Abstract
Thus far I have argued for a metaphysics of fundamental natural properties and relations of the actual world. In particular, I put forward the thesis that fundamentally our world is a categorical–monistic one (henceforth, a C-world). A metaphysics of properties almost always comes together with a corresponding metaphysics of laws of nature. This is obviously true in the case of laws which essentially involve ontologically robust natural (fundamental) properties and relations. Instances of that case is the DTA theory of laws as relations between universals and, more generally, any account of laws as relations between properties construed as belonging to a distinct (from concrete particulars) ontological category. But it is also true even within broadly nominalistic metaphysical contexts where we do not have a substantial notion of a natural property. The reason, in that case, is that one of the main roles of natural properties is to help explain the behaviour of their bearers. It is assumed, however, that laws of nature, if they exist, purport to fill the same role; hence, the inevitable connection. So, in the chapters to follow, I’ll present the basic metaphysical consequences of my preferred account of the nature of fundamental properties for laws of nature.
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.
- 2.
- 3.
The fact that, in a C-world, all nomic relations are external does not preclude the possibility that other, non-nomic, relations between natural properties are internal.
- 4.
No doubt, epistemological problems beset that procedure, but, as far as the metaphysics is concerned, it is a perfectly legitimate way to determine the causal/nomic role of any natural fundamental property.
- 5.
For a detailed exposition of the same problem, though expressed in causal terms, see also Bolender (2006).
- 6.
Moderate, because she only has to admit that the exemplification relation is a metaphysically robust, primitive non-spatiotemporal entity. For an account akin to this but in a non-naturalistic context where universals themselves are abstract, non-spatiotemporal entities, see Moreland (2001).
- 7.
The criterion of dispositionality for fundamental properties of the actual world does not have to be related (as dispositional essentialists claim) to the essentialist claim that causal/nomic roles are essential to properties. Hence, all those philosophers who accept the existence of genuine, irreducible dispositional properties do not have to follow the essentialist course.
- 8.
Of course, this only holds under the assumption that fundamental properties and relations are dispositional in all worlds in which they exist. Anyone (like me) who rejects this assumption must restrict the range of validity of the claim to those worlds in which properties retain their dispositional character.
- 9.
There are at least two different senses of internality. According to the weak sense, internal relations are grounded merely in the numerical identity of their relata, while according to the strong one, they are grounded in the qualitative natures of the relata. In the following discussion, I presuppose the (more popular) strong sense of internality.
- 10.
Armstrong uses a definition of supervenience that does not refer to groups of properties. For him, an entity Q supervenes on entity P iff it is impossible that P could exist and Q not exist, where P is possible (1997, 11). I prefer the more or less standard definition, according to which internal relations supervene on the natures of their relata iff there cannot be a difference in the relations without a difference in the natures of their relata.
- 11.
In his earlier work (1978a, 86), Armstrong presents two reasons in favour of the thesis. First, according to his a posteriori realism, it is a suspicious fact that one can discover the existence of internal relations simply by knowing the properties of their relata. Second, it seems implausible to think that internal relations genuinely exist, given that we have no reason to attribute causal efficacy to them. In his subsequent work, however, Armstrong acknowledges that ‘it is not clear how the thesis that what supervenes is no addition of being is to be proved’ (1997, 12).
- 12.
As in the case of the C-world, the fact that, in a D-world, all nomic relations are internal does not preclude the possibility that other, non-nomic, relations between natural properties are external.
- 13.
The expression ‘nomic realist’, as I use it here, refers to those philosophers who acknowledge the genuine existence of at least some nomic relations in some possible worlds.
- 14.
- 15.
I refer here to the so-called variational symmetries that leave the form of the Lagrangian invariant up to a divergence term. Every such symmetry is also symmetry of the Euler–Lagrange equations that follow from the application of the action principle. However, the converse is not always true.
- 16.
The symmetry-based explanation is not necessarily an ontological explanation. Of course, it can be one provided that fundamental symmetries are properties (not necessarily essential) of the world (or, of its structure).
- 17.
That is not true for the conservation of various charges which is a consequence of invariance under internal symmetry transformations (related to abstract spaces). So in this case we do not have an intuitively well-understood concept to ground the explanation. Nevertheless, I think it is an adequate explanation because it is an instance of (an extension of) an explanatory procedure which is broadly successful.
