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Not all mathematical questions can be resolved, according to Gödel’s famous incompleteness theorems. It turns out that machine learning can be vulnerable to undecidability too, as is illustrated with an example problem where learnability cannot be proved nor refuted.
"The advantages of mathematics, however, sometimes come with a cost. Gödel and Cohen showed, in a nutshell, that not everything is provable. Here we show that machine learning shares this fate. We describe simple scenarios where learnability cannot be proved nor refuted using the standard axioms of mathematics."
PAUL BIRCH THE ENTROPY OF CHOICE
INCOMPLETE DRAFT -- DO NOT DISTRIBUTEThe nature of universal moral law is considered. It is argued that simple formulations, including the utilitarian criterion of the "greatest good of the greatest number" are flawed; that codes of ethics such as the ten commandments, though useful, are only contingent; and that other descriptions appear arbitrary. To overcome these difficulties a new moral concept and a corresponding moral principle are presented: these are the Entropy of Choice, and the Maximisation of the Entropy of Choice.
1. THE NATURE OF MORAL LAW
If Moral Law exists, we might conceive it as either absolute or relative — as universal, or cultural, or personal. However, if it is in fact only relative or contingent, if it is nothing more than the outcome of a particular physical and cultural environment (that might have been otherwise), then although it may have pragmatic value, it can have no fundamental claim on our allegiance. For Morality to have any meaning, it must be Absolute. Or so I contend.
One assumption must be made at the outset: that free will exists. Without free will, there could be no moral law, only physical law. Worse, the whole edifice of reason is based upon the premise that human thought is more than mere computation (since a computer can be programmed even more readily to produce nonsense than to produce sense, yet has of itself no possibility of determining which is which, being as totally confident of its wrong answers as its right ones). This is not to suggest that human actions must be regarded as completely free, unconstrained by our physical or spiritual nature: rather, that they are not wholly predetermined; that some element of choice remains.
In this episode of the podcast, Sam Harris speaks with Renée DiResta about Russia's "Internet Research Agency" and its efforts to amplify conspiracy thinking and partisan conflict in the United States.