Measurement in Psychology: A Critical History of a Methodological Concept (Ideas in Context)
This ebook lines how the sort of probably immutable concept as dimension proved so controversial whilst it collided with the subject material of psychology. This ebook addresses philosophical and social affects (such as scientism, practicalism, and Pythagoreanism) reshaping the idea that of dimension and identifies a basic challenge on the center of this reshaping: the problem of no matter if mental attributes fairly are quantitative. the writer argues that the assumption of size now recommended inside of psychology really subverts makes an attempt to set up a really quantitative technology, and he urges a brand new course. This quantity relates perspectives on dimension through thinkers resembling Hölder, Russell, Campbell, and Nagel to past perspectives, like these of Euclid and Oresme. in the heritage of psychology, it considers contributions by way of Fechner, Cattell, Thorndike, Stevens and Suppes, between others. It additionally features a nontechnical exposition of conjoint size idea and up to date foundational paintings through top dimension theorist R. Duncan Luce. This thought-provoking booklet may be fairly valued through researchers within the fields of mental background and philosophy of technology.
With any symbols. For example, considering geometric axiom systems, 'It must be possible to replace in all geometric statements the words point, line, plane by table, chair, mug' (quoted in Weyl, 1970, p. 264). This is simply the familiar fact that validity depends upon the form of the argument and not its material. For example, the valid conclusion that Socrates is mortal from the facts that All men are mortal and Socrates is a man depends not upon the content of the specific.
Continuous quantity is Page 59 isomorphic to the system of positive real numbers. This makes explicit what is meant by the measure of one magnitude relative to another. Hölder's achievement here cannot be underestimated. Measurement had existed for millennia prior to the publication of his paper. At least since the time of Euclid, it.
Is the ratio of the magnitude, na, to the magnitude, a.19 However, at this point care must be taken. If b is any other magnitude of the same quantity, then 2 = (b + b)/b, or if c is a magnitude of a completely different quantity, then 2 = (c + c)/c. Since (a + a)/a = (b + b)/b = (c + c)/c, 2 is what is common to all of these structures. That is, it is a kind of structure. It is one magnitude's being double or being twice another, and so on, for other natural numbers. Hence, wherever there is.
Each mb (for all natural numbers, m). That is, each step along the a vector precedes, coincides with, or exceeds, any step along the b vector. How these two vectors relate overall (that is, the pattern of how successive steps within each vector relate between vectors) is the ratio between a and b. If at some point these vectors.
Latter sense, he thought, number, 'unlike all other fundamental magnitudes, is considered to have no dimensions' (1920, p. 301). Here he glimpsed the distinction between aggregate size and natural number, but failed to use it and, confusingly, continued to refer to both concepts as number. Aggregate size (the number of things of a kind in an aggregate) is not dimensionless because it is linked to a specific unit. If one concept is dimensionless and the other is not, they cannot be the same.