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 ...
Mathematical Practice And Human Cognition, 2016 Indiana University  Purdue University Fort Wayne
Mathematical Practice And Human Cognition, Bernd Buldt
Philosophy Faculty Presentations
Frank Quinn (of JaffeQuinn fame, see [1]) worked out the basics of his own account of mathematical practice, an account that is informed by an analysis of contemporary mathematics and its pedagogy (see [2]). Taking this account as our starting point, we can characterize the current mathematical practice to acquire and work with new concepts as a cognitive adaptation strategy that, first, emerged to meet the challenges posed by the growing abstractness of its objects and which, second, proceeds according to the following threepronged approach:

(i) sever as many ties to ordinary language as possible and limit ordinary language explanations ...
On Fixed Points, Diagonalization, And SelfReference, 2016 Indiana University  Purdue University Fort Wayne
On Fixed Points, Diagonalization, And SelfReference, Bernd Buldt
Philosophy Faculty Presentations
We clarify the respective role fixed points, diagonalization, and self reference play in proofs of G ̈odel’s first incompleteness theorem. We first show that the usual fixedpoint construction can be reduced to a double diagonalization; this is done to address widely held views such as that fixedpoint are “paradoxical” (Priest), or work by “black magic” (Soare), or that their construction is “intuitively unclear” (Kotlarski). We then discuss three notions of selfreference; this can be seen an extension of a recent study by Halbach and Visser and is meant to show that we do not (yet?) have a robust theory ...
Mathematical Practice And Human Cognition, 2016 Indiana University  Purdue University Fort Wayne
Mathematical Practice And Human Cognition, Bernd Buldt
Philosophy Faculty Presentations
Frank Quinn (of JaffeQuinn fame, see [1]) worked out the basics of his own account of mathematical practice, an account that is informed by an analysis of contemporary mathematics and its pedagogy (see [2]). Taking this account as our starting point, we can characterize the current mathematical practice to acquire and work with new concepts as a cognitive adaptation strategy that, first, emerged to meet the challenges posed by the growing abstractness of its objects and which, second, proceeds according to the following threepronged approach:

(i) sever as many ties to ordinary language as possible and limit ordinary language explanations ...
Rampant NonFactualism: A Metaphysical Framework And Its Treatment Of Vagueness, 2016 Boise State University
Rampant NonFactualism: A Metaphysical Framework And Its Treatment Of Vagueness, Alexander Jackson
Alexander Jackson
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 SelfReference, 2016 Indiana University  Purdue University Fort Wayne
On Fixed Points, Diagonalization, And SelfReference, 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 OrdinaryLanguage Conditional, 2016 Graduate Center, City University of New York
The C3 Conditional: A Variably Strict OrdinaryLanguage Conditional, Monique L. Whitaker
All Graduate Works by Year: Dissertations, Theses, and Capstone Projects
In this dissertation I provide a novel logic of the ordinarylanguage 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 ...
Pascal And Fermat: Religion, Probability, And Other Mathematical Discoveries, 2016 Skidmore College
Pascal And Fermat: Religion, Probability, And Other Mathematical Discoveries, Adrienne E. Lazes
Master of Arts in Liberal Studies (MALS) Student Scholarship
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 ...
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 ...
WabiSabi Mathematics, 2016 Université du Québec à Montréal
WabiSabi Mathematics, JeanFrancois 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 wabisabi values imperfections, temporality, incompleteness, earthly crudeness, and even contradiction. In this paper, I discuss the possibilities of “wabisabi mathematics” by showing (1) how wabisabi mathematics is conceivable; (2) how wabisabi mathematics is observable; and (3) why we should bother about wabisabi 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