Metaphysics and Rasch Measurement

Campbell's Apparent Avoidance of Metaphysics

Norman Campbell (1920) remarks that:

"... one of the chief characteristics which distinguishes science from metaphysics, and the feature which makes men of science so averse from the latter, is that in science, but not in metaphysics, it is possible to obtain universal assent for conclusions, and to present results which do not lose their value because, when they are presented, they are so obvious as to be indubitable. I maintain that the results presented in this work are of that nature." (p. 10)

If "men of science find everything I have to say dull and trite and so familiar that it is not worth saying .... [p. 11:] I shall not be wholly disappointed. It will show at least that I have avoided metaphysics successfully. I am not sure that the most handsome compliment that anyone could pay my work would be to say that he knew it all before."

"But is it true that metaphysics can be avoided wholly in an attempt to probe to the foundations of science? (Now and henceforward I propose to use the word metaphysics, not as a mere term of abuse, but to denote the study which those who accept the status of metaphysician think valuable. So far as I can make out, the study consists in the investigation of reality and existence.) At some stage in our inquiry we must stop and accept judgments without argument; is it certain that these judgments will not be found to be metaphysical? Or again, are we sure that the process of reasoning by which we develop our conclusions from these fundamental judgments does not depend on the acceptance of doctrines that are distinctively metaphysical? The general opinion to-day is that science is in no way dependent on metaphysics; and the proof of independence which seems generally to be thought the most convincing is that persons holding the most diverse metaphysical views all agree in accepting the same scientific conclusion." (p. 11)

"...some men of science [e.g., E. Weichert, 1911, Phys. Zeit. 12:702] hold that science depends on the proposition, apparently metaphysical, that matter is real and exists; and many of those who are ready to assent verbally to the independence [of science from metaphysics] are apt to show great annoyance if any one dares to deny that proposition. Again many metaphysicians agree that science and metaphysics are independent only because they believe that science is not true in the same sense as is their own study; they grant its independence only at the sacrifice of its value." (p. 11)

"...we are all metaphysicians, physicists included. We are all interested in problems which the metaphysician attempts to solve. ... The world is not divided into those who do and those who do not hold metaphysical doctrines, but rather those who hold them for some reason and those who hold them for none." (p.12)

But We Are All Metaphysicians ...

Campbell interestingly takes as his criterion for successfully avoiding metaphysics as telling "men of science" only what they already know. This corresponds quite nicely with Heidegger's (1967) sense of science's mathematical metaphysics as teaching and learning through what is already known. The desire to avoid metaphysics is the same as the desire to base statements and inferences on what is known, and not on untestable or untested conjectures and speculations.

Campbell later claims to find the definition of metaphysical study obscure, saying it "consists in the investigation of reality and existence," but he is perceptive in wondering whether the process of reasoning does not depend on an at least implicit acceptance of metaphysical doctrines. He would even seem wise in recognizing that "we are all metaphysicians" whether we recognize it or not.

Problematic Positivism

As a philosopher of science, and especially as a philosopher of measurement, Campbell is unusual in accepting this point. Western philosophy, especially in matters scientific and mathematical, has a long history of positivism, which rejects metaphysics as nonsense. Positivism thus puts itself in the position of holding that it is possible to apprehend parts with no theory as to the whole to which they belong. This becomes problematic, as Campbell recognizes, as soon as any question arises as to how any instance of a species of thing is recognized. As Burtt (1954, p. 228) puts it, "even the attempt to escape metaphysics is no sooner put in the form of a proposition than it is seen to involve highly significant metaphysical propositions." And similarly, as Derrida (1978, pp. 280-1) wrote,

"There is no sense in doing without the concepts of metaphysics in order to shake metaphysics. We have no language-no syntax and no lexicon-which is foreign to this history; we can pronounce not a single destructive proposition which has not already had to slip into the form, the logic, and the implicit postulations of precisely what it seeks to contest."

Gadamer (1994, p. 187) concurs, and Burtt (1954, p. 229) accordingly asks,

"... what kind of metaphysics are you likely to cherish when you sturdily suppose yourself to be free of the abomination? Of course . . . in this case your metaphysics will be held uncritically because it is unconscious; moreover, it will be passed on to others far more readily than your other notions inasmuch as it will be propagated by insinuation rather than by direct argument."

