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Originally Posted by zelda_pinwheel
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Wikipedia has a better guess (in my opinion) as to the origin of this confusion:
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A possible origin for this confusion in usage is the likeness of the word "beg" to the word "beget", which can mean "to originate." The phrase "to beget the question" might have been confused in time with the similar-sounding (but very different) notion from logic "to beg the question". An example of this usage is found in An Enquiry Concerning Human Understanding by David Hume, published in 1748: "This begets a very natural question; What is meant by a sceptic?" (Section XII).
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http://en.wikipedia.org/wiki/Beg_the_question