Logic and Foundations of Mathematics Commons^™

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, 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.

Frontiers Of Conditional Logic, Yale Weiss

All Dissertations, Theses, and Capstone Projects

Conditional logics were originally developed for the purpose of modeling intuitively correct modes of reasoning involving conditional—especially counterfactual—expressions in natural language. While the debate over the logic of conditionals is as old as propositional logic, it was the development of worlds semantics for modal logic in the past century that catalyzed the rapid maturation of the field. Moreover, like modal logic, conditional logic has subsequently found a wide array of uses, from the traditional (e.g. counterfactuals) to the exotic (e.g. conditional obligation). Despite the close connections between conditional and modal logic, both the technical development and ...

Symmetry And Measuring: Ways To Teach The Foundations Of Mathematics Inspired By Yupiaq Elders, Jerry Lipka, Barbara Adams, Monica Wong, David Koester, Karen Francois

Journal of Humanistic Mathematics

Evident in human prehistory and across immense cultural variation in human activities, symmetry has been perceived and utilized as an integrative and guiding principle. In our long-term collaborative work with Indigenous Knowledge holders, particularly Yupiaq Eskimos of Alaska and Carolinian Islanders in Micronesia, we were struck by the centrality of symmetry and measuring as a comparison-of-quantities, and the practical and conceptual role of qukaq [center] and ayagneq [a place to begin]. They applied fundamental mathematical principles associated with symmetry and measuring in their everyday activities and in making artifacts. Inspired by their example, this paper explores the question: Could symmetry ...

From Solvability To Formal Decidability: Revisiting Hilbert’S “Non-Ignorabimus”, Andrea Reichenberger

Journal of Humanistic Mathematics

The topic of this article is Hilbert’s axiom of solvability, that is, his conviction of the solvability of every mathematical problem by means of a finite number of operations. The question of solvability is commonly identified with the decision problem. Given this identification, there is not the slightest doubt that Hilbert’s conviction was falsified by Gödel’s proof and by the negative results for the decision problem. On the other hand, Gödel’s theorems do offer a solution, albeit a negative one, in the form of an impossibility proof. In this sense, Hilbert’s optimism may still be ...

Recapture, Transparency, Negation And A Logic For The Catuṣkoṭi, Adrian Kreutz

Comparative Philosophy

The recent literature on Nāgārjuna’s catuṣkoṭi centres around Jay Garfield’s (2009) and Graham Priest’s (2010) interpretation. It is an open discussion to what extent their interpretation is an adequate model of the logic for the catuskoti, and the Mūla-madhyamaka-kārikā. Priest and Garfield try to make sense of the contradictions within the catuskoti by appeal to a series of lattices – orderings of truth-values, supposed to model the path to enlightenment. They use Anderson & Belnaps's (1975) framework of First Degree Entailment. Cotnoir (2015) has argued that the lattices of Priest and Garfield cannot ...

Counterfactual Conditional Analysis Using The Centipede Game, Ahmed Bilal

CMC Senior Theses

The Backward Induction strategy for the Centipede Game leads us to a counterfactual reasoning paradox, The Centipede Game paradox. The counterfactual reasoning proving the backward induction strategy for the game appears to rely on the players in the game not choosing that very same backward induction strategy. The paradox is a general paradox that applies to backward induction reasoning in sequential, perfect information games. Therefore, the paradox is not only problematic for the Centipede Game, but it also affects counterfactual reasoning solutions in games similar to the Centipede Game. The Centipede Game is a prime illustration of this paradox in ...

An Introduction To Logic: From Everyday Life To Formal Systems, Albert Mosley, Eulalio Baltazar

Open Educational Resources: Textbooks

An introduction to the discipline of logic covering subjects from the structures of arguments, classical and modern logic, categorical and inductive inferences, to informal fallacies.

• Over 30 years of development provides a sound empirical based pedagogy throughout the text.

• Examples in ordinary language using familiar examples avoids the suggestion of an alien cultural imposition.

• A focus on the basic representational techniques of classical and modern logic.

• Students introduced to basic concepts of set theory, using Venn diagrams to represent statements and evaluate arguments.

• Students introduced to basic concepts of propositional logic and the use of truth-tables.

• Students introduced to basic ...

