Noncomparabilities & Non Standard Logics

Many normative theories set forth in the welfare economics, distributive justice and cognate literatures posit noncomparabilities or incommensurabilities between magnitudes of various kinds. In some cases these gaps are predicated on metaphysical claims, in others upon epistemic claims, and in still others upon political-moral claims. I show that in all such cases they are best given formal expression in nonstandard logics that reject bivalence, excluded middle, or both. I do so by reference to an illustrative case study: a contradiction known to beset John Rawls\u27s selection and characterization of primary goods as the proper distribuendum in any distributively just society. The contradiction is avoided only by reformulating Rawls\u27s claims in a nonstandard form, which form happens also to cohere quite attractively with Rawls\u27s intuitive argumentation on behalf of his claims

How to insulate a reactive site from a perfluoroalkyl group : photoelectron spectroscopy, calorimetric, and computational studies of long-range electronic effects in fluorous phosphines P((CH2)m(CF2)7CF3)3

This study advances strategy and design in catalysts and reagents for fluorous and supercritical CO2 chemistry by defining the structural requirements for insulating a typical active site from a perfluoroalkyl segment. The vertical ionization potentials of the phosphines P((CH2)(m)R-f8)(3) (m = 2 (2) to 5 (5)) are measured by photoelectron spectroscopy, and the enthalpies of protonation by calorimetry (CF3SO3H, CF3C6H5). They undergo progressively more facile (energetically) ionization and protonation (P(CH2CH3)(3) > 5 > 4 approximate to P(CH3)(3) > 3 > 2), as expected from inductive effects. Equilibrations of trans-Rh(CO)(Cl)(L)(2) complexes (L = 2, 3) establish analogous Lewis basicities. Density functional theory is used to calculate the structures, energies, ionization potentials, and gas-phase proton affinities (PA) of the model phosphines P((CH2)(m)CF3)(3) (2'-9'). The ionization potentials of 2'-5' are in good agreement with those of 2-5, and together with PA values and analyses of homodesmotic relationships are used to address the title question. Between 8 and 10 methylene groups are needed to effectively insulate a perfluoroalkyl segment from a phosphorus lone pair, depending upon the criterion employed. Computations also show that the first carbon of a perfluoroalkyl segment exhibits a much greater inductive effect than the second, and that ionization potentials of nonfluorinated phosphines P((CH2)(m)CH3)(3) reach a limit at approximately nine carbons (m = 8)

The Pierre Auger Observatory III: Other Astrophysical Observations

Astrophysical observations of ultra-high-energy cosmic rays with the Pierre Auger Observator