The hardness of the iconic must: Can Peirce’s existential graphs assist modal epistemology?

Charles Peirce’s diagrammatic logic - the Existential Graphs - is presented as a tool for illuminating how we know necessity, in answer to Benacerraf’s famous challenge that most “semantics for mathematics” do not “fit an acceptable epistemology”. It is suggested that necessary reasoning is in essence a recognition that a certain structure has the structure that it has. This means that, contra Hume and his contemporary heirs, necessity is observable. One just needs to pay attention, not just to individual things but to how those things are related in larger structures, certain aspects of which force certain others to be a particular way

The Lean Cuisine+ notation revised

The Lean Cuisine+ notation was developed by Chris Phillips (1995) as an executable semi-formal graphical notation for describing the underlying behaviour of event-based direct manipulation interfaces. Lean Cuisine+ builds on the original Lean Cuisine notation introduced in Apperley & Spence (1989). During the construction of a CASE tool for the notation, as well as further research into the use of the Lean Cuisine+ notation, various changes have been made and the revised notation is presented here. The format and much of the content of this document follows that of Appendix C of Phillips (1993) in order to easily distinguish between the earlier and later versions of the notation

Model atmospheres for massive gas giants with thick clouds: Application to the HR 8799 planets and predictions for future detections

We have generated an extensive new suite of massive giant planet atmosphere models and used it to obtain fits to photometric data for the planets HR 8799b, c, and d. We consider a wide range of cloudy and cloud-free models. The cloudy models incorporate different geometrical and optical thicknesses, modal particle sizes, and metallicities. For each planet and set of cloud parameters, we explore grids in gravity and effective temperature, with which we determine constraints on the planet's mass and age. Our new models yield statistically significant fits to the data, and conclusively confirm that the HR 8799 planets have much thicker clouds than those required to explain data for typical L and T dwarfs. Both models with 1) physically thick forsterite clouds and a 60-micron modal particle size and 2) clouds made of 1 micron-sized pure iron droplets and 1% supersaturation fit the data. Current data are insufficient to accurately constrain the microscopic cloud properties, such as composition and particle size. The range of best-estimated masses for HR 8799b, HR 8799c, and HR 8799d conservatively span 2-12 M_J, 6-13 M_J, and 3-11 M_J, respectively and imply coeval ages between ~10 and ~150 Myr, consistent with previously reported stellar age. The best-fit temperatures and gravities are slightly lower than values obtained by Currie et al. (2011) using even thicker cloud models. Finally, we use these models to predict the near-to-mid IR colors of soon-to-be imaged planets. Our models predict that planet-mass objects follow a locus in some near-to-mid IR color-magnitude diagrams that is clearly separable from the standard L/T dwarf locus for field brown dwarfs.Comment: Accepted for publication in Ap