POM Contributed Paper Sessions
Logic and Intuition in Everyday Mathematics
Many of us likely believe--and teach--that the role of proof is essential to the practice of pure mathematics. However, history is full of examples that suggest intuition may also play a meaningful role in the development of mathematical knowledge. Furthermore, computers can now supply (or at least verify) many of the logical steps in a mathematical proof, and even generate mathematical conjectures. This raises the question: what roles do logic and intuition play in mathematics? Is logic largely a scheme for demonstrating rigor and “correctness” after intuition has led us to a proposition that we believe to be correct? Or is logic more of an essential companion, informing our intuition and the very way think about our subject matter? This contributed paper session welcomes submissions reflecting on the relative roles of logic and intuition in mathematics, based on the contributor's historical/philosophical scholarship or lived experience as a working mathematician.
Jason Douma, University of Sioux Falls
Tom Morley, Georgia Institute of Technology
|1:00 p.m. - 1:15 p.m.||Chris Oehrlein||Re-Imagining Theorem-and-Proof in a Guided-Inquiry Geometry Course for Future K-8 Teachers. Slides.|
|1:20 p.m. - 1:35 p.m.||Benjamin Gaines||Related Rates and Right Triangles: Developing Intuition in a Calculus Course . Slides.|
|1:40 p.m. - 1:55 p.m.||Raul Rojas-Gonzalez||Developing Mathematical Intuition with a History of Math Course. (cancelled)|
|2:00 p.m. - 2:15 p.m.||Paul Christian Dawkins,||Some Ways of Reasoning Productive for the Logic of Mathematical Reasoning . Slides.|
|Kyeong Hah Roh,|
|Steven Ruiz, and|
|2:20 p.m. - 2:35 p.m.||Rick Sommer||Logic, Intuition, and Infinity . Slides.|
|2:40 p.m. - 2:55 p.m.||Rahmat Rashid and||Defining Abstraction. Slides (pptx).|
Special Session on Competing foundations for mathematics: how do we choose?
Does the existence of many possible foundations of mathematics (some of which are mutually incompatible) pose a problem for mathematical realism/platonism? Is set theory or category theory the right foundation? For each, there are different versions. For example, for set theory, there’s Zermelo-Fraenkel (with or without the axiom of choice, with or without large cardinals, etc.), Cantor-von Neumann, Quine's NF, and others. And then there’s category theory, and topos theory. Each is importantly different from the others. But if realism about mathematics is correct, shouldn't there be just one correct foundational system? If so, which is correct? On the other hand, for physicists, a proliferation of theories does not call into question the reality of the external world. Why can mathematicians make important and meaningful contributions to their fields and yet simultaneously avoid, and indeed, often be ignorant of, mathematical foundations? How would we argue that a particular foundation is the correct choice? Or is realism wrong, and there is no one correct foundation? Should fruitfulness be the deciding mechanism? But can this lead to incorrect mathematics? In short, do specific formulations in mathematical foundations matter?
Philosophy of Mathematics, in memory of Reuben Hersh
Philosophy of mathematics since the late 1970s owes a great debt to Reuben Hersh (1927-2020), who, arguably more than anyone else at the time, re-engaged mathematicians with questions on the nature of mathematics and proof. Hersh's writings on social constructivism (that the reality of mathematics is as a social, cultural, and historical construct), on actual proofs done by mathematicians (as opposed to formal proofs) and mathematics as a human activity (as opposed to a platonic ideal or a formal system) were and still are controversial. However, his work inspired many mathematicians to elucidate their own views on such matters, and the resulting discussions remain fruitful today. This session welcomes talks engaging with any of the many topics in the philosophy of mathematics that Hersh discussed.
