Counterfactual conditional

"Counterfactual" redirects here. For other uses, seeCounterfactual (disambiguation).

Counterfactual conditionals(alsocontrafactual,subjunctiveorX-marked) areconditional sentenceswhich discuss what would have been true under different circumstances, e.g. "If Peter believed in ghosts, he would be afraid to be here." Counterfactuals are contrasted withindicatives,which are generally restricted to discussing open possibilities. Counterfactuals are characterized grammatically by their use offake tense morphology,which some languages use in combination with other kinds ofmorphologyincludingaspectandmood.

Counterfactuals are one of the most studied phenomena inphilosophical logic,formal semantics,andphilosophy of language.They were first discussed as a problem for thematerial conditionalanalysis of conditionals, which treats them all as trivially true. Starting in the 1960s, philosophers and linguists developed the now-classicpossible worldapproach, in which a counterfactual's truth hinges on its consequent holding at certain possible worlds where its antecedent holds. More recent formal analyses have treated them using tools such ascausal modelsanddynamic semantics.Other research has addressed their metaphysical, psychological, and grammatical underpinnings, while applying some of the resultant insights to fields including history, marketing, and epidemiology.

Overview

Examples

An example of the difference betweenindicativeand counterfactual conditionals is the followingEnglishminimal pair:

• Indicative conditional:If Sallyownsa donkey, then sheridesit.
• Simple past counterfactual:If Sallyowneda donkey, shewould rideit.

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 thefake tenseform "owned" in the "if" clause and the past-inflectedmodal"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 thepast perfectcounterfactual, which contrasts with indicatives and simple past counterfactuals in its use of pluperfect morphology:

• Past perfect counterfactual:If ithad been rainingyesterday, then Sallywould have beeninside.

Another kind of conditional uses the form "were", generally referred to as theirrealisor subjunctive form.

• Irrealiscounterfactual:If itwere rainingright now, then Sallywould beinside.

Past perfect and irrealis counterfactuals can undergoconditional inversion:

• Had it rained, Sally would have been inside.
• Were it raining, Sally would be inside.

Terminology

The termcounterfactual conditionalis 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 assubjunctive conditionals,though this term is likewise acknowledged as a misnomer even by those who use it.Many languages do not have a morphologicalsubjunctive(e.g.DanishandDutch) and many that do have it do not use it for this sort of conditional (e.g.French,Swahili,allIndo-Aryan languagesthat 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 termscounterfactualandsubjunctivehave 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 termX-Markedhas been proposed as a replacement, evoking theextra marking that these conditionals bear. Those adopting this terminology refer to indicative conditionals asO-Markedconditionals, reflecting theirordinary marking.

Theantecedentof a conditional is sometimes referred to as its"if" -clauseorprotasis.Theconsequentof a conditional is sometimes referred to as a"then"-clause or as an apodosis.

Logic and semantics

Counterfactuals were first discussed byNelson Goodmanas a problem for thematerial conditionalused inclassical logic.Because of these problems, early work such as that ofW.V. Quineheld that counterfactuals are not strictly logical, and do not make true or false claims about the world. However, in the 1960s and 1970s, work byRobert StalnakerandDavid Lewisshowed that these problems are surmountable given an appropriateintensionallogical framework. Work since then informal semantics,philosophical logic,philosophy of language,andcognitive sciencehas built on this insight, taking it in a variety of different directions.

Classic puzzles

The problem of counterfactuals

According to thematerial conditionalanalysis, 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.

1. If that piece of butter had been heated to 150°, it would have melted.
2. If that piece of butter had been heated to 150°, 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 arecontext dependentandvague.For example, either of the following statements can be reasonably held true, though not at the same time:

1. IfCaesarhad been in command in Korea, he would haveused the atom bomb.
2. If Caesar had been in command in Korea, he would have used catapults.

Non-monotonicity

Counterfactuals arenon-monotonicin the sense that their truth values can be changed by adding extra material to their antecedents. This fact is illustrated bySobel sequencessuch as the following:

1. If Hannah had drunk coffee, she would be happy.
2. If Hannah had drunk coffee and the coffee had gasoline in it, she would be sad.
3. 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 ofAntecedent Strengtheningshouldnothold for any connective > intended as a formalization of natural language conditionals.

