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Towards a Philosophy of Chemical Reactivity Through the Molecule in Atoms-of Concept

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Abstract

A novel non-classical mereological concept (Molecule in Atoms-of) built up by blending the Metaphysics of Xavier Zubiri and the Quantum Theory of Atoms in Molecules (QTAIM) of R. F. W. Bader is proposed. It is argued that this philosophical concept is necessary to properly account for what happens in a chemical reaction. From the topology of the gradient of the laplacian of the electronic charge density, \(\nabla \nabla^{2} \rho ( \varvec{r} )\) within the QTAIM framework, different “atomic graphs” (corresponding to different hybridizations) are found for each atom depending on the molecular context, reflecting how the whole molecule affects each atom. In this way, the whole molecular system imposes certain geometry onto each atom, and every atom exhibits different ontological modality. On the Metaphysical side, for X. Zubiri real things (denoted as “de Suyo”) are system of different notes (adventitious, constitutional and essential). The physical essence is the subsystem of essential notes (notes-of) with a coherence unity. Every note is grounded on the essence. The unity of the system is present somehow in every note-of beforehand, and every essential note-of turns towards the other (“respectivity”). The essence determines the position of each note within the system, and hence is the grounding for modality of the notes. By conflating both “theories” and taking the atoms as essential notes, we propose the concept of “Molecule in atoms-of” or “atoms-of in Molecules”. Within the course of a chemical reaction the atoms-of modified their “of” as required by the new molecular unity being formed, and eventually change their modality. The validity to the Zubiri’s statements, is attained by evaluating necessity (□) and possibility (◊) in a set-up of finite accessible “possible worlds”.

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Notes

  1. In this study, Toner seems to deal with “philosophical Atoms”. Nonetheless in p. 287 he refers explicitly to “carbon atoms” and in p. 289 to “sodium atoms”.

  2. Prof. Teófilo Brezmes Brezmes (personal communication).

  3. In Morse theory the CPs are usually designated by just one index (see Matsumoto 2002).

  4. To our knowledge, Bader has taken this condition for granted without a rigorous mathematical demonstration for the gradient of the laplacian.

  5. See SE, pp. 391–395 (OE, pp. 356–360). To this topic devoted Zubiri his last work “Inteligencia Sentiente”, (see IyReal, IyLog, IyRaz, there is an English translation by Fowler: SI).

  6. Some recent authors, such as Oderberg, acknowledge the difference in the essence of “natural kinds” and “artefacts” (Oderberg 2011, note 30, p. 94; see also Bhushan 2006, p. 477) but do not restrict the essentiable domain.

  7. Zubiri prefers the word “thing” as “object”  being  the latter within the discussion of the sentient intelligence (see his digression on “objectuality” in IyR, p. 200).

  8. We encounter this conception easier to assimilate than that contended by van Inwagen (van Inwagen 1990). According to this author, real things would be those which constitute a “life” (van Inwagen 1990, p. 145).

  9. It should be kept in mind that Zubiri does not understand “physical” as synonym of “Physics” and hence the essence would not be reducible (see SE, p. 276, OE p. 267 and Caponigri 1980, pp. 30–31; Gorman 2005, p. 284).

  10. Precisely, expanding the concept of “properties” could solve the riddle regarding the properties that constitute or not the essence (Oderberg 2011, p. 99).

  11. Compare with “aggregates” and “compounds” suggested by Fine (1994b). Surprisingly, without any reference to Chemistry at all.

  12. Broackes trying to rehabilitate the original meaning argues that this “subject underlying" is like a metaphor, not to be taken literally (Broackes 2006, p. 143) and would only denote the “object” that inherits the qualities (Broackes 2006, p. 141).

  13. It should be kept in mind that the Aristotelian substance differs from what is usually understand in Chemistry (Pauling 1970, p. 8; Earley 2009; see also van Brakel 2000).

  14. In fact, for Zubiri “an organism is not one substance but many substances” (SE, 157, OE 171).

  15. This idea clashes with the association of essence with existence, as contended by modal essentialism (Gorman 2005).

  16. Some authors have wondered about this point, from Aristotle: “how something that has many parts can at the same time be one” (Phys I, 2, 185b (1–14)), Fine: “What is it for them to be parts? (Fine 1999, p. 62), Rea: “How is the Ship of Theseus related to its parts?” (Rea 1995, p. 532) Oderberg: “What holds those properties together?” (Oderberg 2011, p. 20).

  17. Furthermore, Zubiri associates the Metaphysics of Aristotle (based on substance and accidents) with the linguistic pattern of the verb to be. In this regard, Zubiri implicitly aligns with Carnap (1931) about the influence of the verb “to be” in occidental Metaphysics.

  18. Note that this statement would be at odds what is the common practice in discussing the emergence/reduction in the mind/body problem (Van Gulick 2001; Kim 2006), where the “mentality” appears to be a property apart from the body, and in some cases “flying over” it (Harré 2015). See also Caponigri (Caponigri 1980 pp. 30–31).

  19. This priority can be also envisaged in the proposal of Koslicki when she states:

    A plurality of objects compose a whole of a particular kind, when the objects (material components) in question satisfy the selection requirements set by the formal components associated with wholes of that particular kind, e.g. requirements concerning, for example, the variety, configuration and sometimes even the number of parts out of which wholes of that particular kind may be composed (Koslicki 2010, 170, italics ours)

  20. Some authors consider this affectation of the rest of the system on each part (Santos 2015, p. 29) but do not envisage the unity of the system. Given that, the “unity is in each note-of” and this conditions each note, it seems that we are dealing with “downward causation”, for according to Schröder (p. 450) “it presupposes parts of a system which are influenced by the way they are related” Nonetheless, this denomination does not adjust properly to what Zubiri bears in mind. Firstly, nor “downward” but “priority”, and secondly, nor “cause” but “causality” (see DSR, pp. 54–56, pp. 59–62). This topic will be developed elsewhere.