|2:15 p.m. MST||1163-I5-1156||Rachel Rupnow||Algebraists' Metaphors for Sameness: Philosophies, Variety, and Commonality|
|2:35 p.m. MST||1163-I5-1276||Thomas Drucker||Why is There a Question About Why There is Philosophy of Mathematics At All?|
Role of Explanation in Mathematical Proofs
Mathematical proofs are a form of argument. We can say of arguments in general--and mathematical proofs specifically--that, when sound, they show us that the claim made is true. But often some arguments--and this includes some mathematical proofs--do more. They also explain to us why it is true. Proposed talks might discuss (but are not limited to) the following topics. What is it to explain why a mathematical theorem is true? Which mathematical proofs explain why the theorem proved is true? Some doubt that proofs by mathematical induction can. Is mathematical explanation different from, say, scientific explanation (which does not involve the use of mathematics)? Is it different from historical explanation? Or is there a unified sense of 'explanation' which is common to its use in all subjects, including mathematics? Are there instances of mathematical theorems which have multiple proofs, some of which are elegant and simple, but not explanatory, while the others are neither elegant nor simple, but explanatory? If so, does being explanatory count as a good reason to prefer one kind of proof over the other? If a mathematician finds a shorter proof of some theorem, will the shorter proof be more explanatory than the longer proof? All paper proposals which discuss the role of explanation in mathematical proofs will be considered.
|8:00 a.m.||1154-O1-487||James Henderson, "Explanatory Proofs"|
|8:35 a.m.||1154-O1-2227||Jeremy Case, "Mathematical Explanation as an Aesthetic"|
|9:10 a.m.||1154-O1-2672||Paul Zorn, "Proofs that explain, proofs that don't, and proofs of the obvious"|
|9:45 a.m.||1154-O1-716||Bonnie Gold, "What makes proofs explanatory? Let's look at some examples"|
|10:20 a.m.||1154-O1-2716||Susan Ruff, "How logic is presented may obscure or enlighten"|
|11:00 a.m.||1154-O1-1421||Jeffrey Buechner, "Are mathematical explanations interest-relative?"|
Philosophy of Mathematics: Do Choices of Mathematical Notation (and Similar Choices) Affect the Development of Mathematical Concepts?
This session invites talks on any topic in the philosophy of mathematics. Our special theme this year is "Do Choices of Mathematical Notation (and Similar Choices) Affect the Development of Mathematical Concepts?" Once mathematical concepts have gelled, they tend to feel "natural" to mathematicians. But in the process of exploring and developing new concepts, mathematicians make choices, including of notation and terminology, that affect how the nascent concept solidifies. For example, to what extent does our decimal notation affect our understanding of numbers? Are there concepts and mathematical practices that can be understood in one notational framework and not in another? This session invites talks that look at this process, and the philosophical implications of the effect of our choice of mathematical notations on the development of mathematical concepts. Talks on the special theme will be given highest priority, but all talks on the philosophy of mathematics are welcome.
|8:00 a.m.||1145-L5-228||Thomas Morley, Feynman's Funny Pictures|
|8:30 a.m.||1145-L5-1466||Daniel Sloughter, What is a measure?|
|9:00 a.m.||1145-L5-1790||James Henderson, Multiplicity of Logical Symbols: Why Is That a Thing?|
|9:30 a.m.||1145-L5-1687||Kevin Iga, What does mathematical terminology say about linguistic determinism?|
|10:00 a.m.||1145-L5-740||Sergiy Koshkin, Mathematical Intuition and the Secret of Platonism|
|10:30 a.m.||1145-L5-1961||Jeffrey Buechner, What makes a notation for the natural numbers a good notation?|
|11:00 a.m.||1145-L5-1343||Ilhan Izmirli, Wittgenstein and Social Constructivism|
|11:30 a.m.||1145-L5-1642||Donald Palmer, Boundary Conditions: Numeric Representation and the Boundary of Pure and Applied Mathematics|
Philosophy of Mathematics as Actually Practiced
The philosophy of mathematics has often failed to account for actual mathematical practice, concentrating only on the finished product, theorems and proofs, and even then, not proofs as mathematicians give them, but the formal proofs by which they could be replaced. In the last quarter of the 20th century, many philosophers of mathematics began to be interested in considering mathematics as it is actually developed, leading to the formation, in 2009, of the Association for the Philosophy of Mathematical Practice. This kind of approach requires that the philosopher of mathematics have a good understanding of mathematics, how it develops, and how it is taught and learned. It therefore requires a significant interaction with the mathematical community. This session invites contributions that discuss philosophical issues involved with mathematics as it is actually practiced. Papers that bring out issues that have not yet been discussed by philosophers but that involve philosophical issues with current mathematical practice are especially welcome. Other topics in the philosophy of mathematics will be considered as time allows.
