This chapter gives a detailed study of diagram-based reasoning in Euclidean plane geometry (Books I, III), as well as an exploration how to characterise a geometric practice. First, an account is given of diagram attribution: basic geometrical claims are classified as exact (equalities, proportionalities) or co-exact (containments, contiguities); exact claims may only be inferred from prior entries in the demonstration text, but co-exact claims may be asserted based on what is seen in the diagram. Diagram control by constructions is necessary (...) for this to work. Case-branching occurs when a construction renders a diagram un-representative. The roles of diagrams in reductio arguments, and of objection in probing a demonstration, are discussed. (shrink)

This chapter provides a survey of issues about diagrams in traditional geometrical reasoning. After briefly refuting several common philosophical objections, and giving a sketch of diagram-based reasoning practice in Euclidean plane geometry, discussion focuses first on problems of diagram sensitivity, and then on the relationship between uniform treatment and geometrical generality. Here, one finds a balance between representationally enforced unresponsiveness (to differences among diagrams) and the intellectual agent's contribution to such unresponsiveness that is somewhat different from what one has come (...) to expect in modern logic. Finally, challenges and opportunities for further work are indicated. (shrink)

In the correspondence with Clarke, Leibniz proposes to construe physical theory in terms of physical (spatio-temporal) relations between physical objects, thus avoiding incorporation of infinite totalities of abstract entities (such as Newtonian space) in physical ontology. It has generally been felt that this proposal cannot be carried out. I demonstrate an equivalence between formulations postulating space-time as an infinite totality and formulations allowing only possible spatio-temporal relations of physical (point-) objects. The resulting rigorous formulations of physical theory may be seen (...) to follow Leibniz' suggestion quite closely. On the other hand, physical assumptions implicit in the postulation of space-time totalities are made explicit in the reconstruction of the space-time versions from the physical-relation versions. (shrink)

This essay examines Meera Margaret Singh’s exhibition Nightingale in the time and place of the liminal space we call “hotel.” In intertexual dialogue with Wayne Koestenbaum’s Hotel Theory, the author not only reviews Singh’s intimate photographs of her mother, she reads the images with and against the architecture in which they are exhibited. The Gladstone as exhibition space redoubles Singh’s emphasis on the tense connectivity of apparent binaries: youth and age, public and private, artist and model, object and spectator, living (...) and dying. The quotidian activities of hotel living—guests’ arrivals, departures, and returns—become inextricable pieces of Singh’s site-specific installation. The author theorizes what Freud calls the “foretaste of mourning” in this work, grappling with what will be but is not yet the death of the mother. Singh’s Nightingale proposes that we do not “work through” mourning: mourning is a perpetual way of being in the present. (shrink)

An infinitary characterisation of the first-order sentences true in all substructures of a structure M is used to obtain partial reduction of the decision problem for such sentences to that for Th(M). For the relational structure $\langle\mathbf{R}, \leq, +\rangle$ this gives a decision procedure for the ∃ x∀ y-part of the theory of all substructures, yet we show that the ∃ x 1x 2 ∀ y-part, and the entire theory, is Π 1 1 -complete. The theory of all ordered subsemigroups (...) of $\langle\mathbf{R}, \leq, +\rangle$ is also shown Π 1 1 -complete. Applications in the philosophy of science are mentioned. (shrink)

We suggest that there can be epistemologically significant reasons why certain mathematical structures - such as the Real numbers - are more important than others. We explore several contexts in which considerations bearing on the choice of a fundamental numerical domain might arise. 1) Set theory. 2) Historical cases of extension of mathematical domains - why were negative numbers resisted, and why should we accept them as part of our fundamental numerical domain? 3) Using fewer reals in physics, without really (...) noticing. (shrink)

Review of Joel Faflak. Romantic Psychoanalysis: The Burden of the Mystery. Albany: State University of New York Press, 2008. 333 pages; paper $29.95. ISBN 978-0-7914-7269-0.

Summary This article seeks to address the question how the Tetrarchic system of four rulers could be presented as legitimate in a society that had never seen this political constellation before. What were the different modes of presenting Tetrarchic rule and how did they help in making the new system acceptable? The article argues that new power structures needed to be formulated in familiar terms, not only for the rulers to legitimate their position, but also for the ruled to understand (...) such new systems. As a result, imperial messages during the Tetrarchic period were strongly influenced by traditional modes of representation from earlier periods. Traditions which were inherent in specific media and locations were determining factors for the way in which a new political system could be presented. The result was a much less coherent ideological Tetrarchic message than is often assumed. The image of group identity was regularly lost in a more complex and messy mode of formulating power. The new and innovative aspects of a collegiate rule by four emperors was less important than linking the power of those rulers to what was traditionally expected of the portrayal of Roman emperorship. (shrink)

Summary Trajan’s status as a model emperor is perhaps most famously expressed in Eutropius’ catchphrase “More fortunate than Augustus, better than Trajan” (Eutr. Brev. 8.5.3). Modern scholarship has similarly stressed Trajan’s exemplary status, assuming that Trajan’s virtues were already a point of departure by which to measure second- and third-century emperors. This article challenges that notion; it argues that Trajan’s status as a model emperor was a late-antique literary construct. Trajan only entered the repertoire of exemplary emperors during the course (...) of the fourth century to become the model emperor in the very late-fourth- and early-fifth century. This development depended on the historical context and ideological demands, as well as on the availability of the then-existing material discussing and depicting the historical Trajan. (shrink)