Abstract
This paper is a reply to Benjamin Smart’s (Philos Stud 162 (2): 319–332, 2013) recent objections to David Armstrong’s solution to the problem of induction (What is a Law of Nature? Cambridge University Press, Cambridge, 1983; Dialogue 30 (4): 503–511, 1991). To solve the problem of induction, Armstrong contends that laws of nature are the best explanation of our observed regularities, where laws of nature are dyadic relations of necessitation holding between first-order universals. Smart raises three objections against Armstrong’s pattern of inference. First, regularities can explain our observed regularities; that is, universally quantified conditionals are required for explanations. Second, if Humean’s pattern of inference is irrational, then Armstrong’s pattern of inference is also irrational. Third, universal regularities are the best explanation of our observed regularities. I defend Armstrong’s solution of induction, arguing against these three claims.
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Notes
I follow Smart’s letters “R” and “B” instead of the traditional letters “F” and “G”.
Supposedly, for the Humean (or at least, for the nominalist Humean), OR and OB are subsets of R and B.
There is a typo in the original paper. I wrote “OB” instead of “BR”.
In this paper, “natural properties” and “universals” are interchangeable terms.
Smart’s argumentation for the chain of explanation is silent about the best explanation. For instance, “N(R,B) explains ∀x(ORx→OBx)” Smart (2013: 323)
This relation of contingent necessitation between N(R,B) and ∀x(Rx→Bx) implies an infinite regress. See Bird (2005).
It might be argued that observeness is not a monadic universal but rather a dyadic universal – a relational universal, i.e., something as such “_observes_”. It seems to me that this is not an issue for my proposal.
Actually, Smart also notes that we want to explain “why all ravens in our sample have been observed to be black” (Smart 2013: 323), but this formulisation of explanandum does not reappear in the remainder of section 2 of the paper, where this point is discussed.
Contrary to Smart, the natural necessitation relation between universals, N(R,B), is not an unobservable entity. The natural necessitation relation is an object of perception. The notion of contingent necessity is postulated by our experience of singular causation relations that are an object of direct perception. This point is beyond the scope of this paper.
Smart takes his explanation, R(F,G), an instance of inference to the best explanation, too.
Armstrong (1983) makes a long discussion that demonstrates why the regularity theory fails to succeed in this point. It is redundant to follow this point.
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Acknowledgments
I am very grateful to the anonymous reviewer whose detailed comments have substantially improved a previous version of this paper.
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Castro, E. Is the Humean Defeated by Induction? A Reply to Smart. Philosophia 44, 435–446 (2016). https://doi.org/10.1007/s11406-016-9700-4
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DOI: https://doi.org/10.1007/s11406-016-9700-4