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 ...

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 Theses*

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 ...

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.

Inferring Inferences: Relational Propositions For Argument Mining, 2022 University of North Alabama

#### Inferring Inferences: Relational Propositions For Argument Mining, Andrew Potter

*Proceedings of the Society for Computation in Linguistics*

Inferential reasoning is an essential feature of argumentation. Therefore, a method for mining discourse for inferential structures would be of value for argument analysis and assessment. The logic of relational propositions is a procedure for rendering texts as expressions in propositional logic directly from their rhetorical structures. From rhetorical structures, relational propositions are defined, and from these propositions, logical expressions are then generated. There are, however, unsettled issues associated with Rhetorical Structure Theory (RST), some of which are problematic for inference mining. This paper takes a deep dive into some of these issues, with the aim of elucidating the problems ...

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 ...

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.

Patrick Aidan Heelan’S The Observable: Heisenberg’S Philosophy Of Quantum Mechanics, 2021 Dublin City University

#### 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 ...

Dimentia: Footnotes Of Time, 2021 Bard College

#### Dimentia: Footnotes Of Time, Zachary Hait

*Senior Projects Spring 2021*

Time from the physicist's perspective is not inclusive of our lived experience of time; time from the philosopher's perspective is not mathematically engaged, in fact Henri Bergson asserted explicitly that time could not be mathematically engaged whatsoever. What follows is a mathematical engagement of time that is inclusive of our lived experiences, requiring the tools of storytelling.

Recognizing Mathematics Students As Creative: Mathematical Creativity As Community-Based And Possibility-Expanding, 2020 Boston University

#### Recognizing Mathematics Students As Creative: Mathematical Creativity As Community-Based And Possibility-Expanding, Meghan Riling

*Journal of Humanistic Mathematics*

Although much creativity research has suggested that creativity is influenced by cultural and social factors, these have been minimally explored in the context of mathematics and mathematics learning. This problematically limits who is seen as mathematically creative and who can enter the discipline of mathematics. This paper proposes a framework of creativity that is based in what it means to know or do mathematics and accepts that creativity is something that can be nurtured in all students. Prominent mathematical epistemologies held since the beginning of the twentieth century in the Western mathematics tradition have different implications for promoting creativity in ...

Don’T Be So Fast With The Knife: A Reply To Kapsner, 2020 San Jose State University

#### Don’T Be So Fast With The Knife: A Reply To Kapsner, Graham Priest

*Comparative Philosophy*

*The is a brief reply to the central objection against the construction of my *The Fifth Corner of Four* **by Andi Kapsner in his “Cutting Corners: A Critical Note on Priest’s Five-Valued *Catuṣkoṭi*. This concerns the desirability of adding a fifth corner (ineffability) to the four of the *catuṣkoṭi.

Cutting Corners: A Critical Note On Priest’S Five-Valued Catuṣkoṭi, 2020 San Jose State University

#### Cutting Corners: A Critical Note On Priest’S Five-Valued Catuṣkoṭi, Andreas Kapsner

*Comparative Philosophy*

*Graham Priest has offered a rational reconstruction of Buddhist thought that involves, first, modeling the *Catuṣkoṭi* by a four valued logic, and then later adding a fifth value, read as “ineffability”. This note examines that fifth value and raises some concerns about it that seem grave enough to reject it. It then sketches an alternative to Priest’s account that has no need for the fifth value.*

A Russellian Analysis Of Buddhist Catuskoti, 2020 San Jose State University

#### A Russellian Analysis Of Buddhist Catuskoti, Nicholaos Jones

*Comparative Philosophy*

*Names name, but there are no individuals who are named by names. This is the key to an elegant and ideologically parsimonious strategy for analyzing the Buddhist *catuṣkoṭi*. The strategy is ideologically parsimonious, because it appeals to no analytic resources beyond those of standard predicate logic. The strategy is elegant, because it is, in effect, an application of Bertrand Russell's theory of definite descriptions to Buddhist contexts. The strategy imposes some minor adjustments upon Russell's theory. Attention to familiar *catuṣkoṭi* from Vacchagotta and Nagarjuna as well as more obscure *catuṣkoṭi* from Khema, Zhi Yi, and Fa Zang motivates ...*

Connecting Ancient Philosophers’ Math Theory To Modern Fractal Mathematics, 2020 College of the Holy Cross

#### Connecting Ancient Philosophers’ Math Theory To Modern Fractal Mathematics, Colin Mccormack

*Parnassus: Classical Journal*

No abstract provided.

