Abstract
This paper examines some possibilities for the laws of nature changing over time. This is done within the context of recent literature on transformational emergence. Transformational emergence is a diachronic account of emergence that does not require the invariance of fundamental objects, properties, and laws. The requirement that no new laws are introduced after the first instance of the universe seems to indicate that all the laws of the universe are present from the outset. By using a dispositional approach to fundamental properties, this restriction can be avoided. An argument appealing to quantitative laws of nature is then used to show that such laws are not, contrary to dispositional essentialism, metaphysically necessary. Further arguments are given to support the possibility of change of laws across time rather than across worlds and why the identity conditions for properties are different in the two cases. The paper is framed by an analysis of John Stuart Mill’s reasons for imposing the invariance requirement on fundamental laws.
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Notes
It has occasionally been suggested that Galileo did identify it as a planet but there is no conclusive evidence of this.
Unless otherwise noted quotations from Mill are from the first edition of A System of Logic (Mill 1843). Mill retained each of these passages unchanged in the last, eighth, edition of 1872.
As far as I know, each of these positions was initially developed independently from the others. All four positions use the expression `transformation' to characterize what is special about their approach.
See Humphreys 2016. The origin of the universe problem has an enhanced version that raises a problem for any position that allows new properties and new laws to come into existence, because it arises each time a new emergent law appears. That version will not be discussed here.
I am following here the common philosophical simplification that nomological regularities consist of discrete sequences. This may be false, but it is not obviously an oversimplification because the intermediate states between the nomologically related states may be constant with no laws needed to maintain the steady state.
There could be lawlike regularities that consist only of monadic properties repeatedly instantiating themselves in more or less interesting patterns but I shall set these aside here as a degenerate case of the general principle.
The standard contrast to dispositional properties is categorical properties but that contrast is neither uniformly drawn nor entirely neutral with respect to the goals in this paper. For example, Bird 2007 holds that fundamental categorical properties are those whose natures are picked out by quiddities (op.cit. p. 3) and for which there are no necessary connections with other entities (op.cit. p. 67). This dichotomy between categorical and dispositional properties is an uncomfortable fit in the present context because fundamental laws may contain mixtures of dispositional and categorical properties. I shall therefore not appeal to that contrast here.
There are arguments that some causal chains are not transitive and there are examples of dispositional properties that do satisfy transitivity, but both types of cases are unusual and all we need are cases in which the two come apart.
Thanks to Alexandre Guay for the first point.
In world W, the spring constant for a given material is a fundamental constant. It is not the result of the internal composition of the material.
The situation is complicated by the fact that Coulomb's Law is often considered not to be a fundamental law but a consequence of the more general Gauss’s Law.
In a similar way, we could say that the repulsive force between two like charges could have an inverse square form in W but an inverse cube form in W*. There is a geometrical explanation of inverse square laws in terms of the distribution of intensity over a spherical surface falling off with the surface area of a region of that surface. But that explanation assumes the conservation of charge intensity, which is itself an empirical fact. In this case, we could acknowledge that it is metaphysically necessary that like charges repel one another but reject the view that the specific mathematical form of Coulomb’s Law is metaphysically necessary, since in W the disposition is to produce a repulsive force of e1Ae2/r2 whereas in W* the disposition is to produce a repulsive force of e1Ae2/r3.
This footnote first appears in the 4th edition of 1856.
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Acknowledgements
I am grateful to Alexandre Guay, Robin Hendry, Andreas Hutteman, Gil Santos, Olivier Sartenaer, Michael Silberstein, Peter Wyss, and David Yates for comments and discussion related to this paper, and to audiences at the Cologne Diachronic Emergence and the Lisbon Rethinking Emergence conferences for critical assessment.
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Humphreys, P. Invariances in transformational emergence. Synthese 199, 2745–2756 (2021). https://doi.org/10.1007/s11229-020-02909-4
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DOI: https://doi.org/10.1007/s11229-020-02909-4