• Antecedent Strengthening:$P>Q\models (P\land R)>Q$

Possible worlds accounts

The most common logical accounts of counterfactuals are couched in thepossible world semantics.Broadly speaking, these approaches have in common that they treat a counterfactualA>Bas true ifBholds 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'svariably strict conditionalis considered the classic analysis within philosophy. The closely relatedpremise semanticsproposed byAngelika Kratzeris often taken as the standard within linguistics. However, there are numerous possible worlds approaches on the market, includingdynamicvariants of thestrict conditionalanalysis originally dismissed by Lewis.

Strict conditional

Thestrict conditionalanalysis treats natural language counterfactuals as being equivalent to themodal logicformula$\Box (P\rightarrow Q)$.In this formula,$\Box$expresses necessity and$\rightarrow$is understood asmaterial implication.This approach was first proposed in 1912 byC.I. Lewisas part of hisaxiomatic approachto modal logic.In modernrelational semantics,this means that the strict conditional is true atwiff the corresponding material conditional is true throughout the worlds accessible fromw.More formally:

• Given a model$M=\langle W,R,V\rangle$,we have that$M,w\models \Box (P\rightarrow Q)$iff$M,v\models P\rightarrow Q$for all$v$such that$Rwv$

Unlike the material conditional, the strict conditional is not vacuously true when its antecedent is false. To see why, observe that both$P$and$\Box (P\rightarrow Q)$will be false at$w$if there is some accessible world$v$where$P$is true and$Q$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.

The strict conditional analysis encounters many known problems, notably monotonicity. In the classical relational framework, when using a standard notion of entailment, the strict conditional is monotonic, i.e. it validatesAntecedent Strengthening.To see why, observe that if$P\rightarrow Q$holds at every world accessible from$w$,the monotonicity of the material conditional guarantees that$P\land R\rightarrow Q$will be too. Thus, we will have that$\Box (P\rightarrow Q)\models \Box (P\land R\rightarrow Q)$.

This fact led to widespread abandonment of the strict conditional, in particular in favor of Lewis'svariably strict analysis.However, subsequent work has revived the strict conditional analysis by appealing to context sensitivity. This approach was pioneered by Warmbrōd (1981), who argued thatSobel sequencesdo not demand anon-monotoniclogic, but in fact can rather be explained by speakers switching to more permissive accessibility relations as the sequence proceeds. In his system, a counterfactual like "If Hannah had drunk coffee, she would be happy" would normally be evaluated using a model where Hannah's coffee is gasoline-free in all accessible worlds. If this same model were used to evaluate a subsequent utterance of "If Hannah had drunk coffee and the coffee had gasoline in it...", this second conditional would come out as trivially true, since there are no accessible worlds where its antecedent holds. 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 ofdynamic semantics,and given a number of linguistic arguments in favor. One argument is that conditional antecedents licensenegative polarity items,which are thought to be licensed only by monotonic operators.

1. If Hannah had drunk any coffee, she would be happy.

Another argument in favor of the strict conditional comes fromIrene Heim'sobservation that Sobel Sequences are generallyinfelicitous(i.e. sound strange) in reverse.

1. If Hannah had drunk coffee with gasoline in it, she would not be happy. But if she had drunk coffee, she would be happy.

Sarah Moss (2012) and Karen Lewis (2018) have responded to these arguments, showing that a version of the variably strict analysis can account for these patterns, and arguing that such an account is preferable since it can also account for apparent exceptions. As of 2020, this debate continues in the literature, with accounts such as Willer (2019) arguing that a strict conditional account can cover these exceptions as well.

Variably strict conditional

In the variably strict approach, the semantics of a conditionalA>Bis given by some function on the relative closeness of worlds where A is true and B is true, on the one hand, and worlds where A is true but B is not, on the other.

On Lewis's account, A > C is (a) vacuously true if and only if there are no worlds where A is true (for example, if A is logically or metaphysically impossible); (b) non-vacuously true if and only if, among the worlds where A is true, some worlds where C is true are closer to the actual world than any world where C is not true; or (c) false otherwise. Although in Lewis'sCounterfactualsit was unclear what he meant by 'closeness', in later writings, Lewis made it clear that he didnotintend the metric of 'closeness' to be simply our ordinary notion ofoverall similarity.

Example:

If he had eaten more at breakfast, he would not have been hungry at 11 am.

On Lewis's account, the truth of this statement consists in the fact that, among possible worlds where he ate more for breakfast, there is at least one world where he is not hungry at 11 am and which is closer to our world than any world where he ate more for breakfast but is still hungry at 11 am.

