Platonism, De Re, And (Philosophy Of) Mathematical Practice,
2023
Chapman University
Platonism, De Re, And (Philosophy Of) Mathematical Practice, Marco Panza
MPP Published Research
The chapter advances a reformulation of the classical problem of the nature of mathematical objects (if any), here called “Plato’s problem,” in line with the program of a philosophy of mathematical practice. It then provides a sketch of a platonist solution, following the same perspective. This solution disregards as nonsensical the question of the existence of abstract, and specifically mathematical, objects, by rather focusing on the modalities of our access to them: objects (in general, both concrete and abstract) are regarded as individual contents that we have (or can have) a de re epistemic access to. The question of the …
Toys As Tools For Good Science,
2023
Singapore Management University
Toys As Tools For Good Science, Joshua Luczak
Research Collection College of Integrative Studies
The primary aim of this paper is to elevate the status of toy models, toy model based reasoning, and to encourage more focused discussions of them. This paper attempts to satisfy this aim by achieving two, secondary goals. First, it attempts elevate the status of toy models by making clear and elaborating on the distinction between them and representational models, and by discussing the connection between user intentionality and scientific representation (i.e. when a model represents something). And second, this paper attempts to elevate the status of toy models by highlighting, through some important historical examples, how they have been …
Moretheless,
2023
Rhode Island School of Design
Moretheless, Abdelghani Alnahawi
Masters Theses
material investigations becoming questions with interjections
Three Essays On Substructural Approaches To Semantic Paradoxes,
2023
CUNY Graduate Center
Three Essays On Substructural Approaches To Semantic Paradoxes, Brian C. Porter
Dissertations, Theses, and Capstone Projects
This thesis consists of three papers on substructural approaches to semantic paradoxes. The first paper introduces a formal system, based on a nontransitive substructural logic, which has exactly the valid and antivalid inferences of classical logic at every level of (meta)inference, but which I argue is still not classical logic. In the second essay, I introduce infinite-premise versions of several semantic paradoxes, and show that noncontractive substructural approaches do not solve these paradoxes. In the third essay, I introduce an infinite metainferential hierarchy of validity curry paradoxes, and argue that providing a uniform solution to the paradoxes in this hierarchy …
Zero, Śūnya And Pūrṇa: A Comparative Analysis,
2023
San Jose State University
Zero, Śūnya And Pūrṇa: A Comparative Analysis, Animisha Tewari
Comparative Philosophy
Due to apparent duality in this world, one has to face a lot of difficulties while searching for the Truth. Our ego is the root cause for perception of duality and this in turn leads to suffering. This suffering can only be extinguished by attainment of the Truth, i.e, non-duality. However, in order to enable the finite intellect to comprehend the incomprehensible non-duality, this undifferentiated whole is sometimes denoted by nothingness (śūnya) or fullness (pūrṇa). Non-duality is usually understood by the numeral ‘1’ which stands for unity or oneness. The main aim of this paper is …
Ineffability, Emptiness And The Aesthetics Of Logic,
2023
San Jose State University
Ineffability, Emptiness And The Aesthetics Of Logic, Andreas Kapsner
Comparative Philosophy
In this essay, I explore the nature of the logical analysis of Buddhist thought that Graham Priest has offered in his book The Fifth Corner of Four (5of4). The paper traces the development of a logical value in- troduced in 5of4, which Priest has called e. The paper points out that certain criticisms I have made earlier still stand, but focuses on a recon- ceptualization of 5of4 in which these arguments carry less weight. This new perspective on the book, inspired by a response to my arguments by Priest himself, sees the logical analysis of Buddhism …
Logic As Applied Mathematics — With Particular Application To The Notion Of Logical Form,
2023
CUNY Graduate Center
Logic As Applied Mathematics — With Particular Application To The Notion Of Logical Form, Graham Priest
Publications and Research
The word ‘logic’ has many senses. Here we will understand it as meaning an account of what follows from what and why. With contemporary methodology, logic in this sense – though it may not always have been thought of in this way – is a branch of applied mathematics. This has various implications for how one understands a number of issues concerning validity. In this paper I will explain this perspective of logic, and explore some of its consequences with respect to the notion of logical form.
