Frontiers Of Conditional Logic, 2019 The Graduate Center, City University of New York

#### 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, 2019 University of Alaska Fairbanks

#### 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”, 2019 Paderborn University

#### 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, 2019 University of St Andrews

#### 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 **Mu**̄**la-madhyamaka-**k**ā**rik**ā**. **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 ...*

Rampant Non-Factualism: A Metaphysical Framework And Its Treatment Of Vagueness, 2018 Boise State University

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

*Alexander Jackson*

Computing, Modelling, And Scientific Practice: Foundational Analyses And Limitations, 2018 The University of Western Ontario

#### 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, 2018 College of the Holy Cross

#### 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, 2018 independent scholar

#### 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, 2018 Lafayette College

#### 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, 2018 Texas A&M University School of Law

#### 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, 2018 Fordham University

#### 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, 2018 Bowdoin College

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

*Honors Projects*

No abstract provided.

Classical Logic, 2018 Old Dominion University

#### 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, 2018 Lafayette College

#### 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, 2018 Lafayette College

#### 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.

Everyone Knows That Someone Knows: Quantifiers Over Epistemic Agents, 2018 Vassar College

#### Everyone Knows That Someone Knows: Quantifiers Over Epistemic Agents, Pavel Naumov, Jia Tao

*Faculty Research and Reports*

Modal logic S5 is commonly viewed as an epistemic logic that captures the most basic properties of knowledge. Kripke proved a completeness theorem for the first-order modal logic S5 with respect to a possible worlds semantics. A multiagent version of the propositional S5 as well as a version of the propositional S5 that describes properties of distributed knowledge in multiagent systems has also been previously studied. This article proposes a version of S5-like epistemic logic of distributed knowledge with quantifiers ranging over the set of agents, and proves its soundness and completeness with respect to a Kripke semantics.

The Logic Of Internal Relations, 2018 Bard College

#### The Logic Of Internal Relations, Jake S. Cardillo

*Senior Projects Spring 2018*

Senior Project submitted to The Division of Social Studies of Bard College.

Fictionalism, Semantics, And Ontology, 2018 Sacred Heart University

#### Fictionalism, Semantics, And Ontology, Gordon Purves

*Philosophy, Theology and Religious Studies Faculty Publications*

This article expands upon the argument of a previous work which defended a variational account of scientific fictions. Specifically, I show that this understanding of scientific fictions can provide guidance for realist interpretations of scientific theories and models. Depending on a model's variational properties, different ontological commitments are appropriate, providing a principled way for a realist to moderate her views according to the structural properties of a given model. This reasoning is then applied the Lee-Yang theory and Kubo-Martin-Schwinger statistics, two foundational models in quantum statistical mechanics. The Lee-Yang theory is analyzed in a way that permits a robust ...

Quantification And Paradox, 2018 University of Massachusetts Amherst

#### Quantification And Paradox, Edward Ferrier

*Doctoral Dissertations*

I argue that absolutism, the view that absolutely unrestricted quantification is possible, is to blame for both the paradoxes that arise in naive set theory and variants of these paradoxes that arise in plural logic and in semantics. The solution is restrictivism, the view that absolutely unrestricted quantification is not possible.

It is generally thought that absolutism is true and that restrictivism is not only false, but inexpressible. As a result, the paradoxes are blamed, not on illicit quantification, but on the ``logical'' conception of *set* which motivates naive set theory. The accepted solution is to replace this with the ...

The Fraïssé Construction, 2017 Wesleyan University