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Philosophy of Chemistry pp 5–22Cite as

Reduction for a Dappled World: Connecting Chemical and Physical Theories

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Part of the book series: Boston Studies in the Philosophy and History of Science ((BSPS,volume 306))

Abstract

In this paper I argue that there are good reasons to construct the connection between theories of chemistry and theories of physics in terms of a Nagelian reductionist model. I use the machinery of belief revision to investigate the reduction relation in terms of a structuralist and conceptual space approach. An important aspect of the current paper is that it has the potential to unite reductive and non-reductive views on science.

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Notes

  1. 1.

    The resulting disconnects have led some to question the role of physics and theory in chemistry, for instance, in the paper by Hoffmann (2007).

  2. 2.

    See for instance Woody (2000), Scerri (1998) and Needham (2010) as examples.

  3. 3.

    And separates them from a number of informal conditions which he also specifies in great detail.

  4. 4.

    See for instance Kuipers (1990) for an example of reductions from many sciences, most of which are not based on strict identities.

  5. 5.

    For instance, Nagel (1961) discussed three kinds of linkages postulated by reduction postulates

    1. 1.

      The links are logical connections, such that the meaning of ‘A’ as ‘fixed by the rules or habits of usage’ is explicable in terms of the established meanings of the theoretical primitives in the primary discipline.

    2. 2.

      The links are conventions or coordinating definitions, created by ‘deliberate fiat’, which assigns a meaning to the term ‘A’ in terms of the primary science, subject to a criterion of consistency with other assignments.

    3. 3.

      The links are factual or material, or physical hypotheses, and assert that existence of a state ‘B in the primary science is sufficient (or necessary and sufficient) condition for the state of affairs designated by ‘A’. In this scenario, the meanings of ‘A’ and ‘B’ are not related analytically.

  6. 6.

    A similar point was made in a somewhat neglected paper by Horgan (1978), who argues that the reduction postulates supervene on the reducing theory.

  7. 7.

    See Balzer and Sneed (1977, 1978) for an introduction of this relation and the corresponding notion of a theory net.

  8. 8.

    In addition, belief revision has been introduced into the structuralist model by Enqvist (2011). Enqvist develops a highly specific alternative to the notion of ‘reduction postulates’ qua ‘linking commitments’ which I developed in Hettema (2012a). Enqvist’s construction relies on a construction of specialisation theory nets, to which he applies the AGM belief revision strategies. Enqvist does not fully develop the AGM theory in a structuralist model, and ignores the stratification between theoretical / non-theoretical levels of the theory. In general, developing complex notions in the stratified model adds complications which are usually ignored in the first ‘step’ of the development of such models, see for instance the development of truthlikeness developed by Kuipers (1992).

  9. 9.

    As the book by Nye (2011) illustrates, this theory was sometimes jokingly referred to as the ‘absolute’ theory of reaction rates. Many of his contemporaries found Eyring’s ideas too radical, as the proceedings of the 1937 workshop at the University of Manchester illustrate. In my earlier paper (Hettema (2012b)) I had this wrong, and used the designation of ‘absolute theory’ throughout. At the time I was unaware of the earlier ironic use, and thought that ‘absolute theory of reaction rates’ was a neater choice to designate the theory than the somewhat more clumsy sounding ‘theory of absolute reaction rates’. Of course, I now see the error of my ways.

  10. 10.

    The notion of a (reactive) potential energy surface for the nuclear motion is key to the development of the theory. While the idea was introduced by Born and Heisenberg (1924) and Born and Oppenheimer (1927) it may be argued that the idea of a potential energy surface only reached its full fruition with the development of a theory of chemical reaction rates. The idea of a potential energy surface is part of Wigner’s ‘three threes’ (see below).

  11. 11.

    Especially illustrative for this is the motivation Eyring (1938) gave for his introduction of various ‘semi-empirical’ methods in quantum chemistry, which lead to various inconsistencies between these semi-empirical theories and quantum theory.

    For the purposes of calculating the potential energy surface for a chemical reaction, Eyring first classifies theories as ‘semi-empirical’ when they have the following characteristics:

    (a) that each electron can be assigned a separate eigenfunction which involves the coordinates of only this one electron. (b) Multiple exchange integrals are negligible, (c) Normalising integrals for overlapping orbitals are negligible in comparison with unity. (d) The exchange and coulombic integrals for a complicated molecular system may be estimated from a potential curve for the isolated pair of atoms. (e) For distances involved in activation energy calculations this percentage is around 20 per cent. coulombic and 80 per cent. exchange binding, and this varies but little from atom pair to atom pair. (Eyring 1938, p. 8)

    Eyring then remarks that more detailed calculations, as well as principled considerations, give no support for the construction of these theories:

    None of these assumptions have been rigorously derived from theory, and, as has been emphasised by Coolidge and James, if one assumes for H3, the approximate eigenfunctions used by Heitler and London and Sugiura for H2, the assumptions can all be shown to fail badly. (Eyring 1938, p. 8)

    Thus stated, these sort of theories seem to be counterexamples to a theory of reduction: the sort of reduction that derives chemical ‘laws’ directly from basic quantum theory can only be achieved on the basis of theoretical assumptions that are unjustified from the viewpoint of basic theory and which can moreover be shown up as factually wrong in a large number of practical cases.

  12. 12.

    The article appears in translated form in Back and Laidler (1967).

  13. 13.

    A modified collision theory often introduces a ‘probability factor’ P which measures the probability that a collision will lead to a completed chemical reaction. Hence, in the modified collision theory

    $$ \mathrm{k}=PZ\; \exp \left(\frac{-E}{RT}\right) $$
    (2.3)

    The ‘fudge factor’ P is introduced since the collision cross section of a molecule bears no clear relationship to the probability for a chemical reaction. While the collision theory works well for reactions between mono-atomic gases, it breaks down for reactions between more complex molecules. In this respect, the collision theory is not capable of clarifying the internal mechanisms of chemical reactions in the necessary detail.

  14. 14.

    Wigner refers to the theory in this paper as ‘The Transition State Method’. The paper by Laidler and King (1983) contains a brief discussion of this conference and the role it played in the subsequent adoption of the theory.

  15. 15.

    A detailed discussion of why this is so falls outside the scope of this paper, but can easily be determined by stepping through the mathematics.

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Authors and Affiliations

  1. Department of Philosophy, The University of Auckland, Private Bag 92019, Auckland, New Zealand

    Hinne Hettema

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  1. Department of Chemistry and Biochemistry, University of California, Los Angeles, California, USA

    Eric Scerri

  2. Center for Philosophy and History of Science, Boston University, Boston, Massachusetts, USA

    Lee McIntyre

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Hettema, H. (2015). Reduction for a Dappled World: Connecting Chemical and Physical Theories. In: Scerri, E., McIntyre, L. (eds) Philosophy of Chemistry. Boston Studies in the Philosophy and History of Science, vol 306. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9364-3_2

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