Abstract
This chapter discusses the ‘reformed’ nuclear theory of trope bundles. The main difference of the reformed theory with the theory considered above is that the nucleus of a bundle is constituted by a unique nuclear trope. The reformed nuclear theory does not require a relation of ontological dependence with especial, non-standard characteristics. Even more, the unique nuclear trope is a substratum. The reformed nuclear theory is, then, a conception in which particular objects are, at the same time, a bundle of tropes, and have a substratum. Finally, structural nuclear bundles are considered in connection to the requirements that have motivated forms of ‘ontic structural realism’ in philosophy of physics.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
More precisely: [∀w1∀w2∀x ((x-@-w1 = x-@-w2) ↔ ∀T ((T < n(x-@-w1)) ↔ (T < n(x-@-w2)))]. Operators of necessity have been omitted here because it is a statement that establishes relations between different possible worlds, which cannot be expressed by such standard modal operators. It should be assumed, therefore, that the variables ‘x’ and ‘T’ have as range objects and tropes, respectively, of any possible world. The variables ‘w1’ and ‘w2’ have as range possible worlds.
- 2.
Recall that in a ‘pregnant whole’ all tropes depend on all the others of the bundle. In a nuclear bundle, on the other hand, only the tropes of the nucleus depend reciprocally between each other. The peripheral tropes are, however, connected by ontological dependence with the tropes of the nucleus because they are dependent on them, which makes the nuclear tropes under the converse of ontological dependence with peripheral tropes.
- 3.
For every moment of time in which Socrates exists, on the other hand, there will be the mereological fusion of Socrates and the peripheral tropes he possesses at such times. For every possible world in which Socrates exists, there will be the mereological fusion of Socrates and the peripheral tropes that he owns in such a possible world. Socrates can be conceived, then, as exactly the mereological product of all the ‘accidental’ unities in all possible worlds and at all times in each of those worlds of which he is a part.
- 4.
Something analogous happens with tropes concerning determinable universals. A trope must always be the instantiation of a super-determinate universal property. At the same time, however, this same trope will be the instantiation of each of the determinable universals under which the super-determinate universal falls. A color will be the instantiation of a super-determinate universal of color corresponding to a maximally specific tone, but also of the determinable universal of being of blue color and of the determinable universal of being a color. See for a comparison between gender-species and determinable-determinate relationships, Funkhouser, 2014, 52–54.
- 5.
Interestingly, however, even when an object ‘constituted’ by others could be made from other objects different the first instant of its existence, it remains true that a table could not be made of a different material, as it usually has been proposed. This applies in a general way to any artifact. The reason is that a table is a sequence of ‘continuants’, as explained above (see § 83). A sequence of continuants is a sequence of mereological fusions, each of which has its identity conditions fixed by its parts. For a table, then, it will be essential what its parts are at a given time because whatever the mereological fusion maybe that counts as ‘continuant’ of the table at that time, that fusion will have its parts essentially. This applies to any of the times of existence of the table, so it is obviously valid for the first moment of its existence.
- 6.
It is known that several argumentative strategies have been proposed to defend the necessity of origin that have depended on the assumption that the material that constitutes an object at a time could only have constituted this object (see Kripke, 1980, 115, note 56). This principle is, of course, false, so it should not be strange that these strategies have not been successful. See for a detailed discussion and a general presentation, Mackie, 2006, 47–69, 94–95; Alvarado, 2005, 2007.
- 7.
No discrimination is being made here between different reductivist and non-reductivist theories about causality (see § 13). This is not a question that can be explored with sufficient detention here, but it is curious to note that the necessity for causal antecedents seems a thesis that is hardly acceptable if one admits some or another reductivist conception. Indeed, why should we assume that an object must be preceded by certain events with which its beginning of existence satisfies some regularity? Such a requirement seems arbitrary. The same happens if a counterfactual conception of causality is adopted. Why should it be necessary that the beginning of the existence of every object must be preceded by events for which there is counterfactual dependence? If instead, a non-reductivist conception of causality according to which causality is a primitive ontological relation is adopted, it is trivial that it is necessary for the existence of an object those causal antecedents that are—indeed—necessary for its existence.
