Fatalism and Future Contingents

In this paper I address issues related to the problem of future contingents and the metaphysical doctrine of fatalism. Two classical responses to the problem of future contingents are the third truth value view and the all-false view. According to the former, future contingents take a third truth value which goes beyond truth and falsity. According to the latter, they are all false. I here illustrate and discuss two ways to respectively argue for those two views. Both ways are similar in spirit and intimately connected with fatalism, in the sense that they engage with the doctrine of fatalism and accept a large part of a standard fatalistic machinery

Thermal Wave Measurements with a Mirage Detection for Investigation of Thermal Diffusivity of GdCa4O(BO3)3 Single Crystals

Single crystals of GdCa4O(BO3)3 were examined to determine their thermal properties. Samples were grown by the Czochralski pulling technique. There were three types of samples: a pure crystal, the crystal doped with neodymium (4 at.% of Nd), and the third one doped with ytterbium (7 at.% of Yb). All samples were rectangular prisms with edges parallel to the axes of the optical indicatrix X, Y , Z (principal axes). The thermal diffusivity was determined by means of the thermal wave method with the optical detection of the temperature disturbance based on a mirage effect. Experimental results showed anisotropy of the thermal diffusivity. The thermal diffusivity along Y direction has the highest value while values obtained in X and Z axes are much lower. Dopants cause decrease in the thermal diffusivity for all investigated directions

Studying Algebraic Structures Using Prover9 and Mace4

In this chapter we present a case study, drawn from our research work, on the application of a fully automated theorem prover together with an automatic counter-example generator in the investigation of a class of algebraic structures. We will see that these tools, when combined with human insight and traditional algebraic methods, help us to explore the problem space quickly and effectively. The counter-example generator rapidly rules out many false conjectures, while the theorem prover is often much more efficient than a human being at verifying algebraic identities. The specific tools in our case study are Prover9 and Mace4; the algebraic structures are generalisations of Heyting algebras known as hoops. We will see how this approach helped us to discover new theorems and to find new or improved proofs of known results. We also make some suggestions for how one might deploy these tools to supplement a more conventional approach to teaching algebra.Comment: 21 pages, to appear as Chapter 5 in "Proof Technology in Mathematics Research and Teaching", Mathematics Education in the Digital Era 14, edited by G. Hanna et al. (eds.), published by Springe

33000 Photons per MeV from Mixed (Lu0.75Y0.25)3Al5O12:Pr Scintillator Crystals

(LuxY1-x)3Al5O12:Pr (x = 0.25, 0.50, 0.75) crystals have been grown by the Czochralski method and their scintillation properties have been examined. Compared to the well-respected LuAG:Pr scintillator, which has so extensively been studied in the recent years, the new mixed LuYAG:Pr crystals display markedly higher light yields, regardless of the value of x. In particular, (Lu0.75Y0.25)3Al5O12:0.2%Pr characterized by a yield of 33000 ph/MeV, an energy resolution of 4.4% (at 662 keV), and a density of 6.2 g/cm3, seems to be an ideal candidate to supercede Lu3Al5O12:0.2%Pr (19000 ph/MeV, 4.6%, 6.7 g/cm3) in various applications. The observed enhancement of light output following the partial substitution of lutetium by yttrium is most probably related to some specific differences in distributions of shallow traps in particular materials