  21. Within other splitting schemes the molecule—or “promolecule”—is also define beforehand (see for instance: Sukumar 2013).

  22. Thence the idea of the Ontic Structural Realism of objects + relation (Wolff 2012), being the latter external to the relata (probably because of it is based in subatomic particles without internal structure and entanglement) does not match with the idea of Zubiri, and neither with the disposition of the atoms within the molecules, as we have already pointed out in view of the topology of \(\nabla \nabla^{2} \rho ( \varvec{r} )\) (inner respectivity in Zubiri’s words) are incardinated somehow in the structure of every atom. Nevertheless, the amendment introduced by Esfeld (Esfeld 2011) is more in line with Zubiri’s philosophy.

  23. Precisely, recently Santos acknowledges that the units forming the whole should be subgraphs (Santos 2015, p. 7) And also the proposal of Koslicki to expand the Aristotle’s hylemorphism consists succinctly on introducing the “structure” within the form (Koslicki 2008).

  24. Van Inwagen speaks about “parthood essentially involves causation” (Van Inwagen 1990, p. 81.).

  25. From a Molecular Orbital Theory point of view, each atom would contribute to the molecular unity by means of the bonding MOs, being the frontier orbitals that more involved (Fukui 1975; Flemming 1976). On the contrary, the antibonding MOs highlight the “atomic presence” by concentrating the electronic density within the atomic domains (Atkins and de Paula 2006, p. 371). In fact, in the MOs the atoms vanished into thin air (Harré and Llored 2011, p. 73, cf. with Bader 1994).

  26. Prof. Tian Lu and Prof. Biegler-König (personal communications).

  27. Thence, the relational ontology of Santos does not hold in our scheme since the whole is “left behind” (Santos 2015, p. 28).

  28. It remains to be ascertained what sort of mereological operation is this “gluing”: sum, product, fusion (Fine 1994b; Koslicki 2008).

  29. Notice that here we are departing somewhat from Zubiri’s thinking at least for molecular essences. The note “structure” or “shape” will not be determined exclusively by the essence of the molecule (Shallow Essentialism, Paul 2006).

  30. This kind of emergence could be dubbed “ontological”, which is ascribed to the creation of a new entity (see Bunge 2003, p. 31), in this way it would be a “micro derived from micro”(cf. with Mclaughlin 1997, p. 2). Usually, the emergence is related with the appearance of novel properties (Kim 2006, p. 548) or as a property that emerges from other (Shrader 2005, see criticism in Bunge 2003, p. 31). In this way, in Chemistry, another type of emergence is usually envisaged in the aggregation of molecules, which exhibits macroscopic properties (boiling point, density, etc.) the isolated molecules lack (let us refer to it as “aggregation emergence”, see Bunge 2010, p. 73, cf. with Earley 2016, p. 209). Precisely, this aggregate is what chemists usually refer to as “substance” (see Harré and Llored 2013, p. 129; van Brakel suggests to call it “species”, van Brakel 1997). Nevertheless, within Zubiri’s metaphysics, what would be “de Suyo” (in its own right) would be each molecule, therefore a chemical substance would consist of substantivities.

  31. Notice that a molecule would not be just a “composite” (according to Goldwater 2015) since every atom-of is actually an arrangement (conditioned by the unity) as manifested in its atomic graph. Nonetheless, this “arrangement” differs from that proposed recently by Goldwater (2015).

  32. It is obvious that the many molecules would have coincident atomic graphs (the transferability holds!). Nevertheless, the value of \(\nabla^{2} \rho ( \varvec{r} )\) evaluated at the CPs would be different.

  33. Note that this ungrounded character would entail the “unexplained” character of essential features as contended by Gorman (2005, p. 285).

  34. The non-compactness of the topology of the atomic graphs, due to infinity gradient lines, would entail a Čech Homology (Prof. Viruel at Malaga’s University, personal communication).

  35. This is assertion will be important in a future discussion about emergence, for all the discussion about emergent properties by Kim is based on considering the following definition of Emergent properties: “A property is emergent if it has novel causal powers” (cited by Humphreys 1999, p. 8; Kim 2006).

  36. Note that this idea is what lies behind Entanglement (Horodecki 2009). In Esfeld’s words: Entanglement is to say that the quantum systems in question do not have state-dependent properties each independent of one another” (Esfeld 2004, pp. 603–604). In this way, “be entangled with” would be, in our framework, synonym of “to be particle-of”.

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Acknowledgements

SCL wants to thank to: Prof. R. F. W. Bader (in memoriam) for kindly providing a reprint of one of his papers, the SCAI (Picasso Supercomputer) at Malaga’s University and especially to Rafael Larrosa, Prof. Fowler for providing a preprint of one of his papers, A. Madinaveitia (in memoriam) for every warmful welcome at the Zubiri’s Foundation, Prof. A. Hortal for providing a copy of the Ellacuría’s Ph. D. thesis, Prof. Lorenzo Pueyo (in memoriam) and his group at Oviedo’s University from whom I was firstly aware of the QTAIM, Prof. Teófilo Brezmes Brezmes (in memoriam) for transmitting his enthusiasm towards Mathematics, Manuela Jiménez Garcés for her infinite patience and my child Covadonga.

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    Saturnino Calvo-Losada & José Joaquín Quirante

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Dedicated to my parents: in memoriam.

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Calvo-Losada, S., Quirante, J.J. Towards a Philosophy of Chemical Reactivity Through the Molecule in Atoms-of Concept. Axiomathes 32, 1–41 (2022). https://doi.org/10.1007/s10516-020-09497-5

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