Quine classified counterfactual conditionals as “creatures of darkness,” precisely because they did not correspond to any of the formulas of classical extensional logic (Quine 1960). The truth-value of a counterfactual conditional is not a function of the truth-value of its parts. The parts of (2) are both false, but there are many false counterfactuals that also have false antecedents (‘if’-clauses) and consequents (‘then’-clauses):
(5) If Oswald had not killed Kennedy, the earth would have stopped revolving on its axis.
Work by Robert Stalnaker (Stalnaker 1968) and David Lewis (Lewis 1973b), however, rescued counterfactuals from Quine's ban. The rehabilitation of counterfactual conditionals led to a revival of the conditional theory of dispositions, which had been proposed by Gilbert Ryle (1949) but had been largely abandoned as a result of Quinean anxieties about the meaning of the relevant conditional. The conditional theory of dispositions suggests that having a disposition like fragility consists in making true a conditional. Thus, the truth of (6) was supposed to be grounded in (7):
(6) The vase is fragile.
(7) If struck, the vase would break. (The word ‘fragile’ is derived from a Latin word meaning ‘breakable’.)
Ryle applied the conditional theory very widely, since he believed that nearly all mental states, such as beliefs, desires, and even experiences, were merely behavioral dispositions of one kind or another. Whether there is hope for this sort of analysis, then, is a very important question for a number of philosophical areas.
First, we must ask, is there any reason to believe that (7) is the fundamental truth and (6) derived, rather than the other way around? Can there in fact be fundamental conditional truths? There seem to be two options here.
4.1T Hypotheticalism. There are fundamentally conditional or hypothetical truths.
4.1A Anti-Hypotheticalism. All conditional truths are grounded in non-conditional facts.
The sort of grounding that is relevant here seems to be what we called conceptual grounding in Section 3.4: can reflecting on the essence of the logical if-then construction reveal that conditional truths are grounded in non-hypothetical facts and entities? Or must there be some entities or primitive facts in the world that correspond directly to that if-then structure?
But before we examine directly the question whether Hypotheticalism or Anti-Hypotheticalism (also called ‘categoricalism’) is correct, it will be worth making a foray into how we evaluate counterfactual conditionals.
So: how do we evaluate counterfactual conditionals? By ‘evaluate’ we don't mean: how do we know or judge them to be true? What we mean is: what are the conditions under which such counterfactual conditionals are in fact true? In the mid-twentieth century, Nelson Goodman (1954) and J.L. Mackie (1973) both proposed argument models for the truth or falsity of counterfactual conditionals. A conditional of the form ‘if p, then q’ is true if q can be validly deduced from:
p itself,
the laws of nature, and
other true propositions that are “co-tenable” (in Goodman's terms) with p.
If q cannot be deduced from this set of propositions, then the conditional is false. Both (b) and (c) are important: it is very rare to find a conditional in which the consequent can be deduced from the antecedent alone. Statement (3), noted above, would be one of these rare examples.
Laws of nature are relevant. Such laws are said to support corresponding counterfactuals. Consider (8):
(8) If this sample of water were cooled to 0° C, then it would freeze.
In (8), the consequent (‘it would freeze’) is a consequence of the antecedent plus certain laws of chemistry, together with facts about the chemical composition of water. This seems sufficient to make (8) true. In contrast, mere accidental regularities do not support counterfactuals in this way. Suppose it is true that every coin in my pocket is made of bronze. (9) would certainly not follow:
(9) If this dime were in my pocket, it would be made of bronze.
Finally, we must also consider so-called ‘co-tenable’ propositions. These are background facts that we believe would not have been disturbed had the antecedent been true. Recall (4):
(4) If McCain had won the vote in Michigan and Florida, he would have been elected President in 2008.
