Toward a Markedly More Accurate Geography of Minds, Machines, and Math

The research will produce answers to the two Templeton Foundation-posed questions (both of which are sharpened in the Project Description, to among other things bring them in line with the research expertise and prior accomplishments of Bringsjord's lab). The answers can be encapsulated as follows. A1: The advance of human knowledge via mathematics has apparently encountered three limits: Limit 1: Human knowledge and intelligence appears to make use of extensional infinitary content and reasoning. Limit 2: In the intensional sphere, human knowledge and intelligence appears to call for a logical system having many, many intensional operators-many more than have been successfully formalized in any extant system. Limit 3: The formal science of human knowledge and intelligence appears to be limited by the fact that current frameworks do not allow the integration of symbolic/linguistic content and reasoning, with visual content/reasoning. A2: The difficulties of AI, when viewed objectively, have taught us three significant lessons, namely: Lesson 1: While computing machines can be given knowledge and corresponding programs by clever humans so as to enable these machines to produce human-level behavior, this shows only that humans are clever enough to mechanize some of their own intelligence, not that machines can themselves be human-level intelligent. Lesson 2: AI needs high-expressivity computational intensional logics that would exceed Limit 2 from above. And Lesson 3: Natural language processing is astonishingly difficult-which explains why no computational artifact is even close to being a conversational computer that genuinely understands natural language given to it as input, nor natural language that it generates.