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First you have to give a specific definition for thinking and reasoning before determining if they definitely do or don't do such a thing.
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Fair enough, I should have phrased that less strongly. Until you show that your neural net does "thinking" or "reasoning" I'll disregard that and prefer to think about it in terms of what we actually know neural nets actually do. Does that work?
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Just start with your definition for reasoning. If A implies B, and B implies C, does A imply C? Does that count as reasoning?
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