Generalism and the Metaphysics of Ontic Structural Realism

Ontic structural realism (OSR) claims that all there is to the world is structure. But how can this slogan be turned into a worked-out metaphysics? Here I consider one potential answer: a metaphysical framework known as generalism (Dasgupta, 2009, 2016). According to the generalist, the most fundamental description of the world is not given in terms of individuals bearing properties, but rather, general facts about which states of affairs obtain. However, I contend that despite several apparent similarities between the positions, generalism is unable to capture the two main motivations for OSR. I suggest instead that OSR should be construed as a meta-metaphysical position

Justifications-on-demand as a device to promote shifts of attention associated with relational thinking in elementary arithmetic

Student responses to arithmetical questions that can be solved by using arithmetical structure can serve to reveal the extent and nature of relational, as opposed to computational thinking. Here, student responses to probes which require them to justify-on-demand are analysed using a conceptual framework which highlights distinctions between different forms of attention. We analyse a number of actions observed in students in terms of forms of attention and shifts between them: in the short-term (in the moment), medium-term (over several tasks), and long-term (over a year). The main factors conditioning students´ attention and its movement are identified and some didactical consequences are proposed

Topology on cohomology of local fields

Arithmetic duality theorems over a local field $k$ are delicate to prove if $\mathrm{char} k > 0$. In this case, the proofs often exploit topologies carried by the cohomology groups $H^n(k, G)$ for commutative finite type $k$-group schemes $G$. These "\v{C}ech topologies", defined using \v{C}ech cohomology, are impractical due to the lack of proofs of their basic properties, such as continuity of connecting maps in long exact sequences. We propose another way to topologize $H^n(k, G)$: in the key case $n = 1$, identify $H^1(k, G)$ with the set of isomorphism classes of objects of the groupoid of $k$-points of the classifying stack $\mathbf{B} G$ and invoke Moret-Bailly's general method of topologizing $k$-points of locally of finite type $k$-algebraic stacks. Geometric arguments prove that these "classifying stack topologies" enjoy the properties expected from the \v{C}ech topologies. With this as the key input, we prove that the \v{C}ech and the classifying stack topologies actually agree. The expected properties of the \v{C}ech topologies follow, which streamlines a number of arithmetic duality proofs given elsewhere.Comment: 36 pages; final version, to appear in Forum of Mathematics, Sigm

Easing the transition from paper to screen: an evaluatory framework for CAA migration

Computer assisted assessment is becoming more and more common through further and higher education. There is some debate about how easy it will be to migrate current assessment practice to a computer enhanced format and how items which are currently re-used for formative purposes may be adapted to be presented online. This paper proposes an evaluatory framework to assess and enhance the practicability of large-scale CAA migration for existing items and assessments. The framework can also be used as a tool for exposing compromises between delivery mechanism and validity-exposing the limits of validity of modified paper based assessments and highlighting the crucial areas for transformative assessments