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    The languages are designed like that because the math makes sense. That came first. Commented May 15, 2013 at 19:57
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    @Morwenn, it goes back to the 19th century and George Boole. People have been representing False as 0 and True as !0 for longer than there have been computers. Commented May 15, 2013 at 20:03
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    I don't see why the math doesn't work the other way if you merely change all of the definitions so that AND is + and OR is *. Commented May 15, 2013 at 21:49
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    Exactly: the math works both ways and the answer to this question seems to be that it is purely conventional. Commented May 15, 2013 at 21:51
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    @Robert It'd be great if you could spell out the "mathematical underpinnings" in your post. Commented May 15, 2013 at 21:59