Williams college student course survey form: Instructor modified version

Opening a copy of The Mathematical Intelligenceryou may ask yourself uneasily, “What is this anyway—a mathematical journal, or what?” Or you may ask, “Where am I?” Or even “Who am I?” This sense of disorientation is at its most acute when you open to Colin Adams’s column. Relax. Breathe regularly. It’s mathematical, it’s a humor column, and it may even be harmless.     

Non-branching Clause

The central claim of the Parfitian psychological approach to personal identity is that the fact about personal identity is underpinned by a “non-branching” psychological continuity relation. Hence, for the advocates of the Parfitian view, it is important to understand what it is for a relation to take or not take a branching form. Nonetheless, very few attempts have been made in the literature of personal identity to define the “non-branching clause.” This paper undertakes this task. Drawing upon a recent debate between Anthony Brueckner and Harold Noonan on the issue, I present three candidates for the non-branching clause.     

A subprime lending market primer

Opening a copy of TheMathematical Intelligencer you may ask yourself uneasily, “What is this anyway—a mathematical journal, or what?” Or you may ask, “Where am I?” Or even “Who am I?” This sense of disorientation is at its most acute when you open to Colin Adams’s column. Relax. Breathe regularly. It’s mathematical, it’s a humor column, and it may even be harmless.     

The mathematical ethicist

Opening a copy ofThe Mathematical Intelligencer you may ask yourself uneasily, “What is this anyway—a mathematical journal, or what?” Or you may ask, “Where am I?” Or even “Who am I?” This sense of disorientation is at its most acute when you open to Colin Adams’s column. Relax. Breathe regularly. It’s mathematical, it’s a humor column, and it may even be harmless.     

Don’t Touch the Button

Opening a copy of The Mathematical Intelligenceryou may ask yourself uneasily, “What is this anyway—a mathematical journal, or what?” Or you may ask, “Where am I?” Or even “Who am I?” This sense of disorientation is at its most acute when you open to Colin Adams’s column. Relax. Breathe regularly. It’s mathematical, it’s a humor column, and it may even be harmless.     

More from the mathematical ethicist

Opening a copy ofThe Mathematical Intelligencer you may ask yourself uneasily, “What is this anyway—a mathematical journal, or what?” Or you may ask, “Where am I?” Or even “Who am I?” This sense of disorientation is at its most acute when you open to Colin Adams’s column.Relax. Breathe regularly. It’s mathematical, it’s a humor column, and it may even be harmless.     

The three little pigs

Opening a copy ofThe Mathematical Intelligencer you may ask yourself uneasily, “What is this anyway—a mathematical journal, or what?” Or you may ask, “Where am I?” Or even “Who am I?” This sense of disorientation is at its most acute when you open to Colin Adams’s column.Relax. Breathe regularly. It’s mathematical, it’s a humor column, and it may even be harmless.     

Can a Single Property Be Both Dispositional and Categorical? The “Partial Consideration Strategy”, Partially Considered

One controversial position in the debate over dispositional and categorical properties maintains that our concepts of these properties are the result of partially considering unitary properties that are both dispositional and categorical. As one of its defenders (Heil 2005, p. 351) admits, this position is typically met with “incredulous stares”. In this paper, I examine whether such a reaction is warranted. This thesis about properties is an instance of what I call “the Partial Consideration Strategy”—i.e., the strategy of claiming that what were formerly thought of as distinct entities are actually a unified entity, partially considered. By evaluating its use in other debates, I uncover a multi-layered prima facie case against the use of the Partial Consideration Strategy in the dispositional/categorical properties debate. In closing, I describe how the Partial Consideration Strategy can be reworked in a way that would allow it to sidestep this prima facie case.     

Comments on “Statistical reasoning with set-valued information: Ontic vs. epistemic views”

In this comment, several paragraphs from the paper “Statistical reasoning with set-valued information: Ontic vs. epistemic views” have been selected and discussed. The selection has been based, on one side, on a personal view of what can be considered the most clarifying points in the paper and, on the other side, on the aspects I am more familiar with and interested in and being quite unequivocally ontic-oriented. For sure, it is a biased selection, but the aim of these comments is that of sharing what I have found to be more appealing within the discussion and I would like to point out in connection with my own expertise.     

A Posteriori Physicalism and the Discrimination of Properties

According to a posteriori physicalism, phenomenal properties are physical properties, despite the unbridgeable cognitive gap that holds between phenomenal concepts and physical concepts. Current debates about a posteriori physicalism turn on what I call “the perspicuity principle”: it is impossible for a suitably astute cognizer to possess concepts of a certain sort—viz., narrow concepts—without being able to tell whether the referents of those concepts are the same or different. The perspicuity principle tends to strike a posteriori physicalists as implausibly rationalistic; further, a posteriori physicalists maintain that even if the principle is applicable to many narrow concepts, phenomenal concepts have unique features that render them inferentially isolated from other narrow concepts (a dialectical move known as “the phenomenal concept strategy” (PCS)). I argue, on the contrary, that the case for the perspicuity principle is quite strong. Moreover, not only have versions of the PCS repeatedly failed, likely, all versions will, given the strange combination of lucidity and opacity that the PCS has to juggle (it requires that we come up with a lucid explanation of an irremediable cognitive blindspot). I conclude that a posteriori physicalists currently lack a principled objection to classic anti-physicalist arguments.     