Rampant Non-Factualism: A Metaphysical Framework And Its Treatment Of Vagueness, Alexander Jackson

Alexander Jackson

Computing, Modelling, And Scientific Practice: Foundational Analyses And Limitations, Filippos A. Papagiannopoulos

Electronic Thesis and Dissertation Repository

This dissertation examines aspects of the interplay between computing and scientific practice. The appropriate foundational framework for such an endeavour is rather real computability than the classical computability theory. This is so because physical sciences, engineering, and applied mathematics mostly employ functions defined in continuous domains. But, contrary to the case of computation over natural numbers, there is no universally accepted framework for real computation; rather, there are two incompatible approaches --computable analysis and BSS model--, both claiming to formalise algorithmic computation and to offer foundations for scientific computing.

The dissertation consists of three parts. In the first part, we ...

The Logical Fallacies In Political Discourse, Zilin Cidre Zhou

Summer Research Program

I examined the use of logical fallacies in political discourse. Logical fallacies are fraudulent tricks people use in their argument to make it sound more credible while what they really do is to fool the audience. Out of more than 300 kinds of fallacies, I focused on 18 common ones by analyzing their use in debates about political issues. During conducting my research, I noted that being aware of my mental state is very important if I want to accurately detect the fallacies. Furthermore, while watching two sides debating, being impartial is as significant as staying calm. I also need ...

Dialetheism, Paradox, And Nāgārjuna’S Way Of Thinking, Richard H. Jones

Comparative Philosophy

Nāgārjuna’s doctrine of emptiness, his ideas on “two truths” and language, and his general method of arguing are presented clearly by him and can be stated without paradox. That the dialetheists today can restate his beliefs in paradoxical ways does not mean that Nāgārjuna argued that way; in fact, their restatements misrepresent and undercut his arguments.

Second-Order Know-How Strategies, Pavel Naumov, Jia Tao

Faculty Research and Reports

The fact that a coalition has a strategy does not mean that the coalition knows what the strategy is. If the coalition knows the strategy, then such a strategy is called a know-how strategy of the coalition. The paper proposes the notion of a second-order know-how strategy for the case when one coalition knows what the strategy of another coalition is. The main technical result is a sound and complete logical system describing the interplay between the distributed knowledge modality and the second-order coalition know-how modality.

Flag-Waving: Visual Arguments, Verbal Reconstruction, And Speaker Intentions, Brian Larson

Brian Larson

Radical Social Ecology As Deep Pragmatism: A Call To The Abolition Of Systemic Dissonance And The Minimization Of Entropic Chaos, Arielle Brender

Student Theses 2015-Present

This paper aims to shed light on the dissonance caused by the superimposition of Dominant Human Systems on Natural Systems. I highlight the synthetic nature of Dominant Human Systems as egoic and linguistic phenomenon manufactured by a mere portion of the human population, which renders them inherently oppressive unto peoples and landscapes whose wisdom were barred from the design process. In pursuing a radical pragmatic approach to mending the simultaneous oppression and destruction of the human being and the earth, I highlight the necessity of minimizing entropic chaos caused by excess energy expenditure, an essential feature of systems that aim ...

Non-Naturalism And Naturalism In Mathematics, Morality, And Epistemology, Nicholas Distefano

Honors Projects

No abstract provided.

Classical Logic, Stewart Shapiro, Teresa Kouri Kissel

Philosophy Faculty Publications

[From introductory section]

Typically, a logic consists of a formal or informal language together with a deductive system and/or a model-theoretic semantics. The language has components that correspond to a part of a natural language like English or Greek. The deductive system is to capture, codify, or simply record arguments that are valid for the given language, and the semantics is to capture, codify, or record the meanings, or truth-conditions for at least part of the language.

The following sections provide the basics of a typical logic, sometimes called “classical elementary logic” or “classical first-order logic”....

Information Flow Under Budget Constraints, Pavel Naumov, Jia Tao

Faculty Research and Reports

Although first proposed in the database theory as properties of functional dependencies between attributes, Armstrong's axioms capture general principles of information flow by describing properties of dependencies between sets of pieces of information. This article generalizes Armstrong's axioms to a setting in which there is a cost associated with information. The proposed logical system captures general principles of dependencies between pieces of information constrained by a given budget.

Strategic Coalitions With Perfect Recall, Pavel Naumov, Jia Tao

Faculty Research and Reports

The paper proposes a bimodal logic that describes an interplay between distributed knowledge modality and coalition know-how modality. Unlike other similar systems, the one proposed here assumes perfect recall by all agents. Perfect recall is captured in the system by a single axiom. The main technical results are the soundness and the completeness theorems for the proposed logical system.