Introduction. Measurement, the use of quantitative structures to represent empirical phenomena, is probably the most basic notion in all of science. The landmark three-volume series Foundations of Measurement (FoM) is perhaps the single most influential treatment of this topic. Given its enormous impact, it would be worth reading for purely historical reasons. However, the material developed in FoM continues to be of considerable contemporary importance, and is also the basis of much current research.  The goal of this course is to get a solid overview of this remarkable work. Because of its size, some compromises will be necessary; our emphasis will be on breadth over depth. We will try to get a "big picture" of FoM and the general project it undertakes, recognizing that this comes at the cost of careful inspection of many details. In particular, we will spend little time on the proofs of the theorems. Instead, we will focus on how the definitions and theorems are developed into certain kinds of apparatus, and on the applications of the latter. (Rigorous proofs are supplied in the text, though, and persons wishing to delve into them will have ample opportunities.)

Reading. Foundations of Measurement (Volumes 1, 2, and 3) was relatively recently reissued as inexpensive Dover paperbacks, available from Amazon here, here, and here.

Requirements. This seminar will have the format of a reading group, and those enrolled in the course will be expected to be active and informed participants. Enrollees will also be expected to do their share of presenting of the material, and to prepare accordingly. Satisfaction of the above two requirements is sufficient. However, students who wish to complete the course in some alternative way should feel free to negotiate with me for an alternative strategy. Auditors, of course, are welcome.

  1. March 28: Vol. 1, Chapters 1 - 2: Introduction, Construction of numerical functions, Extensive measurement [Kent] Presentation
  2. April 4: Vol. 1, Chapters 3 - 4: Extensive measurement, Difference measurement [Tucker] Chap03  Chap04
  3. April 11: Vol. 1, Chapters 5 - 6: Probability representations, Additive conjoint measurement [Brett] Presentation
  4. April 18: Vol. 1, Chapters 7 - 8: Polynomial conjoint measurement, Conditional expected utility [Skyler] Presentation
  5. April 25: Vol. 1, Chapters 9 - 10: Measurement inequalities, Dimensional analysis and numerical laws [Greg] Presentation
  6. May 2: Vol. 2, Chapters 11 - 13: Overview, Geometrical representations, Axiomatic geometry and applications [Bennett]
  7. May 9: Vol. 2, Chapters 14 - 15: Proximity measurement, Color and force measurement [Cailin] Presentation
  8. May 16: Vol. 2, Chapters 16 - 17: Representations with thresholds, Representations of choice probabilities [Jenny] Presentation
  9. May 23: Vol. 3, Chapters 18 - 20: Overview, Nonadditive representations, Scale types [Bennett, Tucker] Chap19 Chap20
  10. May 30: Vol. 3, Chapters 21 - 22: Axiomatization, Invariance and meaningfulness [Jenny, Brett]
  11. June 6:
Further Reading. There has been a substantial literature on measurement since Foundations of Measurement. Some good examples include: