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Natural languages have words for all the operators of first-order logic, modal logic, and many logics that have yet to be invented. They also have words and phrases for everything that anyone has ever discovered, assumed, or imagined. Aristotle invented formal logic as a tool (organon) for analyzing and reasoning about the ontologies implicit in language. Yet some linguists and logicians took a major leap beyond Aristotle: they claimed that there exists a special kind of logic at the foundation of all NLs, and the discovery of that logic would be the key to harnessing their power and implementing them in computer systems. Projects in artificial intelligence developed large systems based on complex versions of logic, yet those systems are fragile and limited in comparison to the robust and immensely expressive natural languages. Formal logics are too inflexible to be the foundation for language; instead, logic and ontology are abstractions from language. This reversal turns many theories about language upside down, and it has profound implications for the design of automated systems for reasoning and language understanding. This article analyzes these issues in terms of Peirce's semiotics and Wittgenstein's language games. The resulting analysis leads to a more dynamic, flexible, and extensible basis for ontology and its use in formal and informal reasoning.

DOI: 10.1007/978-90-481-8845-1_11

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