All this notwithstanding, the philosopher Hume famously proposed that all works of metaphysics lacking quantity, number, and matters of fact be burned (Ayer, 1952, p. 54), and his attitude is apparently shared by the vast majority of today's working scientists. Campbell, in contrast, does well to point out that questions concerning the real existence of what scientists purport to measure are metaphysical questions that often provoke great annoyance when asked of some researchers.

Intentional and Unintentional Metaphysics

And here we encounter a subtle irony. A work can be metaphysical in two ways, one intentional and the other not, as Campbell notes. Overtly metaphysical works are those that make and test explicit metaphysical postulates concerning reality and existence. Criteria for recognizing when something is real, as in able to persistently resist tests of its strength and so exist in stable states across samples, instruments, laboratories, investigators, time, space, etc., make a work metaphysical in a positive, though not positivist, sense by not attempting to avoid the inevitable.

Covertly metaphysical works are those that deny any role for metaphysics and that ignore or hide their metaphysical assumptions concerning the real existence of their objects of study. In this negative sense, a work is metaphysical to the extent that it leaves untested its assumptions concerning the nature of what is supposedly a matter of fact. The danger here is, of course, that science cannot rest content with merely confirming a researcher's prejudices and biases, but ought instead to subject these to close scrutiny and critical evaluation.

Overcoming metaphysics is then a matter of taking it up and using it (Gadamer, 1976, p. 240), since metaphysics must be presupposed even as we "get over it" (Heidegger, 1973, pp. 84-110; Gadamer, 1994, p. 164), a point missed by some commentators on the subject (Friedman, 1996). This is because, as Gadamer (1991) points out, even should we succeed in overcoming positivism's insufficient reductions and metaphysical blindness, there remains the constant danger

"of the systematic problem of philosophy itself: that the part of lived reality that can enter into the concept is always a flattened version-like every projection of a living bodily existence onto a surface. The gain in unambiguous comprehensibility and repeatable certainty is matched by a loss in stimulating multiplicity of meaning." (p. 7)

In other words, "all interpretation makes its object univocal and, by providing access to it, necessarily also obstructs access to it" (Gadamer 1991, p. 8).

Measurement and Metaphysics

In the human sciences, researchers persist in avoiding a positive use of metaphysics, and so wind up being metaphysical in the negative sense. As Michell (for instance, 2000) points out in his body of work, the most popular statistical methods in use leave untested vital hypotheses as to the quantitative structure of the variables purportedly measured by tests, surveys, and assessments. Unexamined metaphysics then remain uncritically insinuated within the measures and their rationales, with unknown potential consequences.

Rasch measurement, in contrast, especially when situated within a fully conceived and interconnected metrological system (Fisher, 2000), advances the work of overcoming metaphysics by starting from an explicit mathematical theory of what counts as real existence, applying that theory in tests of the quantitative hypothesis, and vigilantly persisting in attempting to prevent a fall into negative metaphysics (though this cannot be guaranteed) by routinely checking for adherence to the theory and by supporting decision making with replicable measures.

The Metaphysics of Meaning

Campbell says that we are all metaphysicians, but some of us take metaphysics seriously, and have good reasons for adhering to particular doctrines, while others dismiss metaphysics and wind up adhering to unarticulated doctrines for no reason. In the case of Rasch measurement, Campbell's observation is particularly apt, since the metaphysics of meaning hinge on being able to demonstrate an understanding in one's own words, or to translate representations across media (Latour, 1987). To put it more technically,

"The hallmark of a meaningless proposition is that its truth-value depends on what scale or coordinate system is employed, whereas meaningful propositions have truth-value independent of the choice of representation, within certain limits. The formal analysis of this distinction leads, in all three areas [measurement theory, geometry, and relativity], to a rather involved technical apparatus focusing upon invariance under changes of scale or changes of coordinate system" (Mundy, 1986, p. 392; also see Luce, 1978; Narens, 1981, 2002; Roberts, 1985).

By connecting numbers with invariantly additive amounts of the thing measured, Rasch models make generally accessible a heretofore only rarely attained level of meaningfulness. And meaningfulness is the most fundamental metaphysical assumption made in academic and scientific discourse. Even the most ardent deconstructionist writes, and in writing must assume that understandable meaning is communicable. This was well understood by Derrida (2003, p. 62) when he said that, in "playing with or transgressing norms," and in taking "liberties, it's always by measuring the distance from the standards I know or that I've been rigorously trained in."