- 18.
Alan Chalmers (1999, 14) raises two more worries about Bigelow et al.’s suggestion. He points out, first, that conservation laws—just like the other (non-cosmological) laws—are applied to local systems in the world, not to the world as a whole. Though he admits that conservation laws apply exactly only to isolated systems, he does not regard this as a cogent reason to suppose that those laws apply only to the whole universe; for all laws apply exactly only in idealised contexts (in his words, ‘there is no causal factor governed by any law which operates totally unhindered’). The second worry is that, by appealing to the world-essence, Bigelow et al. do not eventually succeed in offering a single unified account of laws of nature. For, while conservation laws impose (often strong) constraints on the physical processes in the universe, they do not ‘describe powers and capacities that are exercised in a law-like way in bringing about the phenomena of the world as causal laws do’.
- 19.
According to Hamilton’s principle, the action integral \( I=\underset{t_0}{\overset{t_1}{{\displaystyle \int }}}L\cdot dt \)of the Lagrangian function of a physical system is stationary under arbitrary variations dqi of the generalised co-ordinates which vanish at the limits of integration.
- 20.
The application of Hamilton’s principle yields the Euler–Lagrange equations. They are in general second-order differential equations for the Lagrangian function.
- 21.
For more details about that, see Earman (2004).
- 22.
Recall (from Sect. 2.2.2) the two main approaches concerning the interpretation of fundamental symmetries, the ontological and the epistemic.
- 23.
French (forthcoming) is a recent investigation of the prospects of orthodox dispositionalism as a metaphysical account of the nature of fundamental symmetries. He examines various ways of implementing standard stimulus-manifestation dispositionalism in the context of physical symmetries and finds them problematic.
- 24.
The two difficulties (the one related to conservation laws discussed in the preceding section and the one associated with fundamental constants to be examined here) do not exhaust the problems that DEAL should meet. There is also a problem related to the least action principles (for a discussion, see Katzav (2004) and Ellis (2005a)) and another difficulty concerning properties (such as inertial and gravitational mass) which, though they seem to be involved in laws in accordance with the dispositional conception, are nomically related by a law that most probably is not an expression of their dispositional natures. All these issues are briefly discussed in Bird (2007).
- 25.
Of course, extremely important is also the discovery of new fundamental constants that always accompany the introduction of novel fundamental theories (for instance, Planck’s constant h in quantum theory and string tension λ in String Theory). Barrow’s list is supplemented with the discovery that the value of one constant is determined by the values of others, the discovery that a physical phenomenon is governed by a new combination of constants, and, finally, the discovery that a quantity believed to be a constant is not really constant. For more details and examples, see Barrow (2002).
- 26.
An implicit assumption of the argument is that the laws of the possible world in premise (2) differ from the corresponding actual laws. This assumption, however, is not controversial because if the constants appearing in the laws assume different values, then the propositional contents of the laws are surely different and that means (on any tenable account of laws of nature) that laws themselves have changed.
- 27.
For a scientifically informed metaphysician, this association fits nicely her core belief that the only reliable source for discovering the inventory of fundamental entities of the world is our best current physical theories. Of course, there are disagreements about the appropriate theoretical frameworks, but what I think is undisputed is that the examination of the case of fundamental constants within a science-sensitive metaphysical context should be grounded in the findings and practice of modern physical science.
- 28.
We may arrive to the same conclusion following Levy-Leblond’s interesting views about the fate of all dimensional constants. Levy-Leblond (1979) classifies physical constants into three distinct types: Type-A includes properties of particular (types of) physical objects (such as the masses of elementary particles); type-B constants characterise classes of phenomena (such as the coupling constants of fundamental interactions); and type-C constants characterise the most general theoretical frameworks in the context of which we can describe any physical phenomena (such as ħ). According to Levy-Leblond, all type-C constants undergo a shift (as theories evolve) from a dominant conceptual status to an almost invisible one. They are ‘progressively incorporated into the implicit common background of physical ideas, then play a role of mere unit conversion factors and often finally forgotten altogether by a suitable redefinition of physical units’ (1979, 246).
