# Logic and Foundations of Mathematics Commons™

## All Articles in Logic and Foundations of Mathematics

374 full-text articles. Page 6 of 12.

The C3 Conditional: A Variably Strict Ordinary-Language Conditional, 2016 Graduate Center, City University of New York

#### The C3 Conditional: A Variably Strict Ordinary-Language Conditional, Monique L. Whitaker

##### Dissertations, Theses, and Capstone Projects

In this dissertation I provide a novel logic of the ordinary-language conditional. First, however, I endeavor to make clearer and more precise just what the objects of the study of the conditional are, as a lack of clarity as to what counts as an instance of a given category of conditional has resulted in deep and significant confusions in subsequent analysis. I motivate for a factual/counterfactual distinction, though not at the level of particular instances of the conditional. Instead, I argue that each individual instance of the conditional may be interpreted either factually or counterfactually, rather than these instances dividing …

Primality Proving Based On Eisenstein Integers, 2016 Union College - Schenectady, NY

#### Primality Proving Based On Eisenstein Integers, Miaoqing Jia

##### Honors Theses

According to the Berrizbeitia theorem, a highly efficient method for certifying the primality of an integer N ≡ 1 (mod 3) can be created based on pseudocubes in the ordinary integers Z. In 2010, Williams and Wooding moved this method into the Eisenstein integers Z[ω] and defined a new term, Eisenstein pseudocubes. By using a precomputed table of Eisenstein pseudocubes, they created a new algorithm in this context to prove primality of integers N ≡ 1 (mod 3) in a shorter period of time. We will look at the Eisenstein pseudocubes and analyze how this new algorithm works with the …

Cantor's Infinity, 2016 Union College - Schenectady, NY

#### Cantor's Infinity, Michael Warrener

##### Honors Theses

At the heart of mathematics is the quest to ﬁnd patterns and order in some set of similar structures, whether these be shapes, functions, or even numbers themselves. In the late 1800’s, there was a strong focus in the mathematical community on the study of real numbers and sequences of real numbers. Mathematicians quickly realized, however, that in order to do any meaningful investigation into the properties of sequences of real numbers, they needed a better deﬁnition of real numbers than the loose intuitions that had been sucient for the generations prior. This led Georg Cantor (March 3, 1845 - …

Reading Between The Lines: Verifying Mathematical Language, 2016 Union College - Schenectady, NY

#### Reading Between The Lines: Verifying Mathematical Language, Tristan Johnson

##### Honors Theses

A great deal of work has been done on automatically generating automated proofs of formal statements. However, these systems tend to focus on logic-oriented statements and tactics as well as generating proofs in formal language. This project examines proofs written in natural language under a more general scope of mathematics. Furthermore, rather than attempting to generate natural language proofs for the purpose of solving problems, we automatically verify human-written proofs in natural language. To accomplish this, elements of discourse parsing, semantic interpretation, and application of an automated theorem prover are implemented.

The Polysemy Of ‘Fallacy’—Or ‘Bias’, For That Matter, 2016 Lund University

#### The Polysemy Of ‘Fallacy’—Or ‘Bias’, For That Matter, Frank Zenker

##### OSSA Conference Archive

Starting with a brief overview of current usages (Sect. 2), this paper offers some constituents of a use-based analysis of ‘fallacy’, listing 16 conditions that have, for the most part implicitly, been discussed in the literature (Sect. 3). Our thesis is that at least three related conceptions of ‘fallacy’ can be identified. The 16 conditions thus serve to “carve out” a semantic core and to distinguish three core-specifications. As our discussion suggests, these specifications can be related to three normative positions in the philosophy of human reasoning: the meliorist, the apologist, and the panglossian (Sect. 4). Seeking to make these …

Compassion, Authority And Baby Talk: Prosody And Objectivity, 2016 Trent University

#### Compassion, Authority And Baby Talk: Prosody And Objectivity, Leo Groarke, Gabrijela Kišiček

##### OSSA Conference Archive

Recent work on multimodal argumentation has explored facets of argumentation which have no obvious analogue in the written arguments which were emphasized in traditional accounts of argument. One of these facets is prosody: the structure and quality of the sound of spoken language. Prosodic features include pitch, temporal structure, pronunciation, loudness and voice quality, rhythm, emphasis and accent. In this paper, we explore the ways that prosodic features may be invoked in arguing.

