Abstract
The exploration of chemical periodicity over the past 250 years led to the development of the Periodic System of Elements and demonstrates the value of vague ideas that ignored early scientific anomalies and instead allowed for extended periods of normal science where new methodologies and concepts are developed. The basic chemical element provides this exploration with direction and explanation and has shown to be a central and historically adaptable concept for a theory of matter far from the reductionist frontier. This is explored in the histories of Prout’s hypothesis, Döbereiner Triads, element inversions necessary when ordering chemical elements by atomic weights, and van den Broeck’s ad-hoc proposal to switch to nuclear charges instead. The development of more accurate methods to determine atomic weights, Rayleigh and Ramsey’s gas separation and analytical techniques, Moseley’s X-ray spectroscopy to identify chemical elements, and more recent accelerator-based cold fusion methods to create new elements at the end of the Periodic Table point to the importance of methodological development complementing conceptual advances. I propose to frame the crossover from physics to chemistry not as a loss of accuracy and precision but as an increased application of vague concepts such as similarity which permit classification. This approach provides epistemic flexibility to adapt to scientific anomalies and the continued growth of chemical compound space and rejects the Procrustean philosophy of reductionist physics. Furthermore, it establishes chemistry with its explanatory and operational autonomy epitomized by the periodic system of elements as a gateway to other experimental sciences.
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Notes
Superconductors are described using a phenomenological theory like BCS with few parameters (i.e. critical temperature Tc) that are experimentally determined but cannot be calculated as materials properties from first principles.
There are about 700 different periodic tables of elements (Mazurs 1974). Leal and Restrepo (2019) point to thousands of possible periodic tables of elements using different chemical classifications within the Mendeleev-type system. Therefore, I prefer to use the plural and have PTE understood as plural throughout the text when not specifically indicated by a qualifier. Periodic table of elements are n-dimensional mappings of periodic systems of elements (PSE), n being mostly 2 or 3. See further details in 2.1.
Defining a Kuhnian anomaly and paradigm is often plagued by the fact that these terms are used for a wide range of cases and concepts and have vague definitions.
This creates confusion teaching as we introduced different types of chemical bonds (i.e. metallic, ionic, covalent, polar covalent) but cannot provide clear boundaries for their existence.
Chemical valences are the number of hydrogen atoms that can combine with an element in a binary hydride, or twice the number of oxygen atoms combining with an element in its oxide or oxides.
A hypergraph is a generalization of a graph in which an edge can join any number of vertices. In an ordinary graph an edge connects two vertices.
Basic elements are also called abstract, metaphysical or transcendental elements. I will use the term basic here.
The concept of an ether has a long history stretching from Plato and Aristotle over Descartes’s theory of gravity to the many Michelson-Morley experiments searching for a medium for the propagation of electromagnetic waves. Walter Nernst proposed that radioactive atoms are created in an ether (Kragh 2012) and Mendeleev (Mendeleev 1904) claimed that there are two chemical elements, the element X (Newtonium) and Y (Coronium) with lower atomic weights than hydrogen that make up the ether.
Friedrich Adolph Paneth’s dual concept of element (1962) distinguished between the transcendental Grundstoff (basic substance) and einfacher Stoff (simple substance), which is the form in which the former manifests itself to our senses. The term transcendental was introduced as a nod to Kant (Ruthenberg 2009).
We exclude radiochemical transmutations occurring in radiochemistry.
The English chemist Humphrey Davy already forwarded such an idea in 1808. In 1815 no atomic weight was known to even the nearest integer so the term Prout’s speculation might be better. By the 1830 the discrepancies of the weight ratios from integer became larger and larger.
The equivalent weight of an element is its gram atomic weight divided by its valence.
This term refers to proto-hyle meaning ‘first stuff’ in Greek.
Triads of chemical compounds such as the oxides CaO, SrO and BaO were also found and therefore Döbereiner triads also reflect chemical similarity.
