus, in order to defend the function of mathematics as a prodaideutic to dialectic, Proclus rejects Aristotelian abstractionism in favor of an elaborate account in terms of Nous projecting images of its Forms through the medium of the imagination. In metaphorical terms, he replaces the Aristotelian image of the soul as a blank tablet with that of a tablet that has always been inscribed and is always writing itself, while also being written on by Nous. The mediating function of mathematics for understanding the higher realities is grounded in the fact that its central principles of Limit and Unlimited have a universal provenance in Proclus's whole system of reality.


2021 ◽  
pp. 017084062110354
Author(s):  
William Roth Smith

Recent organizational theorizing contends that loosely structured fluid social collectives may attain degrees of “organizationality” (Dobusch & Schoeneborn, 2015) depending on whether or not they achieve certain organization-like elements. The organizationality approach offers a compelling account for the persistence of fluid social collectives, but the framework could be strengthened by moving beyond language-centered explanations and including into theorizing a plurality of ‘entities’ that differ in ontological status. Based on a case study within the context of a fluid user-built recreation space, this study adopts a relational ontology viewpoint on materiality to show how dynamic aspects of natural elements, expectations, feelings, and the cyclicality of nature can be theorized as material, and thus mattering, to organizing processes. Findings reveal that the degree of durability of these entities is key for understanding interconnected decision making, identity, and ultimately how the fluid collective achieves or degrades organizationality.


2021 ◽  
Vol 2 (1) ◽  
pp. 26-32
Author(s):  
Nia Sutrisna ◽  
Surya Amami Pramuditya ◽  
Jajo Firman Raharjo ◽  
Setiyani Setiyani

This study aims to determine the ability of reflective mathematical abstraction which consists of the ability to apply concepts, the ability to make relationships between concepts to form new meanings, and the ability to manipulate abstract mathematical objects. This research is a qualitative research with type of case study. The sample used in this study was one senior high school student of class X. The method of collecting data to find the results of the study was to use a test instrument for building questions and interviews. These instruments are validated first using Expert Judgment Validation. The results obtained by indicator one and indicator two, student still find it difficult to understand the concept and choose which other concept is suitable to obtain a solution. Meanwhile, on the third indicator student can manipulate abstract mathematical objects. So that the student' mathematical abstraction ability is still quite good.


PARADIGMA ◽  
2020 ◽  
pp. 112-138
Author(s):  
Nehemías Moreno Martínez ◽  
Luis Enrique Hernández Zavala

Se propone una interpretación de la técnica de representación del Mapa Conceptual Híbrido a partir de la extensión a la química escolar de algunos elementos teóricos del Enfoque Ontosemiótico de la Matemática Educativa. Para mostrar la viabilidad de la propuesta, se planteó el objetivo de analizar de manera gráfica, mediante un estudio de casos de carácter descriptivo, el sistema de prácticas implicado en la resolución de un problema químico, por parte de un docente y uno de sus estudiantes, que implicaba el uso del concepto de reactivo limitante. El análisis muestra que, en la resolución del problema, los sujetos se apoyan en objetos químicos como en objetos de tipo químico-matemático, los cuales son conectados y organizados en el sistema de prácticas; el docente llevó a cabo un sistema de prácticas predominantemente interpretativo mientras que el alumno realizó uno mayormente operativo; los sujetos también realizaron cierto conjunto de procesos cognitivos que se encuentran implicados en la producción del conocimiento químico.Palabras clave: Mapa conceptual híbrido, resolución de problemas, reactivo limitante, química escolar, objetos químico-matemáticos.Análise gráfica da resolução de um problema químico de reagente limitanteResumo: É proposta uma interpretação da técnica de representação do Mapa Conceitual Híbrido a partir da extensão à química escolar de alguns elementos teóricos da Abordagem Ontosemiótica à Matemática Educacional. Para mostrar a viabilidade da proposta, o objetivo foi analisar graficamente, por meio de um estudo de caso descritivo, o sistema de prática envolvido na resolução de um problema químico, por um professor e um de seus alunos. , o que implicou na utilização do conceito de reagente limitante. A análise mostra que, para resolver o problema, os sujeitos contam com objetos químicos, bem como objetos químico-matemáticos, que estão conectados e organizados no sistema de prática; o professor realizou um sistema de prática predominantemente interpretativo, enquanto o aluno realizou um sistema predominantemente operacional; os sujeitos também realizaram um determinado conjunto de processos cognitivos que estão envolvidos na produção do conhecimento químico.Palavras-chave: Mapa conceitual híbrido, solução de problemas, reagente limitante, química escolar, objetos químico-matemáticos.Graphical analysis of the resolution of a limiting reagent problemAbstract: An interpretation of the representation technique of the Hybrid Concept Map is proposed from the extension to the school chemistry of some theoretical elements of the Ontosemiotic Approach of Educational Mathematics. In order to show the viability of the proposal, the objective was raised to analyze graphically, through a descriptive case study, the system of practices involved in solving a chemical problem posed in a textual way, by a teacher and one of his students, which involved the use of the concept of limiting reagent. The analysis shows that, in solving the problem, the subjects rely on chemical and chemical-mathematical objects, which are connected and organized in the system of practices; the teacher carried out a predominantly interpretive practice system while the student carried out an operational one; subjects also perform a certain set of cognitive processes that are involved in the production of chemical knowledge.Keywords: Hybrid conceptual map, problem solving, limiting reagent, schoolar chemistry, chemical-mathematical objects.


2014 ◽  
Vol 38 (01) ◽  
pp. 102-129
Author(s):  
ALBERTO MARTÍN ÁLVAREZ ◽  
EUDALD CORTINA ORERO

AbstractUsing interviews with former militants and previously unpublished documents, this article traces the genesis and internal dynamics of the Ejército Revolucionario del Pueblo (People's Revolutionary Army, ERP) in El Salvador during the early years of its existence (1970–6). This period was marked by the inability of the ERP to maintain internal coherence or any consensus on revolutionary strategy, which led to a series of splits and internal fights over control of the organisation. The evidence marshalled in this case study sheds new light on the origins of the armed Salvadorean Left and thus contributes to a wider understanding of the processes of formation and internal dynamics of armed left-wing groups that emerged from the 1960s onwards in Latin America.


2020 ◽  
Vol 43 ◽  
Author(s):  
Michael Lifshitz ◽  
T. M. Luhrmann

Abstract Culture shapes our basic sensory experience of the world. This is particularly striking in the study of religion and psychosis, where we and others have shown that cultural context determines both the structure and content of hallucination-like events. The cultural shaping of hallucinations may provide a rich case-study for linking cultural learning with emerging prediction-based models of perception.


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