|8:00 a.m.||1135-A5-144||David M. Shane, "The Eroding Foundation of Mathematics"|
|8:30 a.m.||1135-A5-362||James Henderson, "When Physicists Teach Mathematics"|
|9:00 a.m.||1135-A5-609||Daniel C. Sloughter, "Hardy, Bishop, and Making Hay"|
|9:30 a.m.||1135-A5-301||Jae Yong John Park, "Fictionalism, Constructive Empiricism, and the Semantics of Mathematical Language"|
|10:00 a.m.||1135-A5-814||Chandra Kethi-Reddy, "Gian-Carlo Rota and the Phenomenology of Mathematics"|
|10:30 a.m.||1135-A5-1883||sarah-marie belcastro, "Does Inclusivity Matter in Mathematical Practice?"|
Do Mathematicians Really Need Philosophy?
Nobel physicist Steven Weinberg famously declared that philosophers were useful to him only to defend him from other philosophers. Weinberg was complaining mostly about logical positivists, who don't seem to deal with mathematics much. But the philosophy of mathematics is a battleground for a number of warring schools, most prominently Platonists and constructivists. Does a practicing mathematician have to choose which school to join? Philosophical questions have been shown to have a huge positive effect in the teaching of mathematics, but need they come up during the development of a new branch of mathematics? Philosophy of mathematics has recently seen a movement toward "pluralism": let's accept everyone's philosophies, no matter how contradictory they may be. Is that a useful trend? Is it just a futile attempt to sweep a problem under the rug? This session, sponsored by POMSIGMAA, will give a forum for views from all sides of the issue, whether from the perspective of doing mathematical research, teaching mathematics, or more general philosophical fruitfulness. Other topics in the philosophy of mathematics will be considered as time allows.
|1:00 p.m.||1125-C5-248||James R. Henderson, "Otavio Bueno's Mathematical Fictionalism"|
|1:30 p.m.||1125-C5-2521||Thomas Drucker, "Why Can't Those With Conflicting Views on the Foundations of Mathematics Just Get Along?"|
|2:00 p.m.||1125-C5-1670||Katalin Bimbó, "The unexpected usefulness of epistemological skepticism"|
|2:30 p.m.||1125-C5-507||Bonnie Gold, "Melding realism and social constructivism"|
Using Philosophy to Teach Mathematics
Courses in the philosophy of mathematics are rare, but philosophical questions frequently arise in the regular curriculum, often presenting difficulties to teachers who haven’t prepared to respond to them. In recent years a growing number of teachers of mathematics are discovering that addressing philosophical issues deliberately in their courses not only eases the strain but also enhances students’ ability to grasp difficult mathematical concepts. The upcoming MAA Notes volume, Using the Philosophy of Mathematics in Teaching Collegiate Mathematics, illustrates the ways a wide variety of teachers have found to introduce philosophical questions as an exciting part of presenting standard mathematical material. This session invites teachers at all levels to discuss ways they have found to include philosophy in the mathematics classroom. Papers on other topics in the philosophy of mathematics will be considered as time permits.