This does not imply that one-dimensional sequences of atoms cannot contain chemical similarities as Mendeleev numbers show.
The Madelung Aufbau principle is valid up to Ca (Z = 20). Attempts to expand this heuristic rule to elements with higher Z has created wrong statements about an apparent energetic stability of full or half filled d-shells which unfortunately the majority of freshman chemistry books contain. Those that advance in chemistry are then required to ‘unlearn’ these myths.
The same positional switch had already been done by William Odling in 1864 and most other PTE also had these two elements switched.
Helium was detected during a solar eclipse in 1868 by the astronomers Georges Rayet, C. T. Haig, Norman R. Pogson and John Hershel and confirmed by Jules Janssen and Norman Lockyer who named it.
All together there were 4 chemical inversions: Te/I, Co/Ni, Ar/K and Th/Pa.
Carbon has 15 isotopes from 8 to 22C with only 14C, 13C and 12C occurring naturally and only the latter two are stable. The half-life times of most unstable isotopes are seconds and below with the exception of 11C and 14C with life times of about 20 min and 5730 years, respectively. Tying elemental existence to their half-life times becomes philosophically important in super heavy elements.
This is problematic for elements with low Z, in particular hydrogen with its isotopes deuterium and tritium where certainly the chemical reactivity is impacted and referred to as an ‘isotope effect’.
Size dependent ‘intrinsic’ properties such as melting points of simple elements add a further dimension to PTE: 2.5 nm spheres of gold particles melt near 300 °C whereas bulk gold melts at 1064 °C.
References
Allahyari, Z., & Oganov, A. (2020). Non-empirical definition of the Mendeleev Numbers: Organizing the chemical space. Journal of Physical Chemistry C, 124, 23867–23878.
Anderson, P. W. (1972). More is different. Science, 177(4047), 393–396.
Aristotle De caelo, 302 a16.
Bächtold, M. (2010). Saving Mach’s view on atoms. Journal for General Philosophy of Science, 41(1), 1–19.
Bensaude-Vincent, B. (1998). Éloge du Mixte. Paris: Hachette.
Cavendish, H. (1785). Experiment on air. Philosophical Transactions of the Royal Society of London, 75, 372–384.
Cahn,R. M. (2002). Philosophische und historische Aspekte des Periodensystems der chemischen Elemente. Hyle Publication, Karlsruhe. www.hyle.org/publications/books/cahn/index.html. Retrieved from November 28, 2020.
Chang, H. (2014). Is water H2O? Evidence, realism and pluralism. New York: Springer.
Cole, S. (1970). Professional standing and the reception of scientific discoveries. American Journal of Sociology, 76, 286–306.
Dirac, P. A. M. (1929). The quantum mechanics of many-electron systems. Proceedings of the Royal Society of London, A123, 714–733.
Djerassi, C., & Hoffmann, R. (2001). Oxygen. New York: Wiley.
Döbereiner, J. W. (1829). Versuch zu einer Gruppierung der elementaren Stoffe nach ihrer Analogie. Annalen Der Physik Und Chemie, 15(2), 301–307.
Du, J., & Wu, Y. (2016). A bibliometric framework for identifying princes who wake up sleeping beauty in challenge-type scientific discoveries. Journal of Data and Information Science, 1(1), 50–68.
Galison, P. (1997). Image and logic: A material culture of microphysics. Chicago: University of Chicago Press.
Geiger, H., & Mardsen, E. (1913). The laws of deflection of α-particles through large angles. Philosophical Magazine, 25, 604–628.
Glawe, H., Sanna, A., Gross, E. K. U., & Marques, M. A. L. (2016). The optimal one dimensional periodic table: A modified Pettifor chemical scale from data mining. New Journal of Physics, 18(9), 093011.
Harré, R. (2005). Chemical kinds and essences revisited. Foundations of Chemistry, 7, 7–30.
Heitler, W., & London, F. (1927). Wechselwirkung neutraler Atome und homöopolare Binding nach der Quantenmechanik. Zeitschrift Für Physik, 44, 455–472.
