Fine and Antonelli introduce two generalizations of permutation invariance — internal invariance and simple/double invariance respectively. After sketching reasons why a solution to the Bad Company problem might require that abstraction principles be invariant in one or both senses, I identify the most fine-grained abstraction principle that is invariant in each sense. Hume’s Principle is the most fine-grained abstraction principle invariant in both senses. I conclude by suggesting that this partially explains the success of Hume’s Principle, and the comparative lack (...) of success in reconstructing areas of mathematics other than arithmetic based on non-invariant abstraction principles. (shrink)

This essay argues that Hume's political and historical thought is well read as skeptical and skeptical in a way that roots it deeply in the Hellenistic traditions of both Pyrrhonian and Academical thought. It deploys skeptical instruments to undermine political rationalism as well as theologically and metaphysically political ideologies. Hume's is politics of opinion and appearance. It labors to oppose faction and enthusiasm and generate suspension, balance, tranquility, and moderation. Because Hume advocate the use of reflectively generated but epistemically and (...) metaphysically suspensive general rules, his political thought is not intrinsically conservative. While it valorizes stability and peace, Humean politics accepts a contested and open-ended political order, one that requires continuous maintenance and revision but does not pretend to any ultimate or final progress or end. (shrink)