“History reflects a gradual ‘externalization’ of measurement in terms of Carnap’s terminology (1950): the development of measurement instruments is initially for ‘internal questions’ and moves gradually towards ‘external questions’. For example, parameters are internal within models, whereas the existence of models is external with respect to the parameters. Econometric research has moved from the issue of how to optimally estimate parameters to the harder issue of how to measure and hence evaluate the efficiency, fruitfulness and simplicity of the models, i.e. the relevance of models as measuring instruments.”
“[I]f a count of correct answers or a sum of ratings can provide a meaningful basis for invariant, additive quantification, then a Rasch model holds. Even when data are not evaluated for fit to a Rasch model, even when the invariance and additivity properties of quantitative measurement are ignored, use of test, survey, or assessment scores as though they are [unweighted] measures inherently implies acceptance of Rasch’s separability theorem.
This is because the parameter separation theorem is nothing less than a formal representation of the rigorous independence of figure and meaning, or of name and concept (Fisher, 2003a, 2003b, 2004b), that must be assumed in any communication, even in the discourses of deconstruction (Ricoeur, 1977, p. 293; Derrida, 1982, p. 229; Derrida, 1989, p. 218; Gasché, 1987, p. 5). Though not obvious on first blush, postmodern philosophy has multiple points of contact and potentially productive associations to be found in mathematics (Tasić, 2001). Rasch’s mathematics, for instance, make tests of the qualitative hypothesis of quantitative meaningfulness (Narens, 2002) more accessible and practical than most work in this area. And in so doing, it taps deeply into the history of measurement and deploys rich possibilities for mathematical thinking that remain largely unexplored (Wright, 1988, 1997).”
“Irving Fisher is widely known for what is called a separation theorem (I. Fisher, 1930, ch. 6-8). The basic principle is fundamentally the same as Rasch’s separability theorem, but with an economic twist. The theorem separates managerial opportunities for productivity from entrepreneurial market opportunities. The point is that a firm’s basic objective is the maximization of its current value, no matter what the investment preferences & financing sources of the owners happen to be
The Fisher Separation Theorem posits that investment budgeting decisions are made in a two-stage process. First, entrepreneurial capital investment decisions are held to be independent of the preferences of the owner, and second, the investment decision is independent of the financing decision. The story told by these relations became the basis of neoclassical macroeconomic theory, and each of them could be written as a multifaceted Rasch model (Linacre, 1989)”
“But, strictly speaking, it cannot be claimed that [social] contradictions and their fusion are merely the pure phenomena of the general contradiction. The circumstances and currents constituting it are more than its phenomena pure and simple. They derive from the relations of production, which are, of course, one of the terms of the contradiction, but at the same time its conditions of existence; from the superstructures, instances deriving from it, but with their own consistency and efficacy; from the international conjuncture itself, which intervenes as a determination with a specific role to play.
[…] The unity they constitute in this ‘fusion’ into a revolutionary rupture, is constituted by their own essence and efficacy, by what they are according to the specific modalities of their action. In constituting this unity, they reconstitute and consummate their basic animating unity, but at the same time they also bring out its nature: the ‘contradiction’ is inseparable from the total structure of the social body in which it is found, inseparable from its formal conditions of existence, even from the instances it governs; it is radically affected by them, determining and determined in one and the same movement by the various levels and instances of the social formation it animates; it might be called in principle overdetermined.”