Arts and Humanities Commons^™

“What Line Can’T Be Measured With A Ruler?” Riddles And Concept-Formation In Mathematics And Aesthetics, William H. Brenner, Samuel J. Wheeler

Philosophy Faculty Publications

We analyze two problems in mathematics – the first (stated in our title) is extracted from Wittgenstein’s “Philosophy for Mathematicians”; the second (“What set of numbers is non-denumerable?”) is taken from Cantor. We then consider, by way of comparison, a problem in musical aesthetics concerning a Brahms variation on a theme by Haydn. Our aim is twofold: first, to bring out and elucidate the essentially riddle-like character of these problems; second, to show that the comparison with riddles does not reduce their solution to an exercise in bare subjectivity

Pluralistic Perspectives On Logic: An Introduction, Colin R. Caret, Teresa Kouri Kissel

Philosophy Faculty Publications

(First paragraph) Logical pluralism is the view that there are distinct, but equally good logics. Recent years have witnessed a sharp upswing of interest in this view, resulting in an impressive literature. We only expect this trend to continue in the future. More than one commentator has, however, expressed exasperation at the view: what can it mean to be a pluralist about logic of all things? [see, e.g., Eklund (2017); Goddu (2002); Keefe (2014)]. In this introduction, we aim to set out the basic pluralist position, identify some issues over which pluralists disagree amongst themselves, and highlight the topics at …

Logical Instrumentalism And Concatenation, Teresa Kouri Kissel

Philosophy Faculty Publications

Logical pluralism is the theory that there is more than one right logic. Logical instrumentalism is the view that a logic is a correct logic if it can be used to fruitfully pursue some deductive inquiry. Logical instrumentalism is a version of logical pluralism, since more than one logic can be used fruitfully. In this paper, I will show that a logical instrumentalist must accept linear logic as a correct logic, since linear logic is useful for studying natural language syntax. I further show that this means that the logical instrumentalist must accept a wide range of connectives, in particular …

Susan Stebbing, Teresa Kouri Kissel

Philosophy Faculty Publications

Susan Stebbing (1885-1943) was a founder of Analysis and had a large influence on philosophy during the early 20th century. Recently, the work of Michael Beaney (2000), Siobhan Chapman (2013) and Frederique Janssen- Lauret (2017), amongst others, has begun a resurgence of interest in Stebbing. This paper serves as a brief introduction to some of the major features of her philosophical work.

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”....

Logical Pluralism From A Pragmatic Perspective, Teresa Kouri Kissel

Philosophy Faculty Publications

This paper presents a new view of logical pluralism. This pluralism takes into account how the logical connectives shift, depending on the context in which they occur. Using the Question-Under-Discussion Framework as formulated by Craige Roberts, I identify the contextual factor that is responsible for this shift. I then provide an account of the meanings of the logical connectives which can accommodate this factor. Finally, I suggest that this new pluralism has a certain Carnapian flavour. Questions about the meanings of the connectives or the best logic outside of a specified context are not legitimate questions.

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.

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 …

A Reply To Heathcote's "On The Exhaustion Of Mathematical Entities By Structures", Teresa Kouri

Philosophy Faculty Publications

In this article I respond to Heathcote’s "On the Exhaustion of Mathematical Entities by Structures". I show that his ontic exhaustion issue is not a problem for ante rem structuralists. First, I show that it is unlikely that mathematical objects can occur across structures. Second, I show that the properties that Heathcote suggests are underdetermined by structuralism are not so underdetermined. Finally, I suggest that even if Heathcote’s ontic exhaustion issue if thought of as a problem of reference, the structuralist has a readily available solution.

Denying Antecedents And Affirming Consequents: The State Of The Art, David Godden, Frank Zenker

Philosophy Faculty Publications

Recent work on conditional reasoning argues that denying the antecedent [DA] and affirming the consequent [AC] are defeasible but cogent patterns of argument, either because they are effective, rational, albeit heuristic applications of Bayesian probability, or because they are licensed by the principle of total evidence. Against this, we show that on any prevailing interpretation of indicative conditionals the premises of DA and AC arguments do not license their conclusions without additional assumptions. The cogency of DA and AC inferences rather depends on contingent factors extrinsic to, and independent of, what is asserted by DA and AC arguments. © David …

Philosophy Of Mathematics In The Twentieth Century: Selected Essays, Stewart Shapiro, Teresa Kouri Kissel

Philosophy Faculty Publications

No abstract provided.

A Logistic Approximation To The Cumulative Normal Distribution, Shannon R. Bowling, Mohammad T. Khasawneh, Sittichai Kaewkuekool, Byung R. Cho

Engineering Management & Systems Engineering Faculty Publications

This paper develops a logistic approximation to the cumulative normal distribution. Although the literature contains a vast collection of approximate functions for the normal distribution, they are very complicated, not very accurate, or valid for only a limited range. This paper proposes an enhanced approximate function. When comparing the proposed function to other approximations studied in the literature, it can be observed that the proposed logistic approximation has a simpler functional form and that it gives higher accuracy, with the maximum error of less than 0.00014 for the entire range. This is, to the best of the authors’ knowledge, the …