Abstract
Measurement theory in (Hand in The world through quantification. Oxford University Press, 2004; Suppes and Zinnes in Basic measurement theory. Psychology Series, 1962) is concerned with the assignment of number to objects of phenomena. Representational aspect of measurement is the extent to which the assigned numbers and arithmetics truthfully represent the underlying objects and their relations, and is characteristic to natural sciences; pragmatic aspect is the extent to which the assigned numbers serve purposes other than representing the underlying phenomena, and is characteristic to social sciences (Hand in The world through quantification. Oxford University Press, 2004). Here I criticise this distinction of representational and pragmatic measurements on the basis of the earlier history of the periodic system of chemical elements, viewed in terms of a practice based philosophy of science by Rein Vihalemm. I argue that the periodic system, although a natural scientific system interpretable as a measurement system, has considerable, in Hand’s terms pragmatic, aspects in it. Those aspects include: tampering with the material measurement results for the theoretical ideal of systematicity; adopting metaphysical assumptions that cannot be experimentally proven, like individuality of elements and atomicity; theoretical construction of the abstract entity—element—as the reference of the measurement system amenable to mathematically elegant ordering. Contrary to Suppes and Zinnes (Basic measurement theory. Psychology Series, 1962) I also argue for the dependence of the assigned numerical system on the material-procedural base of the measurement.
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Notes
Philosophy of science in the Soviet Union was strongly influenced by Karl Marx’s “Theses on Feuerbach”, as all Soviet scholars were required to include obligatory references to Marxism-Leninism in their academic research (so-called ‘foreword Marxism’). The philosophers of science turned this requirement to their advantage by developing the practical realist approach to science (Vihalemm 2011, 2015; personal communication).
Not all mathematics is quantitative, and the mathematicity of empirical sciences can be understood more broadly than numericalness (cf. Vihalemm 2016). However, in the context of measurement theory and practice, numbers do matter, as they did for Mendeleev (see next chapter).
Clearly the product of this concatenation is equivalent to other objects in the same equivalence class only in terms of its atomic number, as e.g. Z(Cl) = 17, similarly Z(O + H) = 17, but Cl ≠ OH.
In Mendeleev’s (1869) parlance, ‘valency’ is ’atomicity’ (атомность), and ’univalent’ –’monatomic’ (одноатомный; accordingly he had the terms 'biatomic’, ’triatomic’ etc.).
Mendeleev knew of this variation: for instance he puts phosphor that is „3–5 atomic“ into group V (Mendeleev 1869).
An attempt of a full deployment of a possible arithmetic system of valencies would exceed the space limitations of this paper, particularly taking into account the complexities of this topic.
Absolute scale means “unique up to the identity transformation.” (Suppes and Zinnes 1962, p. 17).
Prout’s hypothesis: (1) “all atomic weights were integral number of hydrogen’s”, and (2) “all elements were composed of some form of primary matter […], [namely] hydrogen” (Gordin 2004, p. 215).
The modern generally accepted standard for the atomic mass unit is 1/12th of the atomic mass of 12C.
I will not go into the difficulties related to determining the atomic number here, but focus on those of the pre-atomic-number-era.
Although, perhaps, the concept of element would have gained a different meaning.
Hand does not delve into the difference between understanding and prediction. From his brief statements I conclude that the former is concerned with the real structure of the phenomenona, the latter with what is going to be done on the basis of the received model.
Hand (ibid, p. 17) admits that the discriminations between indirect, representational and pragmatic measurements may be fuzzy, because in what he calls indirect representational measurement, theoretical constructs are used to connect directly manifest and measurable properties with the variables which are not directly measurable (i.e. they are latent), and theories are nowadays considered not true or false but more or less adequate. Hence, not the truth but the effectiveness of the latent variable matters.
Although these two procedures measure different quantities, therefore pertaining to different measuring systems altogether, and cannot be compared in that sense, nonetheless, due to my interest here in the interpretation of the entire periodic system as a measuring system, these procedures are comparable in terms of their purpose, which is the primary ordering of elements and the determination of the scale which shapes and is shaped by the order of the elements.
Marian Przełęcki (1974) also considers an ERS to be an idealised system, in contrast to Suppes (1959). He argues that an NRS entails an infinite set, therefore presupposing the possibility of measuring arbitrarily large values of a given attribute (in his case, mass), which is not possible materially. That is, no material ERS can correspond to such an NRS, thence its idealised character.
Atomic weight = valency * equivalent weight (Scerri 2007, p. 37).
