Counterfactual conditional
Encyclopedia
A counterfactual conditional, subjunctive conditional, or remote conditional, abbreviated , is a conditional (or "if-then") statement
indicating what would be the case if its antecedent
were true (although it is not true). This is to be contrasted with an indicative conditional
, which indicates what is (in fact) the case if its antecedent is (in fact) true (which it may or may not be).
The protasis
(the if clause) of the first sentence may or may not be true according to the speaker, so the apodosis (the then clause) also may or may not be true; the apodosis is said by the speaker to be true if the protasis is true. In this sentence the if clause and the then clause are both in the past tense of the indicative mood. In the second sentence, the speaker is speaking with a certainty that Oswald did shoot Kennedy (according to the speaker, the protasis is false), and therefore the main clause deals with the counterfactual result — what would have happened. In this sentence the if clause is in the pluperfect subjunctive form of the subjunctive mood
, and the then clause is in the conditional perfect
form of the conditional mood
.
A corresponding pair of examples with present time reference uses the present indicative in the if clause of the first sentence but the past subjunctive in the second sentence's if clause:
Here again, in the first sentence the if clause may or may not be true; the then clause may or may not be true but certainly (according to the speaker) is true conditional on the if clause being true. Here both the if clause and the then clause are in the present indicative. In the second sentence, the if clause is not true, while the then clause may or may not be true but certainly would be true in the counterfactual circumstance of the if clause being true. In this sentence the if clause is in the past subjunctive form of the subjunctive mood, and the then clause is in the conditional mood.
frequently. Experimental evidence indicates that people's thoughts about counterfactual conditionals differ in important ways from their thoughts about indicative conditionals.
inference 'there was no circle' more often than they do from an indicative conditional (Byrne and Tasso, 1999). Given the counterfactual conditional and the subsequent information 'in fact there was a circle', participants make the modus ponens
inference as often as they do from an indicative conditional.
s 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'. 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' (Byrne, 2005). According to the mental model theory of reasoning
, they construct mental models of the alternative possibilities (Johnson-Laird and Byrne, 1991).
The truth value of a material conditional
, A → B, is determined by the truth values of A and B. This is not so for the counterfactual conditional A > B, for there are different situations agreeing on the truth values of A and B but which yield different evaluations of A > B. For example, if Keith is in Germany
, the following two conditionals have both a false antecedent and a false consequent:
Indeed, if Keith is in Germany, then all three conditions "Keith is in Mexico", "Keith is in Africa", and "Keith is in North America" are false. However, (1) is obviously false, while (2) is true as Mexico
is part of North America
.
and Robert Stalnaker
modeled counterfactuals using the possible world semantics of modal logic
. The semantics of a conditional A > B are 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's Counterfacutals it was unclear what he meant by 'closeness', in later writings, Lewis made it clear that he did not intend the metric of 'closeness' to be simply our ordinary notion of overall similarity.
Consider an example:
On Lewis's account, the truth of this statement consists in the fact that, among possible worlds where I ate more for breakfast, there is at least one world where I am not hungry at 11am and which is closer to our world than any world where I ate more for breakfast but am still hungry at 11am.
Stalnaker's account differs from Lewis's most notably in his acceptance of the Limit and Uniqueness Assumptions. The Uniqueness Assumption is the thesis that, for any antecedent A, there is a unique possible world where A is true, while the Limit Assumption is the thesis that, for a given antecedent A, there is a unique set of worlds where A is true that are closest. (Notice that the Uniqueness Assumption entails the 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 I eat more breakfast, I don't feel hungry at 11am. 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 my 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 the law of excluded middle
is 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). Consider the following example:
If the coin had been flipped, it would have landed heads. If the coin had been flipped, it would have landed tails (i.e. not heads).
On Stalnaker's analysis, there is a closest world where the 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 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.'
, as the evaluation of A > B can be done by first revising the current knowledge with A and then checking whether B is true in what results. Revising is easy when A is 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.
e, considering the maximal sets of these formulae that are consistent with A, and adding A to each. The rationale is that each of these maximal sets represents a possible state of belief in which A is true that is as similar as possible to the original one. The conditional statement A > B therefore holds if and only if B is true in all such sets.
methods for establishing causality
in the natural and
social sciences, e.g., whether taking antibiotics helps cure bacterial
infection. For every individual, u, there is a function
that specifies the state of us infection under two
hypothetical conditions: had u taken antibiotic and had u
not taken antibiotic. Only one of these states can be
observed, since the other one is literally "counter factual."
The overall effect of antibiotic
on infection is defined as the difference between these two states,
averaged over the entire population. If the treatment
and control groups are selected at random,
the effect of antibiotic can be estimated by
comparing the rates of recovery in the two groups.
causal and counterfactual relations has prompted Judea Pearl
(2000) to reject both the possible world
semantics and those of Ramsey and Ginsberg.
