Language and Ontology
Russell's model for a "logically perfect language" is the language of symbolic logic. I will use the "blocks language" in Barwise and Etchemendy, Language, Proof, and Logic, to illustrate.
| language | ontology |
| names (a, b, c, d, e, f) | particulars |
| predicates (arity 1: Tet, Dodec, Large, Small, etc. arity 2: Larger, LeftOf, etc.) |
properties and relations |
| atomic sentences (Tet(a), Larger(a, b)) | atomic facts (positive and negative) |
| truth-functional compounds (Tet(a) & Large(a)) | no new facts needed |
| propositional functions (Tet(x) & Large(x)) | don't express facts (incomplete) |
| universally quantified sentences Ax (Tet(x) -> Large(x)) | general facts |
| existentially quantified sentences Ex (Tet(x) & Large(x)) | existence facts |
Existence: Russell claims that it makes no sense to say that a particular exists. The concept of existence only makes sense in relation to propositional functions, when we say there exists something that satisfies the function. (What's a propositional function? Something like "Tet(x)" i.e. "x is a tetrahedron." You can think of this as a function that takes particulars as arguments and returns a proposition as value. A particular satisfies a propositional function if the proposition which is the value of the propositional function for that argument is true.)
Last
update: January 23, 2007 |