Abstract
A well-known difficulty that affects all accounts of laws of nature according to which the latter are higher-order facts involving relations between universals (the so-called DTA accounts, from Dretske in Philosophy of Science 44:248–268, 1977; Tooley in Canadian Journal of Philosophy 7:667–698, 1977 and Armstrong (What is a Law of Nature?, Cambridge University Press, Cambridge, 1983)) is the Inference Problem: how can laws construed in that way determine the first-order regularities that we find in the actual world? Bird (Analysis 65:147–55, 2005) has argued that there is no solution to the Inference Problem which is consistent with both categorical monism (that is, the view that all natural properties are categorical) and basic tenets of Armstrong’s account of the laws of nature. This paper shows that, given Armstrong’s view about laws as first-order structural universals whose instantiation ‘produce’ nomic regularities and under specific plausible metaphysical assumptions concerning nomic relations which are consistent with a broadly construed DTA approach to laws, there is no extra difficulty regarding the Inference Problem in a categorical monistic context besides the ones that beset structural universals in general.
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Notes
The inference is taken to be an entailment that strictly holds only for deterministic and exceptionless laws.
In his (1989, 96), van Fraassen has also presented the so-called Identification Problem which, in rough terms, concerns the identification of a proper entity that can play the governing role of N.
As I will mention in the sequel, this characterisation cannot be construed as implying that under any conception of structural universals the latter are literally composed by other simpler universals. Structural universals ‘involve’ their ‘constituents’ at least in the minimal sense that there are necessary connections between their instances and the instances of their ‘constituents’.
Nevertheless, for a defence of indiscernible universals, see Rodriguez-Pereyra (2017).
For a proposal of how this can be done, see Bennett (2013).
For a useful review of the main arguments, see Fisher (2018).
For Armstrong, the fundamental ontological units are states of affairs. Universals are state-of-affairs types: that is, abstractions in which particulars have been ‘eliminated’ from states of affairs.
Bolender explains: “Armstrong’s point is that a causal relation between particulars instantiates a structural property. For example, states of affairs of the form A-caused-B are particulars (thick particulars) instantiating structural properties of a temporal sort. It is the nature of a causal sequence to instantiate a special kind of structural property, one in which the structure unfolds through time just as a flag (with a design on it) or a molecule is an instantiation of a structural property in which the structure is extended through space. In some cases, these particular causal relations essentially involve structural extension through time and in some cases they do not, but they are in all cases structures.” (2006, 407).
According to Lewis (1999, 89), we should reject the linguistic conception for all structural universals on the grounds that it cannot accommodate the possibility of infinite complexity in the world (that is, the possibility that there are no simples).
Perhaps, however, one could provide an essentialist explanation of this fact. For further discussion, see Sect. 6.
To avoid misunderstandings, Coates herself does not suggest that. Her suggestion is that it is the nomic necessitation relation N that may have as a matter of brute fact the necessary property of being such that if it relates F and G then R(F,G) (2021, 927). Furthermore, although that at this point we appeal to Coates’ view in the case of simple categorical properties, there is nothing regarding the view itself that would prohibit its application in the case of complex categorical properties.
In the recent literature, the concept of metaphysical explanation is most often related to grounding. For the purposes of this paper, a less specific notion of metaphysical explanation is sufficient. According to this conception, an explanation is metaphysical if its explanans involves ‘pure’ metaphysical notions such as essences, relations of ontological dependency, etc. Given that, the metaphysical explanation can be seen as a family of kinds of explanation which includes (perhaps among others) the grounding explanation.
For an akin proposal, where the entailment in question is the strict implication from laws to corresponding regularities, see Wilsch (2021). Hireche et al. (2021) propose that it is part of the nature of the nomic relation N that it gives rise to the corresponding regularities. In their words: “It is essential to N that, if F stands in the relation N to G, then everything which is F is G.” (2021, 10, 228). Note however that this proposal concerns the essence of N, not the essence of laws whose ‘constituent’ is N.
The adicity of a first-order universal is the number of ‘slots’ that need to be filled by particulars in order for an instance of the universal to exist. Properties of objects are monadic universals (they have adicity 1), whereas relations among objects are polyadic universals (they have adicity greater than or equal to 2). The definition of adicity can be generalised for universals of any order n: the adicity of a universal of order n is the number of ‘slots’ that need to be filled by entities of order n-1 in order for an each instance of the universal to exist.