The latter was rejected because causal information cannot
be encoded as a set of beliefs, and the former
because it is difficult to fine-tune Lewis's similarity
measure to match causal intuition.
Pearl defines counterfactuals directly in terms
of a "structural equation model" -- a set of equations,
in which each variable is assigned a value
that is an explicit function of other variables in the system.
Given such a model, the sentence
"Y would be y had X been x" (formally, X = x > Y = y ) is defined as the assertion: If we replace the equation
currently determining X with a constant X = x,
and solve the set of equations for variable Y, the
solution obtained will be Y = 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.
Conditional sentence
In grammar, conditional sentences are sentences discussing factual implications or hypothetical situations and their consequences. Languages use a variety of conditional constructions and verb forms to form such sentences....
indicating what would be the case if its antecedent
Antecedent (logic)
An antecedent is the first half of a hypothetical proposition.Examples:* If P, then Q.This is a nonlogical formulation of a hypothetical proposition...
were true (although it is not true). This is to be contrasted with an indicative conditional
Indicative conditional
In natural languages, an indicative conditional is the logical operation given by statements of the form "If A then B". Unlike the material conditional, an indicative conditional does not have a stipulated definition...
, which indicates what is (in fact) the case if its antecedent is (in fact) true (which it may or may not be).
Examples
The difference between indicative and counterfactual conditionals, in a context of past time reference, can be illustrated with a pair of examples in which the if clause is in the past indicative in the first example but in the pluperfect subjunctive in the second:- If OswaldLee Harvey OswaldLee Harvey Oswald was, according to four government investigations,These were investigations by: the Federal Bureau of Investigation , the Warren Commission , the House Select Committee on Assassinations , and the Dallas Police Department. the sniper who assassinated John F...
did not shoot KennedyJohn F. KennedyJohn Fitzgerald "Jack" Kennedy , often referred to by his initials JFK, was the 35th President of the United States, serving from 1961 until his assassination in 1963....
, then someone else did. - If Oswald had not shot Kennedy, then someone else would have.
The protasis
Protasis (linguistics)
In linguistics, a protasis is the subordinate clause in a conditional sentence. For example, in "if X, then Y", the protasis is "if X"...
(the if clause) of the first sentence may or may not be true according to the speaker, so the apodosis (the then clause) also may or may not be true; the apodosis is said by the speaker to be true if the protasis is true. In this sentence the if clause and the then clause are both in the past tense of the indicative mood. In the second sentence, the speaker is speaking with a certainty that Oswald did shoot Kennedy (according to the speaker, the protasis is false), and therefore the main clause deals with the counterfactual result — what would have happened. In this sentence the if clause is in the pluperfect subjunctive form of the subjunctive mood
Subjunctive mood
In grammar, the subjunctive mood is a verb mood typically used in subordinate clauses to express various states of irreality such as wish, emotion, possibility, judgment, opinion, necessity, or action that has not yet occurred....
, and the then clause is in the conditional perfect
Conditional perfect
In linguistics, the conditional perfect is the composed form of the conditional mood. It refers to a hypothetical action in the past, contingent on something else that did not occur in the past...
form of the conditional mood
Conditional mood
In linguistics, the conditional mood is the inflectional form of the verb used in the independent clause of a conditional sentence to refer to a hypothetical state of affairs, or an uncertain event, that is contingent on another set of circumstances...
.
A corresponding pair of examples with present time reference uses the present indicative in the if clause of the first sentence but the past subjunctive in the second sentence's if clause:
- If it is raining, then he is inside.
- If it were raining, then he would be inside.
Here again, in the first sentence the if clause may or may not be true; the then clause may or may not be true but certainly (according to the speaker) is true conditional on the if clause being true. Here both the if clause and the then clause are in the present indicative. In the second sentence, the if clause is not true, while the then clause may or may not be true but certainly would be true in the counterfactual circumstance of the if clause being true. In this sentence the if clause is in the past subjunctive form of the subjunctive mood, and the then clause is in the conditional mood.
Psychology
People engage in counterfactual thinkingCounterfactual thinking
Counterfactual thinking is a term of psychology that describes the tendency people have to imagine alternatives to reality. Humans are predisposed to think about how things could have turned out differently if only..., and also to imagine what if?....
frequently. 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' (Fillenbaum, 1974). 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 conditional 'primed' them to read the sentence corresponding to the presupposed facts very rapidly; no such priming effect occurred for indicative conditionals (Santamaria, Espino, and Byrne, 2005). They spend different amounts of time 'updating' a story that contains a counterfactual conditional compared to one that contains factual information (De Vega, Urrutia, and Riffo, 2007) and they focus on different parts of counterfactual conditionals (Ferguson and Sanford, 2008).Reasoning
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 the modus tollensModus tollens
In classical logic, modus tollens has the following argument form:- Formal notation :...
inference 'there was no circle' more often than they do from an indicative conditional (Byrne and Tasso, 1999). Given the counterfactual conditional and the subsequent information 'in fact there was a circle', participants make the modus ponens
Modus ponens
In classical logic, modus ponendo ponens or implication elimination is a valid, simple argument form. It is related to another valid form of argument, modus tollens. Both Modus Ponens and Modus Tollens can be mistakenly used when proving arguments...
inference as often as they do from an indicative conditional.
