Counterfactual conditionals (also contrafactual/subjunctive/X-marked conditionals) are conditional sentences that describe what would have been true if circumstances had been different, typically when the antecedent is taken to be false or incompatible with what actually happened. In English they are often formed with a past or irrealis morphology, as in "If Peter believed in ghosts, he would be afraid to be here", and are standardly contrasted with indicative conditionals, which are generally used to discuss live or open possibilities.
The name subjunctive conditionals is sometimes preferred because counterfactuals are not always "contrary to fact" as the word "counterfactual" implies, but the name counterfactual conditionals is sometimes preferred because counterfactuals are not always grammatically subjunctive. Hence the name X-marking has been developed as a compromise, although it is newer in the literature; see .
Counterfactuals are central topics in philosophical logic, formal semantics, and philosophy of language. In particular, several conditional logics have been developed specifically to study counterfactuals. Early work treated them as a challenge for the analysis of conditionals in terms of the material conditional, which would make all counterfactuals with false antecedents trivially true. Subsequent research developed a range of non-truth-functional accounts, especially possible world approaches such as David Lewis's variably strict analysis and Stalnaker's closest-world semantics, as well as alternatives based on strict conditionals, causal models, and belief revision and the Ramsey test.
From a linguistic perspective, counterfactuality is closely tied to the grammatical marking of tense, aspect, and mood. Many languages use so-called fake tense and fake aspect to signal a counterfactual interpretation, sometimes analyzed as instances of more general X-marking that distinguishes these conditionals from their indicative or O-marked counterparts. Research in psychology and cognitive science studies how people understand and reason with counterfactual conditionals, how they differ from indicatives in comprehension and inference, and how they relate to more general patterns of counterfactual thinking and mental simulation.
Overview
Examples
An example of the difference between indicative and counterfactual conditionals is the following English minimal pair:
Indicative conditional: If Sally owns a donkey, then she rides it. Simple past counterfactual: If Sally owned a donkey, she would ride it.
These conditionals differ in both form and meaning. The indicative conditional uses the present tense form "owns" and therefore conveys that the speaker is agnostic about whether Sally in fact owns a donkey. The counterfactual example uses the fake tense form "owned" in the "if" clause and the past-inflected modal "would" in the "then" clause. As a result, it conveys that Sally does not in fact own a donkey. English has several other grammatical forms whose meanings are sometimes included under the umbrella of counterfactuality. One is the past perfect counterfactual, which contrasts with indicatives and simple past counterfactuals in its use of pluperfect morphology:
Past perfect counterfactual: If it had been raining yesterday, then Sally would have been inside.
Another kind of conditional uses the form "were", generally referred to as the irrealis or subjunctive form.There is no standard system of terminology for these grammatical forms in English. Pullum and Huddleston (2002, pp. 85-86) adopt the term "irrealis" for this morphological form, reserving the term "subjunctive" for the English clause type whose distribution more closely parallels that of morphological subjunctives in languages that have such a form.
Irrealis counterfactual: If it were raining right now, then Sally would be inside.
Past perfect and irrealis counterfactuals can undergo conditional inversion:
Had it rained, Sally would have been inside. Were it raining, Sally would be inside.
Terminology
The term counterfactual conditional is widely used as an umbrella term for the kinds of sentences shown above. However, not all conditionals of this sort express contrary-to-fact meanings. For instance, the classic example known as the "Anderson Case" has the characteristic grammatical form of a counterfactual conditional, but does not convey that its antecedent is false or unlikely. Anderson Case: If Jones had taken arsenic, he would have shown just exactly those symptoms which he does in fact show.
Such conditionals are also widely referred to as subjunctive conditionals, though this term is likewise acknowledged as a misnomer even by those who use it.See for instance Ippolito (2002): "Because subjunctive and indicative are the terms used in the philosophical literature on conditionals and because we will refer to that literature in the course of this paper, I have decided to keep these terms in the present discussion... however, it would be wrong to believe that mood choice is a necessary component of the semantic contrast between indicative and subjunctive conditionals." Also, von Fintel (2011) "The terminology is of course linguistically inept ([since] the morphological marking is one of tense and aspect, not of indicative vs. subjunctive mood), but it is so deeply entrenched that it would be foolish not to use it." Many languages do not have a morphological subjunctive (e.g. Danish and Dutch) and many that do have it do not use it for this sort of conditional (e.g. French, Swahili, all Indo-Aryan languages that have a subjunctive). Moreover, languages that do use the subjunctive for such conditionals only do so if they have a specific past subjunctive form. Thus, subjunctive marking is neither necessary nor sufficient for membership in this class of conditionals.
