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Articles 1 - 10 of 10
Full-Text Articles in Logic and Foundations of Mathematics
On Probabilistic Reasoning Of Actual Causation, Jingzhi Fang
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, Tom Archibald, Richard T. W. Arthur, Giovanni Ferraro, Jeremy Gray, Douglas Jesseph, Jesper Lützen, Marco Panza, David Rabouin, Gert Schubring
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, Dongwoo Kim
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, Richard Spindler
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, Gregor Nickel
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, Marietta Joleen Watson
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, Caroline Tvardy
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, Ian Ray
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?, Rahmat Rashid
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, Ksenia Tatarchenko, Anya Yermakova, Liesbeth De Mol
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. …