Psychology | Introduction to Foundational Measurement and Scaling
P747 | 3888 | Townsend, J.

There are not a lot of good books that are in print,
but we will copy sections, primarily from an excellent book by Fred
Roberts entitled simply "Measurement Theory".
FORMAT: I will do some lecturing and some of the material will
be presented by participants. We will do enough problems to understand
the material, but the atmosphere will be low-key. I expect plenty
of discussion.
BACKGROUND: Some modicum of mathematical maturity is requisite,
e.g., in calculus (analysis), abstract algebra, and/or set theory.
One might take a look at a copy of Roberts' book or such texts
as "Foundations of Measurement, Vol. I" by Krantz, Luce, Suppes &
Tversky (1971) to get a feel for the kind of material with which we
will deal.
NATURE OF SEMINAR: Foundational measurement has as its goal the
establishment of the theory of how (and perhaps "why" to some extent)
science should go about assigning numbers to objects and entities
(e.g., the mass of a diamond, the extremity of hunger, the
intelligence of a person) in such a way that certain properties and
operations of the number system accurately reflect underlying
physical (physiological, psychological, etc.) aspects and
relationships and operations carried out by the observing scientist.
As we shall see, in essence there are two basic types of theorems.
1. Existence theorems. 2. Uniqueness theorems. The first demonstrates
the existence of a certain kind of measurement scale applicable to a
given environment. The second expresses the degree of invariance
enjoyed by the numbers attached to the natural objects.  This program
leads to the formulation of the allowable kinds of measurement scales
and their various properties.  In addition to familiarizing yourself
with the quantitative apparatus, we will discuss a bit of the
history, philosophy and present limitations of this approach to