Epistemic norms, closure, and no-Belief hinge epistemology

Recent views in hinge epistemology rely on doxastic normativism to argue that our attitudes towards hinge propositions are not beliefs. This paper has two aims; the first is positive: it discusses the general normative credentials of this move. The second is negative: it delivers two negative results for No-Belief hinge epistemology such construed. The first concerns the motivation for the view: if we’re right, doxastic normativism offers little in the way of theoretical support for the claim that our attitudes towards hinge propositions are anything but garden-variety beliefs. The second concerns theoretical fruitfulness: we show that embracing a No-Belief view will either get us in serious theoretical trouble, or loose all anti-sceptical appeal

Pattern Avoidance in Poset Permutations

We extend the concept of pattern avoidance in permutations on a totally ordered set to pattern avoidance in permutations on partially ordered sets. The number of permutations on $P$ that avoid the pattern $\pi$ is denoted $Av_P(\pi)$. We extend a proof of Simion and Schmidt to show that $Av_P(132) \leq Av_P(123)$ for any poset $P$, and we exactly classify the posets for which equality holds.Comment: 13 pages, 1 figure; v2: corrected typos; v3: corrected typos and improved formatting; v4: to appear in Order; v5: corrected typos; v6: updated author email addresse

Geometric combinatorial algebras: cyclohedron and simplex

In this paper we report on results of our investigation into the algebraic structure supported by the combinatorial geometry of the cyclohedron. Our new graded algebra structures lie between two well known Hopf algebras: the Malvenuto-Reutenauer algebra of permutations and the Loday-Ronco algebra of binary trees. Connecting algebra maps arise from a new generalization of the Tonks projection from the permutohedron to the associahedron, which we discover via the viewpoint of the graph associahedra of Carr and Devadoss. At the same time that viewpoint allows exciting geometrical insights into the multiplicative structure of the algebras involved. Extending the Tonks projection also reveals a new graded algebra structure on the simplices. Finally this latter is extended to a new graded Hopf algebra (one-sided) with basis all the faces of the simplices.Comment: 23 figures, new expanded section about Hopf algebra of simplices, with journal correction

Knowledge‐first functionalism

This paper has two aims. The first is critical: I identify a set of normative desiderata for accounts of justified belief and I argue that prominent knowledge first views have difficulties meeting them. Second, I argue that my preferred account, knowledge first functionalism, is preferable to its extant competitors on normative grounds. This account takes epistemically justified belief to be belief generated by properly functioning cognitive processes that have generating knowledge as their epistemic function

Upward and Downward Counterfactual Thought After Loss:A Multiwave Controlled Longitudinal Study

Counterfactual thoughts, mental simulations about how a situation may have turned out differently (i.e., “if only …, then …”), can reduce mental health after stressful life-events. However, how specific counterfactual thought types relate to post-loss mental health problems is unclear. We hypothesized that self-referenced upward counterfactuals (i.e., “If only I had done …, then the current situation would be better”) may serve as cognitive avoidance, thereby perpetuating loss-related distress. Conversely, downward counterfactuals (i.e., “If … had happened, then the current situation could have been [even] worse”) may facilitate benefit finding, thereby reducing distress. In a longitudinal survey, self-referent, other-referent, and nonreferent upward counterfactuals, and nonreferent downward counterfactuals were assessed at baseline. Prolonged grief and depression symptoms were assessed at baseline, and 6- and 12-month follow-ups. Multiple regression analyses assessed associations between counterfactual thoughts and symptom levels in 65 recently bereaved people who generated counterfactual thoughts about the loss-event. Moderator analyses assessed the unicity of significant effects in the previous step, by comparing these effects in 59 people generating loss-related counterfactuals with those in 59 propensity-score matched participants generating counterfactuals about other negative life-events. Multivariate analyses showed that nonreferent upward counterfactuals were uniquely strongly positively associated with prolonged grief and depression symptoms concurrently. Self-referent upward counterfactuals were uniquely positively associated with prolonged grief and depression symptoms longitudinally. Moderator analyses confirmed that thinking about how one's (in)actions could prevent a death uniquely exacerbated prolonged grief and depression severity. Prolonged grief treatment may be improved by targeting self-blame and guilt

A parametric description of the 3D structure of the Galactic bar/bulge using the VVV survey

© 2017 The Authors. We study the structure of the inner Milky Way using the latest data release of the VISTA Variables in the Via Lactea (VVV) survey. The VVV is a deep near-infrared, multi-colour photometric survey with a coverage of 300 square degrees towards the bulge/bar. We use red clump (RC) stars to produce a high-resolution dust map of the VVV's field of view. From dereddened colour-magnitude diagrams, we select red giant branch stars to investigate their 3D density distribution within the central 4 kpc. We demonstrate that our best-fitting parametric model of the bulge density provides a good description of the VVV data, with a median percentage residual of 5 per cent over the fitted region. The strongest of the otherwise lowlevel residuals are overdensities associated with a low-latitude structure as well as the so-called X-shape previously identified using the split RC. These additional components contribute only ~5 per cent and ~7 per cent respectively to the bulge mass budget. The best-fitting bulge is 'boxy' with an axial ratio of [1:0.44:0.31] and is rotated with respect to the Sun-Galactic Centre line by at least 20°. We provide an estimate of the total, full sky, mass of the bulge of MbulgeChabrier= 2.36 × 1010M⊙for a Chabrier initial mass function. We show that there exists a strong degeneracy between the viewing angle and the dispersion of the RC absolute magnitude distribution. The value of the latter is strongly dependent on the assumptions made about the intrinsic luminosity function of the bulge