For a discussion of this issue in the case of powerful qualities, see Livanios (2021).
According to Bird, powers are fundamental natural properties that have dispositional essences.
Coates scrutinizes the idea that the nomic necessitation relation N (not the law N(F, G) itself) can essentially be such that if it relates F and G, then R(F,G) and finds it wanting for the same reason: “Indeed, it is possible for N to be instantiated without F or G being instantiated at all, as well as for F or G to be instantiated without N being instantiated. Consequently, that N stands in an essential connection with F and G cannot be explained by N’s having F and G as constituents.” (2021, 926).
The notion of the relata-specific first-order relation has been used by Weiland and Betti (2008) to account for the unity of first-order facts. Livanios (2012) has suggested that relata-specificity is an essential characteristic of external second-order nomic relations (see also Ioannidis et al. 2021).
It is interesting to note that Armstrong himself allows the existence of more than one type of nomic relations (nomic necessitation, nomic probabilification and perhaps nomic exclusion) in order to accommodate all possible laws of nature. (In fact, under a specific interpretation of his account of probabilistic laws, the number of distinct nomic/causal relations is the same as the number of laws with different objective probabilities of being instantiated in favourable conditions, see Jacobs and Hartman 2017). He does not however hold that each fundamental law involves a distinct nomic relation.
Bartels (2019) argues that these ‘laws’ are not counterexamples to the causal interpretation of laws of nature. For him, the lawful status belongs to types of interactions which are represented by specific Lagrangians and the equations of motion derived from them. Furthermore, the modal force that characterised laws is grounded in the contingent fact that their causal productivity is stable on the basis of their mutual independence. Constraint and composition ‘laws’, as well as the symmetry principles (both global and local), are not laws in Bartels’ sense.
Armstrong’s view is not the only DTA account that has failed to provide an adequate and illuminating answer to the Identification Problem. Tooley (1987) suggested two ways to solve the problem (the account by stipulation and the speculative account) which are both problematic. The latter proposal has been severely criticised by Sider (1992) and Hildebrand (2013) and Tooley himself (1987, 127) admitted that the former is inadequate on the grounds that it gives no account of the intrinsic nature of nomic relations. (I would add that even if the proposed account were to offer an illuminating view about the nature of nomic relations, it would certainly give no metaphysically illuminating ‘solution’ to the Inference Problem given that the crucial entailment that raises the problem is included by definition in the functional role of any relation that according to Tooley would legitimately be called nomic.) According to Dretske (1977), laws are the relationships between properties or magnitudes that are asserted to exist by true law-like statements which are singular statements of fact. The nomic relation between properties F and G (symbolised as F − > G) is an extensional relation between those properties, with the terms “F-ness” and “G-ness” occupying transparent positions. Beyond that, however, no extra information is given regarding the nature of nomic relations. As Dretske himself admits: “I attach no special significance to the connective→. I use it here merely as a dummy connective or relation. The kind of connection asserted to exist between the universals in question will depend on the particular law in question, and it will vary depending on whether the law involves quantitative or merely qualitative expressions”.
According to the composition-as-identity view for a structural universal, the latter is identical to the plurality of universals that compose it. In a weak version of the view, the relation of identity is replaced by another relation of ‘weak identity’ which is sufficiently similar to ‘strict’ identity in the sense that just as in the case of the latter, necessarily, when two properties are related by this identity-like relation they are co-extensional. For details, see Azzano (2021).
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Acknowledgements
Earlier versions of this paper were presented at the 4th conference of East European Network for Philosophy of Science (Tartu 2022) and 6th Italian Conference in Analytic Ontology and Metaphysics (L’Aquila 2022). I would like to thank the participants of both conferences as well as the anonymous referees for their useful comments. This study was funded by A.G. Leventis Foundation (Grant number 912876).
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This study was funded by A.G. Leventis Foundation (912876).
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Livanios, V. Categorical Monism, Laws, and the Inference Problem. J Gen Philos Sci 54, 599–619 (2023). https://doi.org/10.1007/s10838-023-09638-5
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DOI: https://doi.org/10.1007/s10838-023-09638-5