The Logic Of Concessive Statements, 2016 Touro College

#### The Logic Of Concessive Statements, Aharon Grenadir

##### School for Lifelong Education Publications

Concessive statements appear frequently in everyday reasoning. They are one of the eleven types of statement mentioned in the Ramchal‟s Sefer Derech Tevunos. In addition, in Talmudic discussions, every statement has a presupposition (hava-amina) and a conclusion (ka mashma lan). This goal of this research is to organize the categorizations of concessive statements that are stated in the technical literature. Using the distintinction in lomdus between dechiyah (overriding a law) and hutrah (removal of a law), a novel categorization can be added, according to the type of denial of the expectation by the main clause. That is the subject of …

2016 Skidmore College

#### Pascal And Fermat: Religion, Probability, And Other Mathematical Discoveries, Adrienne E. Lazes

##### MALS Final Projects, 1995-2019

This final project primarily discusses how Blaise Pascal and Pierre de Fermat, two French seventeenth century mathematicians, founded the field of mathematical Probability and how this area continued to evolve after their contributions. Also included in this project is an analysis of how Pascal and Fermat were affected, or not, in their mathematical work by the widespread impact that the Catholic Church had on life in France during this time period. I further discuss two other central discoveries by these theorists: Pascal’s Triangle and Fermat’s Last Theorem. Lastly, the project analyzes how all of these aspects: the influence of the …

Avatars Of Oneself, 2016 Duquesne University

#### Avatars Of Oneself, Patrick L. Miller

##### Sophia and Philosophia

Zoe is an American woman who has found that “drawing the line and standing firm has always made me feel like a bitch, and, actually, I feel that people saw me as one too.”[3] For two years, however, she played an online role-playing game using a male character where “as a man I was liberated from all that.” She made mistakes in her unfamiliar role, but learned from them. “I got better at being firm but not rigid,” she says; “I practiced, safe from criticism.” Case is an American man, who plays a similar game but always appears as a …

Xanthippe To Her Mother, 2016 Belmont University

#### Xanthippe To Her Mother, Ginger Osborn

##### Sophia and Philosophia

The following is a translation of an ancient manuscript, presumably a late-Hellenistic school exercise, recovered from the so-called Villa of the Papyri in Herculaneum, which was entombed by the eruption of Vesuvius in 79 BCE. The library was well-stocked with philosophical works, mostly of an Epicurean bent, but with a variety of other traditions represented as well. The text below is the result of the editorial work and translation of the Italo-Brtitish philosophical eccentric Michael Tommasi, completed presumably in Cambridge in the 1940s, but never published; his literary executors discovered the manuscript among his posthumous papers. Several revisions to Tommasi's …

Jane Austen Meets The Gps: Place And Space, 2016 Bates College

#### Jane Austen Meets The Gps: Place And Space, David Kolb

##### Sophia and Philosophia

When one reads Jane Austen’s novels, one finds that her heroines’ lives center around a beloved and comfortable home, in a local region including a small town, some neighboring estates, and local hills and valleys. It is a detailed and textured home area of nearby places reachable on foot or horse. One to three miles are walkable to a friend’s house or a favorite scenic hill. Beyond this region is no longer “home.” Fifteen or twenty-five miles can be distant.

2016 Elon College

#### Empty Souls: Confession And Forgiveness In Hegel And Dostoevsky, Ryan Johnson

##### Sophia and Philosophia

“Towards the end of a sultry afternoon early in July a young man came out of his little room in Stolyarny Lane and turned and in the direction of Kameny Bridge in central St. Petersburg.”[1] Right then, this young man, a former law student named Rodion Raskolnikov, is caught in an agonizing conversation with himself over whether or not to commit the ultimate crime: to murder an innocent person. Exasperated, wondering what to do with such a weighty decision, he cried aloud, “that’s why I don’t act, because I am always talking. Or perhaps I talk so much just because …

Nietzsche And Heraclitus: Notes On Stars Without An Atmosphere, 2016 National Hellenic Research Foundation

#### Nietzsche And Heraclitus: Notes On Stars Without An Atmosphere, Niketas Siniossoglou

##### Sophia and Philosophia

I awake estranged from everyone. Words have lost their meaning; they sound indifferent and homonymous. The word No appears to mean Yes, or rather: Yes and No are malleable, ephemeral, and transparent. A decades-old or perhaps centuries-old movement of miry clay has resulted in a miscarriage of words. Iinquire whether anyone still holds the resources needed for a direct, sincere affirmation of life—a Yes that is definitively and essentially affirmative—or a No that is definitively and essentially negative—words bursting forth splendour like a crystal. I am told that formulations of this sort are incomprehensible; they are too metaphorical and, …