Hoffmann, R. (1995). The same and not the same. Columbia: Columbia University Press.
Hofffmann, R., & Laszlo, P. (1991). Representation in chemistry. Angewandte Chemie (international Ed. in English), 30, 1–16.
Ihde, J. (1964). The development of modern chemistry (pp. 161–231). New York: Dover Publications.
IUPAC. (2018). https://iupac.org/tag/transfermium-working-group/.
Jensen, W. B. (1986). Classification, symmetry and the periodic table. Computers & Mathematics with Applications, 12B(1/2), 487–510.
Jensen, W. B. (Ed.). (2002). Mendeleev on the periodic law: Selected writings, 1869–1905 (pp. 135–137). New York: Dover.
Jerabek, P., Schuetrumpf, B., Schwerdtfeger, P., & Nazarewicz, W. (2018). Electron and nucleon localization functions of oganesson: Approaching the Thomas-Fermi limit. Physical Review Letters, 120, 053001.
Kultgen, J. H. (1958). Philosophical conceptions in Mendeleev’s principles of chemistry. Philosophy of Science, 25, 177–183.
Kragh, H. (2000). Conceptual changes in chemistry: The notion of chemical elements, ca. 1900–1925. Studies in History and Philosophy of Physics, 31, 435–450.
Kragh, H. (2012). Walter Nernst: Grandfather of dark energy? Astronomy & Geophysics, 53(1), 1.24-1.26.
Kragh, H. (2017). On the ontology of superheavy elements. Substantia. https://doi.org/10.13128/Substantia-25
Kragh, H. (2019). Plentitude philosophy and chemical elements. HYLE International Journal for Philosophy of Chemistry, 25(1), 1–20.
Ke, Q., Ferrara, E., Radicchi, F., & Flammini, A. (2015). Defining and identifying sleeping beauties in science. Proceedings of the National Academy of Sciences, 112(24), 7426–7431.
Klein, U. (2003). Experiments, models, paper tools: Cultures of organic chemistry in the nineteenth century. Stanford: Stanford University Press.
Kuhn, T. S. (1962). The structure of scientific revolutions. Chicago: University of Chicago Press.
Kuhn,T. S. (1977). Objectivity, value judgment, and theory choice. In The essential tension (Ch. 13, pp. 320–339). Chicago: University of Chicago Press.
Lakatos, I. (1980). In J. Worrall & G. Currie (Eds.), The methodology of scientific research programs: Volume 1: Philosophical papers. Cambridge: Cambridge University Press.
Laughlin, R. B. (2005). A different universe: Reinventing physics from the bottom down. New York: Basic Books.
Laughlin, R. B., & Pines, D. (2000). The theory of everything. Proceedings of the National Academy of Sciences of the United States of America, 97(1), 28–31.
Laughlin, R. B., Pines, D., Schmalian, J., Stojković, B. P., & Wolynes, P. (2000). The middle way. Proceedings of the National Academy of Sciences of the United States of America, 97(1), 32–37.
Leal, W., & Restrepo, G. (2019). Formal structure of periodic system of elements. Proceedings of the Royal Society A, 475, 20180581.
Lemonick, S. (2020). Exploring chemical space: Can AI takes us where no human has gone before? Chemical & Engineering News, 98(13), 30–35.
Lombardi, O., & LaBarca, M. (2005). The ontological autonomy of the chemical world. Foundations of Chemistry, 7, 125–148.
Marcum, J. A. (2015). Thomas Kuhn’s revolutions. A historical and evolutionary philosophy of science? Chapter 6. London: Bloomsbury Academic.
Martin, J. D. (2018). Solid State insurrection. Pittsburgh, PA: University of Pittsburgh Press.
Mazurs, E. G. (1974). Graphic representations of the periodic system during one hundred years. Alabama: University Alabama Press.
Mendeleev, D. I. (1904). An attempt towards a chemical conception of the ether. London: Longmans, Green, and Co.
