Frege's Ten Organizing Principles
1. Anti-psychologism
Words are not marks or indicators of psychological states ('ideas', for Locke).
2. The Compositionality Principle
The meaning of a sentence is a function of the meanings of its parts.
3. The Context Principle
The meaning of an expression is given by the linguistic contexts into which it enters.
4. Sense and Reference
Any fully meaningful expression has two kinds of meaning: The reference of the expression and the sense of the expression which determines its reference.
5. Transparency and Objectivity of Sense
Senses are objective, real, mind-independent, and secure the capacity of language users to communicate.
6. Concept and Object
Names refer to objects, if they refer at all, while predicates refer to concepts, which Frege construes as functions mapping objects to truth values.
7. Substitutivity of Identicals
Co-referring names may be replaced one for the other, salva veritate, in any statement in which they occur.
8. Extensionality
Co-extensional predicates may be replaced one for the other, salva veritate, in any statement in which they occur.
9. Ideal Language
In a perfectly regimented language, names and predicates would be mapped one-to-one and onto objects and concepts, respectively.
10. Logicism
In an ideal mathematical language (but see his "Begriffschrift"), the truths of mathematics would be shown to be entirely reducible to truths of logic.