Hi Julio, What you said was, "A "mapping" is just a symbolic concept to denote a relationship or transformation." I understood a mapping in mathematics to be: basically, a relationship between two sets, such that every element of one set corresponds to another element in the other set. We could express the relationship as some kind of function, and that function could I suppose have a fixed point. When you survey and compile e.g. national accounts aggregates, it looks very much like an empirical or empiricist exercise. In fact, it is not really so much that, because what you are actually doing is collecting data to fit with prior concepts to get your measure. You have this prior grid of concepts and classifications, and you collect observations which, turned into data using a classification grid, can be converted into aggregates that are consistent with the prior concepts. So really, the process is not: Experiential data -> formed concept. But: Concept -> experiential data -> measure of the concept. The mathematical analysis only gets off the ground, once you have defined the appropriately classified measuring units. It assumes that you have the measuring units. Mathematical analysis can reveal the quantitative implications, and therefore the logical coherence, of the measures, but the initial conceptual step of defining the measurement units is not a purely mathematical operation. You have to assume some conceptual distinctions before you begin to perform your mathematical operations. If there are disputes about what the concepts ought to be, mathematical analysis will not solve a great deal. At most you might be able to prove, that the quantitative consequences of adopting particular concepts are such, that some concepts seem more plausible or credible than others. And indeed nowadays this plays a big role in e.g. producing national accounts, since mathematical models are constructed to extrapolate the data for the aggregates from partial or incomplete data, which are used as valid and relevant indicators (a cost-saving method). To obtain e.g. quarterly GDP measures, for example, it is rarely possible to run full surveys four times a year. You have to extrapolate and adjust the data as more information becomes available. >From a data set, we can draw synthetic or inductive conclusions which are generalisations not fully reducible to particular data. A "theory" typically goes well beyond the data - there is typically much more theory, than relevant data to back up the theory. In social science, we frequently encounter the problem that a multiplicity of individual behaviours leads to an aggregate social result, a social condition which can be a "social force", such that the individual behaviours and the total social effect coexist and influence each other. Simply put, the parts act on the whole and the whole acts on the parts. The whole is then not reducible to the particular parts, but coexists with them. That is the sort of thing I had in mind. Dialectical analysis is typically concerned with these kinds of reciprocal causation. I personally think the vexed concept of abstract labour has been much misunderstood, because it is thought of as a fixed condition, rather than as an evolutionary category which gains additional dimensions as it develops. J.
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