The Laws of Nature and the Metaphysical Multiverse

by Max Andrews

Regularity theory (RT) attempts to account for laws in a descriptive manner contra the necessitarian position (NT), which expresses the laws of nature as nomic necessity.  According to the RT the fundamental regularities are brute facts; they neither have nor require an explanation.  Regularity theorists attempt to formulate laws and theories in a language where the connectives are all truth functional.  Thus, each law is expressed with a universal quantifier as in [(x) (Px ⊃ Qx)].[1]  The NT states that there are metaphysical connections of necessity in the world that ground and explain the most fundamental regularities.  Necessitarian theorists usually use the word must to express this connection.[2]  Thus, NT maintains must-statements are not adequately captured by is-statements (must ≠ is, or certain facts are unaccounted for).[3]

The role of counterfactuals serves to make distinctions in regularities.  Concerning the RT and counterfactuals the regularist may claim that laws do not purport what will always occur but what would have occurred if things were different.  NT claims that it is difficult for RT to account for certain counterfactual claims because what happens in the actual world do not themselves imply anything about what would have happened had things been different.[4]  This is only a mere negative assertion on behalf of NT and carries no positive reason to adopt the NT position.  However, RT does have a limited scope in explanation. C.D. Broad argued that the very fact that laws entail counterfactuals is incompatible with regularity theory.[5]  He suggests that counterfactuals are either false or trivially true. If it is now true that Q occurs if P causally precedes Q then the regularist may sufficiently account for past counterfactual claims.  Given the present antecedent condition of P at tn and P implies Q at tn and it was true that P implied Q at tn-1 then using P as an antecedent for R at hypothetical tn-1’ then R is true if P was a sufficient condition R at tn-1’. Thus, RT accounts for past counterfactuals, but this is trivially true.  However, in positive favor of the NT, there is no reason to expect the world to continue to behave in a regular manner as presupposed by the practice of induction.  Consider Robin Collins’ illustration of this point:

Suppose that a coin were tossed one thousand times and each time it came up heads.  Both [NT and RT proponents] would agree that such an occurrence cries out for explanation, such as that the coin was biased strongly in favor of heads; such an occurrence would constitute too grand of a coincidence to be plausibly ascribed by chance.  Moreover, only if we believed that there was some such explanation would we have any reason to believe that the coin would continue to come up heads in the future; if we discovered that it had landed on heads by mere accident, we would have no reason to believe that it would continue to land on heads.[6]

The regularist may point out that generalizations from finite sample sets cannot be warranted unless the appropriate necessary connections are postulated, which is this problem of induction.  This is a problem whose examination has often been the occasion for the introduction of NT. Unless a necessitarian is prepared to say that the relation of necessity is actually observed in the instances of some law, the inference to a necessary law creates the problem of induction just as easily.[7]

Thus, NT and RT fall short of explanatory scope at some point or another.  The regularist can only account for past and present occurrences of laws but such universal implication and induction for future instances do not promise certainty in prediction.  With [(x) (Px ⊃ Qx)] the necessitarian will claim that Qx is just a brute fact of necessity while the regularist will claim that the regularities are due to a brute fact.[8]  The regularist can certainly account for past and, to an extent, present behavior of laws but the necessitarian has no basis for even asserting necessity. At least the regularists may take their position from previous empirical evidence and argue that even though there is no guarantee that [(x) (Px ⊃ Qx)] they can still make probability claims.

Gold has an atomic weight of 196.966543.  This follows necessarily from gold’s atomic structure but gold is contingent.  With this being an analytic a posteriori claim there is no counterfactual claim that is true about the atomic weight.  The law of alpha particle decay in the half-life of a uranium atom is purely probabilistic.  The probability remains constant over time and is the same in every uranium atom, and there is no difference at all between two uranium atoms one of which decays and the other doesn’t in the next minute.[9]  It is the case that introducing a laser into the atomic nucleus of 232U, which alters the stability of the atom and accelerates the alpha and beta decay, can alter the rate of decay.[10]  However, the fact remains that when the decay occurs is determined by the quantum world of probability (depending on one’s interpretation of quantum mechanics). In either of these two neither NT nor RT provide a preferred explanation for such counterfactual states of affairs. Such counterfactual claims are empty with certain laws.  Some may have counterfactual truth and others are vacuous.  If one were to attempt to express such alpha decay as [(x) (Px ⊃ Qx)], for every alpha particle, if an alpha particle of uranium obtains then the alpha particle will decay is true but cannot be causally or temporally indexed.

