Ante Rem Structuralism And The No-Naming Constraint, 2016 Old Dominion University

#### 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.

A New Interpretation Of Carnap's Logical Pluralism, 2016 Old Dominion University

#### 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 …

Restall's Proof-Theoretic Pluralism And Relevance Logic, 2016 Old Dominion University

#### 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 …

What Do We Mean By Logical Consequence?, 2016 University of Puget Sound

#### What Do We Mean By Logical Consequence?, Jesse Endo Jenks

*Summer Research*

In the beginning of the 20th century, many prominent logicians and mathematicians, such as Frege, Russell, Hilbert, and many others, felt that mathematics needed a very rigorous foundation in logic. Many results of the time were motivated by questions about logical truth and logical consequence. The standard approach in the early part of the 20th century was to use a syntactic or proof-theoretic definition of logical consequence. This says that "for one sentence to be a logical consequence of [a set of premises] is simply for that sentence to be derivable from [them] by means of some standard system of …

The Philosophy Of Mathematics: A Study Of Indispensability And Inconsistency, 2016 Scripps College

#### 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 …

Vol 7 No 1 Contents Page, 2015 San Jose State University

Vol 7 No 1 Information Page, 2015 San Jose State University

Vol 7 No 1 Cover Page, 2015 San Jose State University

Why Brilliant People Believe Nonsense: A Practical Text For Critical And Creative Thinking, 2015 Kennesaw State University

#### 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 …

How Does “Collaboration” Occur At All? Remarks On Epistemological Issues Related To Understanding / Working With ‘The Other’, 2015 Northern Michigan University

#### How Does “Collaboration” Occur At All? Remarks On Epistemological Issues Related To Understanding / Working With ‘The Other’, Don Faust, Judith Puncochar

*Conference Presentations*

Collaboration, if to occur successfully at all, needs to be based on careful representation *and communication *of each stakeholder’s knowledge. In this paper, we investigate, from a foundational logical and epistemological point of view, how such representation and communication can be accomplished. What we tentatively conclude, based on a careful delineation of the logical technicalities necessarily involved in such representation and communication, is that *a complete representation is not possible. *This inference, if correct, is of course rather discouraging with regard to what we can hope to achieve in the knowledge representations that we bring to our collaborations. We suggest …

Book Review: How To Bake Pi: An Edible Exploration Of The Mathematics Of Mathematics, 2015 Gettysburg College

#### Book Review: How To Bake Pi: An Edible Exploration Of The Mathematics Of Mathematics, Darren B. Glass

*Math Faculty Publications*

If you think about it, mathematics is really just one big analogy. For one example, the very concept of the number three is an drawing an analogy between a pile with three rocks, a collection of three books, and a plate with three carrots on it. For another, the idea of a group is drawing an analogy between adding real numbers, multiplying matrices, and many other mathematical structures. So much of what we do as mathematicians involves abstracting concrete things, and what is abstraction other than a big analogy? [*excerpt*]

The Square Of Opposition: Innovations In Teaching Logic, 2015 uri

#### The Square Of Opposition: Innovations In Teaching Logic, Marc R. Dimartino

*Senior Honors Projects*

Teaching classical logic can often be challenging, especially when working with students who lack any prior experience with the more technical aspects of critical thinking. The abstraction of statements into logical symbols and the implementation of various diagramming methods can be enough to frustrate novice logicians, leading to a lack of hope and sometimes failure of mastery. The unique difficulties in teaching classical logic can, in addition, exacerbate tricky pedagogical issues that arise on a day to day basis in the critical thinking classroom. For example, it can be challenging to convey complex information in a meaningful way when dealing …

Thriving, Not Just Surviving, On Food Stamps, 2015 University of Rhode Island

#### Thriving, Not Just Surviving, On Food Stamps, Sam L. Mccaughey

*Senior Honors Projects*

Food insecurity has been a persistent element in the history of the United States. Efforts to address the problem - and the larger issue of poverty - have been wide-ranging, but the debate about how best to respond to hunger has often centered on the relative roles of government and charity. Often that debate has led to hybrid solutions that combine government sponsored welfare such as food stamps and community-based food relief programs such as food banks. Yet, even such complementary approaches leave many people’s needs unmet, and there remains a significant population, both across the country and in Rhode …

A Formalization Of Topical Logic, 2015 Touro College

#### A Formalization Of Topical Logic, Aharon Grenadir

*School for Lifelong Education Publications*

The author discusses the history of topical logic.

On Pi Day, A Serving Of Why We Need Math, 2015 Gettysburg College

#### On Pi Day, A Serving Of Why We Need Math, Darren B. Glass

*Math Faculty Publications*

Today, our Facebook feeds will be peppered with references to Pi Day, a day of celebration that has long been acknowledged by math fans and that Congress recognized in 2009. Every high schooler learns that pi is the ratio of the circumference of a circle to its diameter and that its decimal expansion begins 3.14 and goes on infinitely without repeating. [*excerpt*]

Denying Antecedents And Affirming Consequents: The State Of The Art, 2015 Old Dominion University

#### 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 …

A Reply To Heathcote's "On The Exhaustion Of Mathematical Entities By Structures", 2015 Old Dominion University

#### 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.

Philosophy Of Mathematics: Theories And Defense, 2015 University of Akron Main Campus

#### Philosophy Of Mathematics: Theories And Defense, Amy E. Maffit

*Williams Honors College, Honors Research Projects*

In this paper I discuss six philosophical theories of mathematics including logicism, intuitionism, formalism, platonism, structuralism, and moderate realism. I also discuss problems that arise within these theories and attempts to solve them. Finally, I attempt to harmonize the best features of moderate realism and structuralism, presenting a theory that I take to best describe current mathematical practice.

An Argument For A Neutral Free Logic, 2015 Wayne State University

#### An Argument For A Neutral Free Logic, Daniel Yeakel

*Wayne State University Dissertations*

I argue for a neutral free logic is a logic wherein sentences containing non-referring terms do not have truth value. The primary support for this conclusion comes by way of criticism of the alternatives. If every sentence of the form `a = a' is a logical truth and is consequently knowable a priori then it will follow absurdly that `a exists' is knowable a priori. There are several alternatives for avoiding this intolerable conclusion and I argue that, with the exception of neutral free logic which holds that `a = a' can lack truth value, their successes are not sufficient …

Forall X: An Introduction To Formal Logic 1.30, 2014 University at Albany, State University of New York

#### Forall X: An Introduction To Formal Logic 1.30, P.D. Magnus

*Philosophy Faculty Books*

In formal logic, sentences and arguments in English are translated into mathematical languages with well-defined properties. If all goes well, properties of the argument that were hard to discern become clearer. This book covers translation, formal semantics, and proof theory for both sentential logic and quantified logic. Each chapter contains practice exercises; solutions to selected exercises appear in an appendix.