A fundamental change in the way we think about science is taking place. This change primarily involves our understanding of the role of measurement in the relation between theory and data; the new understanding of measurement and scientific instrumentation seems to point decisively toward a model with features quite like those Rasch has brought together.
The work of philosophers of science such as Thomas Kuhn, Stephen Toulmin and Patrick Heelan, among many others, seriously questions the long-held view that the data of science are absolutely objective - that is, that data exists in an eternally given state, always factually self-evident to anyone, anywhere, anytime. That traditional view of scientific data is broadly called positivism. Auguste Comte, a nineteenth-century French philosopher, was largely responsible for explicating and popularizing positivism, though its elements were prominent in the work of many scientists, especially that of Isaac Newton.
In his work on optics, Newton disdained the need for any hypotheses to guide the accumulation of data in scientific research. Later social researchers, such as Emile Durkheim, wanted to bring the success of natural science in the establishment of facts to their field, and followed Newton's example, asserting the brute givenness of the data involved.
This view had become so much a part of scientific thinking that when Ronald Fisher recommended statistical methods to social researchers as the sole means by which social studies would be raised to the level of sciences, he completely overlooked the differences that exist between data in the natural sciences and that of the social sciences. Quantitative data of the sort used in Fisher's examples come from studies in biology or agriculture, and are read off calibrated instruments - instruments with an invariant additive structure.
The quantitative data of the social sciences are almost never of that sort. The data of social research are usually made up of numbers simply assigned to qualities with no attempt to justify that assignment through the establishment of structural correspondences between the conceptual measurement apparatus and the phenomenon measured. Of course, according to positivism, this was never done in the natural sciences, either; the factuality of the data was just naturally given. With the changes that have taken place in physics in this century, however, the historicality of what counts as a fact in the natural sciences has been made evident and has raised the problem of just what facts are if they can change from time to time.
Philosophy has turned more and more toward investigations of language in its attempts to resolve this problem. Workers such as Ludwig Wittgenstein and Martin Heidegger have changed the philosophy of science by showing that the conceptual status of things in language is of primary interest when the factuality of those things is in question. Concepts do not exist in nature, but we are born into a conceptual world insofar as language is the means through which we learn about life. Thus, scientific researchers become scientific researchers through socialization and training; the socialization and training are themselves constituted historically and conceptually, changing through time.
Following this line of thought, philosophy has arrived at an explanation of factuality that relies on contextualization for criteria as to what can count as data. The problem now is to reconcile this general context-dependency with a specific context- independency. Understandings are situated in general historical, cultural and linguistic contexts, but if these understandings are to mean anything at all they must be shared in a more specific fashion that is repeatable and relatively free from the influence of minor contextual changes.
Study of these issues led Heidegger to examine Plato's reasons for emphasizing the importance of keeping philosophy near to mathematics. In ancient Greek, ta mathemata is the mathematical, and mathesis means both learning and science. In his MENO dialogue, Plato makes plain that mathematical entities have two main features: they are those things that can be taught and learned, and they are learned through a reorganization of what is already known.
Hans-Georg Gadamer and Paul Ricoeur make some things explicit at this point that Heidegger leaves unexamined. They show that for something to be teachable and learnable in the Platonic sense the words and signs used to convey meaning must separate from that meaning. In a broad and relative way, words and signs must have a constancy to them that does not depend upon who is using them or upon where or when they are used, as long as everyone has been trained to understand the language involved.
This constancy constitutes a specific context-independence that is most evident in mathematics: when a geometrical analysis of a circle is performed anyone with a rudimentary appreciation of what is going on is thoroughly aware that what is being studied is not the property of this particular circle drawn in the dust, on the blackboard or on the page. Instead, we are all aware that it is the general idea of a circle that is involved, an idea that stands relatively and probabilistically independent of every particular example of it.
This combination of a general linguistic context-dependence with a specific context-independence is so essential for perceiving or conceiving anything that, in retrospect, it seems completely natural for it to have been overlooked by those who have tried to understand science in the past. Being a fundamental presupposition of conceptualization, it was bound to be overlooked until enough anomalous information emerged to highlight the outline of something lacking.
From this point of view, the importance of Plato's linking of philosophy and mathematics resides in the way that language provides the condition of the possibility of teaching and learning. It does this by fostering a convergence and correspondence between things and thought that can persist and endure beyond the instance of its inception. The idea that dominates the interaction in which correspondence occurs is seen to persist when its meaning is shared by others in a wider context. This is to say that when the original convergence of thing and thought takes a place in the history, culture and language involved something is said to someone about something such that what is said takes on a life of its own and becomes a part of the world into which others are born.
Plato's link between mathematics and the philosophical considerations of the possibility of this happening persists in our language today. Our very concept of rationality refers to the mathematical ratio between what something probably is and what it probably is not that goes into every act of recognition and learning. Beyond this, we commonly speak of understanding in terms of getting something straight, of delineating an idea, of the dimensions of experience, of how things figure or add up, and of ruling something out, or putting things in proper order.
Scientific measurement is always uni-dimensional because the only way to tell what counts in life is to take things one at a time. For things to add up, conceptually as well as numerically, the arrow of meaning can go only in one direction - otherwise its path is impossible to follow. Multi-dimensional analyses of raw data make no effort toward knowing just what it is they are dealing with; the variables may be mixtures of things that the researcher ought to be concerned with but is oblivious to.
Definition of the variable remains incomplete so long as Plato's sense of the instructiveness of mathematics is left out of our instruments. Data that do not take on a life of their own, separating from the particular respondents to be measured and the particular items used to measure, remain mired in specific context-dependencies that prevent generality from being attained. When Rasch and Wright speak of specific objectivity, the separability theorem, sample-free instrumentation, instrument-free measurement or the convergence of items and persons in an MSCALE analysis, they are speaking of a realization of new potentials in the historical possibilities presented to us by science that have remained implicit until now. No other measurement models or quantitative methods reach as far into the history of science or grasp as much concerning our possibilities as those gathered together under the name of Rasch.
Philosophy of science and objectivity. Fisher WP Jr. Rasch Measurement Transactions 2:2 p.22-3
Philosophy of science and objectivity. Fisher WP Jr. Rasch Measurement Transactions, 1988, 2:2 p.22-3
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