In
natural languages, an indicative conditional is a
conditional sentence
Conditional sentences are natural language sentences that express that one thing is contingent on something else, e.g. "If it rains, the picnic will be cancelled." They are so called because the impact of the main clause of the sentence is ''con ...
such as "If Leona is at home, she isn't in Paris", whose grammatical form restricts it to discussing what could be true. Indicatives are typically defined in opposition to
counterfactual conditional
Counterfactual conditionals (also ''subjunctive'' or ''X-marked'') are conditional sentences which discuss what would have been true under different circumstances, e.g. "If Peter believed in ghosts, he would be afraid to be here." Counterfactua ...
s, which have extra grammatical marking which allows them to discuss eventualities which are no longer possible.
Indicatives are a major topic of research in
philosophy of language
In analytic philosophy, philosophy of language investigates the nature of language and the relations between language, language users, and the world. Investigations may include inquiry into the nature of meaning, intentionality, reference, ...
,
philosophical logic, and
linguistics
Linguistics is the science, scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and structure ...
. Open questions include which
logical operation
In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. They can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary ...
indicatives denote, how such denotations could be
composed from their grammatical form, and the implications of those denotations for areas including
metaphysics
Metaphysics is the branch of philosophy that studies the fundamental nature of reality, the first principles of being, identity and change, space and time, causality, necessity, and possibility. It includes questions about the nature of conscio ...
,
psychology of reasoning
The psychology of reasoning (also known as the cognitive science of reasoning) is the study of how people reason, often broadly defined as the process of drawing conclusions to inform how people solve problems and make decisions. It overlaps w ...
, and
philosophy of mathematics
The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in peop ...
.
Formal analyses
Early analyses identified indicative conditionals with the
logical operation
In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. They can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary ...
known as the
material conditional
The material conditional (also known as material implication) is an operation commonly used in logic. When the conditional symbol \rightarrow is interpreted as material implication, a formula P \rightarrow Q is true unless P is true and Q i ...
. According to the material conditional analysis, an indicative "If A then B" is true unless A is true and B is not. Although this analysis covers many observed cases, it misses some crucial properties of actual conditional speech and reasoning.
One problem for the material conditional analysis is that it allows indicatives to be true even when their antecedent and
consequent
A consequent is the second half of a hypothetical proposition. In the standard form of such a proposition, it is the part that follows "then". In an implication, if ''P'' implies ''Q'', then ''P'' is called the antecedent and ''Q'' is called ...
are unrelated. For instance, the indicative "If Paris is in France then trout are fish" is intuitively strange since the location of Paris has nothing to do with the classification of trout. However, since its antecedent and the consequent are both true, the material conditional analysis treats it as a true statement. Similarly, the material conditional analysis treats conditionals with false antecedents as
vacuously true
In mathematics and logic, a vacuous truth is a conditional or universal statement (a universal statement that can be converted to a conditional statement) that is true because the antecedent cannot be satisfied. For example, the statement "she d ...
. For instance, since Paris is not in Australia, the conditional "If Paris is in Australia, then trout are fish" would be treated as true on a material conditional analysis. These arguments have been taken to show that no
truth-functional
In logic, a truth function is a function that accepts truth values as input and produces a unique truth value as output. In other words: The input and output of a truth function are all truth values; a truth function will always output exactly one ...
operator will suffice as a semantics for indicative conditionals. In the mid-20th century, work by
H.P. Grice,
Frank Cameron Jackson
Frank Cameron Jackson (born 31 August 1943) is an Australian analytic philosopher and Emeritus Professor in the School of Philosophy (Research School of Social Sciences) at Australian National University (ANU) where he had spent most of the l ...
, and others attempted to maintain the material conditional conditional as an analysis of indicatives' literal semantic denotation, while appealing to
pragmatics
In linguistics and related fields, pragmatics is the study of how context contributes to meaning. The field of study evaluates how human language is utilized in social interactions, as well as the relationship between the interpreter and the in ...
in order to explain the apparent discrepancies.
Contemporary work in
philosophical logic and
formal semantics generally proposes alternative denotations for indicative conditionals. Proposed alternatives include analyses based on
relevance logic Relevance logic, also called relevant logic, is a kind of non-classical logic requiring the antecedent and consequent of implications to be relevantly related. They may be viewed as a family of substructural or modal logics. It is generally, but ...
,
modal logic,
probability theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set ...
,
Kratzerian modal semantics, and
dynamic semantics Dynamic semantics is a framework in logic and natural language semantics that treats the meaning of a sentence as its potential to update a context. In static semantics, knowing the meaning of a sentence amounts to knowing when it is true; in dynam ...
.
Psychology
Most behavioral experiments on conditionals in the psychology of reasoning have been carried out with indicative conditionals, causal conditionals, and
counterfactual conditionals
Counterfactual conditionals (also ''subjunctive'' or ''X-marked'') are conditional sentences which discuss what would have been true under different circumstances, e.g. "If Peter believed in ghosts, he would be afraid to be here." Counterfactual ...
. People readily make the
modus ponens inference, that is, given ''if A then B'', and given ''A'', they conclude ''B'', but only about half of participants in experiments make the
modus tollens
In propositional logic, ''modus tollens'' () (MT), also known as ''modus tollendo tollens'' (Latin for "method of removing by taking away") and denying the consequent, is a deductive argument form and a rule of inference. ''Modus tollens' ...
inference, that is, given ''if A then B'', and given ''not-B'', only about half of participants conclude ''not-A'', the remainder say that nothing follows (Evans ''et al.'', 1993). When participants are given counterfactual conditionals, they make both the modus ponens and the modus tollens inferences (Byrne, 2005).
See also
*
Counterfactual conditional
Counterfactual conditionals (also ''subjunctive'' or ''X-marked'') are conditional sentences which discuss what would have been true under different circumstances, e.g. "If Peter believed in ghosts, he would be afraid to be here." Counterfactua ...
*
Logical consequence
*
Material conditional
The material conditional (also known as material implication) is an operation commonly used in logic. When the conditional symbol \rightarrow is interpreted as material implication, a formula P \rightarrow Q is true unless P is true and Q i ...
*
Strict conditional In logic, a strict conditional (symbol: \Box, or ⥽) is a conditional governed by a modal operator, that is, a logical connective of modal logic. It is logically equivalent to the material conditional of classical logic, combined with the necess ...
References
{{reflist
Further reading
* Byrne, R.M.J. (2005). ''The Rational Imagination: How People Create Counterfactual Alternatives to Reality.'' Cambridge, MA: MIT Press.
* Edgington, Dorothy. (2006). "Conditionals". ''The Stanford Encyclopedia of Philosophy'', Edward Zalta (ed.). http://plato.stanford.edu/entries/conditionals/.
* Evans, J. St. B. T., Newstead, S. and Byrne, R. M. J. (1993). ''Human Reasoning: The Psychology of Deduction.'' Hove, Psychology Press.
Conditionals in linguistics
Logical connectives
Reasoning