Abstract
Bird reveals an important problem at the heart of Armstrong’s theory of laws of nature: to explain how a law necessitates its corresponding regularity, Armstrong is committed to a vicious regress. In his very brief response, Armstrong gestures towards an argument that, as he admits, is more of a “speculation.” Later, Barker and Smart argue that a very similar problem threatens Bird’s dispositional monist theory of laws of nature and he is committed to a similar vicious regress. In this paper, first, I construct Armstrong’s would-be argument in response to Bird. Second, I argue that his response makes his account of laws and natural properties incompatible with science. Finally, I argue that Armstrong’s strategy to address Bird’s criticism can be used, quite ironically, to defuse Barker and Smart’s argument against Bird.
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Notes
As Lewis (1983, 366) famously writes, “N[−relation] deserves the name of ‘necessitation’ only if, somehow, it really can enter into the requisite necessary connections. It can’t enter into them just by bearing a name, any more than one can have mighty biceps just by being called ‘Armstrong’.”
This, obviously, does not mean that we can never revise (even) our best scientific theories and most well-established laws of nature. The point is that an inconsistency between a well-established law and one’s metaphysical theory of laws is hardly a proper reason for such a revision.
Here, I primarily focus on the scientific ramifications of Armstrong’s principle of instantiation. For a discussion on its metaphysical problems, see (Moreland, 2001, chap. 6).
It might be suggested that “a sphere made of californium-251 with a mass of more than five kilograms explodes as a result of a chain reaction” is reducible to some instantiated fundamental law(s) governing the interactions of subatomic particles and the atomic nucleus. And this makes the uninstantiated status of the law governing the critical mass of californium-251 unproblematic. This is a scientifically substantial claim that can be accepted only if one shows that this alleged reduction can be really done in a theoretically acceptable manner. I am not aware of any such reduction. In fact, from different models that have been developed for calculating the critical mass of fissionable elements in nuclear physics, one gets a strong impression that such a reduction is by no means readily available. Nuclear fission occurs when a nucleus is struck by a neutron. This process results in releasing energy and emitting other neutrons which, in turn, can bring about more fissions. Now, imagine a sample of a radioactive material that emits neutrons. These released neutrons can be divided into three groups: (i) neutrons that reach the surface of the fissionable material sample and escape, (ii) neutrons that strike nuclei and cause fissions, and (iii) neutrons that strike nuclei but scatter from them without causing fissions. To have a chain reaction, we need a large enough sample—i.e., a sample that reaches the critical mass—in which “the number of neutrons that do not escape is just high enough to induce fission in all nuclei” (Reed, 1996, 162). In calculating the critical mass of uranium-235, if we don’t take group (iii) into account—in other words, if we assume that all the “scattered” neutrons are “scaped” neutrons—the final result is about twice the real critical mass of uranium-235. This shows that in calculating the critical mass, we must take “scattered” neutrons into account. For this reason, we should take into account the average distance that these scatterings travel within the sample (Reed, 1996, 163). This average distance, however, is a function of the shape of the sample. Thus, the critical mass of a fissionable element changes depending on, say, whether it is spherical or cylindrical. Since shape plays a crucial role in the models suggested for calculating the critical mass—besides Reed (1996), see also Serber (1992) and Derringh (1990)—it seems quite unlikely that we can easily “reduce” the laws governing the critical mass to more fundamental laws in which, presumably, the shape of the sample cannot play a role.
Bird focuses on fundamental natural properties and fundamental laws of nature (2007, chap. 3). For the sake of brevity, I omit fundamentality here.
Here, I intentionally use what can be considered a qualitative expression of Coulomb’s law. It is a matter of dispute whether Bird’s dispositional essentialism can make a good sense of the quantitative expression of the Coulomb’s law, i.e., “F = −ε0(pq/r2)” where ε0 is a constant, p and q are the values of two charges whose distance is r, and F is the force between the charges. This issue goes beyond the scope of my paper but suffice to say that even some of those who argue that Bird’s account cannot make a good sense of quantitative laws, admit that the qualitative form of the Coulomb’s law “looks amenable to dispositional essentialism” (Sartenaer et al., 2020, 10).
Or, if one adopts Hendry and Rowbottom’s (2009) permissive dispositional essentialism, the same SR-relation holds in every possible world that contains properties with similar actual dispositional profiles.
A stimulus property is also dispositional and hence its instantiation requires the instantiation of a preceding disposition and stimulus. In Figure 1, for the sake of brevity, I overlook the stimulus properties’ “chain” of instantiation.
cf. Price (2004)
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Acknowledgments
Earlier versions of this work were presented at the meetings of Canadian Society for the History and Philosophy of Science (2021) and APA Eastern Division (2021). I thank the audience for their helpful comments. I am also grateful to Anjan Chakravartty, Mack Sullivan, Raghwinder Singh Grewal, and two anonymous reviewers for their helpful comments and suggestions.
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Mohammadian, M. An Armstrongian defense of dispositional monist accounts of laws of nature. Euro Jnl Phil Sci 12, 52 (2022). https://doi.org/10.1007/s13194-022-00481-x
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DOI: https://doi.org/10.1007/s13194-022-00481-x