EVEN—equal volumes of gases contain equal number of particles (Scerri 2007, p. 38).
However, Przełęcki (1974) argues that even if units are uniquely determined, ambiguity may remain in the meaning of sentences due to material operations of measurement.
For extensive properties (mass, length), proportionality is rather obvious and easily defined through the concatenation procedure; for intensive properties (temperature, pressure), the proportionality can be established through more hidden and indirect relations (between the underlying processes or properties defining it).
Bensaude-Vincent (1982) understands interpolation in the context of the periodic table as deriving values between the known, observed values of properties of elements, and extrapolation as deriving values exceeding the maximum of observed values.
‘E’ stands for ‘element’. Following the rule of simplicity, Dalton presumed compounds’ particles to contain one atom of each constituent element (Scerri 2007, p. 36).
See also (Bensaude-Vincent and Stengers 1996, p. 115) on this.
“…the atomic weight of each element was the gravimetric proportion that combined with a gram of hydrogen to form the most stable combination” (Bensaude-Vincent and Stengers 1996, p. 114).
I replace Brooks’ ‘R’ with ‘E’ for unity of this paper.
Although I have not demonstrated the necessity of the concept of atom for (reaching) the periodic system, a proper discussion of this question would exceed the limits of this article.
References
Baird, D. C. (1964). Experimentation: An introduction to measurement theory and experiment design. Englewood Cliffs, NJ: Prentice-Hall.
Bensaude-Vincent, B. (1982). L’éther, élément chimique: un essai malheureux de Mendéléev? The British Journal for the History of Science, 15(2), 183–188.
Bensaude-Vincent, B. (1986). Mendeleev’s periodic system of chemical elements. The British Journal for the History of Science, 19(1), 3–17.
Bensaude-Vincent, B. (1997). Dix-neuvième bifurcation : anticipation ou résumé du passé? Mendeleïev: histoire d’une découverte. In Serres, Michel (ed.) (1997). Éléments d’histoire des sciences (pp. 665–696). Paris: Larousse-Bordas.
Bensaude-Vincent, B., & Simon, J. (2008). Chemistry: The impure science. London: Imperial College Press.
Bensaude-Vincent, B., & Stengers, I. (1996). A history of chemistry. Cambridge: Harvard University Press.
Brescia, F., Arents, J., Meislich, H., & Turk, A. (1975). Fundamentals of CHEMISTRY. New York, San Francisco, London: Academic Press.
Brooks, N. M. (2002). Developing the periodic law: Mendeleev’s work during 1869–1871. Foundations of Chemistry, 4, 127–147.
Campbell, N.R. (2012/1920). Physics, the elements. Forgotten Books/London: Cambridge University Press.
Chang, H. (2012). Is water H 2 O? Evidence, realism and pluralism. Boston Studies in the Philosophy of Science 293. Dordrecht: Springer.
D’Agostini, G. (1999). Bayesian reasoning in high-energy physics: Principles and applications. Geneva: CERN—Cervice d’information scientifique.
De Chancourtois, A.-É. B. (1862). Mémoire sur un classement des corps simples ou radicaux appelé vis tellurique. (Extraits par l’auteur). Comptes rendus hebdomadaires des séances de l’Académie des sciences, tome 54, janvier-juin 1862 (pp. 757–761). Paris: imprimerie de Mallet-Bachelier. Available: http://gallica.bnf.fr/ark:/12148/bpt6k30115/f757.image.
Döbereiner, J. W. (1895/1829). Versuch zu einer Gruppirung der elementaren Stoffe nach ihrer Analogie. In Meyer, J. L. (ed.) Die Anfänge des natürlichen Systemes der chemischen Elemente (pp. 3–8). Leipzig: Verlag von Wilhelm Engelmann.
Dumas, J.-B. (1859). Mémoire sur les équivalents des corps simples. Paris: Mallet-Bachelier. Available http://gallica.bnf.fr/ark:/12148/bpt6k90419b/f3.image.
Edwards, P. N. (1999). Global climate science, uncertainty and politics: Data-laden models, model-filtered data. Science as Culture, 8(4), 437–472.
Ellis, B. (1968). Basic concepts of measurement. Cambridge: Cambridge University Press.
Gordin, M. D. (2004). A well-ordered thing. Dmitrii Mendeleev and the shadow of the periodic table. New York: Basic Books.
Hand, D. J. (2004). Measurement theory and practice. The world through quantification: Oxford University Press.
