Abstract
A monist theory of explanation is one that seeks a common definition for all speech acts answering why-questions. One recent example is the counterfactual theory of explanation (CTE), which assumes that an ideal explanation can be characterized by the familiar Hempelian criteria for a scientific explanation plus a certain counterfactual that is supported by the laws mentioned in the explanans. I show that the CTE fails. My discussion leads to a critique of the CTE’s key concept of counterfactual dependence and to the suggestion of an alternative: For an argument to be a scientific explanation, a certain necessary-condition claim must be true. For an answer to a why-question to be an explanation, it must express a certain necessary condition.
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Notes
Define that a generalization ‘∀x (Fx → Gx)’ is structurally similar to a counterfactual iff the open formula ‘Fx → Gx’, on changing ‘x’ into ‘a’ and ‘→’ into ‘□→’, becomes that counterfactual.
Explicitly, (Graph 2) runs: ‘If there were an Euler path through KG, then KG would be an Euler graph’, which, given our simple theory of counterfactual support is supported by G1 in Sect. 3.1.1.
Explicitly, (Königsberg 2) runs: ‘If there had been an Euler walk through Königsberg in 1735, then the city would have been well-connected’, which is supported by G1 in Sect. 3.1.2.
Why is this a generalization? G1 should be understood as including a tacit quantification over situations. In any situation, where the sun is at an angle x above the horizon, the flagpole’s shadow is z meters long iff the flagpole is y meters high, where z = y cot x and y = z tan x.
Recall the brief discussion about reading off a counterfactual from a law at the end of Sect. 2.
Introduce a new predicate ‘A’ via the claim ‘Ax ↔ Px & ¬ Hx’, such that the generalitation has the form ‘∀x (Ax → ¬ Ex)’. By the technique of note 1 above, this generalization is structurally similar to the counterfactual ‘Aa □→ ¬ Ea’, which can be re-translated into (Pa & ¬ Ha □→ ¬ Ea).
Introduce a new predicate ‘B’ via the claim ‘Bx ↔ Px & ¬ Ex’ and proceed as in note 8. Note that (Hempel 1) and (Hempel 2) are not mutual inverses.
Usually? For an exception see the previous note.
With Lewis; see his well-known priority list in (1986, 47–48).
My proposal is indebted to the quantificational account of natural-language indicative conditionals presented in Lycan (2001, Ch. 2), and Kratzer (2012, Ch. 4). My notion of a situation deciding a proposition A is inspired by Lycan's quantifier restriction to situations (cases) that make a certain proposition B either true or false.
Suppose that ‘[A] is a necessary (sufficient) condition of [B]’ are simply defined as ‘only (all) A-situations contain [B]’, where ‘simply’ means that no specific restrictions on the quantifiers are assumed. Then, if [A] is a sufficient condition of [B], then [B] is a necessary condition of [A].
Here is the argument. It is plausible to assume that ‘x contains [B]’ entails ‘x is a B-situation (contains a truthmaker of B)’, but not vice versa. Assume that x contains [A]. Then, by the plausible assumption just considered, x is an A-situation. Then, given the simple definition of ‘[A] is a sufficient condition of [B]’, it follows that x contains [B]. By the plausible assumption, again, x is a B-situation. Since x was arbitrary, it follows that all situations containing [A] are B-situations. By contraposition, only B-situations contain [A], which is the definition of ‘[B] is a necessary condition of [A]’.
As in the previous note, assume that x contains [A]. Then, again by the plausible assumption, x is an A-situation. Then, given the definition of ‘[A] is a sufficient condition of [B]’ with quantifier restriction, it follows that x contains [B] only if x decides A. In this case, again by the plausible assumption, x is a B-situation. Since x was not arbitrary, it follows that all situations containing [A] are B-situations only if these situations decide A. By contraposition, only B-situations contain [A], but this is the definition of ‘[B] is a necessary condition of [A]’ only for situations deciding B. Since the sets of situations deciding A or B may be distinct, the inference from sufficient to necessary condition is blocked.
The assumption that ‘x is a B-situation (contains a truthmaker of B)’ entails ‘x contains [B]’ (the reverse of our above plausible assumption) is implausible. We attempt to show that ‘[A] is a necessary condition of [B]’ entails ‘[B] is a sufficient condition of [A]’. Assume that x is a [B]-situation. Using the implausible assumption, we could infer that x contains [B] and then bring into play the necessary condition (‘only A-situations contain [B]’), which, by contraposition, would yield that x is an A-situation. But since the assumption is implausible we are entitled to resist it and the inference fails. A quantifier restriction plays no role.
Assume that, for a condition claim to be true the condition-sense associated with the first position is required, i.e. it is necessary that the clause ‘that A’ (or the noun-phrase ‘[A]’ proxying for it) refers to an arbitrary, not a particular, member of the set of potential truthmakers of A. Assume now that [A] is a condition of [B]. Consider whether it is also true that [B] is a condition of [A]. For the first to be true, the speaker must refer, via the first position, to an arbitrary, not a particular, truthmaker of [A]; for the second to be true, the speaker must refer, via the second position, to [A], a particular truthmaker of [A]—a contradiction.
First, ignore the quantifier restriction. We have the following chain of equivalences. Assume that E[A] is a necessary condition of E[B]. Thus, by definition, only situations containing [A] contain [B]. Thus, all situations containing [B] contain [A]. Thus, again by definition, E[B] is a sufficient condition of E[A].
Now observe the quantifier restriction. Again, we have a chain of equivalences. Assume that E[A] is a necessary condition of E[B]. Thus, with a restriction to situations deciding A, only the ones containing [A] contain [B]. Thus, with a restriction to situations deciding A, all of them if they contain [B] also contain [A]. But here the chain ends and its last element is not the definition of sufficiency (of E[B] for E[A]), which runs: with a restriction to situations deciding B, all of them if they contain [B] also contain [A]. Hence, in the special case where a proposition is of the form ‘[A] exists’, where [A] is a certain truthmaker of another proposition A, the quantifier restriction to situations deciding A conserves the asymmetry of conditionship.
A comparable case is familiar from van Fraassen’s story of the tower and the shadow (1980, Ch. 5, § 3.2).
Given my approach to conditionship, I should say, more precisely, that a cause is an event that is a truthmaker of a necessary condition of another event but this claim and its defense would clutter my treatment of the example.
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Held, C. Towards a Monist Theory of Explanation. J Gen Philos Sci 50, 447–475 (2019). https://doi.org/10.1007/s10838-019-09458-6
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DOI: https://doi.org/10.1007/s10838-019-09458-6