- 8.
Recall that an object x is exactly located in the region r if and only if x is located in r, there are no parts of x located in any region r’ such that it is not the case that r’ ⊂ r and there is no subregion r” ⊂ r where no part of x is located.
- 9.
If one were not willing to accept that the content of concepts such as ‘substratum’ or ‘characterization’ are analysed by their theoretical roles, it should at least be admitted that a nuclear trope satisfies the same theoretical functions as a substratum (see Benovsky, 2008, 183–184).
- 10.
Lowe has argued that a natural law should be understood as the characterization of a universal of substance by a non-substantial universal (see Lowe, 2006, 127–133). Probably for Lowe the relation of ‘characterization’ between universals is something that would be fulfilling functions similar to the relation of ‘necessitation’ (see Armstrong, 1983, 85–99) or ‘nomological’ relation (see Tooley, 1987, 88) between universals. The problem with this assimilation is that a non-substantial universal has no ontological dependence on a substantial universal—perhaps we should say that it is dependent on a single nomic network, as explained above (see §§ 75–77), but this is a very different matter. It happens, moreover, that it is very doubtful that all laws should be connecting a non-substantial universal to a substantial universal. Paradigmatic examples of natural law have nothing to do with the sortal property of the objects in question, but, for example, only with their masses and their distances.
- 11.
Of course, there would be important ontological issues to face for a substantialist conception of spacetime from the perspective of the nuclear theory. However, such an ontologically independent structure is understood, it should be made up of tropes and the connections by which they should form such a structure must be a collection of ontological dependencies. Normally, substantialist perspectives tend to think of spacetime as a set of points. A set of ‘points’ that are small independent substrata does not seem coherent with nuclear theory. When the structuralist ontologies are considered below (see §§ 93–94) it will become more understandable how a substantial spacetime ‘structure’ could be given from the perspective of an ontology of tropes.
- 12.
This type of analogical predication or attribution has been traditionally denominated as an “analogy of attribution” or analogy ad unum / pros hén. Another form of analogical predication has been called of proportionality (see St. Thomas Aquinas, De veritate, q. 2, a. 11, c.). In this second form of analogy the same concept is attributed to several cases because, although these cases are different from each other, there is in each of them certain ‘ratio’ or ‘proportion’ similar between certain elements or constituents. In the same way, as it is said that 2:4 and 3:6 are the same ratio, it has been maintained that, for example, between perceptive knowledge and sensory qualities there is the same ‘ratio’ as between intellectual knowledge and universal properties. Attention will be focused here in the analogy of ‘attribution’.
- 13.
It has also been maintained that there is an analogy in the attributions of ‘being’ to God and creatures. God is the focal case of ‘being’, while creatures are derivative attributions (see St. Thomas Aquinas, Summa theologiae I, q. 13).
- 14.
Part of the motivations for adopting this approach has been the assumption that the only intelligible concept of ‘being’ or ‘existence’ is a second-level concept such as existential quantification. From this perspective, it does not make sense to attribute to a particular object ‘existence’ in the same way that shape or color is attributed to a particular object. What would be intelligible is to attribute cases to a concept. It would not make sense to say that “Tom exists” but it would make sense to say that “there is a cat”. Although the reasons for adopting this point of view have already been well answered (see Salmon, 1987), the discussion will be developed here in terms of existential quantifications so as not to introduce unnecessary complexity.
- 15.