|8:00 a.m.||1116-T5-103||Daniel C. Sloughter, "Making Philosophical Choices in Statistics"|
|8:30 a.m.||1116-T5-608||Sally Cockburn, "Senior Seminar in Set Theory as a Springboard for Mathematical Philosophy"|
|9:00 a.m.||1116-T5-2355||Thomas Drucker, "Role of Real Numbers in an Introduction to Analysis"|
|9:30 a.m.||1116-T5-2376||Brian R Zaharatos, "Statistics as a Liberal Art"|
|10:00 a.m.||1116-T5-177||James R Henderson, "Strange Bedfellows: Thomae's Game Formalism and Developmental Algebra"|
|10:30 a.m.||1116-T5-2300||Luke Wolcott, "Gardens of Infinity: Cantor meets the real deep Web"|
|11:00 a.m.||1116-T5-2556||Martin Flashman, "Is Philosophy of Mathematics Important for Teachers?"|
MathFest Centennial joint with Canadian Society for the History and Philosophy of Mathematics
Special Session on Philosophy of Mathematics
|2:30 p.m.||Elaine Landry, "Mathematical Structuralism and Mathematical Applicability"|
|3:00 p.m.||Jean-Pierre Marquis, "Designing Mathematics: The Role of Axioms"|
|3:30 p.m.||Alex Manafu, "Does the Indispensability Argument Leave Open the Question of the Causal Nature of the Mathematical Entities?"|
|4:00 p.m.||Carl Behrens, "How Does the Mind Construct/Discover Mathematical Propositions?"|
|4:30 p.m.||Jeff Buechner, "What is an Adequate Epistemology for Mathematics?"|
Discovery and Insight in Mathematics
One new development in the philosophy of mathematics that mathematicians should welcome is an interest in the philosophy of mathematics as actually practiced by mathematicians. This session invites talks addressing philosophical issues concerning two related topics: how mathematics is discovered, and the role of insight in mathematical understanding and discovery. Epistemology studies how we come to know things. A distinction has been made between methods of discovery and methods of justification: that is, the way one discovers a mathematical truth – a conjecture, for example – may be quite different from how it is later justified (by a proof). What are the methods and grounds for such discoveries? What is the role insight plays in these discoveries? How do interconnections between mathematical concepts or subjects lead to discoveries? Talks addressing any of these issues within the philosophy of mathematics are appropriate for this session. Papers on other topics in the philosophy of mathematics will be considered as time permits.
Organizers: Dan Sloughter and Bonnie Gold
|8:00 a.m.||1106-C5-583||Daniel C Sloughter, “Insights Gained and Lost”|
|8:30 a.m.||1106-C5-443||James R Henderson, “Kepler's Mysterium Cosmographicum”|
|9:00 a.m.||1106-C5-2535||Horia I Petrache, “Removing bias: the case of the Dirac equation”|
|9:30 a.m.||1106-C5-1961||Ruggero Ferro, “An analogy to help understanding Discovery, Insight and Invention in Mathematics”|
|10:00 a.m.||1106-C5-1803||Carl E. Behrens, “How does the mind construct/discover mathematical propositions?”|
|1:00p.m.||106-C5-1594||Reuben Hersh, “Mathematicians’ proof: ‘The kingdom of math is within you’”|
|1:30 p.m.||1106-C5-1714||Thomas Drucker, “Explanatory and Justificatory Proofs”|
|2:00 p.m.||1106-C5-249||Bonnie Gold, “George Polya on methods of discovery in mathematics”|
|2:30 p.m.||1106-C5-2391||Tom Morley, “Some proofs and discoveries from Euler and Heaviside”|
|3:00 p.m.||1106-C5-2763||Kira Hylton Hamman, “Intuition: A History”|
|3:30 p.m.||1106-C5-838||Steven R Benson, “If you’re hoping for discovery, put away the handouts!”|
Is Mathematics the Language of Science?
In 1960 physicist Eugene Wigner published an article entitled: “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” in which he raised the question of the relationship between mathematics and the empirical sciences. Discussions of Wigner’s article often reflect the assumption that mathematics has relevance only as a means of exploring the physical world: as Wigner puts it, “in discovering the laws of inanimate nature.” Many mathematicians would find this an unacceptable restriction on the definition of their pursuits and activities. This session will explore the extent to which Wigner’s approach defines the role of mathematics, and entertain alternative or additional functions and purposes.