Nietzsche's Views On Plato Pre-Basel, 2016 Belmont University

#### Nietzsche's Views On Plato Pre-Basel, Daniel Blue

##### Sophia and Philosophia

In an essay published in 2004[1] Thomas Brobjer surveyed Nietzsche’s attitudes toward Plato and argued that, far from entering into a dedicated agon with that philosopher, he had little personal engagement with Plato’s views at all. Certainly, he did not grapple so immediately and fruitfully with him as he did with Emerson, Schopenhauer, Lange, and even Socrates. Instead, he merely “set up a caricature of Plato as a representative of the metaphysical tradition … to which he opposed his own.”[2] This hardly reflects the view of Nietzsche scholarship in general, but Brobjer argued his case vigorously by ranging broadly over …

2016 Belmont University

#### On The Relationship Of Alcibiades’ Speech To The Rest Of The Speeches In Plato’S Symposium[1], Andy Davis

##### Sophia and Philosophia

To get to the point immediately concerning how I think about the relationship between the first five speeches and Socrates’ speech: it seems to me the claim that Plato has only brought together inadequate perspectives on Eros in order to present Socrates’ speech over and against them as the only correct one is completely in error. Socrates himself does not deny these speeches their accolades, he comes back to many things in them as he assigns each single perspective its own due place. Much more, I believe that from the first speech to the last a decisive progress takes place, …

Kirkos, 2016 Eureka College

#### Kirkos, Prabhu Venkatarama

##### Sophia and Philosophia

Yesterday morning I received a newspaper clipping that changed the course of my life. It arrived in a small grey envelope, my mother’s Cyrillic handwriting on the front instantly recognizable by its beautiful loops and arches. I was expecting it; my mother had told me it was in the mail. The clipping was of an obituary, that of Robert Mascas, a younger cousin of mine who’d lived in my former hometown of Kirkos. He had turned eighteen three months ago, precisely seven years to the day after I had. The obituary didn’t mention what my mother had on the phone, …

Review Of Swimming Home, By Vincent Katz, 2016 Woodland Community College

#### Review Of Swimming Home, By Vincent Katz, Phillip Barron

##### Sophia and Philosophia

After a reading in San Francisco, I asked Katz about the significance of using the term “poetry” repeatedly throughout “Sidewalk Poem.” He answered, “poetry is about making, as much as any hand skill like carpentry or welding, but the craft of poetry is not respected.” For Charles Reznikoff and Federico Garcia Lorca, walking the streets of New York was integral to the act of writing poetry. The craft of poetry contains not only those moments when pen smears ink on paper or keyboard presses pixel on screen. Making poetry is more sensuous and active than the still, quiet moments that …

Toward A Kripkean Concept Of Number, 2016 Graduate Center, City University of New York

#### Toward A Kripkean Concept Of Number, Oliver R. Marshall

##### Dissertations, Theses, and Capstone Projects

Saul Kripke once remarked to me that natural numbers cannot be posits inferred from their indispensability to science, since we’ve always had them. This left me wondering whether numbers are objects of Russellian acquaintance, or accessible by analysis, being implied by known general principles about how to reason correctly, or both. To answer this question, I discuss some recent (and not so recent) work on our concepts of number and of particular numbers, by leading psychologists and philosophers. Special attention is paid to Kripke’s theory that numbers possess structural features of the numerical systems that stand for them, and to …

Wabi-Sabi Mathematics, 2016 Université du Québec à Montréal

#### Wabi-Sabi Mathematics, Jean-Francois Maheux

##### Journal of Humanistic Mathematics

Mathematics and aesthetics have a long history in common. In this relation however, the aesthetic dimension of mathematics largely refers to concepts such as purity, absoluteness, symmetry, and so on. In stark contrast to such a nexus of ideas, the Japanese aesthetic of wabi-sabi values imperfections, temporality, incompleteness, earthly crudeness, and even contradiction. In this paper, I discuss the possibilities of “wabi-sabi mathematics” by showing (1) how wabi-sabi mathematics is conceivable; (2) how wabi-sabi mathematics is observable; and (3) why we should bother about wabi-sabi mathematics

Explanatory Proofs And Beautiful Proofs, 2016 University of North Carolina at Chapel Hill

#### Explanatory Proofs And Beautiful Proofs, Marc Lange

##### Journal of Humanistic Mathematics

This paper concerns the relation between a proof’s beauty and its explanatory power – that is, its capacity to go beyond proving a given theorem to explaining why that theorem holds. Explanatory power and beauty are among the many virtues that mathematicians value and seek in various proofs, and it is important to come to a better understanding of the relations among these virtues. Mathematical practice has long recognized that certain proofs but not others have explanatory power, and this paper offers an account of what makes a proof explanatory. This account is motivated by a wide range of examples …