FIRST ORDER THEORIES OF INDIVIDUAL CONCEPTS AND PROPOSITIONS

John McCarthy, Stanford University

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Abstract:

We discuss first order theories in which individual concepts are admitted as mathematical objects along with the things that reify them. This allows very straightforward formalizations of knowledge, belief, wanting, and necessity in ordinary first order logic without modal operators. Applications are given in philosophy and in artificial intelligence. We do not treat general concepts, and we do not present any full axiomatizations but rather show how various facts can be expressed.

• Introduction
• Knowing What and Knowing That
• Functions from Things to Concepts of them
• Relations between Knowing What and Knowing That
• Replacing Modal Operators by Modal Functions
• More Philosophical Examples-Mostly Well Known
• Propositions Expressing Quantification
• Possible Applications to Artificial Intelligence
• Abstract Languages
• Remarks and Acknowledgements
• References
• About this document ...