This theorem is big

Opening a copy of The Mathematical Intelligencer you may ask yourself uneasily, “What is this anyway—a mathematical journal, or what?” Or you may ask, “Where am I?” Or even “Who am I?” This sense of disorientation is at its most acute when you open to Colin Adams’s column. Relax. Breathe regularly. It’s mathematical, it’s a humor column, and it may even be harmless.     

Rumpled stiltskin

Opening a copy of The Mathematical Intelligencer you may ask yourself uneasily, “What is this anyway—a mathematical journal, or what?” Or you may ask, “Where am I?” Or even “Who am I?” This sense of disorientation is at its most acute when you open to Colin Adams’s column. Relax. Breathe regularly. It’s mathematical, it’s a humor column, and it may even be harmless.     

Journey to the center of mathematics

Opening a copy of The Mathematical Intelligencer you may ask yourself uneasily, “What is this anyway—a mathematical journal, or what?” Or you may ask, “Where am I?” Or even “Who am I?” This sense of disorientation is at its most acute when you open to Colin Adams’s column. Relax. Breathe regularly. It’s mathematical, it’s a humor column, and it may even be harmless.     

The Math fall fashion preview

Opening a copy of The Mathematical Intelligencer you may ask yourself uneasily, “What is this anyway—a mathematical journal, or what?” Or you may ask, “Where am I?” Or even “Who am I?” This sense of disorientation is at its most acute when you open to Colin Adams’s column. Relax. Breathe regularly. It’s mathematical, it’s a humor column, and it may even be harmless.     

A killer theorem

Opening a copy of The Mathematical Intelligencer you may ask yourself uneasily, “What is this anyway—a mathematical journal, or what?” Or you may ask, “Where am I?” Or even “Who am I?” This sense of disorientation is at its most acute when you open to Colin Adams’s column. Relax. Breathe regularly. It’s mathematical, it’s a humor column, and it may even be harmless.     

Mangum,P.I.

Opening a copy of The Mathematical Intelligencer you may ask yourself uneasily, “What is this anyway —a mathematical journal, or what? ” Or you may ask, “Where am I? ” Or even “Who am I? ” This sense of disorientation is at its most acute when you open to Colin Adams ’s column. Relax. Breathe regularly. It ’s mathematical, it ’s a humor column, and it may even be harmless.     

Violence Hexagon

In this article I will show why and how it is useful to exploit the hexagon of opposition to have a better and new understanding of the relationships between morality and violence and of fundamental axiological concepts. I will take advantage of the analysis provided in my book Understanding Violence. The Intertwining of Morality, Religion, and Violence: A Philosophical Stance. Springer, Heidelberg/Berlin, 2011) to stress some aspects of the relationship between morality and violence, also reworking some ideas by John Woods concerning the so-called epistemic bubbles, to reach and describe my own concept of moral bubbles. The study aims at providing a simple theory of basic concepts of moral philosophy, which extracts and clarifies the strict relationship between morality and violence and more, for example the new philosophical concept of overmorality. I will also conclude that this kind of hybrid diagrammatic reasoning is a remarkable example of manipulative explanatory abduction—through drawing—in the spirit of “conceptual structuralism”, promoted by Robert Blanché and further developed by Jean-Yves Béziau.     

Trial and error

Opening a copy of The Mathematical Intelligencer you may ask yourself uneasily, “What is this anyway—a mathematical journal, or what?” Or you may ask, “Where am I?“ Or even “Who am I?” This sense of disorientation is at its most acute when you open to Colin Adams’s column. Relax. Breathe regularly. It’s mathematical, it’s a humor column, and it may even be harmless.     

Connecting theories in mathematics education: challenges and possibilities

This paper is a commentary on the problem of networking theories. My commentary draws on the papers contained in this ZDM issue and is divided into three parts. In the first part, following semiotician Yuri Lotman, I suggest that a network of theories can be conceived of as a semiosphere, i.e., a space of encounter of various languages and intellectual traditions. I argue that such a networking space revolves around two different and complementary “themes”—integration and differentiation. In the second part, I advocate conceptualizing theories in mathematics education as triplets formed by a system of theoretical principles, a methodology, and templates of research questions, and attempt to show that this tripartite view of theories provides us with a morphology of theories for investigating differences and potential connections. In the third part of the article, I discuss some examples of networking theories. The investigation of limits of connectivity leads me to talk about the boundary of a theory, which I suggest defining as the “limit” of what a theory can legitimately predicate about its objects of discourse; beyond such an edge, the theory conflicts with its own principles. I conclude with some implications of networking theories for the advancement of mathematics education.     

On the cusped fan in a planar portrait of a manifold

Stable maps into the plane are good tools to obtain “views” of higher dimensional manifolds. We introduce the planar portraits to define the “view” properly. To start studying their relation to manifolds, we restrict our attention to their basic piece called the cusped fan. Fibreing structures over the cusped fan are studied and given a geometric characterisation. As by-products, we supply various stable maps and planar portraits of closed manifolds. In particular, two infiniteness properties of planar portraits are shown by using these examples.