Organizers: Carl Behrens, Tom Drucker, Dan Sloughter
|1:00 p.m.||1096-G1-1195||Carl E. Behrens,"Mathematics Is a Science in its Own Right"|
|1:30 pm:||1096-G1-149||James R Henderson, "The Mathematics of Quantum Mechanics: Making the Math Fit the Philosophy"|
|2:00 pm:||1096-G1-2359||Horia I. Petrache, "A group theory perspective of mathematical constructs in physics"|
|2:30 pm:||1096-G1-842||Mate Szabo, "The Roots Of Kalmar's Empiricism"|
|3:00 pm:||1096-G1-2034||Ruggero Ferro,"No Surprise for the Effectiveness of Mathematics in the Natural Sciences"|
|3:30 pm:||1096-G1-743||Ronald E. Mickens, "Mathematics as an Emergent Feature of the Physical Universe"|
|3:55 pm:||1096-G1-1414||Jeff Buechner, "A New Look at Wigner's `The Unreasonable Effectiveness of Mathematics in the Natural Sciences'"|
There were two types of sessions in Hartford: a session running throughout the meeting, of talks in either the history or philosophy of mathematics, and a session of talks on the interactions between history and philosophy of mathematics. Of the former, only the specifically philosophical talks during the daily sessions are listed.
Philosophy of Mathematics:
Friday, August 2
|9 a.m.||Matthew Clemens, "Fictionalism and Mathematical Practice," Keene State College|
|10 a.m.||Robert H C Moir, "Rational Discovery of the Natural World: An Algebraic and Geometric Answer to Steiner"|
|11 a.m.||Jean-Pierre Marquis, "Canonical Maps: Where Do They Come From and Why Do They Matter?"|
|3 p.m.||Martin E Flashman, "Logic is Not Epistemology: Should Philosophy Play a Larger Role in Learning about Proofs?"|
Interactions Between History and Philosophy of Mathematics
This session is geared specifically to interactions between the history and philosophy of mathematics. Talks will be expected either to approach specifically how each discipline informs the other in particular or general contexts, or to discuss issues and episodes that have implications for both the philosophy and the history of mathematics.
Organizers: Thomas Drucker, University of Wisconsin-Whitewater and Glen Van Brummelen, Quest University
Saturday, August 3
|10:30 a.m.||Thomas Drucker, "Zeno Will Rise Again"|
|11:00 a.m.||Amy Ackerberg-Hastings,"Analysis and Synthesis in Geometry Textbooks: Who Cares?"|
|2:30 p.m.||Robert S D Thomas, "Assimilation in Mathematics and Beyond|
|3:00 p.m.||Lawrence D'Antonio, "Euler and the Enlightenment|
|3:30 p.m.||Maryam Vulis, "Persecution of Nikolai Luzin"|
|4:00 p.m.||Roger Auguste Petry,"Philosophy Etched in Stone: The Geometry of Jerusalem's 'Absalom Pillar'"|
|4:30 p.m.||Jeff Buechner, "Understanding the Interplay between the History and Philosophy of Mathematics in Proof Mining"|
Philosophy, Mathematics and Progress.
Mathematics as a discipline seems to make progress over time, while philosophy is often taken to task for not having made such progress over the millennia. When philosophy comes to tackle issues related to mathematics, one natural topic is how mathematics succeeds in making progress while philosophy does not. One question to be addressed in this session is whether philosophy can help to explain the apparent progress displayed by mathematics. Another is whether the mismatch in progress between the disciplines is more apparent than real. As currents of mathematical change gather speed, perhaps a philosophical perspective is needed to make sure that current practitioners do not lose their footing. Papers addressing issues of progress in mathematics and philosophical ways of understanding that progress will help to continue conversations between mathematicians and philosophers.
