Abstract
We have seen that Dretske explicitly required that laws related items like F-ness and G-ness, which would normally be understood as a reference to universals. However he also referred to laws as relating physical magnitudes. If all physical magnitudes, including refractive indices in particular, count, according to Dretske, as universals, then it seems to me that universals so understood, are in tremendous abundance, and set no limits for the expressive power of physical theories, beyond those set by the use of ordinary mathematical analysis. We noted in Chap. 4, there isn’t any problem with those universals used by Dretske, if they are physical magnitudes.
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Notes
- 1.
Cf, D. Armstrong, What is a Law of Naure, Cambridge University Press, 1983, p. 111, fn.1.
- 2.
Cf. Chap. 2.
- 3.
Armstrong, What is a Law of Nature? Cambridge University Press, 1983, p. 97, and (3). p. 156. While F and G are universals, “¬Fx” and “¬Gx” are the supposedly negative universals “x is not being F”, and “x is not being G” respectively.
- 4.
Though it is assumed, the claim has rightly been subject to severe criticism by Bas Van Fraassen, and David Lewis to the effect that (MP) is not justified by Armstrong.
- 5.
Armstrong, What is a Law of Nature, p. 156,
- 6.
But it does assume that Armstrong has interposed a material conditional horseshoe) between two universals and that raises another problem since Armstrong’s view on universals is that with the exception of conjunction, there are no negations, disjunctions, or conditionals between universals. If we read “F[x]” as “x’s being F” – i.e. what Armstrong calls a state of affairs, then he has to explain what the conditional between states of affairs could possibly mean. We try below to remove that impediment by shifting to (MP∗).
- 7.
Yes, this by fiat. But since it is needed, and Armstrong does not have a proof, then it could be argued that assuming (MP∗) is a maneuver that is no different than what D. Lewis did when he needed to assume that the counterfactual conditional in his system VC satisfied Modus Ponens. He added it on. It was needed since it didn’t follow from the other statements of VC.
- 8.
The insightful proposal of John Carroll for defining a predicate in terms of a universal is in An Introduction to Metaphysics, N. Markosian and J.W. Carroll, Cambridge University Press, 2010, p. 229. Binary relations such as R(xy) are connected by Carroll neatly this way “a Rs b if and only if a and b (in that order) instantiate R-ing”, where ‘R-ing’is understood to be a two-place relation that is a universal. The variable “x” in (C) is understood to range over the particulars of Armstrong’s account of universals.
- 9.
The additional requirement that the equivalence class of all the values of PF are a proper subset of W is guaranteed if there are at least two states of affairs in W that are not equivalent by the equivalence relation E.
- 10.
Armstrong, What is a Law of Nature, Cambridge University Press, 1983.
- 11.
A World of States of Affairs, Cambridge University Press, 1997.
- 12.
For more detailed discussion of this example Cf. WSA, 225 ff.
- 13.
It should be noted that these four formal properties endorsed by Armstrong cover only the case when the laws involve only two universals.
- 14.
We have to be careful in attributing this equivalence to Armstrong. He does say that laws are second order universals relating (first-order) universals, and he also says that laws relate states of affairs by a binary second order universal. So (i) should be seen as a friendly addition that is not explicitly advocated by Armstrong. We do not claim that (i) is the only was of glossing the connections between Armstrong’s account of laws and states of affairs. There are many variations on this theme consistent with what one can glean from (I) and (II).
- 15.
R is a binary universal that Armstrong thinks of as some kind of causal relation. It should be noted that here, unlike familiar notions of that relation, it is not a relation between objects, events or facts, but a relation between states of affairs. It should also be noted that some, writers, eg H.G. Mellor do not regard causation as a relation and R.B. Braithaite (in his Fellowship Thesis for King’s College, A Dissertation on Causality (1923), King’s College Archives, Cambridge, was one of the first to use the causal relation in hypotheticals (asserted conditionals) merely to indicate some kind of relation where one item depends upon another, leaving it open that it could cover various kinds of determination. Armstrong owes an explanation of the relation R between states of affairs, that figures so prominently in his account of laws.
- 16.
A World of States of Affairs, Cambridge University Press, 1997, p. 19.
- 17.
Ibid.
- 18.
Armstrong seems to have held that ontological causation is non-transitive, though its transitive closure is transitive. Cf. A World of States of Affairs, 206–207.
- 19.
A World of States of Affairs, p. 19.
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Koslow, A. (2019). D. Armstrong’s Account of Laws: Identity Lost, Regained, and Lost Again. In: Laws and Explanations; Theories and Modal Possibilities. Synthese Library, vol 410. Springer, Cham. https://doi.org/10.1007/978-3-030-18846-7_6
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