Between Evidence And Facts: An Argumentative Perspective Of Legal Evidence, 2020 East China University of Political Science and Law, Wenbo Academy

#### Between Evidence And Facts: An Argumentative Perspective Of Legal Evidence, Wenjing Du, Minghui Xiong

*OSSA Conference Archive*

In this paper, we will present an argumentative view of legal evidence. In an argumentation-based litigation game, the only purpose of the suitor (S) or the respondent (R) is to maximize their own legal rights while the purpose of the trier (T) is to maintain judicial fairness and justice. Different selections of evidence and different orders of presenting evidence will lead to different case-facts and even adjudicative results, the purpose of litigation is to reconcile a balance among the three parties - S, R, and T.

Real Possibility: Modality And Responsibility, 2020 University of Connecticut

#### Real Possibility: Modality And Responsibility, Julia Gaul

*Honors Scholar Theses*

Imagine: someone is backing out of a parking space and does not look in their rear view mirror. They subsequently hit a car that was passing by. One could argue that they simply could have avoided the accident had they looked in their mirror. This non-actual possibility, that they could have looked in the mirror, seems legally and morally relevant. One could also argue that they could have avoided the accident had they stuck their feet out of their window and sung *La Marseillaise.*

My leading questions is: how do we distinguish possibilities that are legally and morally relevant from ...

An Evolutionary Approach To Crowdsourcing Mathematics Education, 2020 University of Maine

#### An Evolutionary Approach To Crowdsourcing Mathematics Education, Spencer Ward

*Honors College*

By combining ideas from evolutionary biology, epistemology, and philosophy of mind, this thesis attempts to derive a new kind of crowdsourcing that could better leverage people’s collective creativity. Following a theory of knowledge presented by David Deutsch, it is argued that knowledge develops through evolutionary competition that organically emerges from a creative dialogue of trial and error. It is also argued that this model of knowledge satisfies the properties of Douglas Hofstadter’s strange loops, implying that self-reflection is a core feature of knowledge evolution. This mix of theories then is used to analyze several existing strategies of crowdsourcing ...

The Conceptions Of Self-Evidence In The Finnis Reconstruction Of Natural Law, 2020 Campbell University School of Law

#### The Conceptions Of Self-Evidence In The Finnis Reconstruction Of Natural Law, Kevin P. Lee

*St. Mary's Law Journal*

Finnis claims that his theory proceeds from seven basic principles of practical reason that are self-evidently true. While much has been written about the claim of self-evidence, this article considers it in relation to the rigorous claims of logic and mathematics. It argues that when considered in this light, Finnis equivocates in his use of the concept of self-evidence between the realist Thomistic conception and a purely formal, modern symbolic conception. Given his respect for the modern positivist separation of fact and value, the realism of the Thomistic conception cannot be the foundation for the natural law as Finnis would ...

Logical Pluralism And Vicious Regresses, 2020 The Graduate Center, City University of New York

#### Logical Pluralism And Vicious Regresses, Daniel Boyd

*Dissertations, Theses, and Capstone Projects*

This material in this dissertation will be divided into two parts. The first part is a preliminary discussion of vicious regress arguments in the philosophy of logic in the 20th century. The second part will focus on three different versions of logical pluralism, i.e., the view that there are many correct logics. In each case an argument will be developed to show that these versions of logical pluralism result in a vicious regress.

The material in part one will be divided into three chapters, and there are a few reasons for having a preliminary discussion of vicious regress arguments ...

Are Logic And Math Relevant To Social Debates?, 2020 The Silberman School of Social Work at Hunter College

#### Are Logic And Math Relevant To Social Debates?, Michael A. Lewis

*Journal of Humanistic Mathematics*

Social debates, as well as discussions about certain highly charged issues, such as racism, gender identity, and sexuality, usually turn on the uses or mentions of key words. That is, the conclusions we can draw from such discussions depend on how certain terms are used or mentioned in them. Yet participants in social debates may often fail to precisely define their terms or fail to make important distinctions in terms uttered by others. Both logic and mathematics pay attention to the importance of precise definitions when it comes to engaging in discussions, arguments, or proofs. Logic also makes an important ...