On Probabilistic Reasoning Of Actual Causation,
2022
Lingnan University
On Probabilistic Reasoning Of Actual Causation, Jingzhi Fang
Lingnan Theses (MPhil & PhD)
Probabilistic actual causation is a theory about actual causal relations in probabilistic scenarios. Compared with general (or type) causal connections, actual (or token, singular) causation involves specific and actual events occurring in a particular time and space. Halpern and Pearl proposed three mathematical definitions on actual causation via structural equation models (or causal models). Fenton-Glynn extended one of their definitions into a probabilistic version by following the probability-raising principle in the tradition of theorizing about probabilistic causation. The basic idea of this principle is that a cause shall raise the probability of its effect. He adopted interventional probabilities to analyse …
A Question Of Fundamental Methodology: Reply To Mikhail Katz And His Coauthors,
2022
Simon Fraser University
A Question Of Fundamental Methodology: Reply To Mikhail Katz And His Coauthors, Tom Archibald, Richard T. W. Arthur, Giovanni Ferraro, Jeremy Gray, Douglas Jesseph, Jesper Lützen, Marco Panza, David Rabouin, Gert Schubring
Philosophy Faculty Articles and Research
This paper is a response by several historians of mathematics to a series of papers published from 2012 onwards by Mikhail Katz and various co-authors, the latest of which was recently published in the Mathematical Intelligencer, “Two-Track Depictions of Leibniz’s Fictions” (Katz, Kuhlemann, Sherry, Ugaglia, and van Atten, 2021). At issue is a question of fundamental methodology. These authors take for granted that non-standard analysis provides the correct framework for historical interpretation of the calculus, and castigate rival interpretations as having had a deleterious effect on the philosophy, practice, and applications of mathematics. Rather than make this case by reasoned …
Necessity, Essence And Analyticity: Toward An Analytic Essentialist Account Of Necessity,
2022
CUNY Graduate Center
Necessity, Essence And Analyticity: Toward An Analytic Essentialist Account Of Necessity, Dongwoo Kim
Dissertations, Theses, and Capstone Projects
Some truths could not have failed to hold. Such are called metaphysically necessary truths. As Michael Dummett once aptly formulated, the philosophical problem about necessity is twofold: what makes necessary truths necessarily true and how do we recognize them as such? This dissertation aims to address these questions by developing and defending a novel account of necessity, which has the following three main theses: (1) the necessity of a statement about an entity is established as a consequence of a general principle implying that if the entity is a certain way then it is necessarily that way and the fact …
Foundational Mathematical Beliefs And Ethics In Mathematical Practice And Education,
2022
Charles A. Dana Center
Foundational Mathematical Beliefs And Ethics In Mathematical Practice And Education, Richard Spindler
Journal of Humanistic Mathematics
Foundational philosophical beliefs about mathematics in the mathematical community may have an unappreciated yet profound impact on ethics in mathematical practice and mathematics education, which also affects practice. A philosophical and historical basis of the dominant platonic and formalist views of mathematics are described and evaluated, after which an alternative evidence-based foundation for mathematical thought is outlined. The dualistic nature of the platonic view based on intuition is then compared to parallel historical developments of universalizing ethics in Western thought. These background ideas set the stage for a discussion of the impact of traditional mathematical beliefs on ethics in the …
Ethics And Mathematics – Some Observations Fifty Years Later,
2022
University of Siegen
Ethics And Mathematics – Some Observations Fifty Years Later, Gregor Nickel
Journal of Humanistic Mathematics
Almost exactly fifty years ago, Friedrich Kambartel, in his classic essay “Ethics and Mathematics,” did pioneering work in an intellectual environment that almost self-evidently assumed a strict separation of the two fields. In our first section we summarize and discuss that classical paper. The following two sections are devoted to complement and contrast Kambartel’s picture. In particular, the second section is devoted to ethical aspects of the indirect and direct mathematization of modern societies. The final section gives a short categorization of various philosophical positions with respect to the rationality of ethics and the mutual relation between ethics and mathematics.
Narrative Inquiry Of Opt Workers In Manufacturing Engineering Fields,
2022
Indiana State University
Narrative Inquiry Of Opt Workers In Manufacturing Engineering Fields, Marietta Joleen Watson
All-Inclusive List of Electronic Theses and Dissertations
Optional Practical Training (OPT) is a highly valued and highly underutilized program designed to offer international students an opportunity to work in the U.S. and train in their field of study. This qualitative study collected and analyzed the narratives of three alumni of a Midwest university who completed OPT in the manufacturing engineering field. Four themes were identified in the narratives. These themes were inextricable to the premise that OPT is a deeply appreciated opportunity for F-1 students. The first theme is viewing the OPT experience as a system which includes the university, USCIS, and the employer and moreover a …
Unknowable Truths: The Incompleteness Theorems And The Rise Of Modernism,
2022
Belmont University
Unknowable Truths: The Incompleteness Theorems And The Rise Of Modernism, Caroline Tvardy
Honors Scholars Collaborative Projects
This thesis evaluates the function of the current history of mathematics methodologies and explores ways in which historiographical methodologies could be successfully implemented in the field. Traditional approaches to the history of mathematics often lack either an accurate portrayal of the social and cultural influences of the time, or they lack an effective usage of mathematics discussed. This paper applies a holistic methodology in a case study of Kurt Gödel’s influential work in logic during the Interwar period and the parallel rise of intellectual modernism. In doing so, the proofs for Gödel’s Completeness and Incompleteness theorems will be discussed as …
Semantic Completeness Of Intuitionistic Predicate Logic In A Fully Constructive Meta-Theory,
2022
Western Kentucky University
Semantic Completeness Of Intuitionistic Predicate Logic In A Fully Constructive Meta-Theory, Ian Ray
Masters Theses & Specialist Projects
A constructive proof of the semantic completeness of intuitionistic predicate logic is explored using set-generated complete Heyting Algebra. We work in a constructive set theory that avoids impredicative axioms; for this reason the result is not only intuitionistic but fully constructive. We provide background that makes the thesis accessible to the uninitiated.
