Logic and Foundations of Mathematics Commons^™

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, 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, 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, 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, Colin Mccormack

Parnassus: Classical Journal

No abstract provided.

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, 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, 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, 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, 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?, 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 ...

Engaging The Paradoxical: Zeno's Paradoxes In Three Works Of Interactive Fiction, Michael Z. Spivey

Journal of Humanistic Mathematics

For over two millennia thinkers have wrestled with Zeno's paradoxes on space, time, motion, and the nature of infinity. In this article we compare and contrast representations of Zeno's paradoxes in three works of interactive fiction, Beyond Zork, The Chinese Room, and A Beauty Cold and Austere. Each of these works incorporates one of Zeno's paradoxes as part of a puzzle that the player must solve in order to advance and ultimately complete the story. As such, the reader must engage more deeply with the paradoxes than he or she would in a static work of fiction ...

The Rhetorical Structure Of Modus Tollens: An Exploration In Logic-Mining, Andrew Potter

Proceedings of the Society for Computation in Linguistics

A general method for mining discourse for occurrences of the rules of inference would be useful in a variety of natural language processing applications. The method described here has its roots in Rhetorical Structure Theory (RST). An RST analysis of a rule of inference can be used as an exemplar to produce a relational complex in the form of a nested relational proposition. This relational complex can be transformed into a logical expression using the logic of relational propositions. The expression can then be generalized as a logical signature for use in logic-mining discourse for instances of the rule. Generalized ...

Logic, Thought, And Language In Hegel, Marx, And Rosenzweig, Omar Moreno

Open Access Theses & Dissertations

The objective of this Thesis is to open a conversation regarding the role of grammar in two areas of philosophy: interpretation and normative philosophy. The task is divided into three chapters, each of which focuses on one major issue. The first is a demonstration of the use of grammar in understanding and interpreting works of philosophy, namely those of Hegel and Marx. The second chapter is an interpretation of Franz Rosenzweig's renovated grammar as seen in The Star of Redemption. The last uses an analysis of grammar to challenge the role of empirical knowledge in community building. The last ...

Pluralistic Perspectives On Logic: An Introduction, Colin R. Caret, Teresa Kouri Kissel

Philosophy Faculty Publications

(First paragraph) Logical pluralism is the view that there are distinct, but equally good logics. Recent years have witnessed a sharp upswing of interest in this view, resulting in an impressive literature. We only expect this trend to continue in the future. More than one commentator has, however, expressed exasperation at the view: what can it mean to be a pluralist about logic of all things? [see, e.g., Eklund (2017); Goddu (2002); Keefe (2014)]. In this introduction, we aim to set out the basic pluralist position, identify some issues over which pluralists disagree amongst themselves, and highlight the topics ...

The Logic Of Being: An Evaluation Of Arguments For God's Existence, Joshua D. Vaughn

Georgia Undergraduate Research Conference (GURC)

The existence of God and the scholarly debates concerning it have dominated Western philosophy for roughly a millennia and a half with no verifiable conclusions being reached. Rather than throwing another “logical” justification for the existence of higher powers into the ring, the research and analysis I have undertaken concerns itself with the premise that there is no logical argument for the existence of God that will satisfy the debate. This dismissal is accompanied by an in-depth deconstruction of the work of Kurt Gödel, a logician and mathematician credited with the publication of the Incompleteness Theorems. The use of the ...

A Groundwork For A Logic Of Objects, David Winters

Electronic Thesis and Dissertation Repository

The history of philosophy is rich with theories about objects; theories of object kinds, their nature, the status of their existence, etc. In recent years philosophical logicians have attempted to formalize some of these theories, yielding many fruitful results. My thesis intends to add to this tradition in philosophical logic by developing a second-order logical system that may serve as a groundwork for a multitude of theories of objects (e.g. concrete and abstract objects, impossible objects, fictional objects, and others). Through the addition of what we may call sortal quantifiers (i.e. quantifiers that bind individual variables ranging over ...

Maths Living In Social Arenas, From Practice To Foundations, Nigel Vinckier

Journal of Humanistic Mathematics

Maths comes to life in human interaction. This has consequences for the mathematics itself. This paper discusses how this ``coming to life'' of mathematics in different social arenas influences the foundations of maths. We will argue that this influence is profound, to the extent that it is hard to upkeep the idea that there is or should be one foundation on which all mathematics can be built.

The Poetic Function Of Imagination: The Parallel Process Of Poiêsis, Angela Carlson

Expressive Therapies Capstone Theses

In the advent of Postmodernism, modern approaches to understanding the nature of things is being put into question. As the gap between objective and subjective realms of experiences is narrowing, there is an increased need for a more artful approach to science. This paper serves as my attempt to promote the field of Expressive Arts Therapy (ExATh) as a mode of poetic science for understanding the experience of ‘Being’ in the world. Through a critical review of the semantic development of the ancient Greek concepts poiêsis, noêsis, and aisthêsis, the imagination is identified as a function of alêthaic revealing, personified ...

Fatal Attractions, Elective Affinities, And Deadly Epistemologies, Ibpp Editor

International Bulletin of Political Psychology

This article cites film, the novel, and news report to underline the deadly seriousness of the quest for knowledge.