P658 | 4091 | J. Townsend

This will be a seminar on the axiomatic theory of measurment and scaling. The text will be Measurement Theory by Fred Roberts. The topics of types of measurement scale (e.g., absolute, ratio, interval, ordinal and nominal) and proofs of existence, and proving uniqueness of a measurement scale up to some level (e.g., ratio-- >uniqueness up to multiplication by a positive constant). The driving force will be the postulate that in assigning numbers to things in the real world, we are attempting to make quantitative statements that capture important qualitative facts and relationships about those things in said real world. The course will be reasonably mathematical and a good grasp of calculus is necessary. Also helpful, but not required would be some experience with naive set theory and/or real analysis or topology, and modern algebra. We will go through proofs of certain theorems, do some problems, and discuss the ramifications for psychological and cognitive science.