id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
cv43nv9583f	Christopher Porter	Mathematical and Philosophical Perspectives on Algorithmic Randomness	2012		.txt	text/plain	554	13	25	Prior to evaluating the Martin-L f-Chaitin Thesis and related randomness-theoretic theses, in Chapters 8 and 9 we discuss two roles of definitions of randomness, both of which motivated much early work in the development of algorithmic randomness: the resolutory role of randomness, which is successfully filled by a definition of randomness that allows for the solution of problems in a specific theory of probability, and the exemplary role of randomness, which is successfully filled by a definition of randomness that counts as random certain sequences that exemplify the properties typically held by sequences chosen at random. Definitions filling the calibrative role allow us to calibrate the level of randomness necessary and sufficient for certain almost-everywhere results in classical mathematics to hold, while definitions filling the limitative role illuminate a phenomenon known as the indefinite contractibility of the notion of randomness.	cache/cv43nv9583f.txt	txt/cv43nv9583f.txt