A Metaphysics of Platonic Universals and their Instantiations by José Tomás Alvarado

Author:José Tomás Alvarado
Language: eng
Format: epub
ISBN: 9783030533939
Publisher: Springer International Publishing

7.5.2 Necessary Laws

§ 52. Since natural laws, however they may be conceived, must be essential for the universals that constitute them, there are solid reasons to think that those laws must be necessary entities. If they are necessary entities, ontologically dependent on the universals that constitute them, then those universals must also be necessary entities. Bostock’s argument (see Bostock 2003) can be summarized as follows: all the universals of a possible world—assuming that they are universals instantiated in that world, according to the restrictions of the Aristotelian—must belong to a ‘nomic network’. There is a single nomic network for every possible world. If the instantiations of a universal can interact with instantiations of another universal, then those universals must belong to the same nomic network. But the instantiation of any universal can interact with the instantiation of any other. Then, all universals belong to the same nomic network. This nomic network, then, exists invariably in all possible worlds, which is what we wanted to show.

It will now be necessary to examine this argument with more detention. In a general way, it must be understood by a “nomic network” the closure of all and only universals nomologically connected between themselves. For example, suppose that [N(U1, U2)], [N(U2, Conj(U3, U4))] and [N(U4, U1)]. Suppose, also, that these are all the natural laws that the universals U1, U2, U3, and U4 constitute. All of them are connected nomologically, and there is no other universal connected nomologically with any of them. Each of these universals depends ontologically on all the others. For example, U1 depends ontologically on U2, since [N(U1, U2)], and it is essential for U1 to integrate [N(U1, U2)], as explained in the previous section. Like the natural law [N(U1, U2)] depends on its constituents, it turns out that U1 depends on U2, on which depends the natural law essential to U1. But, in turn, U2 depends ontologically for the same reasons on the conjunction of U3 and U4, [Conj(U3, U4)]. As a conjunction of universals depends on the conjunctively linked universals, it follows that U2 depends ontologically on U3 and ontologically depends on U4. But the ontological dependence is transitive, so it follows that U1 depends on U3 and depends on U4, etc. A nomic network, then, is a structure of universals mutually dependent with each other.18 The existence of one of these universals in a possible world makes necessary the existence of all the rest of the same nomic network. The absence of one of the universals of a nomic network makes that none of the others exist.

A premise of importance for Bostock’s argument is that every possible world must have only one nomic network for all universals existing in such a world. The main motivation for this premise is that all the instantiations of the universals in a possible world must be able to interact with each other. For it to be possible for the instantiations of two different universals to interact with each other, it is necessary a nomic connection between these universals.

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