Psychological accounts
Ruth M.J. Byrne proposed that people construct mental representationMental representation
A representation, in philosophy of mind, cognitive psychology, neuroscience, and cognitive science, is a hypothetical internal cognitive symbol that represents external reality, or else a mental process that makes use of such a symbol; "a formal system for making explicit certain entities or types...
s 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'. 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' (Byrne, 2005). According to the mental model theory of reasoning
Mental model theory of reasoning
-Introduction:The mental model theory of reasoning was developed by Philip Johnson-Laird and Ruth M.J. Byrne . It has been applied to the main domains of deductive inference including relational inferences such as spatial and temporal deductions; propositional inferences, such as conditional,...
, they construct mental models of the alternative possibilities (Johnson-Laird and Byrne, 1991).
Connective
In order to distinguish counterfactual conditionals from material conditionals, a new logical connective '>' is defined, where A > B can be interpreted as "If it were the case that A, then it would be the case that B."The truth value of a material conditional
Material conditional
The material conditional, also known as material implication, is a binary truth function, such that the compound sentence p→q is logically equivalent to the negative compound: not . A material conditional compound itself is often simply called a conditional...
, A → B, is determined by the truth values of A and B. This is not so for the counterfactual conditional A > B, for there are different situations agreeing on the truth values of A and B but which yield different evaluations of A > B. For example, if Keith is in Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
, the following two conditionals have both a false antecedent and a false consequent:
- if Keith were in MexicoMexicoThe United Mexican States , commonly known as Mexico , is a federal constitutional republic in North America. It is bordered on the north by the United States; on the south and west by the Pacific Ocean; on the southeast by Guatemala, Belize, and the Caribbean Sea; and on the east by the Gulf of...
then he would be in AfricaAfricaAfrica is the world's second largest and second most populous continent, after Asia. At about 30.2 million km² including adjacent islands, it covers 6% of the Earth's total surface area and 20.4% of the total land area...
. - if Keith were in Mexico then he would be in North AmericaNorth AmericaNorth America is a continent wholly within the Northern Hemisphere and almost wholly within the Western Hemisphere. It is also considered a northern subcontinent of the Americas...
.
Indeed, if Keith is in Germany, then all three conditions "Keith is in Mexico", "Keith is in Africa", and "Keith is in North America" are false. However, (1) is obviously false, while (2) is true as Mexico
Mexico
The United Mexican States , commonly known as Mexico , is a federal constitutional republic in North America. It is bordered on the north by the United States; on the south and west by the Pacific Ocean; on the southeast by Guatemala, Belize, and the Caribbean Sea; and on the east by the Gulf of...
is part of North America
North America
North America is a continent wholly within the Northern Hemisphere and almost wholly within the Western Hemisphere. It is also considered a northern subcontinent of the Americas...
.
Possible world semantics
Philosophers such as David LewisDavid Kellogg Lewis
David Kellogg Lewis was an American philosopher. Lewis taught briefly at UCLA and then at Princeton from 1970 until his death. He is also closely associated with Australia, whose philosophical community he visited almost annually for more than thirty years...
and Robert Stalnaker
Robert Stalnaker
Robert C. Stalnaker is Laurance S. Rockefeller Professor of Philosophy at the Massachusetts Institute of Technology. In 2007, he delivered the John Locke Lectures at Oxford University on the topic of Our Knowledge of the Internal World...
modeled counterfactuals using the possible world semantics of modal logic
Modal logic
Modal logic is a type of formal logic that extends classical propositional and predicate logic to include operators expressing modality. Modals — words that express modalities — qualify a statement. For example, the statement "John is happy" might be qualified by saying that John is...
. The semantics of a conditional A > B are 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's Counterfacutals it was unclear what he meant by 'closeness', in later writings, Lewis made it clear that he did not intend the metric of 'closeness' to be simply our ordinary notion of overall similarity.
Consider an example:
- If I had eaten more at breakfast, I would not have been hungry at 11am.
On Lewis's account, the truth of this statement consists in the fact that, among possible worlds where I ate more for breakfast, there is at least one world where I am not hungry at 11am and which is closer to our world than any world where I ate more for breakfast but am still hungry at 11am.
