Counterfactuals are one of the most studied phenomena in philosophical logic, formal semantics, and philosophy of language.
Other research has addressed their metaphysical, psychological, and grammatical underpinnings, while applying some of the resultant insights to fields including history, marketing, and epidemiology.
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.
For instance, the term "counterfactual" is sometimes applied to conditionals that express a contrary-to-fact meaning, regardless of their grammatical structure.
[14][8] 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.
[14][15] Recently the term X-Marked has been proposed as a replacement, evoking the extra marking that these conditionals bear.
Counterfactuals were first discussed by Nelson Goodman as a problem for the material conditional used in classical logic.
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, philosophy of language, and cognitive science has built on this insight, taking it in a variety of different directions.
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.
For example, either of the following statements can be reasonably held true, though not at the same time:[20] Counterfactuals are non-monotonic in the sense that their truth values can be changed by adding extra material to their antecedents.
David Lewis's variably strict conditional is considered the classic analysis within philosophy.
However, there are numerous possible worlds approaches on the market, including dynamic variants of the strict conditional analysis originally dismissed by Lewis.
The strict conditional analysis treats natural language counterfactuals as being equivalent to the modal logic formula
In the classical relational framework, when using a standard notion of entailment, the strict conditional is monotonic, i.e. it validates Antecedent Strengthening.
However, subsequent work has revived the strict conditional analysis by appealing to context sensitivity.
Warmbrōd's idea was that speakers will switch to a model with a more permissive accessibility relation in order to avoid this triviality.
Subsequent work by Kai von Fintel (2001), Thony Gillies (2007), and Malte Willer (2019) has formalized this idea in the framework of dynamic semantics, and given a number of linguistic arguments in favor.
Another argument in favor of the strict conditional comes from Irene Heim's observation that Sobel Sequences are generally infelicitous (i.e. sound strange) in reverse.
So, the above example is true just in case at the single, closest world where he ate more breakfast, he does not feel hungry at 11 am.
For example, there might be an infinite series of worlds, each with a coffee cup a smaller fraction of an inch to the left of its actual position, but none of which is uniquely the closest.
This definition has been shown to be compatible with the axioms of possible world semantics and forms the basis for causal inference in the natural and social sciences, since each structural equation in those domains corresponds to a familiar causal mechanism that can be meaningfully reasoned about by investigators.
This approach was developed by Judea Pearl (2000) as a means of encoding fine-grained intuitions about causal relations which are difficult to capture in other proposed systems.
[26][31] In formal semantics and philosophical logic, fake past is regarded as a puzzle, since it is not obvious why so many unrelated languages would repurpose a tense morpheme to mark counterfactuality.
It differs from "real" tense only in how it takes scope, i.e. which component of the sentence's meaning is shifted to an earlier time.
"In ordinary non-conditional sentences, such adverbials are compatible with perfective aspect but not with imperfective aspect:[26] Eχtisebuild.PFVaftothisto spitihouse(mesa)inse enaoneminamonthEχtise afto to spiti (mesa) se ena minabuild.PFV this {} house in {} one month"She built this house in one month.
Participants in experiments were asked to read sentences, including counterfactual conditionals, e.g., "If Mark had left home early, he would have caught the train".
[38] In other experiments, participants were asked to read short stories that contained counterfactual conditionals, e.g., "If there had been roses in the flower shop then there would have been lilies".
Byrne argues that people construct mental representations that encompass two possibilities when they understand, and reason from, a counterfactual conditional, e.g., "if Oswald had not shot Kennedy, then someone else would have".