Why Are They Called Real Numbers If They Aren’T Real, And Other Such Questions?,
2022
Rollins College
Why Are They Called Real Numbers If They Aren’T Real, And Other Such Questions?, Rahmat Rashid
Honors Program Theses
This thesis studies the position of mathematical realism (the position that mathematical objects have ontological status) through history, starting with Pythagoras up until W.V.O Quine, and examining how these positions originate from each other. I hope to see how the position has changed and why, and provide an argument against the strongest of the realist positions, drawing on this extensive background. Finally, I advance my own argument against the strongest arguments for mathematical realism, and propose alternatives to a view of mathematical realism.
Russian Logics And The Culture Of Impossible: Part Ii: Reinterpreting Algorithmic Rationality,
2022
Singapore Management University
Russian Logics And The Culture Of Impossible: Part Ii: Reinterpreting Algorithmic Rationality, Ksenia Tatarchenko, Anya Yermakova, Liesbeth De Mol
Research Collection School of Social Sciences
This article reinterprets algorithmic rationality by looking at the interaction between mathematical logic, mechanized reasoning, and, later, computing in the Russian Imperial and Soviet contexts to offer a history of the algorithm as a mathematical object bridging the inner and outer worlds, a humanistic vision that we, following logician Vladimir Uspensky, call the “culture of the impossible.” We unfold the deep roots of this vision as embodied in scientific intelligentsia. In Part I, we examine continuities between the turn-of-the-twentieth-century discussions of poznaniye—an epistemic orientation towards the process of knowledge acquisition—and the postwar rise of the Soviet school of mathematical logic. …
Organizational Culture: An Examination Of The Role Of Leadership In Neutralizing The Negative Effects Of Technostress During Operational Shifts,
2021
Indiana State University
Organizational Culture: An Examination Of The Role Of Leadership In Neutralizing The Negative Effects Of Technostress During Operational Shifts, David P. Kirkland
All-Inclusive List of Electronic Theses and Dissertations
COVID-19 created a support problem for public universities across the United States and required that IT departments and professionals alter how they performed in 2020, and perhaps beyond. IT professionals tasked with safeguarding large amounts of data were required to shift to a teleworking posture to continue offering a similar level of service as previously expected. In addition to the technological shift that organizations experienced because of COVID-19, leadership challenges also impacted IT departments across the United States. The rapid shift of operational duties has the propensity to increase technology-related stress, due to employee perception of being successful in their …
Assessing Risk At The National Strategic Level: Visualization Tools For Military Planners,
2021
US Army War College
Assessing Risk At The National Strategic Level: Visualization Tools For Military Planners, Wade A. Germann, Heather S. Gregg
The US Army War College Quarterly: Parameters
The reemergence of great power competition, conflict with near-peer competitor states below the level of armed conflict, and persisting threats from nonstate actors with transnational ambitions and global reach pose challenges for strategists planning, executing, and assessing military operations and strategy. Building on current visualization tools, two proposed models—the National Strategic Risk Abacus and the National Strategic Risk Radar Chart—address these challenges and better depict how the US military may inadvertently contribute to risk at the national strategic level.
The Agnostic Structure Of Data Science Methods,
2021
Chapman University
The Agnostic Structure Of Data Science Methods, Domenico Napoletani, Marco Panza, Daniele Struppa
MPP Published Research
In this paper we argue that data science is a coherent and novel approach to empirical problems that, in its most general form, does not build understanding about phenomena. Within the new type of mathematization at work in data science, mathematical methods are not selected because of any relevance for a problem at hand; mathematical methods are applied to a specific problem only by `forcing’, i.e. on the basis of their ability to reorganize the data for further analysis and the intrinsic richness of their mathematical structure. In particular, we argue that deep learning neural networks are best understood within …
