Three Essays In Intuitionistic Epistemology, 2016 The Graduate Center, City University of New York

#### Three Essays In Intuitionistic Epistemology, Tudor Protopopescu

*All Graduate Works by Year: 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 ...

Vol 7 No 2 Contents Page, 2016 San Jose State University

Vol 7 No 2 Information Page, 2016 San Jose State University

Vol 7 No 2 Cover Page, 2016 San Jose State University

On Fixed Points, Diagonalization, And Self-Reference, 2016 Indiana University - Purdue University Fort Wayne

#### On Fixed Points, Diagonalization, And Self-Reference, Bernd Buldt

*Philosophy Faculty Publications*

We clarify the respective roles fixed points, diagonalization, and self- reference play in proofs of Gödel’s first incompleteness theorem.

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

*All Graduate Works by Year: 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 ...

Rampant Non-Factualism: A Metaphysical Framework And Its Treatment Of Vagueness, 2016 Boise State University

#### Rampant Non-Factualism: A Metaphysical Framework And Its Treatment Of Vagueness, Alexander Jackson

*Alexander Jackson*

Rampant non-factualism is the view that all non-fundamental matters are non-factual, in a sense inspired by Kit Fine (2001). The first half of this paper argues that if we take non-factualism seriously for any matters, such as morality, then we should take rampant non-factualism seriously. The second half of the paper argues that rampant non-factualism makes possible an attractive theory of vagueness. We can give non-factualist accounts of non-fundamental matters that nicely characterize the vagueness they manifest (if any). I suggest that such non-factualist theories dissolve philosophical puzzlement about vagueness. In particular, the approach implies that philosophers should not try ...

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

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

*All Graduate Works by Year: 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 ...

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 ...

Theorem Proving In Lean, 2016 Carnegie Mellon University

#### Theorem Proving In Lean, Jeremy Avigad, Leonardo De Moura, Soonho Kong

*Department of Philosophy*

Formal verification involves the use of logical and computational methods to establish claims that are expressed in precise mathematical terms. These can include ordinary mathematical theorems, as well as claims that pieces of hardware or software, network protocols, and mechanical and hybrid systems meet their specifications. In practice, there is not a sharp distinction between verifying a piece of mathematics and verifying the correctness of a system: formal verification requires describing hardware and software systems in mathematical terms, at which point establishing claims as to their correctness becomes a form of theorem proving. Conversely, the proof of a mathematical theorem ...

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 ...

New Test Article Wednesday, 2015 bepress university

#### New Test Article Wednesday, Sid Fifteen

*S. B. Fifteen*

It's The First Article - Uploaded By Author On Sw, 2015 bepress university

#### It's The First Article - Uploaded By Author On Sw, Sid Fifteen

*S. B. Fifteen*

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

Character And Object, 2015 Carnegie Mellon University

#### Character And Object, Rebecca Morris, Jeremy Avigad

*Department of Philosophy*

In 1837, Dirichlet proved that there are infinitely many primes in any arithmetic progression in which the terms do not all share a common factor. Modern presentations of the proof are explicitly higher-order, in that they involve quantifying over and summing over Dirichlet characters, which are certain types of functions. The notion of a character is only implicit in Dirichlet’s original proof, and the subsequent history shows a very gradual transition to the modern mode of presentation.

In this essay, we describe an approach to the philosophy of mathematics in which it is an important task to understand the ...

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 ...

Mathematics And Language, 2015 Carnegie Mellon University

#### Mathematics And Language, Jeremy Avigad

*Department of Philosophy*

This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes that we view mathematics as a system of conventions and norms that is designed to help us make sense of the world and reason efficiently. Like any designed system, it can perform well or poorly, and the philosophy of mathematics has a role to play in helping us understand the general principles by which it serves its purposes well.