Organizers: Thomas Drucker, University of Wisconsin-Whitewater and Daniel Sloughter, Furman University
|1:00 p.m.||1086-L5-459||Deborah C. Arangno, “From Intuition to Esoterica”|
|1:30 p.m.||1086-L5-71||Sean F. Argyle, “Mathematical Thinking: From Cacophony to Consensus”|
|2:00 p.m.||1086-L5-618||Thomas Drucker, “Mathematical Progress via Philosophy”|
|2:30 p.m.||1086-L5-1597||Daniel Sloughter, “Philosophical and Mathematical Considerationsof Continua”|
|3:00 p.m.||1086-L5-45||Amy Ackerberg-Hastings, “John Playfair, the Scottish Enlightenment, and ‘Progress’ in the History and Philosophy of Mathematics”|
|3:30 p.m.||1086-L5-365||Ruggero Ferro, “Mathematics versus Philosophy”|
|4:00 p.m.||1086-L5-209||James R. Henderson, “Progress in Mathematics: The Importance of Not Assuming Too Much”|
|4:30 p.m.||1086-L5-874||Mate Szabo, “Kalmar’s Argument Against the Plausibility of Church’s Thesis”|
Philosophy of Mathematics and Mathematical Practice
Philosophers search for insights into the most general epistemological and ontological questions: How do we know, and what is it that we know? Since mathematical knowledge is a significant piece of what we know, an explanation of the nature of mathematics plays an important role in philosophy. To this end, a philosopher of mathematics must pay careful attention to mathematical practice, what it is that mathematicians claim to know and how they claim to know it. A philosopher's explanation of mathematics cannot be a local explanation: it must fit within the larger picture of knowledge as a whole. A mathematician may have an account of mathematics which suffices for her work, but unless this account fits coherently into a larger epistemological and ontological picture, it will not suffice as a philosophy of mathematics. This session will address questions concerning the relationship between the philosophy and the practice of mathematics. We encourage papers to address questions such as: Should the philosophy of mathematics influence, or be influenced by, the practice of mathematics? Is it necessary for the philosophy of mathematics to influence the practice of mathematics for it to be relevant to mathematicians?
Organizers: Daniel Sloughter, Furman University and Bonnie Gold, Monmouth University
|1:00 p.m.||1077-K1-1196||Daniel C. Sloughter, "The Consequences of Drawing Necessary Conclusions"|
|1:30 p.m.||1077-K1-383||Thomas Drucker, "Thought in Mathematical Practice"|
|2:00 p.m.||1077-K1-85||Joshua B. Wilkerson, "Beyond Practicality: George Berkeley and the Need for Philosophical Integration in Mathematics"|
|2:30 p.m.||1077-K1-2002||Bonnie Gold, "Philosophy (But Not Philosophers) of Mathematics Does Influence Mathematical Practice"|
|3:00 p.m.||1077-K1-1287||Sarah-Marie Belcastro, "Epistemological Culture and Mathematics"|
|3:30 p.m.||1077-K1-904||Ruggero Ferro, "How Do I (We) Know Mathematics"|
|4:00 p.m.||1077-K1-800||Jeff Buechner, "Formal mathematical proof and mathematical practice: a new skeptical problem"|
|4:30 p.m.||1077-K1-1744||Nathaniel G. Miller,"CDEG: Computerized Diagrammatic Euclidean Geometry"|
Philosophy of Mathematics in Teaching and Learning.
Mathematicians tend not to think about philosophical issues while teaching. Yet we are making ontological and epistemological commitments in much of what we do in the classroom. Every time we use a proof by induction or contradiction, discuss the existence or non-existence of a mathematical object, or refer to the discovery or creation of some piece of mathematics, we are endorsing some philosophical view of our subject.
The focus of this session is on the recognition and use of the philosophy of mathematics in the teaching and learning of mathematics. Can we understand mathematics without a philosophical context? Papers are encouraged to address questions such as: What philosophical issues (such as the nature of mathematical objects, the method of mathematical proof, and the nature of mathematical knowledge) should be treated in a mathematics course? How? In which course(s)? In what ways does the consideration of philosophical issues enhance a mathematics, or mathematics related, course? What does a learner gain by contact with issues from the philosophy of mathematics?
Other papers of a philosophical nature will be considered for inclusion as time permits.
