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Articles 1 - 7 of 7
Full-Text Articles in Logic and Foundations of Mathematics
Ante Rem Structuralism And The No-Naming Constraint, Teresa Kouri
Ante Rem Structuralism And The No-Naming Constraint, Teresa Kouri
Philosophy Faculty Publications
Tim Räz has presented what he takes to be a new objection to Stewart Shapiro's ante rem structuralism (ARS). Räz claims that ARS conflicts with mathematical practice. I will explain why this is similar to an old problem, posed originally by John Burgess in 1999 and Jukka Keränen in 2001, and show that Shapiro can use the solution to the original problem in Räz's case. Additionally, I will suggest that Räz's proposed treatment of the situation does not provide an argument for the in re over the ante rem approach.
Philosophy Of Mathematics: Theories And Defense, Amy E. Maffit
Philosophy Of Mathematics: Theories And Defense, Amy E. Maffit
Williams Honors College, Honors Research Projects
In this paper I discuss six philosophical theories of mathematics including logicism, intuitionism, formalism, platonism, structuralism, and moderate realism. I also discuss problems that arise within these theories and attempts to solve them. Finally, I attempt to harmonize the best features of moderate realism and structuralism, presenting a theory that I take to best describe current mathematical practice.
Philosophy Of Mathematics In The Twentieth Century: Selected Essays, Stewart Shapiro, Teresa Kouri Kissel
Philosophy Of Mathematics In The Twentieth Century: Selected Essays, Stewart Shapiro, Teresa Kouri Kissel
Philosophy Faculty Publications
No abstract provided.
Anti-Foundational Categorical Structuralism, Darren Mcdonald
Anti-Foundational Categorical Structuralism, Darren Mcdonald
Electronic Thesis and Dissertation Repository
The aim of this dissertation is to outline and defend the view here dubbed “anti-foundational categorical structuralism” (henceforth AFCS). The program put forth is intended to provide an answer the question “what is mathematics?”. The answer here on offer adopts the structuralist view of mathematics, in that mathematics is taken to be “the science of structure” expressed in the language of category theory, which is argued to accurately capture the notion of a “structural property”. In characterizing mathematical theorems as both conditional and schematic in form, the program is forced to give up claims to securing the truth of its …
Loss Of Vision: How Mathematics Turned Blind While It Learned To See More Clearly, Bernd Buldt, Dirk Schlimm
Loss Of Vision: How Mathematics Turned Blind While It Learned To See More Clearly, Bernd Buldt, Dirk Schlimm
Bernd Buldt
To discuss the developments of mathematics that have to do with the introduction of new objects, we distinguish between ‘Aristotelian’ and ‘non-Aristotelian’ accounts of abstraction and mathematical ‘top-down’ and ‘bottom-up’ approaches. The development of mathematics from the 19th to the 20th century is then characterized as a move from a ‘bottom-up’ to a ‘top-down’ approach. Since the latter also leads to more abstract objects for which the Aristotelian account of abstraction is not well-suited, this development has also lead to a decrease of visualizations in mathematical practice.
The Biopolitical Unconscious: Not-All Persons Are Political, Ross G. Shields
The Biopolitical Unconscious: Not-All Persons Are Political, Ross G. Shields
Media and Cultural Studies Honors Projects
It is a tenet of post-structuralist theory that discursive series fail in their attempts to constitute themselves as totalities. A system can fail in two distinct ways—from Kant’s dynamic and mathematic failures of reason, to Jacques Lacan’s equation of the two failures of language with the two failures (male and female) of sex. Biopolitical theory offers the most recent account of failure and collapse, now on the geopolitical scale. Given that the biopolitical subject too is sexed, this thesis asks the question: How does biopolitics fail? Franz Kafka’s aborted novels offer a premonition to a possible answer.
Reconstruction Of Concept Of Paradigm In Thomas S. Kuhn, Fernando Estrada
Reconstruction Of Concept Of Paradigm In Thomas S. Kuhn, Fernando Estrada
Fernando Estrada
This article aims to discuss an evaluation of the concept of paradigm of T. Kuhn in his representative work: The Structure of Scientific Revolutions ERC, [Ku96] and the complementary version by W. Stegmüller, Structure and dynamics of theories EDT, [Steg83]. This refined interpretation of the concept of paradigm allows for a more complete set of central Kuhnian concept.