Krantz, D. H., Duncan Luce, R., Suppes, P., & Tversky, A. (1971). Foundations of measurement. Volume I Additive and polynomial representations. Mineola, New York: Dover Publications.
Mendeléeff, D. (1891). The principles of chemistry volume I. New York and Bombay: Longmans, Green, and Co. Available https://play.google.com/books/reader?id=j9gKAAAAIAAJ&printsec=frontcover&output=reader&hl=en&pg=GBS.PR3.
Mendeléeff, D. (1897). The principles of chemistry volume II. New York and Bombay: Longmans, Green, and Co. Available https://archive.org/details/cu31924012367458.
Mendeléeff, D. (1901). The principles of chemistry (Part One). New York: P.F. Collier and Son. Available https://archive.org/details/principlesofchem01menduoft.
Mendeleev (Meндeлѣeв), D. (1869). Cooтнoщeнie cвoйcтвъ cъ aтoмнымъ вѣcoмъ элeмeнтoвъ (On the Correlation of the Properties and Atomic Weights of the Elements). Жypнaлъ pyccкaгo xимичecкaгo oбщecтвa. Toмъ I. 60–77 (in Russian). Available http://www.knigafund.ru/books/51872/read#page1 (a summary of it can be found in Mendeléeff 1897, footnote on p. 17).
Mukherjee, S. (2011). Applied mineralogy: Application in industry and environment. Dordrecht: Springer.
Pfanzagl, J. (1971). Theory of measurement. Würzburg, Wien: Physica-Verlag.
Przełęcki, M. (1974). Empirical meaningfulness of quantitative statements. Synthese, 26, 344–355.
Scerri, E. R. (2007). The periodic table: Its story and its significance. New York: Oxford University Press.
Stepin, V. (1999/2000). Theoretical knowledge. Moskva (in Russian).
Suppes, P. (1959). Measurement, empirical meaningfulness, and three-valued logic. In C. V. Churchman & P. Ratoosh (Eds.), Measurement: Definitions and theories (pp. 129–143). New York: Wiley.
Suppes, P., & Zinnes, J. L. (1962). Basic measurement theory. Psychology Series.
Tal, E. (2012). The epistemology of measurement: A model-based account (thesis). University of Toronto.
Van Brakel, J. (1984). Norms and facts in measurements. Measurement, 2(1), 45–51.
Van Brakel, J. (1990). Units of measurement and natural kinds: Some Kripkean considerations. Erkenntnis, 33, 297–317.
Van Spronsen, J. W. (1969). The periodic system of chemical elements. A history of the first hundred years. Amsterdam: Elsevier.
Vihalemm, R. (Ed.). (1979). Teaduse metodoloogia (Methodology of science). Eesti Raamat: Tallinn. (in Estonian).
Vihalemm, R. (2007). A. Whitehead’s metaphysical ontology and I. Prigogine’s scientific ontology: From a point of view of a theoretical conception of science. Problemos, 71, 78–89.
Vihalemm, R. (2008). How to understand science (2003). In Vihalemm, R. (Ed.), Teadusfilosoofilisest vaatepunktist (pp. 401–419). Eesti Keele Sihtasutus (in Estonian).
Vihalemm, R. (2011). Towards a practical realist philosophy of science. Baltic Journal of European Studies, 1(9), 46–60.
Vihalemm, R. (2015). Theoretical philosophy and philosophy of science in soviet times. Studia Philosophica Estonica, 8(2), 195–227.
Vihalemm, R. (2016). Science, φ-science, and the dual character of chemistry. In E. Scerri & G. Fisher (Eds.), Essays in the philosophy of chemistry (pp. 352–380). Oxford: Oxford University Press.
Acknowledgements
I would like to extend my gratitude to the referees of this article for their thorough and extensive reviews which provided valuable input to the revision process, to Ain Rada for advice on important aspects of chemical theory, to my supervisor Rein Vihalemm for his ideas and for encouraging me to engage in the philosophy of chemistry, and to my colleagues at the University of Tartu. This article was supported by the Estonian Research Council grants IUT20-5 and ETF7946, Estonian Ministry of Education and Research grant SF0180110s08, University of Tartu grants PFLFI15915 and PHVFI16941, and the European Union through the European Regional Development Fund (Centre of Excellence in Estonian Studies).
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Mets, A. A Philosophical Critique of the Distinction of Representational and Pragmatic Measurements on the Example of the Periodic System of Chemical Elements. Found Sci 24, 73–93 (2019). https://doi.org/10.1007/s10699-018-9567-x
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DOI: https://doi.org/10.1007/s10699-018-9567-x