Again, (4) seems true, given the closeness of the electoral vote in 2008. However, we can deduce the consequent from the antecedent only with the additional supposition that, in the imagined counterfactual scenario, the constitutional rules for electing the President would not have been different, the other forty-eight states voted as they actually had, and so on. As Goodman noted, it is quite difficult to give a non-circular account of which true propositions are co-tenable with an actually false antecedent. Intuitively, we want to include just those propositions that still would have been true had the antecedent been true. If we do that, we have slipped into the subjunctive mood (‘would have been’) in defining the co-tenable proposition. Clearly, this is not going to give us a non-circular account of the truth-conditions of the subjunctive conditionals.
If we want to give an informative account of what it is for these subjunctive conditionals to be true, we must find something more to say about these co-tenable truths. Even if we think (as Hypotheticalists do) that the truth of subjunctive conditionals is irreducible to other truths, it would be nice to have some more information about the relationship between the truth-conditions of one conditional and those of another or between subjunctive conditionals and non-conditional statements about modality (possibility and necessity). For example, (11) seems to follow from (10), and (13) follows from the conjunction of (10) and (12):
(10) If Michigan had voted for McCain, then McCain would have won and Obama would have lost.
(11) If Michigan had voted for McCain, then McCain would have won.
(12) It was possible that Michigan vote for McCain.
(13) It was possible that McCain win.
Ideally, we would like some sort of theory, even if a relatively abstract one, that could explain why these propositions stand in these logical relations to one another.
In 1968, Robert Stalnaker introduced a new approach, which built on the notion of a possible world. Gottfried Leibniz, the seventeenth-century German rationalist, made use of the idea of possible worlds in trying to clarify issues in the metaphysics of possibility, necessity, and actuality, which philosophers refer to as ‘modalities’. A possible world is a total or maximal possibility: a way that the whole of reality could have been. We will take up modality in more detail in Chapters 14–16, but for the purposes at hand we will need to say something about possible worlds semantics. (A semantical theory is a theory about linguistic meaning, including the truth of sentences.) Possible worlds semantics grew out of the work of C.I. Lewis (1932), Rudolf Carnap (1947), and Saul Kripke (1963) as an attempt to exploit the Leibnizian idea of a possible world in giving an explicit, regimented representation of our modal talk, our talk about possibility, necessity, and actuality.
Possible worlds semantics involves specifying a mathematical model with three characteristic features. First, the model must contain a domain of entities that play the role of possible worlds. Second, every atomic sentence—every sentence that ascribes a property to an object or asserts that a relation holds between or among some objects—is assigned a truth-value at each of these worlds. In other words, every sentence like ‘Elsie is a dachshund’, ‘The cat is on the mat’, and ‘The boys formed a circle’ are variously true and false according to these worlds. Finally, one of the worlds is taken to represent the actual world. The atomic sentences true according to our world are just the atomic sentences that really are true. Given a model of this sort, we can specify rules that will tell us which modal claims are true, given the facts about which sentences are true according to which worlds. The rules go like this. A statement of the form ‘possibly p’ is true in the actual world just in case p is true according to at least one world. A statement of the form ‘necessarily p’
is true just in case p is true according to every world.2
Stalnaker applied these models to elucidating the semantics of counterfactual conditionals. He assumed that we can employ a world-selection function, a function which selects a world on the counterfactual supposition that p. When we apply this function to a world (representing the actual world) and a set of worlds (representing some proposition p, the antecedent of the conditional), the world-selection function gives us a unique world—the world that would have been actual had p been the case. We then check to see if the consequent of the conditional is true in the selected world: if it is, the conditional is true; if not, it is false. Here are the truth-conditions for the counterfactual conditional in Stalnaker's semantics (we'll use Lewis's symbol ‘’ to represent the subjunctive conditional connective):
Stalnaker. ‘(p q)’ is true if and only if q is true according to *(p).3
The right-hand side of Stalnaker's definition includes the world-selection function *. This *-function takes a proposition as an input and yields a world as its output. Intuitively, *(p) is the world that would have been actual had proposition p been true. The world-selection function * always picks a world in which the actual laws of nature hold, but it need not maintain the truth of merely accidentally true generalizations. In this way, laws support counterfactuals in a way that accidental regularities (like the coins in my pocket's being bronze) do not. The world-selection function * also changes background facts as little as possible. We make the smallest change necessary to make p true. In this way, the semantics preserves all of the co-tenable truths.