The Princeton philosopher David Lewis and MIT cosmologist Max Tegmark have postulated a metaphysical multiverse (MM) to account for the behavior of natural laws.  Their proposed multiverse scenarios entail modal realism.  This modal realism is, in a sense, modally limited.  The state of affairs of the non-existence of anything cannot be true if something does exist so by definition modal realism must entail ~∃!W with W being the non-existence of anything—nothing, lest it suffer the consequence of being intrinsically incoherent.  Under such a MM different regions of space will exhibit different effective laws of physics (i.e. difference constants, dimensionality, particle content, relation of information, information propagation, etc.) corresponding to different local minima in a landscape of possibilities.[11]  This could obtain in several different ways such as the local bubble location in a string landscape or in unitary quantum physics the wave function does not collapse and all possibilities are actualized.  Such an approach denies counterfactual definiteness.  This means that any counterfactual of what measurements have not been performed are empty of any meaning and truth.

These MM scenarios allows for the proponents to get the best of both worlds (pun intended).  It avoids the problem of RT by having variance in the behavior of laws.  A tropical fish never leaving the ocean might mistakenly conclude that the properties of water are universal, not realizing that there is also ice and steam.  We may be smarter than fish but may just as easily be fooled.[12]  This is a shortcoming of RT for all we know such regularities are localized instantiations.  The problems of NT and RT are avoided but it takes on its own problem similar to the NT problem of accounting for the mechanisms that produce the varying laws and values.  It is a displacement issue.

Following Robin Collins’ third option out of this quagmire would to adopt a theistic approach to either theory.  The theistic view states that the fundamental regularities in the world are explained by the creative and sustaining power of God: God either sustains these regularities directly, or God has created the sort of fundamental powers or necessities in nature that underlie these fundamental regularities.  This is the view undergirding the philosophies of Galileo and Kepler calling God the “great geometer.”[13]  There is a value-based metaphysical import associated with this view but it I am disinterested in that aspect of the explanation.  This isn’t entirely ad hoc given the nature of God; that is, if God is a perfectly free, omniscience, and omnipotent being.[14]  This is by no means an argument for the existence of God but if God does exist then the laws of nature would be regularities in God’s function in nature.

The theistic view can encompass any of the three theories: NT, RT, or the MM.  The NT makes sense given divine simplicity.  If God is simple then transworld simplicity is true, which means God’s interaction transworld is identical and flows necessarily from him.  RT is consistent with the divine sensorium in the laws of nature and not a Kantian categorical projection. The regular course of divine sustainment, regularity, allows for discovery and free invention.  The premises or predicates are not fixed necessarily and the conclusions are drawn out of these regularities in a way that could be described as an exegesis of nature.  The NT, RT, and the MM are explanatorily empty in the end from a non-theistic perspective.  It does seem that RT is quite harmonious with relativity theory, which states that the laws of nature are the same in all reference frames.  This is the best chance at allowing induction to be a legitimate tool for the regularist.  Additionally, as exampled by 232U, quantum mechanics functions on a probabilistic level.  The closest one could get to a reasonable future tense counterfactual or prediction of a consequent could, at best, be a probabilistic claim offered by RT.

[1] Bernard Berofsky, “The Regularity Theory,” Nous Vol. 2 No. 4 (1968): 315.

[2] Robin Collins, “God and the Laws of Nature,” Philo Vol. 12 No. 2 (2009): 2-3. (Preprint).

[3] Berofsky, 316.

[4] Collins, 4.

[5] C.D. Broad, “Mechanical and Teleological Causation,” Proceedings of the Aristotelian Society: Supplementary Volumes (1935, XIV.

[6] Ibid.

[7] Berofsky, 325-26.

[8] Collins., 11.

[9] Alexander Rosenberg, Philosophy of Science (New York: Routeledge, 2012), 92.

[10] A.V. Simakin and G.A. Shafeev, “Accelerated Alpha-Decay of 232U Isotope Achieved by Exposure of its Aqueous Solution with Gold Nanoparticles to Laser Radiation,” (accessed March 6, 2012), 1-2.

[11] Max Tegmark, “The Multiverse Hierarchy,” (accessed March 6, 2012), 1.

[12] Ibid.

[13] Collins, 1, 16.

[14] Ibid., 18.


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