Stalnaker's account differs from Lewis's most notably in his acceptance of thelimitanduniqueness assumptions.The uniqueness assumption is the thesis that, for any antecedent A, among the possible worlds where A is true, there is a single (unique) one that isclosestto the actual world. The limit assumption is the thesis that, for a given antecedent A, if there is a chain of possible worlds where A is true, each closer to the actual world than its predecessor, then the chain has alimit:a possible world where A is true that is closer to the actual worlds than all worlds in the chain. (The uniqueness assumptionentailsthe limit assumption, but the limit assumption does not entail the uniqueness assumption.) On Stalnaker's account, A > C is non-vacuously true if and only if, at the closest world where A is true, C is true. 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. Although it is controversial, Lewis rejected the limit assumption (and therefore the uniqueness assumption) because it rules out the possibility that there might be worlds that get closer and closer to the actual world without limit. 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. (See Lewis 1973: 20.)

One consequence of Stalnaker's acceptance of the uniqueness assumption is that, if thelaw of excluded middleis true, then all instances of the formula (A > C) ∨ (A > ¬C) are true. The law of excluded middle is the thesis that for all propositions p, p ∨ ¬p is true. If the uniqueness assumption is true, then for every antecedent A, there is a uniquely closest world where A is true. If the law of excluded middle is true, any consequent C is either true or false at that world where A is true. So for every counterfactual A > C, either A > C or A > ¬C is true. This is called conditional excluded middle (CEM). Example:

(1) If the fair coin had been flipped, it would have landed heads.

(2) If the fair coin had been flipped, it would have landed tails (i.e. not heads).

On Stalnaker's analysis, there is a closest world where the fair coin mentioned in (1) and (2) is flipped and at that world either it lands heads or it lands tails. So either (1) is true and (2) is false or (1) is false and (2) true. On Lewis's analysis, however, both (1) and (2) are false, for the worlds where the fair coin lands heads are no more or less close than the worlds where they land tails. For Lewis, "If the coin had been flipped, it would have landed heads or tails" is true, but this does not entail that "If the coin had been flipped, it would have landed heads, or: If the coin had been flipped it would have landed tails."

Other accounts

Causal models

Further information:Causal model § Counterfactuals

Thecausal models frameworkanalyzes counterfactuals in terms of systems ofstructural equations.In a system of equations, each variable is assigned a value that is an explicit function of other variables in the system. Given such a model, the sentence "Ywould beyhadXbeenx"(formally,X = x>Y = y) is defined as the assertion: If we replace the equation currently determiningXwith a constantX = x,and solve the set of equations for variableY,the solution obtained will beY = y.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 byJudea Pearl(2000) as a means of encoding fine-grained intuitions about causal relations which are difficult to capture in other proposed systems.

Belief revision

Further information:Belief revision § The Ramsey test

In thebelief revisionframework, counterfactuals are treated using a formal implementation of theRamsey test.In these systems, a counterfactualA>Bholds if and only if the addition ofAto the current body of knowledge hasBas a consequence. This condition relates counterfactual conditionals tobelief revision,as the evaluation ofA>Bcan be done by first revising the current knowledge withAand then checking whetherBis true in what results. Revising is easy whenAis consistent with the current beliefs, but can be hard otherwise. Every semantics for belief revision can be used for evaluating conditional statements. Conversely, every method for evaluating conditionals can be seen as a way for performing revision.

Ginsberg

Ginsberg (1986) has proposed a semantics for conditionals which assumes that the current beliefs form a set ofpropositional formulae,considering the maximal sets of these formulae that are consistent withA,and addingAto each. The rationale is that each of these maximal sets represents a possible state of belief in whichAis true that is as similar as possible to the original one. The conditional statementA>Btherefore holds if and only ifBis true in all such sets.

The grammar of counterfactuality

Languages use different strategies for expressing counterfactuality. Some have a dedicated counterfactualmorphemes,while others recruit morphemes which otherwise expresstense,aspect,mood,or a combination thereof. Since the early 2000s, linguists, philosophers of language, and philosophical logicians have intensely studied the nature of this grammatical marking, and it continues to be an active area of study.

