The curvature argument

Dasgupta (2015) has recently put forward a novel argument, which he calls the ‘curvature argument’, that aims to show that Galilean spacetime is not an ideal setting for our classical theory of motion. This paper examines the curvature argument and argues that it is not sound. The discussion yields a remark about the conditions under which a ‘symmetry argument’ demonstrates that a particular spacetime is a non-ideal setting for our theory of motion.     

“The True” in Gottlob Frege's “Über die Grundlagen der Geometrie”

In this essay, I examine the metaphysical and metalogical ramifications of Gottlob Frege's controversy with David Hilbert and Alwin Korselt, over Hilbert's Grundlagen der Geometrie. These ramifications include(1) Korselt's original appeals to general metatheoretic Deutungen (interpretations);(2) Hilbert's puzzling belief that whatever is consistent in some sense exists; and(3) Frege's semantic monist conviction that theoretical sense and reference (mathematical and other) must be eindeutig lösbar (uniquely solvable).My principal conclusions are(4) that Frege's position in (3) represented a pervasively dogmatic presumption that his newly discovered quantification theory must have a propositional metatheory (the True; the False); and(5) that this needless assumption adversely affected not only his polemic against the moderate semantic relativism of Hilbert and Korselt, but also his reception of type-theoretic ideas, and greatly facilitated his vulnerability to the sort of self-referential inconsistency Russell discovered in Grundgesetz V.These conclusions also seem to me to provide a conceptual framework for several of Frege's other arguments and reactions which might seem more particular and disparate. These include(6) his arbitrary restrictions on the range of second-order quantification, which undercut his own tentative attempts to give accounts of independence and semantic consequence;(7) his uncharacteristic hesitation, even dismay, at the prospect that such accounts might eventuate in a genuinely quantificational metamathematics, whose Gegenstände (objects) might themselves be Gedanken (thoughts); and, perhaps most revealingly(8) his otherwise quite enigmatic, quasi-stoic doctrine that genuine formal deduction must be from premises that are true.A deep reluctance to pluralize or iterate the transition from theory to meta-theory would also be consonant, of course, with Frege's vigorous insistence that there can be only one level each of linguistic Begriffe (concepts) and Gegenstände (objects). With hindsight, such an assumption may seem more gratuitous in the philosophy of language (where it contributed, I would argue, to Wittgenstein's famous transition to the mystical in 6.45 and 6.522 of the Tractatus); but its more implausible implications in this wider context seemed to emerge more slowly.In the mathematical test-case discussed here, however, such strains were immediately and painfully apparent; the first models of hyperbolic geometry were described some thirty years before Frege drafted his polemic against Hilbert's pioneering exposition. It is my hope that a careful study of Frege's lines of argument in this relatively straightforward mathematical controversy may suggest other, parallel approaches to the richer and more ambiguous problems of his philosophy of language.Niemand kann zwei Herren dienen. Man kann nicht der Wahrheit dienen und der Unwahrheit. Wenn die euklidische Geometrie wahr ist, so ist die nichteuklidische Geometrie falsch, und wenn die nichteuklidische wahr ist, so ist die euklidische Geometrie falsch.No one can serve two masters. One cannot serve truth and untruth. If Euclidean geometry is true, non-Euclidean geometry is false, and if non-Euclidean [geometry] is true, Euclidean geometry is false. Über Euklidische Geometrie [Frege 1969], p. 183.     

A massive phytoplankton bloom induced by an ecosystem-scale iron fertilization experiment in the equatorial Pacific Ocean

The seeding of an expanse of surface waters in the equatorial Pacific Ocean with low concentrations of dissolved iron triggered a massive phytoplankton bloom which consumed large quantities of carbon dioxide and nitrate that these microscopic plants cannot fully utilize under natural conditions. These and other observations provide unequivocal support for the hypothesis that phytoplankton growth in this oceanic region is limited by iron bioavailability.     

Detecting MoS2 and MoSe2 with optical contrast simulation

Optical imaging is a promising method to identify and locate 2D materials efficiently and non-invasively. By putting a 2D material on a substrate, the nanolayer will add to an optical path and create a contrast to the case when the nanolayer is absent. This optical contrast imaging can be used to identify the 2D material and its number of layers. To make the optical imaging process in the laboratories an effective tool, Fresnel Law as a model was used to simulate the optical imaging results of 2D materials(graphene, Mo S2 and MoSe_2) on top of different thickness of SiO_2 and Si wafer in the present investigation. The results provide the details of the optimal conditions(optimal light wavelength and optimal SiO_2 thickness) to identify and locate single to few 2D nanolayers, which can be used directly in laboratories. The optical contrasts of 1–5 layers of molybdenum disulfide(MoS_2) and molybdenum diselenide(MoSe_2) were simulated. To the best of our knowledge, it is the first time that the optical contrast results of MoSe_2 have been reported. In particular, this work highlights the sensitivity of the model on the accuracy of the refractive indices used. It is demonstrated that through computational modeling that optical contrast can allow effective determination of number of layers in few layer 2D materials.