The terms counterfactual and subjunctive have sometimes been repurposed for more specific uses. For instance, the term "counterfactual" is sometimes applied to conditionals that express a contrary-to-fact meaning, regardless of their grammatical structure. Along similar lines, the term "subjunctive" is sometimes used to refer to conditionals that bear fake past or irrealis marking, regardless of the meaning they convey.
Recently the term X-Marked has been proposed as a replacement, evoking the extra marking that these conditionals bear. Those adopting this terminology refer to indicative conditionals as O-Marked conditionals, reflecting their marking.von Fintel, Kai; Iatridou, Sabine. Prolegomena to a theory of X-marking Unpublished lecture slides.von Fintel, Kai; Iatridou, Sabine. X-marked desires or: What wanting and wishing crosslinguistically can tell us about the ingredients of counterfactuality Unpublished lecture slides.
The antecedent of a conditional is sometimes referred to as its "if"-clause or protasis. The consequent of a conditional is sometimes referred to as a "then"-clause or as an apodosis.
Logic and semantics
Counterfactuals were first discussed by Nelson Goodman as a problem for the material conditional used in classical logic. Because of these problems, early work such as that of W.V. Quine held that counterfactuals are not strictly logical, and do not make true or false claims about the world. However, in the 1960s and 1970s, work by Robert Stalnaker and David Lewis showed that these problems are surmountable given an appropriate intensional logical framework. Work since then in formal semantics, philosophical logic (especially conditional logic), philosophy of language, and cognitive science has built on this insight, taking it in a variety of different directions.
Classic puzzles
The problem of counterfactuals
According to the material conditional analysis, a natural language conditional, a statement of the form "if P then Q", is true whenever its antecedent, P, is false. Since counterfactual conditionals are those whose antecedents are false, this analysis would wrongly predict that all counterfactuals are vacuously true. Goodman illustrates this point using the following pair in a context where it is understood that the piece of butter under discussion had not been heated.Goodman, N., "The Problem of Counterfactual Conditionals", The Journal of Philosophy, Vol. 44, No. 5, (27 February 1947), pp. 113–28. If that piece of butter had been heated to 150°F, it would have melted. If that piece of butter had been heated to 150°F, it would not have melted.
More generally, such examples show that counterfactuals are not truth-functional. In other words, knowing whether the antecedent and consequent are actually true is not sufficient to determine whether the counterfactual itself is true.
Context dependence and vagueness
Counterfactuals are context dependent and vague. For example, either of the following statements can be reasonably held true, though not at the same time:
If Caesar had been in command in Korea, he would have used the atom bomb. If Caesar had been in command in Korea, he would have used catapults.
Non-monotonicity
Counterfactuals are non-monotonic in the sense that their truth values can be changed by adding extra material to their antecedents. This fact is illustrated by Sobel sequences such as the following:
If Hannah had drunk coffee, she would be happy. If Hannah had drunk coffee and the coffee had gasoline in it, she would be sad. If Hannah had drunk coffee and the coffee had gasoline in it and Hannah were a gasoline-drinking robot, she would be happy.
One way of formalizing this fact is to say that the principle of antecedent strengthening should not hold for any connective > intended as a formalization of natural language conditionals.
Antecedent strengthening:
Possible worlds accounts
The most common logical accounts of counterfactuals are couched in a conditional logic using possible world semantics. Broadly speaking, these approaches have in common that they treat a counterfactual A > B as true if B holds across some set of possible worlds where A is true. They vary mainly in how they identify the set of relevant A-worlds.
David Lewis's variably strict conditional is considered the classic analysis within philosophy. The closely related premise semantics proposed by Angelika Kratzer is often taken as the standard within linguistics. However, there are numerous possible worlds approaches on the market, including dynamic variants of the strict conditional analysis originally dismissed by Lewis.
Strict conditional
The strict conditional analysis treats natural language counterfactuals as being equivalent to the modal logic formula . In this formula, expresses necessity and is understood as material implication. This approach was first proposed in 1912 by C.I. Lewis as part of his axiomatic approach to modal logic. In modern relational semantics, this means that the strict conditional is true at w iff the corresponding material conditional is true throughout the worlds accessible from w. More formally:
Given a model , we have that iff for all such that
Unlike the material conditional, the strict conditional is not vacuously true when its antecedent is false. To see why, observe that both and will be false at if there is some accessible world where is true and is not. The strict conditional is also context-dependent, at least when given a relational semantics (or something similar). In the relational framework, accessibility relations are parameters of evaluation which encode the range of possibilities which are treated as "live" in the context. Since the truth of a strict conditional can depend on the accessibility relation used to evaluate it, this feature of the strict conditional can be used to capture context-dependence.