Organizers: Dan Sloughter, Furman University, and Martin E. Flashman, Humboldt State University
|1:00 p.m.||1067-T1-1395||Martin E. Flashman, "Square Roots: Adding Philosophical Contexts and Issues to Enhance Understanding"|
|1:30 p.m.||1067-T1-2224||Whitney Johnson and Bill Rosenthal, "Precalculus from an Ontological Perspective"|
|2:00 p.m.||1067-T1-1766||Thomas Drucker, "Putting Content into a Fictionalist Account of Mathematics for Non-Mathematicians"|
|2:30 p.m.||1067-T1-2223||Sheila K. Miller, "On the Value of Doubt and Discomfort"|
|3:00 p.m||1067-T1-712||Jeff Buechner, "Mathematical Understanding and Philosophies of Mathematics"|
|3:30 p.m.||1067-T1-1527||Ruggero Ferro, "Abstraction and objectivity in mathematics"|
|4:00 p.m.||1067-T1-159||James R. Henderson, "Causation and Explanation in Mathematics"|
|4:30 p.m.||1067-T1-2327||Andy D. Martin, "Claims Become Theorems, but Who Decides?"|
|5:00 p.m.||1067-T1-2300||Firooz Khosraviyani, Terutake Abe and Juan J Arellano, "Definitions in Their Developmental Stages: What should we call them?"|
Philosophy of Mathematics for Working Mathematicians.
Philosophers have a wide range of views on the nature and existence of mathematical objects. How is it that mathematics continues to flourish, year after year, when philosophical questions about the fundamental nature of mathematical objects remain controversial and unsettled? This session invites papers that address, and clarify the relevance of, this issue, and propose views of mathematical objects that are consistent with mathematical practice.
Organizers: Carl Behrens, Alexandria, Virginia, and Bonnie Gold, Monmouth University
|1:00 p.m.||1056-M5-259||James R. Henderson, “What Is the Character of Mathematical Law?”|
|1:30 p.m.||1056-M5-596||Carl E. Behrens, “John Stuart Mill's "Pebble Arithmetic" and the Nature of Mathematical Objects”|
|2:00 p.m.||1056-M5-1635||Thomas Drucker, “Dummett Down: Intuitionism and Mathematical Existence”|
|2:30 p.m.||1056-M5-1770||Martin Flashman, “The Articulation of Mathematics-A Pragmatic/Constructive Approach to The Philosophy of Mathematics”|
|3:00 p.m.||1056-M5-445||Lawrence A. D’Antonio, “Molyneux's Problem”|
|3:30 p.m.||1056-M5-1015||Jeff Buechner, “Mathematical practice and the philosophy of mathematics”|
|4:00 p.m.||1056-M5-444||Daniel C. Sloughter, “Being a Realist Without Being a Platonist”|
|4:30 p.m.||1056-M5-1918||Ruggero Ferro, “An analysis of the notion of natural number”|
The History of Mathematics and its Philosophy, and Their Uses in the Classroom
Note: this session was joint with HOMSIGMAA. Most of the talks were history of mathematics; the talks listed below involved either only philosophy of mathematics, or both history and philosophy.
Organizers: Janet Beery, University of Redlands; Bonnie Gold, Monmouth University; Amy Shell-Gellasch, Pacific Lutheran University; Charlotte Simmons, University of Central Oklahoma
|1:00 p.m.||Martin E Flashman, "Which Came First? The Philosophy, the History, or the Mathematics?"|
|1:20 p.m.||Daniel Sloughter, "Should My Philosophy of Mathematics Influence My Teaching of Mathematics?"|
|1:40 p.m.||Bonnie Gold, "Philosophical Questions You DO Take a Stand on When You Teach First-year Mathematics Courses"|
|2:00 p.m.||Jeff Buechner, "Using the Philosophy of Intuitionistic Mathematics to Strengthen Proof Skills"|
Organizers: Kevin Iga, Pepperdine University, and Bonnie Gold, Monmouth University
