Internalism externalized. Doxastic Change, the Body, and Causation

One important element of a reliabilist account of knowledge\ud is the causal production of beliefs about the external\ud world. If such beliefs are thus produced they are likely to\ud be true. This is a strategy that is not available to internalism.\ud A strong link to Humean accounts of causation may\ud be implicit in internalist doctrines about justification since\ud they seem to assume the impossibility of justified beliefs\ud about genuine causal facts. But if it can be shown that\ud beliefs about causal facts are justifiable in the internalist\ud sense then this would decisively modify the unsatisfying\ud position of internalism regarding knowledge about the\ud external world. It will be argued that knowledge presupposes\ud doxastic change and that (i) beliefs about doxastic\ud change are indefeasibly justifiable, that (ii) such change is\ud not itself a doxastic entity, and (iii) that it involves causal\ud facts

Cutoff on Graphs and the Sarnak-Xue Density of Eigenvalues

It was recently shown by Lubetzky and Peres (2016) and by Sardari (2018) that Ramanujan graphs, i.e., graphs with the optimal spectrum, exhibit cutoff of the simple random walk in optimal time and have optimal almost-diameter. We prove that this spectral condition can be replaced by a weaker condition, the Sarnak-Xue density of eigenvalues property, to deduce similar results. We show that a family of Schreier graphs of the $SL_{2}\left(\mathbb{F}_{t}\right)$-action on the projective line satisfies the Sarnak-Xue density condition, and hence exhibit the desired properties. To the best of our knowledge, this is the first known example of optimal cutoff and almost-diameter on an explicit family of graphs that are neither random nor Ramanujan

Debt, Deficits and Inflation on the Road to the EU: the case of Turkey.

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