Logic and Foundations of Mathematics Commons^™

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.

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 …

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 …

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 …

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 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, …

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, 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, 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 …

Abstraction And Epistemic Economy, Marco Panza

MPP Published Research

Most of the arguments usually appealed to in order to support the view that some abstraction principles are analytic depend on ascribing to them some sort of existential parsimony or ontological neutrality, whereas the opposite arguments, aiming to deny this view, contend this ascription. As a result, other virtues that these principles might have are often overlooked. Among them, there is an epistemic virtue which I take these principles to have, when regarded in the appropriate settings, and which I suggest to call ‘epistemic economy’. My purpose is to isolate and clarify this notion by appealing to some examples concerning …

Restall's Proof-Theoretic Pluralism And Relevance Logic, Teresa Kouri

Philosophy Faculty Publications

Restall (Erkenntnis 79(2):279–291, 2014) proposes a new, proof-theoretic, logical pluralism. This is in contrast to the model-theoretic pluralism he and Beall proposed in Beall and Restall (Aust J Philos 78(4):475–493, 2000) and in Beall and Restall (Logical pluralism, Oxford University Press, Oxford, 2006). What I will show is that Restall has not described the conditions on being admissible to the proof-theoretic logical pluralism in such a way that relevance logic is one of the admissible logics. Though relevance logic is not hard to add formally, one critical component of Restall’s pluralism is that the relevance logic that gets added must …

A New Interpretation Of Carnap's Logical Pluralism, Teresa Kouri

Philosophy Faculty Publications

Rudolf Carnap’s logical pluralism is often held to be one in which corresponding connectives in different logics have different meanings. This paper presents an alternative view of Carnap’s position, in which connectives can and do share their meaning in some (though not all) contexts. This re-interpretation depends crucially on extending Carnap’s linguistic framework system to include meta-linguistic frameworks, those frameworks which we use to talk about linguistic frameworks. I provide an example that shows how this is possible, and give some textual evidence that Carnap would agree with this interpretation. Additionally, I show how this interpretation puts the Carnapian position …

Ante Rem Structuralism And The No-Naming Constraint, Teresa Kouri

Philosophy Faculty Publications

Tim Räz has presented what he takes to be a new objection to Stewart Shapiro's ante rem structuralism (ARS). Räz claims that ARS conflicts with mathematical practice. I will explain why this is similar to an old problem, posed originally by John Burgess in 1999 and Jukka Keränen in 2001, and show that Shapiro can use the solution to the original problem in Räz's case. Additionally, I will suggest that Räz's proposed treatment of the situation does not provide an argument for the in re over the ante rem approach.

The Philosophy Of Mathematics: A Study Of Indispensability And Inconsistency, Hannah C. Thornhill

Scripps Senior Theses

This thesis examines possible philosophies to account for the practice of mathematics, exploring the metaphysical, ontological, and epistemological outcomes of each possible theory. Through a study of the two most probable ideas, mathematical platonism and fictionalism, I focus on the compelling argument for platonism given by an appeal to the sciences. The Indispensability Argument establishes the power of explanation seen in the relationship between mathematics and empirical science. Cases of this explanatory power illustrate how we might have reason to believe in the existence of mathematical entities present within our best scientific theories. The second half of this discussion surveys …

The Varieties Of Indispensability Arguments, Marco Panza, Andrea Sereni

MPP Published Research

The indispensability argument (IA) comes in many different versions that all reduce to a general valid schema. Providing a sound IA amounts to providing a full interpretation of the schema according to which all its premises are true. Hence, arguing whether IA is sound results in wondering whether the schema admits such an interpretation. We discuss in full details all the parameters on which the specification of the general schema may depend. In doing this, we consider how different versions of IA can be obtained, also through different specifications of the notion of indispensability. We then distinguish between schematic and …

Vol 7 No 1 Contents Page

Comparative Philosophy

No abstract provided.

Vol 7 No 1 Information Page

Comparative Philosophy

No abstract provided.

Vol 7 No 1 Cover Page

Comparative Philosophy

No abstract provided.

Why Brilliant People Believe Nonsense: A Practical Text For Critical And Creative Thinking, J. Steve Miller, Cherie K. Miller

2015 Faculty Bookshelf

The information explosion has made us information rich, but wisdom poor. Yet, to succeed in business and in life, we must distinguish accurate from bogus sources, and draw valid conclusions from mounds of data. This book, written for a general adult audience as well as students, takes a new look at critical thinking in the information age, helping readers to not only see through nonsense, but to create a better future with innovative thinking.

Readers should see the practicality of enhancing skills that make them more innovative and employable, especially in a day when companies increasingly seek original thinkers, global …