Fake tense

Description

In many languages, counterfactuality is marked bypast tensemorphology.Since these uses of the past tense do not convey their typical temporal meaning, they are calledfake pastorfake tense.English is one language which uses fake past to mark counterfactuality, as shown in the followingminimal pair.In the indicative example, the bolded words are present tense forms. In the counterfactual example, both words take their past tense form. This use of the past tense cannot have its ordinary temporal meaning, since it can be used with the adverb "tomorrow" without creating a contradiction.

1. Indicative: If Natalialeavestomorrow, shewillarrive on time.
2. Counterfactual: If Natalialefttomorrow, shewouldarrive on time.

Modern Hebrewis another language where counterfactuality is marked with a fake past morpheme:

im

if

Dani

Dani

haya

be.PST.3S.M

ba-bayit

in-home

maχa ɾ

tomorrow

hayinu

be.PST.1PL

mevakRim

visit.PTC.PL

oto

he.ACC

im Danihayaba-bayit {maχa ɾ}hayinumevakRim oto

if Dani be.PST.3S.M in-home tomorrow be.PST.1PL visit.PTC.PL he.ACC

"If Dani had been home tomorrow, we would've visited him."

Palestinian Arabicis another:

iza

if

kaan

be.PST.3S.M

fi

in

l-bet

the-house

bukra

tomorrow

kunna

be.PST.1PL

zurna-a

visit.PST.PFV.1PL-him

izakaanfi l-bet bukra kunnazurna-a

if be.PST.3S.M in the-house tomorrow be.PST.1PL visit.PST.PFV.1PL-him

"If he had been home tomorrow, we would've visited him."

Fake past is extremely prevalent cross-linguistically, either on its own or in combination with other morphemes. Moreover,theoretical linguistsandphilosophers of languagehave argued that other languages' strategies for marking counterfactuality are actuallyrealizationsof fake tense along with other morphemes. For this reason, fake tense has often been treated as the locus of the counterfactual meaning itself.

Formal analyses

Informal semanticsandphilosophical logic,fake past is regarded as a puzzle, since it is not obvious why so many unrelated languages would repurpose a tensemorphemeto mark counterfactuality. Proposed solutions to this puzzle divide into two camps:past as modalandpast as past.These approaches differ in whether or not they take the past tense's core meaning to be about time.

In thepast as modal approach,thedenotationof the past tense is not fundamentally about time. Rather, it is anunderspecifiedskeleton which can apply either tomodalor temporal content.For instance, the particular past as modal proposal of Iatridou (2000), the past tense's core meaning is what is shown schematically below:

1. Thetopicxis not the contextually-providedx

Depending on how this denotationcomposes,xcan be a time interval or apossible world.Whenxis a time, the past tense will convey that the sentence is talking about non-current times, i.e. the past. Whenxis a world, it will convey that the sentence is talking about a potentially non-actual possibility. The latter is what allows for a counterfactual meaning.

Thepast as past approachtreats the past tense as having an inherently temporal denotation. On this approach, so-called fake tense is not actually fake. It differs from "real" tense only in how it takesscope,i.e. which component of the sentence's meaning is shifted to an earlier time. When a sentence has "real" past marking, it discusses something that happened at an earlier time; when a sentence has so-called fake past marking, it discusses possibilities that wereaccessibleat an earlier time but may no longer be.

Fake aspect

Fakeaspectoften accompanies fake tense in languages that mark aspect. In some languages (e.g.Modern Greek,Zulu,and theRomance languages) this fake aspect isimperfective.In other languages (e.g.Palestinian Arabic) it isperfective.However, in other languages includingRussianandPolish,counterfactuals can have either perfective or imperfective aspect.

Fake imperfective aspect is demonstrated by the twoModern Greeksentences below. These examples form aminimal pair,since they are identical except that the first uses past imperfective marking where the second uses past perfective marking. As a result of this morphological difference, the first has a counterfactual meaning, while the second does not.

An

if

eperne

take.PST.IPFV

afto

this

to

sirpoi

syrup

θa

FUT

γinotan

become.PST.IPFV

kala

well

An eperne afto to sirpoi θa γinotan kala

if take.PST.IPFVthis {} syrup FUT become.PST.IPFVwell

'If he took this syrup, he would get better'

An

if

ipχe

take.PST.PFV

afto

this

to

sirpoi

syrup

θa

FUT

eγine

become.PST.PFV

kala

well

An ipχe afto to sirpoi θa eγine kala

if take.PST.PFVthis {} syrup FUT become.PST.PFVwell

"If he took this syrup, he must be better."