Formulations in this sense of St. Thomas Aquinas are well known. For example: hoc quod dico esse est actualitas omnium actuum, et propter hoc est perfectio omnium perfectionum (De veritate, q. 7, a. 2, ad 9: “This what I call ‘being’ is the actuality of all acts, and for this, it is the perfection of all perfections”). Also: esse est actualitas omnis formae vel naturae (Summa theologiae I, q. 3, a. 4, c.: “being is the actuality of all form or nature”). Also: ipsum esse est perfectissimum omnium, comparatur enim ad omnia ut actus (Summa theologiae I, q. 4, a. 1, ad 3: “being itself is the most perfect of all things since everything is compared to it as an act”). That is, ‘being’ (esse) is the actuality of all acts, that is, the character of ‘act’ of any act.
- 16.
A ‘Hilbert space’ is a generalization of a Euclidean space for finite or infinite dimensions to which the methods of vector algebra and calculus can be applied.
- 17.
These ‘instantiation distributions’ can, moreover, be represented as complex universals. The possibility (i) would be the instantiation of [Conj (U1x1, U2x2, Rx1x2) = Refx2x4 (Refx1x3 (Conj (Conj (U1x1, U2x2)), Rx3x4)))]; (ii) would be the instantiation of [Conj (U2x1, U2x2, Rx1x2)]; and (iii) would be the instantiation of [Conj (U1x1, U1x2, Rx1x2)].
- 18.
A manifold is a topological space in which the neighborhood of each point is homeomorphic to a Euclidean space. A ‘topological space’ is a set of points in which each point is assigned its neighborhood satisfying certain conditions that are not of interest here. A topological space is ‘differentiable’ if differential calculus can be applied, defining directions, tangents and differentiable functions in the manifold.
- 19.
That is, a specification of the distances between points in Minkowski’s tetra-dimensional spacetime.
- 20.
A ‘tensor metric’ of a differentiable manifold can be characterized—very informally—as the ‘measure’ of the curvature of that space for each point of the manifold.
- 21.
This mapping is called a ‘diffeomorphism’, that is, an infinitely differentiable bijective mapping of M to M. This argument has been called the hole argument.
- 22.
Because of these problems, some of the proponents of ontic structuralism have argued that the same philosophical considerations of physics that would make structuralism reasonable would also make reasonable to discard all contemporary analytic metaphysics (see Ladyman & Ross, 2007, 7–27). This conclusion is surprising when it is evident that the indicated problems precisely require developing a metaphysics with the best conceptual and theoretical resources that we have at our disposal. Fortunately, the position of other defenders of ontic structuralism like Steven French has been more sensible on this point (see French, 2014, 48–64). What is required is a work that integrates the cooperation of philosophers of physics—which usually have little sensitivity to the more general ontological problems—and metaphysicians—which usually have little sensitivity for the specific problems of philosophy of physics.
References
Alvarado, J. T. (2005). Necesidad de origen y metafísica modal. Diánoia, 50(54), 3–32.
Alvarado, J. T. (2007). Cómo podrían ser las cosas. Nota crítica. Philosophica, 32, 203–219.
Alvarado, J. T. (2015). Dos teorías nucleares de la sustancia. Cuadernos de filosofía, 33, 29–51.
Alvarado, J. T. (2016). Nuclear trope bundles and ontological dependence. Disputatio Philosophical Research Bulletin, 5(6), 205–224.
Aquinas, Thomas, Summa theologiae (1952). Cura et studio Petri Caramello cum texto ex recensione leonina. Roma: Marietti.
Aristotle, Metaphysica (1998). Metafísica. Introducción, traducción y notas de Tomas Calvo Martínez. Madrid: Gredos.
Aristotle, Categories (2009). Categorías. Sobre la interpretación. Introducción, traducción y notas de Jorge Mittelmann. Buenos Aires: Losada.
Armstrong, D. M. (1978). Universals and scientific realism, Volume II, A Theory of Universals. Cambridge: Cambridge University Press.
Armstrong, D. M. (1983). What is a law of nature? Cambridge: Cambridge University Press.
Benovsky, J. (2008). The bundle theory and the substratum theory: Deadly enemies or twin brothers? Philosophical Studies, 141, 175–190.
