The Claremont History and Philosophy Seminar will be meeting online on Friday mornings for the entirety of the "virtual" year. For more information about the Seminar, to suggest speakers, or to obtain the relevant zoom information, please contact Jemma Lorenat, Friday January 22 10:00 am Paola Cantu Aix-Marseille University and CNRS Peano's formalization and semantics
ABSTRACT: This talk develops one issue contained in a paper that investigates Peano's philosophical views through a detailed analysis of several
mathematical practices that can be fruitfully investigated to compare Peano's philosophical views with logicism and structuralism: the link between functions and
relations, the role of metatheoretical investigations, the kind of semantics, the use of definitions by
abstraction, and the foundational or non-foundational value of axiomatics. In the paper Peano's view is
characterized as a form of structural algebraism, which differs from both the algebra of logic tradition
using mathematical symbols to express logical calculi, and from Frege's logical investigation centered
on the effort to understand the functional nature of predication.
This talk will focus on Peano's semantics, which radically differs both from Frege's and from Padoa's semantics, as described in the 1902 paper on formal deductive systems.
The influence of Leibniz can be seen
both in the development of a kind of semantics that is neither representational nor conceptualist
(symbols mean linguistic items of ordinary language), and in the consideration of symbolic signs as
mirroring what they stand for.
Friday January 29 9:15 am Matthew Jones Columbia University Learning to Love Opacity: Decision Trees and the Genealogy of the Algorithmic Black Box
ABSTRACT: My talk concerns the genesis and the development of one of the foremost kinds of algorithms for supervised learning: decision trees. A series of researchers, each slightly askew to the dominant practices and epistemic virtues of their fields, came obliquely to trees in the 1970s: a data-driven statistician, a machine learning expert focused on large data sets, social scientists unhappy with multivariate statistics, a physicist interested mostly in computers who eventually was tenured in a statistics department. In case after case, the creators of different forms of trees deployed "applied" philosophies of science in critiquing contemporary practices, epistemic criteria and even promotion practices in academic disciplines. Faced with increasing amounts of high-dimensional data, these authors time and again advocated a data-focused positivism. The history of trees does not cleanly divide into a theoretical and an applied stage; an academic and a commercial phase; a statistical and a computational stage; or even an algorithm design and an implementation stage. This history is iterative: the implementation of algorithms on actually existing computers with various limitations drives the development and transformation of the techniques. Before the very recent renaissance and current triumph of neural networks, decision trees were central to the transformation of artificial intelligence and machine learning of recent years: the shift in the central goal to a focus on prediction at the expense of concerns with human intelligibility, and of a shift from symbolic interpretation to potent but inscrutable black-boxes. Trees exploded in the late 1980s and 1990s as paragons of interpretable algorithms but developed in the late 1990s into a key example of powerful but opaque ensemble models, predictive but almost unknowable. We need to explain, rather than take as given, the shift in values to prediction---to an instrumentalism---central to the ethos and practice of the contemporary data sciences. Opacity needs its history---just as transparency does.
Friday February 19 9:15 am Vincent Peluce City University of New York The Perception of Time in Intuitionistic Arithmetic
ABSTRACT: In L.E.J. Brouwer's first act of intuitionism, the subject's perception of time is put forth as the foundation on which arithmetic will be built. According to Brouwer, proper intuitionistic arithmetic, as with the rest of intuitionistic mathematics, is not tied to any particular formal system. When we try to axiomatically approximate an intuitionistic arithmetical system, we are faced with the problem of incorporating the subject and their perception into the axiom system itself. We discuss some unsatisfactory responses to this problem and then offer a solution.
Friday February 26 10:00 am Laura Turner Monmouth University Women as data and as individuals: public dialogues on sexism in mathematics
during the 1970s, 1980s, and 1990s
ABSTRACT: The Association for Women in Mathematics (AWM) came of age in the 1980s, emerging by the early 1990s as a serious mathematics organization engaged in improving the status of women in mathematics. The same period also saw resistance to amelioratory measures and high-profile claims of sexism in mathematical practice. Through the public dialogues surrounding these episodes, in this talk we explore aspects of how the AWM and its members addressed the complex issue of sexism in mathematics in the contexts of reactions to affirmative action mandates; sex-linked theories of mathematical ability; anti-science gender essentialism; the Jenny Harrison tenure dispute; and the myth of objectivity in mathematical practice. As we will see, the deeply-held and widespread belief in the inability of women to do mathematics, exacerbated by the myth of the canonical feminine woman and the understanding that mathematics as a discipline was essentially unbiased, simultaneously emphasized the importance of treating each woman mathematician as an individual, instead of as a representative of her sex, and left her vulnerable to the same discrimination the AWM sought to combat. In particular, while women as data held the power for reform, the perspectives of individual women were vulnerable to controversy.
Friday April 2 10:00 am Dirk Schlimm McGill University 'Calculus' as Method or 'Calculus' as Rules? Boole and Frege on the aims of a logical calculus
ABSTRACT: It is an interesting fact about the history of modern logic, that both Boole and Frege (and others) gave solutions to the same logical problem in order to show the power of their respective notations. In this talk I will present the problem and discuss Boole and Frege's solutions. This will highlight an underappreciated aspect of Boole's work and of its difference with Frege's better-known approach, which sheds light on the concepts of 'calculus' and 'mechanization' and on their history. While Frege's outlook has dominated philosophical thinking about logical symbolism, Boole's idea of an intrinsic link between a 'calculus' and a 'directive method' to solve problems presents a new perspective on the role of notations in logic and mathematics. (This talk is based on joint work with David Waszek.)
Friday April 30 10:00 am Ellen Abrams Cornell University 'Which shall be regarded as the best?': Axiom Systems and American Mathematics
ABSTRACT: In the early twentieth century, researchers in the United States engaged with foundational studies in mathematics by building and evaluating axiom, otherwise known as postulate, systems. At the same time, their contemporaries were evaluating the meaning and politics of knowledge more broadly. In this talk, I explore the ways in which the study of postulates in the United States was tied to important Progressive Era questions about the nature of knowledge, the status of the knower, and the development of American Pragmatism. While most investigations of postulate studies have considered their implications within mathematical research and education, I look instead to the role of postulate studies in the professionalization of mathematics in the United States and to its cultural status more broadly.
Friday May 14 10:00 am Jessica Carter Aarhus University The Philosophy of Mathematics as Practiced
ABSTRACT: For some time now part of the philosophy (and related studies) of mathematics has been referred to as 'the philosophy of mathematical practice'. Although a number of contributions have offered characterisations of this new area, it is still not entirely clearly defined. Moreover, a number of similar terms, such as 'mathematical philosophy' and the 'philosophy of mathematics as practiced', have been used to refer to related areas within the philosophy of mathematics. The talk will present and discuss some of these characterisations. I shall start by giving a brief account of mathematical philosophy as coined by Russell and as part of scientific philosophy at the beginning of the 20th century. The second part will discuss two quite different accounts of the philosophy of mathematical practice, offered by Paolo Mancosu (2008) and Jean-Paul Van Bendegem (2014). In the final part I propose a characterisation of the philosophy of mathematics as practiced as the part of philosophy that actively engages with the actual practice of mathematics --- past and present. This means, for example, that philosophical questions are based on mathematics itself, or the activities of mathematicians. Furthermore, answers to philosophical questions may draw on mathematical tools or (historical) case studies. The 'activities of mathematicians' could, for example, include what mathematicians say or write about their work or how they go about finding new results. This part will propose some questions that could be relevant to contemporary mathematical practice and presents some illustrative examples.
Spring 2020 Schedule
Date
Speaker
Title and Abstract