Let's run through an example to clarify Stalnaker's machinery. Recall (4) once again:
(4) If McCain had won the vote in Michigan and Florida, he would have been elected President in 2008.
In this case, p is ‘McCain won the vote in Michigan and Florida’ and q is ‘McCain is elected President in 2008’. According to Stalnaker, for (4) to be true, the proposition that McCain is elected President in 2008 must be true according to *(McCain won the vote in Michigan and Florida), which is, intuitively, just the world most like ours but according to which McCain won the Michigan and Florida votes. Given that the *-function changes background facts as little as possible in order to make its input proposition true at the output world, *(McCain won the vote in Michigan and Florida) will be a world according to which McCain won all the states he actually did win (in our world). But given that the proposition that McCain won the vote in Michigan and Florida must be true according to *(McCain won the vote in Michigan and Florida), that world will be such that McCain got all of the electoral votes he actually got (in our world), plus the electoral votes of Michigan and Florida. As it happens, this means that according to *(McCain won the vote in Michigan and Florida), McCain won the 2008 Presidential election. Which is just to say that our q is true at our *(p). (4), according to Stalnaker, is true. This matches our intuition about (4).
David Lewis (1973b) proposed some modifications and extensions of Stalnaker's semantics. Lewis argued that we could envisage a system of concentric spheres around the actual world, representing the various degrees of similarity these worlds bear to ours. The worlds in the closest sphere to the actual world are more similar to the actual world than any other worlds, and they are each as similar to the actual world as any other world within that sphere. The worlds in the next closest sphere (and that are not in the closer sphere) are less similar to the actual world than every world in the closer sphere, but they are each as similar to the actual world as any other world within that sphere (and not within the closer sphere). And so on, out to very distant worlds that are very much unlike the actual world.
A counterfactual conditional (p q) is true for Lewis just in case there is a p-permitting sphere of worlds such that every p-verifying world within that sphere is also a q-verifying world. In other words, to evaluate the truth of (p q), Lewis says we must first go out to the closest spheres in which there is at least one world according to which p is true. Then one checks whether every one of the worlds in that sphere according to which p is true is also a world according to which q is true. If every p-world in that sphere is also a q-world, then the counterfactual (p q) is true. If in all of the closest spheres, there is a p-world that is not a q-world, then (p q) is false.4 We can summarize Lewis's view like this:
Lewis. ‘(p q)’ is true if and only if the closest sphere containing a p-world such that every p-world in that sphere is also a q-world.
There is one significant difference between Stalnaker's logic and Lewis's. Stalnaker assumes in effect that for every world w and proposition p there is a unique p-world w' that is closest, most similar, to the actual world. Lewis instead assumes that there is a non-empty set of closest worlds. This semantic difference results in a logical difference: Stalnaker accepts, and Lewis rejects, the Law of Conditional Excluded Middle, (p q) ∨ (p ∼q). (14) is an instance of this law:
(14) Either: (a) if this coin had been flipped a minute ago, it would have landed heads, or (b) if this coin had been flipped a minute ago, it would not have landed heads.
(14) must be true on Stalnaker's semantics, since we can find the one world closest to the actual world in which the coin is flipped. In that world, the coin must either have landed heads or not. On Lewis's approach, there is typically a set of closest worlds, any one of which might equally have been actual had the coin been flipped. The coin might have landed heads in some of those worlds but not in others. For Lewis, it is (15) rather than (14) that is logically valid:
(15) Either: (a) if this coin had been flipped a minute ago, it would have landed heads, or (b) if this coin had been flipped a minute ago, it might not have landed heads.
