Logic and Foundations of Mathematics Commons^™

Reflections On Williamson On Logic And Validity, Graham Priest

Publications and Research

Over many years now, Tim Williamson and I have engaged in debates over fundamental issues concerning logic. On some things, we have disagreed strongly; on others, we have agreed.

Networking For Mid-Level Administrators In Higher Education: Increase Job Performance And Reduce Burnout, Laura Glasbrenner

All-Inclusive List of Electronic Theses and Dissertations

Mid-level administrators occupy a complex position within higher education institutions, a role defined by “middleness” (Gleeson & Shain, 1999, p. 488), which characterizes their place in institutional hierarchies between superiors and subordinates. Mid-level administrators often feel isolated since they cannot be seen as having close personal relationships with those above or below them in the rankings. Consequently, mid-level administrators are subject to burnout, a psychological condition resulting from isolation compounded by working long hours reconciling the competing and conflicting needs of supervisors and subordinates, which leaves them emotionally exhausted, physically depleted, and feeling like they have reached a professional dead-end. …

Adolescent Well-Being And Exclusionary Discipline: A Resiliency Model, Rachel Ballard

All-Inclusive List of Electronic Theses and Dissertations

Adolescents, especially those with a mental illness, often behave in ways judged to be impulsive, overly emotional, and irresponsible (Gogtay et al., 2004; Lawrence et al., 2015; Tamnes et al., 2010). Many teen behaviors which concern adults can be related to underdeveloped skills or competencies, rate of brain development, or expressions of mental disorders (Casey et al., 2011; Serbin et al., 2011; Spear, 2000). Behaviors commonly associated with adolescence, such as impulsivity, risk-taking, and efforts to fit in with peers, are often seen as a serious threat to school harmony, learning, and student safety, necessitating a disciplinary response from school …

The Hidden Quality Cost Resulting From Food And Drug Administration Inspection Failures In Mid To Large Companies, Jonathan Walston

All-Inclusive List of Electronic Theses and Dissertations

An approach to identify and validate hidden quality costs associated with regulatory non-compliance from inspections by the Food and Drug Administration (FDA) has not been previously researched. This dissertation presents a robust quantitative methodology to analyze the daily cumulative abnormal returns (CAR) on populations of publicly traded mid-to-large cap companies around FDA inspection events having negative outcomes. Three hypotheses have been tested focusing only on inspection events from companies falling under the biologics product type category. Hypothesis 1 states that there is no statistically significant correlation between the sum of CAR around inspection windows for such companies when a negative …

The Relationship Between Principal Perceptions On Leadership And Inclusive Education With Growth Model Outcomes For Students With Disabilities, Jason Bletzinger

All-Inclusive List of Electronic Theses and Dissertations

Now more than ever, school principals play a critical role in effective implementation of inclusive education programs in their schools, as inclusive practices are becoming tightly embedded in a school’s culture (Sailor, 2016; Shogren et al., 2015). The success of inclusive education programs has been primarily supported by school principals’ positive attitudes toward inclusion (Romanuck Murphy, 2018; Urton et al., 2014). With increasing pressure to provide legally compliant and quality inclusive special education services in schools, it has become more critical than ever that school principals not only recognize the roles and responsibilities they play in leading inclusive education programs …

Deontics And Time In Contracts: An Executable Semantics For The L4 Dsl, Seng Joe Watt, Oliver Goodenough, Meng Weng (Huang Mingrong) Wong

Research Collection Yong Pung How School Of Law

Existing approaches to modelling contracts often rely on deontic logic to reason about norms, and only treat time qualitatively. Using L4, a textual domain specific language (DSL) for the law, we offer a more operational interpretation of norms, based on states and transitions, that also accounts for the granular timing of events. In this paper, we present a higher-level rendering of the loan agreement from Flood & Goodenough in L4, and an accompanying operational semantics amenable to execution and static analysis. We also implement this semantics in Maude and show how this lets us visualize the execution of the loan …

Japanese-English Translation: Miki Kiyoshi —Thinking With Master Nishida (First Published In Fujin Kōron, August 1941) Complete Draft; Translated, Edited, And Revised By Christopher Southward, October 2022-September 2023 「西田先生のことども」、三木清著（初発 婦人公論、昭和十六年八月）, Christopher Southward

Comparative Literature Faculty and Student Scholarship

Japanese-English Translation: Miki Kiyoshi —Thinking with Master Nishida (First Published in Fujin Kōron, August 1941) Complete Draft; Translated, Edited, and Revised by Christopher Southward, October 2022-September 2023「西田先生のことども」、三木清著（初発 婦人公論、昭和十六年八月）

Source text transcribed and published by Aozora Bunko–a compendium of public-domain Japanese literature, philosophy, and criticism

General website: https://www.aozora.gr.jp

Current text: https://www.aozora.gr.jp/cards/000218/files/50538_37481.html

Tarski And Bachmann In Regina: A Magical Connection, James T. Smith

Journal of Humanistic Mathematics

This is a personal account of an intersection of the schools of research in foundations of geometry founded by Alfred Tarski and Friedrich Bachmann. Their academic lineages and the origins of the schools are also described, as well as the mathematics that resulted from this intersection.

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, 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, Abdelghani Alnahawi

Masters Theses

material investigations becoming questions with interjections

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, 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, 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, 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, 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

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

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

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

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

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

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

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

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

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, 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, 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, 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 …

Patrick Aidan Heelan’S The Observable: Heisenberg’S Philosophy Of Quantum Mechanics, Paul Downes

Research Resources

The publication of Patrick Aidan Heelan’s The Observable, with forewords from Michel Bitbol, editor Babette Babich and the author himself, offers a timely invitation to reconsider the relation between quantum physics and continental philosophy.

Patrick Heelan does so, as a contemporary of and interlocutor with Werner Heisenberg on these issues, as a physicist himself who trained with leading figures of quantum mechanics (QM), Erwin Schrödinger and Eugene Wigner. Moreover, Heelan highlights Heisenberg’s interest in phenomenology as ‘a friend and frequent visitor of Martin Heidegger’ (55). Written originally in 1970 and unpublished then for reasons Babich explicates in her foreword, …

Diagrams In Intra-Configurational Analysis, Marco Panza, Gianluca Longa

MPP Published Research

In this paper we would like to attempt to shed some light on the way in which diagrams enter into the practice of ancient Greek geometrical analysis. To this end, we will first distinguish two main forms of this practice, i.e., trans-configurational and intra-configurational. We will then argue that, while in the former diagrams enter in the proof essentially in the same way (mutatis mutandis) they enter in canonical synthetic demonstrations, in the latter, they take part in the analytic argument in a specific way, which has no correlation in other aspects of classical geometry. In intra-configurational analysis, diagrams represent …