Mewes, J.-M., Jerabek, P., Smits, O. R., & Schwerdtfeger, P. (2019). Oganesson is a semiconductor: On the relativistic band-gap narrowing in the heaviest noble gas solids. Angewandte Chemie International Edition, 58, 14260–14264.
Moseley, H. G. J. (1913). The high-frequency spectra of the elements. Philosophical Magazine, 26, 1024–1034.
Nye, M. J. (1981). Berthelot’s anti-atomism: A matter of taste? Annals of Science, 38(5), 585–590.
Paneth, F. A. (1916). Über den Element- und Atombegriff in Chemie und Radiologie. Zeitschrift Für Physikalische Chemie, 91, 171–198.
Paneth, F. A. (1962). The epistemological status of the chemical concept of an element. The British Journal of the Philosophy of Science, 13(1–14), 144–160.
Petrusevski, V. M., & Cvetkovic, J. (2018). On the ‘true position’ of hydrogen in the periodic table. Foundations of Chemistry, 20, 251–260.
Pettifor, D. G. (1984). Solid State Communications, 51, 31.
Polanyi, M. (1936). The value of vague ideas. The Philosophy of Science, 13, 233–234.
Popper, K. (1963). Conjectures and refutations. The growth of scientific knowledge. New York: Routledge and Kegan Paul.
Prout, W. (1815). On the relation between the specific gravities of bodies in their gaseous state and the weights of their atoms. Annals of Philosophy, 6, 321–330.
Prout, W. (1816). Correction of a mistake in the essay on the relation between the specific gravities of bodies in their gaseous state and the weights of their atoms. Annals of Philosophy, 7, 111–113.
Pyykkö, P. (2011). A suggested periodic table up to Z ≤ 172, based on Dirac-Fock calculations on atoms and ions. Physical Chemistry Chemical Physics: PCCP, 13, 161–168.
Railsback, L. B. (2003). An earth scientist’s periodic table of the elements and their ions. Geology, 31(9), 737–740.
Rayleigh, L. (1892). Density of nitrogen. Nature, 46, 512–513.
Rayleigh, L., & Ramsay, W. (1896). Argon, a new constituent of the atmosphere. Washington, DC: Smithsonian Institution.
Restrepo, G. (2019a). Compounds bring back chemistry to the system of chemical elements. Substantia, 3(2), 115–124.
Restrepo, G. (2019b). Challenges for the periodic systems of elements: Chemical, historical and mathematical perspectives. Chemistry: A European Journal, 25, 15430–15440.
Restrepo, G., & Pachon, L. A. (2007). Mathematical aspects of the periodic law. Foundations of Chemistry, 9, 189–214.
Rocke, A. (1984). Chemical atomism in the nineteenth century: From Dalton to Cannizzaro. Columbus: Ohio State University Press.
Rocke, A. (2013). What did theory mean to nineteenth-century chemists? Foundations of Chemistry, 15, 145–156.
Russell, B. (1923). Vagueness. The Australasian Journal of Psychology and Philosophy, 1(2), 90.
Ruthenberg, K. (2009). Paneth, Kant, and the philosophy of chemistry. Foundations of Chemistry, 11, 79–91.
Rutherford, E. (1911). The scattering of α and β particles by matter and the structure of the atom. Philosophical Magazine, 21, 669–688.
Scerri, E. R. (2005). Some aspects of the metaphysics of chemistry and the nature of the elements. Hyle: International Journal of Philosophy of Chemistry, 11(2), 127–145.
Scerri, E. R. (2007a). The periodic table. Its story and its significance (pp. 38–42). Oxford: Oxford University Press.
Scerri, E. R. (2007b). The periodic table. Its story and its significance (p. 142). Oxford: Oxford University Press.
Scerri, E. R. (2007c). The periodic table. Its story and its significance (p. 117). Oxford: Oxford University Press.
Scerri, E. R. (2007d). The periodic table. Its story and its significance (p. 182). Oxford: Oxford University Press.