Approaches to measurement that leave the quantitative hypothesis untested, in contrast, put their users in the ironic position of being more metaphysical than those who take up and use their metaphysics. In valuing quantitative methods, and in writing and publishing reports of their research, the vast majority of investigators in the human sciences are transgressing their own metaphysical doctrines concerning the transparency and generalizability of their results. But in opposition to Derrida's deconstructionist strategy, they do so in a way that blindly does not measure their distance from the measure-value standards they take for granted in any grocery store purchasing decision.

A Metaphysical Faith

Rasch measurement practitioners are sometimes criticized for being zealous adherents to what is said to be but one metaphysical faith among many equal faiths. But it seems to me that it is much more a matter of deciding where one's faith is best invested, in empirically tested and theoretically informed, generalizable, invariant meaningful mathematical structures, or in blindly assumed, atheoretical, and ungeneralizable scale-dependent scores? To paraphrase Derrida (1989, p. 218), as soon as you give up metaphysics, or the word metaphysics, and you think you have overcome it, defeated it, what happens is not something new or beyond metaphysics. Instead, what happens is that some old hidden metaphysics persists under the cover of another name, such as this new method or that collection of test items, or what have you, and the same old metaphysics goes on dominating the research in an implicit or dogmatic way. When you want to make this implicit metaphysics as clear as possible by establishing the invariance of truth-values over representations, you have to accept being a metaphysician and go on philosophizing.

Successful Scientific Metaphysics

In a field like ours, where the objects of investigation are still so early in their conceptual, gestational, and maturational processes that successful birthings are far from certainties, we must be as vigilant as possible in providing the nurturing environment needed to bring them to life. My bets are on the methods that take up and use the metaphysical assumptions that have proven foundational to the history of science. The ancient Greek metaphysics of learning through what is already known (sign and symbol systems), and what is learned in this way (writable meaning), comprise "the fundamental presupposition of all 'academic' work" and "of the knowledge of things" (Heidegger, 1967, pp. 75, 76). To be an academic is to accept in practice, if not in theory, "that we today, after two thousand years, are still not through with this academic work and never will be so long as we take ourselves seriously" (Heidegger, 1967, p. 76). The integration of theory and practice would seem to require further attention to our metaphysics, and efforts aimed toward achieving Campbell's goals of telling ourselves only what we already know, of not being annoyed by questions as to the reality of our objects of study, and of being prepared with good answers to those questions.

William P. Fisher, Jr.

Ayer, A. J. (1952). Language, Truth and Logic (2d). New York, New York: Dover.

Burtt, E. A. (1954/1932). The metaphysical foundations of modern physical science (Rev. ed.) [First edition published in 1924]. Garden City, New York: Doubleday Anchor.

Campbell, N. R. (1920). Physics, the elements. Cambridge, England: Cambridge University Press.

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Falmagne, J.-C., & Narens, L. (1983). Scales and meaningfulness of quantitative laws. Synthese, 55, 287-325.

Fisher, W. P., Jr. (2000). Objectivity in psychosocial measurement: What, why, how. Journal of Outcome Measurement, 4(2), 527-563.

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Gadamer, H.-G. (1976). Philosophical hermeneutics (D. E. Linge, Trans.). Berkeley: University of California Press.

Gadamer, H.-G. (1991). Plato's dialectical ethics: Phenomenological interpretations relating to the Philebus (R. M. Wallace, Trans.). New Haven, Connecticut: Yale University Press.

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Luce, R. D. (1978). Dimensionally invariant numerical laws correspond to meaningful qualitative relations. Philosophy of Science, 45, 1-16.

Michell, J. (2000, October). Normal science, pathological science and psychometrics. Theory & Psychology, 10(5), 639-667.

Mundy, B. (1986). On the general theory of meaningful representation. Synthese, 67, 391-437.

Narens, L. (1981). A general theory of ratio scalability with remarks about the measurement-theoretic concept of meaningfulness. Theory and Decision: An International Journal for Philosophy and Methodology of the Social Sciences, 13, 1-70.

Narens, L. (2002). Theories of meaningfulness (S. W. Link & J. T. Townsend, Eds.). Scientific Psychology Series. Mahwah, New Jersey: Lawrence Erlbaum Associates.

Roberts, F. S. (1985). Applications of the theory of meaningfulness to psychology. Journal of Mathematical Psychology, 29, 311-32.

Metaphysics and Rasch Measurement, W. P. Fisher, Jr. … Rasch Measurement Transactions, 2005, 18:4 p. 9

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