This imperfective marking has been argued to be fake on the grounds that it is compatible withcompletive adverbialssuch as "in one month":

An

if

eχtizes

build.IPFV

to

the

spiti

house

(mesa)

se

in

ena

one

mina

month

θa

FUT

prolavenes

have-time-enough.IPFV

na

to

to

it

pulisis

sell

prin

before

to

the

kalokeri

summer

An eχtizes to spiti (mesa) se ena mina θa prolavenes na to pulisis prin to kalokeri

if build.IPFVthe house {} in one month FUT have-time-enough.IPFVto it sell before the summer

"If you built this house in a month, you would be able to sell it before the summer."

In ordinary non-conditional sentences, such adverbials are compatible with perfective aspect but not with imperfective aspect:

Eχtise

build.PFV

afto

this

to

spiti

house

(mesa)

in

se

ena

one

mina

month

Eχtise afto to spiti (mesa) se ena mina

build.PFVthis {} house in {} one month

"She built this house in one month."

*

Eχtize

build.IPFV

afto

this

to

spiti

house

(mesa)

in

se

ena

one

mina

month

* Eχtize afto to spiti (mesa) se ena mina

{} build.IPFVthis {} house in {} one month

"She was building this house in one month."

Psychology

People engage incounterfactual thinkingfrequently. Experimental evidence indicates that people's thoughts about counterfactual conditionals differ in important ways from their thoughts about indicative conditionals.

Comprehension

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". Afterwards, they were asked to identify which sentences they had been shown. They often mistakenly believed they had been shown sentences corresponding to the presupposed facts, e.g., "Mark did not leave home early" and "Mark did not catch the train".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". Later in the story, they read sentences corresponding to the presupposed facts, e.g., "there were no roses and there were no lilies". The counterfactual conditionalprimedthem to read the sentence corresponding to the presupposed facts very rapidly; no such priming effect occurred for indicative conditionals.They spent different amounts of time 'updating' a story that contains a counterfactual conditional compared to one that contains factual informationand focused on different parts of counterfactual conditionals.

Reasoning

Main article:Counterfactual thinking

Experiments have compared the inferences people make from counterfactual conditionals and indicative conditionals. Given a counterfactual conditional, e.g., "If there had been a circle on the blackboard then there would have been a triangle", and the subsequent information "in fact there was no triangle", participants make themodus tollensinference "there was no circle" more often than they do from an indicative conditional.Given the counterfactual conditional and the subsequent information "in fact there was a circle", participants make themodus ponensinference as often as they do from an indicative conditional.

Psychological accounts

Byrneargues that people constructmental representationsthat 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". They envisage the conjecture "Oswald did not shoot Kennedy and someone else did" and they also think about the presupposed facts "Oswald did shoot Kennedy and someone else did not".According to themental model theory of reasoning,they constructmental modelsof the alternative possibilities.

See also

• Alvin Goldman
• Angelika Kratzer
• Causality
• Conditional sentence
• David Lewis (philosopher)
• Import-Export
• Indicative conditional
• Sabine Iatridou
• Modal logic
• Robert Nozick
• Similarity (philosophy)
• Simplification of disjunctive antecedents

References

• Bennett, Jonathan (2003).A Philosophical Guide to Conditionals.doi:10.1093/0199258872.001.0001.ISBN9780199258871.
• Morgan, Stephen L.; Winship, Christopher (2007).Counterfactuals and Causal Inference.doi:10.1017/CBO9780511804564.ISBN9780511804564.
• Ginsberg, Matthew L. (1986). "Counterfactuals".Artificial Intelligence.30:35–79.doi:10.1016/0004-3702(86)90067-6.S2CID241535532.
• Kożuchowski, Adam (2015). "More than true: The rhetorical function of counterfactuals in historiography".Rethinking History.19(3): 337–356.doi:10.1080/13642529.2014.893663.S2CID143617647.
• Judea Pearl(2000).Causality: Models, Reasoning, and Inference.Cambridge University Press.ISBN978-0-521-77362-1.
• Thompson, Valerie A.; Byrne, Ruth M. J. (2002). "Reasoning counterfactually: Making inferences about things that didn't happen".Journal of Experimental Psychology: Learning, Memory, and Cognition.28(6): 1154–1170.doi:10.1037/0278-7393.28.6.1154.PMID12450339.