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Hume proposed critical ways of investigating phenomenon. You need to indicate which Mill. The intersection of John Stuart Mill and David Hume's philosophy lies not in skeptical inquiry.
BUT if you are talking about utilitarianism, then that is easy!
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Hume proposed critical ways of investigating phenomenon? In what way? Did it cover things that a naturally non-falsifiable (or is that irrelevant here)? As for J.S. Mill it was just noted in the footnotes, so as Wright so I though they must somehow be related.
IT STARTS with this
Correct me if I am going wrong here, but what is being said is that Hume thought sensory perception was valuable (which is unlike Descartes), correct?
I wouldn't put it that way. Senses perception has a great deal of unreliability is the proper way to put it.
If you read carefully the abstract or intro in italics, this was almost a continuation of Locke's Essay Concerning Human Understanding.