Benovsky, J. (2016). Meta-metaphysics. On metaphysical equivalence, primitiveness, and theory choice. Berlin: Springer.
Brower, J. (2010). Aristotelian Endurantism: A new solution to the problem of temporary Intrinsics. Mind, 119, 883–905.
Chisholm, R. M. (1967). Identity through possible worlds: Some questions. Noûs, 1, 1–8.
Dainton, B. (2001). Time and space. Chesham: Acumen.
French, S. (2014). The structure of the world. Metaphysics and representation. Oxford: Oxford University Press.
French, S., & Krause, D. (2006). Identity in physics: A historical, philosophical, and formal analysis. Oxford: Clarendon Press.
Funkhouser, E. (2014). The logical structure of kinds. Oxford: Oxford University Press.
Garcia, R. K. (2014). Bundle’s theory black box: Gap challenges for the bundle theory of substance. Philosophia, 42, 115–126.
Garcia, R. K. (2015a). Two ways to particularize a property. Journal of the American Philosophical Association, 1(4), 635–652.
Garcia, R. K. (2015b). Is trope theory a divided house? In G. Galluzzo & M. J. Loux (Eds.), The problem of universals in contemporary philosophy (pp. 133–155). Cambridge: Cambridge University Press.
Keinänen, M. (2005). Trope theory and the problem of universals. Helsinki: Philosophical Studies from the University of Heksinki.
Keinänen, M. (2011). Tropes: The basic constituents of powerful particulars? Dialectica, 65(3), 419–450.
Kripke, S. (1980). Naming and necessity. Oxford: Blackwell.
Ladyman, J., & Ross, D. (2007). Every thing must go. Metaphysics naturalized. Oxford: Oxford University Press.
Lam, V. (2017). Structuralism in the philosophy of physics. Philosophy Compass, 12(6). https://doi.org/10.1111/phc3.12421.
Lowe, E. J. (1999). The possibility of metaphysics. Substance, identity, and time. Oxford: Clarendon Press.
Lowe, E. J. (2006). The four-category ontology. A metaphysical Foundation for Natural Science. Oxford: Clarendon Press.
Mackie, P. (2006). How things might have been. Individuals, kinds, and essential properties. Oxford: Clarendon Press.
Maurin, A.-S. (2002). If tropes. Dordrecht: Kluwer.
McDaniel, K. (2010a). A return to the analogy of being. Philosophy and Phenomenological Research, 81, 688–717.
McDaniel, K. (2010b). Being and almost nothingness. Noûs, 44, 628–649.
McDaniel, K. (2013). Degrees of Being. Philosopher’s Imprint, 13(19), 1–18.
Salmon, N. (1987). Existence. Philosophical Perspectives, 1, 49–108.
Shapiro, S. (1997). Philosophy of mathematics. Structure and ontology. Oxford: Oxford University Press.
Strawson, P. F. (1992). Analysis and metaphysics. An introduction to philosophy. Oxford: Oxford University Press.
Tooley, M. (1987). Causation. A realist approach. Oxford: Clarendon Press.
Westerhoff, J. (2005). Ontological categories. Their nature and significance. Oxford: Clarendon Press.
Wiggins, D. (2001). Sameness and substance renewed. Cambridge: Cambridge University Press.
Worrall, J. (1989). Structural realism: The best of both worlds? Dialectica, 43, 99–124. Reprinted in David Papineau (ed.), Philosophy of Science, Oxford: Oxford University Press, 1996, 139–165.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2020 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Alvarado, J.T. (2020). The Reformed Nuclear Theory. In: A Metaphysics of Platonic Universals and their Instantiations. Synthese Library, vol 428. Springer, Cham. https://doi.org/10.1007/978-3-030-53393-9_13
Download citation
DOI: https://doi.org/10.1007/978-3-030-53393-9_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-53392-2
Online ISBN: 978-3-030-53393-9
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)