First Order Theories of Individual Concepts and Propositions
Reference: John McCarthy (1979b). “First Order Theories of Individual Concepts and Propositions.” In J. E. Hayes, D. Michie, and L. I. Mikulich (eds.), Machine Intelligence 9, Ellis Horwood, pp. 129-147. (Version fetched is the revised 2000 reprint.) URL
Summary
McCarthy argues that knowledge, belief, wanting, and necessity can be formalised in ordinary sorted first-order logic — without modal operators, quotation, or possible-worlds machinery — by admitting individual concepts as first-class objects alongside the things that reify them. Where Frege had distinguished sense (the concept) from reference (the denotation), and where Carnap, Church, and Montague responded by extending logic, McCarthy responds by keeping logic ordinary and adding a domain of concepts plus a denot function mapping concepts to their denotations.
Thus Mike is the concept of Mike, mike is Mike himself, Telephone Mike is the concept of Mike’s telephone number, and telephone mike is the number. Know(Pat, Telephone Mike) is the proposition that Pat knows Mike’s telephone number; true Know(Pat, Telephone Mike) asserts it. Extensionality is expressed by explicit axioms: Know is extensional in its first (knower) argument but not its second, which is precisely why substituting equal telephone numbers inside Know fails. The paper works through knowing what vs knowing that, iterated knowledge, non-denoting concepts (Pegasus), belief, wanting, existence (via an Exists predicate that does not presuppose existence of the concept’s referent), and necessity — all in sorted FOL, with standard model theory available to study which concept-spaces satisfy which axioms.
The paper is McCarthy’s most developed statement of his reificationist, logicist methodology for mental attitudes: rather than extend the logic, extend the ontology. This is directly the substrate Elephant 2000 uses when it talks about speech acts committing agents to propositions and referring to past events and future obligations.
Key Ideas
- Reify concepts as objects in sorted FOL; no modal operators, no quotation.
denot function maps concepts to their referents; extensionality becomes an axiom about particular functions rather than a global property of the logic.Know(P, X) is extensional in P (the knower) but not in X (the knowand), explaining failure of substitutivity for knowledge.knowing what vs knowing that are distinct; both are expressible.- Non-existent referents (Pegasus) handled by
denotes(X, x) predicate rather than denot function, and by Exists/exists pair.
- Concept-valued variables, functions, and constants (capitalisation convention) vs object-valued lowercase counterparts.
Connections
Conceptual Contribution