- 29.
The multiverse proposal is not a theory but a ground hypothesis (or prediction) of several modern explanatory physical theories in cosmology and high-energy physics. The core idea is that our universe is just one of a (possibly infinite) ensemble of ‘parallel’ universes; the latter could differ from ours in various features, ranging from different initial conditions (at their Big Bangs) to different fundamental laws and constants. In the cosmological field, there are various views on how the universes of the multiverse might arise. The most popular one nowadays is provided by inflation theory: under the assumptions of a spatially infinite universe and a uniform distribution of matter at large scales, a consequence of inflation theory is that our observable universe is part of a ‘bubble’ which underwent an extra-fast expansion phase at some early time. There are many other ‘bubbles’, each with the same laws but different initial conditions which are most possibly created by quantum fluctuations during the period of inflation (Guth 1981). Another proposal on how new universes may arise is a variant of the above theory, the so-called eternal inflation scenario, according to which each ‘bubble’ universe is continually self-reproducing (Linde (1986), Vilenkin (1983)). For other cosmological theories based on varieties of the multiverse hypothesis, see Wheeler (1974), Misner, Thorne and Wheeler (1973), G.F.R. Ellis (1979) and Smolin (1997). Recently, the multiverse hypothesis has been used in high-energy physics as a ground assumption of the new version of String Theory, the so-called Landscape Scenario. For a recent volume dedicated to the multiverse hypothesis, see Carr (2007).
- 30.
Of course, if one is willing to explain necessity as discussed here with the assistance of a Great Designer, she may follow a theistic version of SAP, according to which there exists one possible universe especially designed with the goal of generating and sustaining (human) observers. In that case the claim for the metaphysical necessity of the values of constants is trivially true.
- 31.
The logic of anthropic reasoning does not indicate any special preference for human (or intelligent) life. Furthermore, there is disagreement about the scope of the notion of life and the elements which are capable of being the building blocks for the type of complex systems that might develop life-like features. Much of the argumentation in this area concerns cosmological and astrophysical features that could make life (broadly conceived) more likely. Typical habitable universes are characterised by big bang nucleosynthesis and large-scale structure, and allow for star formation, long stellar lifetimes and reasonable means to produce and disperse heavy chemical elements into the interstellar medium.
- 32.
Note here that, though a specific constant may be involved in the individual essence of the property, the latter may also appear in laws without constants or with different constants.
- 33.
For the notion of reciprocal disposition partners, see Martin (2008).
- 34.
Recall (from fn. 28) that type-C constants characterise the most general theoretical frameworks in which we can describe physical phenomena. Since each of these constants is present in most of the laws of the framework that it characterises, it should be involved in the individual essence of a large number of fundamental properties. Furthermore, since fundamental properties appear in laws of different theoretical frameworks, they should involve in their individual essences all the type-C constants that characterise the frameworks they appear in.
- 35.
Variation of the constant results in this case from its functional dependence on d which, in turn, is due to the geometric origin of the constants under consideration.
- 36.
Of course, we may arrive at the same conclusion by considering the role of fundamental constants in non-fundamental laws. For instance, according to Newton’s gravitational law, the strength of the gravitational force depends on the value of the fundamental constant G. So, according to dispositional essentialists, the identity of mass must somehow depend on the value of G.
- 37.
Despite its initial appeal, this claim is not defensible after all. To see why, recall my argument from the application of the renormalisation procedures in QFT.
- 38.
In order to be persuasive, the reasoning should have the form of the following argument:
-
a)
The individual essence of fundamental properties involves the values of coupling constants.
-
b)
The individual essence of coupling constants involves the topology/geometry of the space with compactified dimensions.
\( \therefore \) The individual essence of fundamental properties involves the topology/geometry of the space with compactified dimensions.
It is not clear, however, why the determination of coupling constants by ‘topological/geometric’ ones implies that the individual essence of the former involves the latter. Furthermore, the conclusion is only valid provided that a controversial principle of transitivity for individual essences holds.
-
a)
- 39.