Both agree, of course, that if the coin had been flipped, it would have landed either hand or tails. That disjunction (heads or tails) is true in all of the closest worlds. The difference is that Stalnaker is committed to the view that, even when the process is indeterministic, so the laws of nature and the intrinsic natures of the coin and its environment do not determine whether coin would lead heads or tails, it is always true that there is some one result (either heads or tails) which is the result that would happen if the coin were flipped.
One difficulty with Stalnaker-Lewis semantics: it doesn't handle conditionals with impossible antecedents well. Suppose the number 3 exists necessarily (a plausible assumption!). Consider the following:
(16) If there were no number 3, the number 2 would still have the same successor it does have.
(17) If there were no number 3, the number 2 would have no successor or a different successor from the one it does have.
If there is no possible world containing no number 3, then both (16) and (17) count as true (vacuously true) according to Lewis-Stalnaker semantics.5
This is a problematic result: we seem to be able to evaluate some per impossibile conditionals as true (like (17)) and others as false (like (16)).
4.2 Hypotheticalism
So much for the logic and semantics of the counterfactual conditional (see Lewis 1973b for the details). Let's get back to the metaphysical question: are counterfactual truths fundamental, or are they grounded or made true by other truths? There are, to repeat, the two obvious options: Hypotheticalism (some conditional truths are fundamental) and Anti-Hypotheticalism (no conditional truth is fundamental).
4.1T Hypotheticalism. There are fundamentally conditional or hypothetical truths.
4.1A Anti-Hypotheticalism. All conditional truths are grounded in non-conditional facts.
What would the world be like if Hypotheticalism were true? One possibility would be for there to be simple conditional truthmakers: basic, irreducible facts to the effect that if p (subjunctive mood), then q (subjunctive mood). Alternatively, there could be basic facts of comparative closeness between worlds, facts of something like this form: world w′ is one of the closest p-worlds to w′′. These facts of closeness would be very much like simple conditional facts, since they tell us which worlds might
have been actual (from the viewpoint of w′) had p been the case. These facts about closeness between worlds could exist, if possible worlds were themselves fundamental entities, as David Lewis believed them to be (a position we will discuss more thoroughly in Chapter 14). Or, to use Stalnaker's semantics, there might be fundamental truths about which one world would have been actual, had some member of a set of worlds been actual.
Hypotheticalism has had its defenders, both historically (Luis de Molina, 1535–1600) and among contemporary metaphysicians (Alvin Plantinga). We don't know of any knockdown objections to it. It does stand in some tension with both truthmaker theory and Truth Supervenes on Being. However, it is possible to believe in Hypotheticalism while embracing either TSB or a stronger truthmaker theory. One way of doing this would be to treat possible worlds as real, concrete entities existing in “logical space,” a view called Concretism (which we will discuss in detail in Chapter 14). Alternatively, one could posit simple hypothetical truthmakers in the actual world whose existence is sufficient to make some counterfactual conditional true. One way of doing this would follow the lead of Luis Molina, introducing special, primitive properties, which Molina called ‘habitudes’. If it's true, to use Plantinga's example, that Curley the mayor would have accepted a $300,000 bribe, had he been offered one, we could suppose that this conditional is made true by virtue of Curley's having the appropriate habitude property: the property of being the sort of person who would accept a $300,000 bribe if offered one.6
An important point: although these habitudes are properties of individuals, they are not intrinsic properties of them (see our discussion of intrinsic properties in Section 3.1.4). If a habitude were part of the intrinsic nature of a thing, then the unique result associated with the habitude (like accepting the bribe) would be pre-determined by Curry's nature. Habitudes, however, are supposed to be the sort of thing that fills the gap between what is pre-determined to happen and what would happen. If we suppose the truth of conditionals to be grounded in the intrinsic natures of things, we've moved to a Strong Powerist (4.4A.3) position (see Chapter 6), not Hypotheticalism. Consequently, for Hypotheticalists a habitude must be an external relation, rather than an internal relation (Def D2.2), between an individual (like Curley) and some non-actual state of affairs (like being offered the bribe).
The Atlas of Reality Page 14