Scerri, E. R. (2007e). The periodic table. Its story and its significance (pp. 42–58). Oxford: Oxford University Press.
Scerri, E. R. (2012). What is an element? What is the periodic table? And what does quantum mechanics contribute to the question? Foundations of Chemistry, 14, 69–81.
Scerri, E. R. (2013). A tale of seven elements. New York: Oxford University Press.
Scerri, E. R. (2015). The Constitution of Group 3 of the Periodic Table. IUPAC project number 2015-039-2-200. https://iupac.org/projects/project-details/?project_nr=2015-039-2-200. Retrieved from November 28, 2020.
Scerri, E. R. (2016). A tale of seven scientists and a new philosophy of science (pp. 41–62). New York: Oxford University Press.
Scerri, E. R. (2018). Letter to the editor. Hyle International Journal for Philosophy of Chemistry, 24, 101–104.
Scerri, E. R. (2021). Reassessing the notion of a Kuhnian revolution. What happened in twentieth-century chemistry. In K. Brad Wray (Ed.), Interpreting Kuhn. Critical essays. Cambridge: Cambridge University Press.
Schädel, M. (2015). Chemistry of the superheavy elements. Philosophical Transactions of the Royal Society A, 373, 20140191.
Schmidt, H.-W., & Würthner, F. (2020). A periodic system of supramolecular elements. Angewandte Chemie International Edition, 59, 8766–8775.
Schummer, J. (1996). Realismus und Chemie. Philosophische Untersuchungen der Wissenschaft von den Stoffen. Würzburg: Königshausen & Neumann.
Schummer, J. (1998). The chemical core of chemistry. Hyle International Journal for Philosophy of Chemistry, 4(2), 129–162.
Stent, G. (1972). Prematurity and uniqueness in scientific discovery. Scientific American, 227(6), 84–93.
van den Broek, A. (1911). The number of possible elements and Mendeléff’s “Cubic” periodic system. Nature, 87, 78.
Van den Broek, A. (1913). Intra-atomic charge. Nature, 92, 372–373.
Van Brakel, J. (2000). Philosophy of chemistry: Between the manifest and the scientific image (Louvain Philosophical Studies). Leuven University Press: Leuven.
Villars, P., Cenzual, K., Daamsa, J., Chen, Y., & Iwatac, S. (2004). Binary, ternary and quaternary compound former/nonformer prediction via Mendeleev number. Journal of Alloys and Compounds, 367, 167–175.
Vogt, T. (2017). Book review of Eric Scerri: A tale of seven scientists and a new philosophy of science. Hyle International Journal for Philosophy of Chemistry, 23, 107–109.
Weinberg, S. (2008). From BCS to the LHC. International Journal of Modern Physics A, 23, 1627–1635.
Weininger, S. J. (1998). Contemplating the finger: Visuality and the semiotics of chemistry. HYLE: an International Journal for the Philosophy of Chemistry, 4, 3–27.
Wray, K. B. (2018). The atomic number revolution in chemistry: A Kuhnian analysis. Foundations of Chemistry, 20, 209–217.
Yakushev, A., Gates, J. M., Türler, A., Schädel, M., Düllmann, C. E., Ackermann, D., et al. (2014). Superheavy element Flerovium (Element 114) is a volatile metal. Inorganic Chemistry, 53, 1624–1629.
Zapffe, C. A. (1969). Gustavus Hinrichs, Precursor of Mendeleev. Isis, 60(4), 461–476.
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This article belongs to the topical collection "Simplicity out of Complexity? Physics and the Aims of Science", edited by Florian J. Boge, Martin King, Paul Grünke and Miguel Ángel Carretero Sahuquillo.
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Vogt, T. The value of vague ideas in the development of the periodic system of chemical elements. Synthese 199, 10587–10614 (2021). https://doi.org/10.1007/s11229-021-03260-y
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DOI: https://doi.org/10.1007/s11229-021-03260-y