Laws such as L@ and L# are functional because the nomically related properties/relations q and r can take infinite values. (See, for instance, Armstrong’s (1997, 242) account of such laws as relations between determinables having infinite—probably mostly uninstantiated—determinate values falling under them.) L* is a functional law as well, though it has the extra argument d.
- 40.
The mode of expression presupposes the common assumption that all natural properties are transworld entities. Anyone who believes instead that they are world-bound must re-express the syllogism in terms of counterpart theory, where the de re modal representation is achieved by counterparts of properties, rather the properties themselves. Similar remarks hold for the use of the expressions ‘same properties’ and ‘transworld identity’.
- 41.
The strong coupling constant αs is also energy-dependent but, unlike α, decreases at high energies (asymptotic freedom). The difference from the electromagnetic case is due to the nature of gluons (mediators of the strong force) which, unlike photons, are self-interacting.
- 42.
This is the case according to the cosmological inflation theory.
References
Adams, F. (2008). Stars in Other Universes: Stellar Structure with Different Fundamental Constants. Journal of Cosmology and Astroparticle Physics 08, 0810.
Armstrong, D.M. (1978a). Universals and Scientific Realism: A Theory of Universals. Cambridge: Cambridge University Press.
Armstrong, D.M. (1983). What Is a Law of Nature? Cambridge: Cambridge University Press.
Armstrong, D.M. (1997). A World of States of Affairs. Cambridge: Cambridge University Press.
Armstrong, D.M. (2004a). How Do Particulars Stand to Universals? In Zimmerman, D.W. (Ed.) Oxford Studies in Metaphysics, Vol. 1. Oxford: Clarendon Press, 139–154.
Barrow, J. (2002). The Constants of Nature: From Alpha to Omega-The Numbers That Encode the Deepest Secrets of the Universe. New York: Pantheon Books.
Barrow, J. & Tipler, F. (1986). The Anthropic Cosmological Principle. Oxford: Clarendon Press.
Bigelow, J., Ellis, B. & Lierse, C. (1992). The World as One of a Kind. British Journal for the Philosophy of Science 43, 371–388.
Bird, A. (2007). Nature’s Metaphysics: Laws and Properties. Oxford: Clarendon Press.
Bird, A. (2012). Monistic Dispositional Essentialism. In Bird, A., Ellis, B. & Sankey, H. (Eds.) Properties, Powers and Structures. New York: Routledge, 35–41.
Bolender, J. (2006). Nomic Universals and Particular Causal Relations: Which Are Basic and Which Are Derived? Philosophia 34, 405–410.
Carr, B. (Ed.) (2007). Universe or Multiverse. Cambridge: Cambridge University Press.
Chalmers, A. (1999). Making Sense of Laws of Physics. In Sankey, H. (Ed.) Causation and Laws of Nature. Kluwer Academic Publishers, 3–18.
Cohen-Tannoutji, G. (2009). Universal Constants, Standard Models and Fundamental Metrology. European Physical Journal (Special Topics) 172, 5–24.
Dretske, F. (1977). Laws of Nature. Philosophy of Science 44, 248–268.
Duff, M.J. (2004). Comment on the Time-Variation of Fundamental Constants. ArXiv:hep-th/0208093v3 (11 July 2004).
Duff, M.J., Okun, L.B & Veneziano, G. (2002). Trialogue on the Number of Fundamental Constants. Journal of High Energy Physics 03(2002), 023. Also in arXiv: physics/0110060v2 [physics.class-ph] (28 Feb 2002).
Earman, J. (2004). Laws, Symmetry, and Symmetry Breaking: Invariance, Conservation Principles, and Objectivity. Philosophy of Science 71(5), 1227–1241.
Ellis, B. (2001). Scientific Essentialism. New York: Cambridge University Press.
Ellis, B. (2005a). Katzav on the Limitations of Dispositionalism. Analysis 65(1), 90–92.
Ellis, G.F.R. (1979). The Homogeneity of the Universe. General Relativity and Gravitation 11(4), 281–289.
French, S. (forthcoming). Doing Away with Dispositions: Powers in the Context of Modern Physics. In Meincke-Spann, A.S. (Ed.) Dispositionalism: Perspectives from Metaphysics and the Philosophy of Science. Springer Synthese Library, Springer.