|8:30 a.m.||1035-Q1-1936||Laura Mann Schueller, Mathematical Rigor in the Classroom|
|9:00 a.m.||1035-Q1-25||Andrew G. Borden, Mathematics is a Meme(plex)|
|9:30 a.m.||1035-Q1-1360||Carl E. Behrens, Are Euclid’s Postulates Really Essences?|
|10:00 a.m.||1035-Q1-181||Daniel C. Sloughter, The De Continuo of Thomas Bradwardine|
|10:30 a.m.||1035-Q1-1461||Jeff Buechner, Ignoring the Obvious in Philosophical Applications of the Gödel Incompleteness theorems|
|11:00 a.m.||1035-Q1-94||James R Henderson, What Does It Mean for One Problem to Reduce to Another?|
|11:30 a.m.||1035-Q1-1722||Ruggero Ferro, Remarks about the notion of EXISTENCE in mathematics|
Organizers: Bonnie Gold, Monmouth University, Charles Hampton, The College of Wooster
Organizers: Roger A. Simons, Rhode Island College, Satish C. Bhatnagar, University of Nevada
|8:00 a.m.||1014-A1-1158||Carl E. Behrens, What Are Mathematical Objects? An Empiricist Hypothesis|
|8:30 a.m.||1014-A1-276||Bonnie Gold, Mathematical objects may be abstract, but they're NOT acausal|
|9:00 a.m.||1014-A1-1352||Sarah-Marie Belcastro, How the way we `see' mathematics changes mathematics|
|9:30 a.m.||1014-A1-1010||Martin E. Flashman, The Square Root of 2, Pi, and the King of France: Ontological and Epistemological Issues Encountered (and Ignored) in Introductory Mathematics Courses|
|10:00 a.m.||1014-A1-626||Sam Stueckle, Mathematics: An Aesthetic Endeavor|
|10:30 a.m.||1014-A1-500||James R Henderson, Propensities and the Two Varieties of Occult Qualities|
Organizers: Charles Hampton, The College of Wooster, Bonnie Gold, Monmouth University
|1:00 p.m.||1003-P1-488||Bonnie Gold, What Is Mathematics II: A Possible Answer|
|1:25 p.m.||1003-P1-652||David W. Henderson, Daina Taimina, Strands in the history of geometry and how they affect our views as to what geometry is|
|1:50 p.m.||1003-P1-830||Robert E. Bradley, Object and Attribute: the case of Curves and Equations|
|2:15 p.m.||1003-P1-522||Homer S. White, Philosophy of Mathematics in Classical India: an Overview|
|2:40 p.m.||1003-P1-655||Daniel C. Sloughter, Realism and Mathematics: Peirce and Infinitesimals|
|3:05 p.m.||1003-P1-405||Thomas Drucker, Fictionalism and the interpretation of mathematical discourse|
|3:30 p.m.||1003-P1-409||Troy D. Riggs, Linguistic Relativity in Applied Mathematics|
|3:55 p.m.||1003-P1-708||Charles R. Hampton, Applied Mathematics---A Philosophical Problem|
|4:20 p.m.||1003-P1-597||Frederik S. Herzberg, Generalised likelihoods, ideals and infinitesimal chances - how to approach the "zero-fit problem,"|
|1:00 p.m.||983-S1-49||Thomas Drucker, Why Plato was not a Platonist|
|1:30 p.m.||983-S1-351||Daniel C Sloughter, Peirce, Zeno, Achilles, and the Tortoise|
|2:00 p.m.||983-S1-544||Kenneth Manders, Structuralist Mathematics and Mathematical Understanding|
|2:30 p.m.||983-S1-546||Roger A. Simons, Are Mathematical Objects Inside or Outside a Human Mind?|
|3:00 p.m.||983-S1-341||Bonnie Gold, What is Mathematics I: The Question|
|3:30 p.m.||983-S1-429||Sarah-marie Belcastro, A Conjecture about... Feminist Mathematics?|
|4:00 p.m.||983-S1-137||Michael J. Bossé, Defining Mathematical Esthetics within the NCTM Standards|
|4:30 p.m.||983-S1-482||John E Beam, Unfair Gambles in Probability (Preliminary Report)|
|5:00 p.m.||983-S1-551||Satish C Bhatnagar, The Pedagogical Challenges of One to One Correspondence|
|5:30 p.m.||983-S1-545||M Anne Dow, A Unifying Principle Describing How Mathematical Knowledge Unfolds|