Stalnaker's account differs from Lewis's most notably in his acceptance of the Limit and Uniqueness Assumptions. The Uniqueness Assumption is the thesis that, for any antecedent A, there is a unique possible world where A is true, while the Limit Assumption is the thesis that, for a given antecedent A, there is a unique set of worlds where A is true that are closest. (Notice that the Uniqueness Assumption entails the 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 I eat more breakfast, I don't feel hungry at 11am. 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 my 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 the law of excluded middle
Law of excluded middle
In logic, the law of excluded middle is the third of the so-called three classic laws of thought. It states that for any proposition, either that proposition is true, or its negation is....
is 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). Consider the following example:
If the coin had been flipped, it would have landed heads. If the coin had been flipped, it would have landed tails (i.e. not heads).
On Stalnaker's analysis, there is a closest world where the 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 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.'
Ramsey
Counterfactual conditionals may also be evaluated using the so-called Ramsey test: A > B holds if and only if the addition of A to the current body of knowledge has B as a consequence. This condition relates counterfactual conditionals to belief revisionBelief revision
Belief revision is the process of changing beliefs to take into account a new piece of information. The logical formalization of belief revision is researched in philosophy, in databases, and in artificial intelligence for the design of rational agents....
, as the evaluation of A > B can be done by first revising the current knowledge with A and then checking whether B is true in what results. Revising is easy when A is 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 of propositional formulaPropositional formula
In propositional logic, a propositional formula is a type of syntactic formula which is well formed and has a truth value. If the values of all variables in a propositional formula are given, it determines a unique truth value...
e, considering the maximal sets of these formulae that are consistent with A, and adding A to each. The rationale is that each of these maximal sets represents a possible state of belief in which A is true that is as similar as possible to the original one. The conditional statement A > B therefore holds if and only if B is true in all such sets.
Within empirical testing
The counterfactual conditional is the basis of experimentalmethods for establishing causality
Causality
Causality is the relationship between an event and a second event , where the second event is understood as a consequence of the first....
in the natural and
social sciences, e.g., whether taking antibiotics helps cure bacterial
infection. For every individual, u, there is a function
that specifies the state of us infection under two
hypothetical conditions: had u taken antibiotic and had u
not taken antibiotic. Only one of these states can be
observed, since the other one is literally "counter factual."
The overall effect of antibiotic
on infection is defined as the difference between these two states,
averaged over the entire population. If the treatment
and control groups are selected at random,
the effect of antibiotic can be estimated by
comparing the rates of recovery in the two groups.
Pearl
The tight connection betweencausal and counterfactual relations has prompted Judea Pearl
Judea Pearl
Judea Pearl is a computer scientist and philosopher, best known for developing the probabilistic approach to artificial intelligence and the development of Bayesian networks ....
(2000) to reject both the possible world
semantics and those of Ramsey and Ginsberg.
The latter was rejected because causal information cannot
be encoded as a set of beliefs, and the former
because it is difficult to fine-tune Lewis's similarity
measure to match causal intuition.
Pearl defines counterfactuals directly in terms
of a "structural equation model" -- a set of equations,
in which each variable is assigned a value
that is an explicit function of other variables in the system.
Given such a model, the sentence
"Y would be y had X been x" (formally, X = x > Y = y ) is defined as the assertion: If we replace the equation
currently determining X with a constant X = x,
and solve the set of equations for variable Y, the
solution obtained will be Y = 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.
See also
- Indicative conditionalIndicative conditionalIn natural languages, an indicative conditional is the logical operation given by statements of the form "If A then B". Unlike the material conditional, an indicative conditional does not have a stipulated definition...
- Irrealis moodsIrrealis moodsIrrealis moods are the main set of grammatical moods that indicate that a certain situation or action is not known to have happened as the speaker is talking.Every language has a formula for the unreal...
- Logical implication
- Material conditionalMaterial conditionalThe material conditional, also known as material implication, is a binary truth function, such that the compound sentence p→q is logically equivalent to the negative compound: not . A material conditional compound itself is often simply called a conditional...
- Optative moodOptative moodThe optative mood is a grammatical mood that indicates a wish or hope. It is similar to the cohortative mood, and closely related to the subjunctive mood....
- Principle of explosionPrinciple of explosionThe principle of explosion, or the principle of Pseudo-Scotus, is the law of classical logic and intuitionistic and similar systems of logic, according to which any statement can be proven from a contradiction...
- Subjunctive moodSubjunctive moodIn grammar, the subjunctive mood is a verb mood typically used in subordinate clauses to express various states of irreality such as wish, emotion, possibility, judgment, opinion, necessity, or action that has not yet occurred....
- Thought experimentThought experimentA thought experiment or Gedankenexperiment considers some hypothesis, theory, or principle for the purpose of thinking through its consequences...
- Possible world semantics