Guth, A. (1981). Inflationary Universe: A Possible Solution to the Horizon and Flatness Problem. Physical Review D 23, 347–356.
Harnik, R., Kribs, G. & Perez, G. (2006). A Universe Without Weak Interaction. Physical Review D 74(3), 035006.
Hawthorne, J. (2001). Causal Structuralism. Philosophical Perspectives 15, 361–378.
Katzav, J. (2004). Dispositions and the Principle of Least Action. Analysis 64(3), 206–214.
Levy-Leblond, J.M. (1979). The Importance of Being (a) Constant. In Toraldo di Francia, G. (Ed.) Problems in the Foundations of Physics. Enrico Fermi School LXXII. Amsterdam: North Holland Publications, 237–263.
Lewis, D.K. (1986). On the Plurality of Worlds. Oxford: Blackwell.
Linde, A.D. (1986). Eternally Existing Self-Reproducing Chaotic Inflationary Universe. Physics Letters B 175(4), 395–400.
Martin, C.B. (2008). The Mind in Nature. Oxford: Clarendon Press.
Moffat, J.W. (2002). Comment on the Variation of Fundamental Constants. ArXiv: hep-th/0208109v2 (7 Nov 2002).
Moreland, J.P. (2001) Universals. Chesham: Acumen.
Mumford, S. (2004). Laws in Nature. London: Routledge.
Noether, E. (1918). Invariante Variationsprobleme. Nachr. d. Konig. Gesellschd. d.Wiss. Zu Gottingen, Math-phys. Klasse, 235–57.
Rees, M. (1999). Just Six Numbers. New York: Basic Books.
Simons, P. (2010). Relations and Truthmaking. Proceedings of the Aristotelian Society, Supplementary Volume LXXXIV, 199–213.
Smolin, L. (1997). The Life of the Cosmos. Oxford: Oxford University Press.
Smolin, L. (2006). The Trouble with Physics. Boston/New York: Houghton Mifflin Co.
Stenger, V. (2004). Is the Universe Fine-Tuned for Us?. In Young, M. & Edis T. (Eds.) Why Intelligent Design Fails: A Scientific Critique of the New Creationism. New Brunswick, NJ: Rutgers University Press, 172–84.
Tegmark, M., Aguirre, A., Rees, M.J. & Wilczek, F. (2006). Dimensionless Constants, Cosmology, and Other Dark Matters. Physical Review D 73(2), 023505.
Tooley, M. (1977). The Nature of Laws. Canadian Journal of Philosophy 7, 667–698.
Uzan, J.P. (2002). The Fundamental Constants and Their Variation: Observational Status and Theoretical Motivations. Reviews of Modern Physics 75(2), 403–455. Also in arXiv: hep ph/0205340v1(30 May 2002).
Uzan, J.P & Leclercq, B. (2008). The Natural Laws of the Universe: Understanding Fundamental Constants. Chichester, UK: Praxis Publishing.
Vilenkin, A. (1983). Birth of Inflationary Universes. Physical Review D 27, 2848–2855.
Weinberg, S. (1992). Dreams of a Final Theory. New York: Pantheon Books.
Weinberg, S., Nielsen, H.B. and Taylor, J.G. (1983). Overview of Theoretical Prospects for Understanding the Values of Fundamental Constants. Philosophical Transactions of the Royal Society of London A 310, 249–252.
Wheeler, J.A. (1974). Beyond the End of Time. In Rees, M., Ruffini, R. & Wheeler, A.J. (Eds.) Black Holes, Gravitational Waves and Cosmology. New York: Gordon and Breach.
Wilczek, F. (2007). Fundamental Constants. ArXiv: 0708.4361v1 [hep-ph] (31 Aug 2007).
Zwiebach, B. (2009). A First Course in String Theory. Cambridge: Cambridge University Press.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 The Author(s)
About this chapter
Cite this chapter
Livanios, V. (2017). Do Nomic Relations Exist?. In: Science in Metaphysics . New Directions in the Philosophy of Science. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-41291-7_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-41291-7_7
Published:
Publisher Name: Palgrave Macmillan, Cham
Print ISBN: 978-3-319-41290-0
Online ISBN: 978-3-319-41291-7
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)