Logic and Foundations of Mathematics Commons^™

Three Essays In Intuitionistic Epistemology, Tudor Protopopescu

Dissertations, Theses, and Capstone Projects

We present three papers studying knowledge and its logic from an intuitionistic viewpoint.

An Arithmetic Interpretation of Intuitionistic Verification

Intuitionistic epistemic logic introduces an epistemic operator to intuitionistic logic which reflects the intended BHK semantics of intuitionism. The fundamental assumption concerning intuitionistic knowledge and belief is that it is the product of verification. The BHK interpretation of intuitionistic logic has a precise formulation in the Logic of Proofs and its arithmetical semantics. We show here that this interpretation can be extended to the notion of verification upon which intuitionistic knowledge is based. This provides the systems of intuitionistic epistemic logic …

The Rhetoric Of Tyranny: Callicles The Rhetor And Nietzsche's Zarathustra, Greg Whitlock

Sophia and Philosophia

Here I will work through the rhetoric of tyranny as practiced by Callicles and as reflected in Nietzsche’s Zarathustra, in particular. In Part 2 it will be shown that Nietzsche’s account of Plato as the complex figure with a Socratic exterior but a latent alternative ego of the tyrant, arrived at an image consistent with E.R. Dodds’ later thesis. Callicles the rhetor, featured as a student of Gorgias, embodies this alter-ego. In Part 3 we find Callicles and Zarathustra shared very similar beliefs once they overcame shame and gained honesty. Indeed, Callicles expounded a number of propositions foundational to …

"Part Of That Force That Always Wills The Evil And Always Produces The Good" On A Devilish Incoherence, Peter Baumann

Sophia and Philosophia

When Mephisto was asked by Faust, "Well now, who are you then?" (“Nun gut, wer bist Du denn?”), he gave the well-known answer, "Part of that force that always wills the evil and always produces the good" (“Ein Teil von jener Kraft, die stets das Böse will und stets das Gute schafft”: Goethe, Faust, 1334-1336). This answer raises some important questions which in turn lead to interesting answers. Let us start by looking at the content of Mephisto's utterance.

The Problem Of Obviousness, Benjamin Goldberg

Sophia and Philosophia

1. The Problem of Obviousness
There’s no such thing as obviousness.

This isn’t, of course, itself obvious; nor is it clear why it should be a problem. So let me start elsewhere, with the anti-vaccine movement. A friend of mine laid out the ‘obvious’ position: there are facts and rationality on one side, unenlightened ignorance and bigotry on the other. Scientists versus fools, and the fools don’t even know what game is being played.

Poetic Justice: Apology Overdue, Stephen Faison

Sophia and Philosophia

Jurors of our republic, I do not know whether you were persuaded by the case made against me, but I certainly hope that you were not. Some of what the prosecutor told you is accurate, though much of it is untrue. To put it another way, some of his facts are correct, yet the conclusions he presented were usually misleading distortions and in some cases simply incorrect. If the indictment is clarified to its essentials, I am accused of corrupting the young and not believing in the gods in whom the city believes. I intend to show that these charges …

‘To Warm Our Hands’, Emmanuel O. Angulo

Sophia and Philosophia

Lovers often die shortly one after the other. Romeo and Juliet. June Carter and Johnny Cash. My grandfather and my grandmother. Leonard Cohen and Marianne Ihlen.

Marianne was the inspiration, most famously, of Cohen’s song “So long, Marianne”, but also of “Bird on the wire” and poems from the collection Flowers for Hitler. Cohen’s last words for her reached her just two days before her death—and a few months before his own. They said: ‘you know that I’ve always loved you for your beauty and your wisdom, but I don't need to say anything more about that because you know …

Cindy, Ken Clatterbaugh

Sophia and Philosophia

Cindy Norton sang loud in slightly accented Spanish. The song was “Perfidia” (“Wicked Woman”). She remembered the melody, and the Spanish language radio reminded her of the lyrics, although she could hardly hear the radio or herself above the grinding, popping, and rattling of her Volkswagen Rabbit. Her radio picked up only one station.

The Descent Of Winter: William Carlos Williams Under The Influence Of Paris, Phillip Barron

Sophia and Philosophia

The Descent of Winter, published in Ezra Pound’s magazine The Exile in 1928, is an uneven experiment in unclassifiable writing. Williams began writing the diaristic entries aboard the SS Pennland “in the fall of 1927. He was returning from Europe, where he had left Florence Williams with their two sons, who were to attend school in Geneva.” (Imaginations, 231) The slim book alternates between spare, image driven poems composed of short lines and diaristic prose. Most entries are titled only with the dates of their composition. In aesthetics, Williams always concerned himself with form. The variety of …

Keats, Truth, And Empathy, Peter Shum

Sophia and Philosophia

At one level, Keats’s sonnet entitled On Peace (1814) is full of philosophical certainties. The speaker believes, for example, that a nation’s people have a right to live in freedom under the rule of law, and that the rule of law should be applicable to everybody. Political and philosophical commitments of this kind do not seem to be called into question in this poem, or made the subject of an enquiry. On the contrary, it is as though we are confronted with somebody who, in certain central thematic respects at least, appears to know his own mind.

Vol 7 No 2 Contents Page

Comparative Philosophy

No abstract provided.

Vol 7 No 2 Information Page

Comparative Philosophy

No abstract provided.

Vol 7 No 2 Cover Page

Comparative Philosophy

No abstract provided.

Clearing Up Calculus With Adaptive Learning Habits, Jennifer Patterson

Honors Theses

No abstract provided.

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, 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 …

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.

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 - …

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 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 …

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 …

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 …

Gronwall’S Inequality And Systems Of Integral Equations, Bradford Garcia

Honors Theses

No abstract provided.

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 …

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.

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, …

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, 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, …

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 …

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 …

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 …