Modal operator
Encyclopedia
In modal logic
, a modal operator is an operator
which forms proposition
s from propositions. In general, a modal operator has the "formal" property of being non-truth-functional, and is "intuitively" characterised by expressing a modal attitude (such as necessity
, possibility
, belief
, or knowledge
) about the proposition to which the operator is applied. The concrete examples in this entry relate modality to literary theory
.
in Heterocosmica (1998), a book that articulates a complete theory of literary fiction based on the idea of possible worlds
. Dolezel works with the concept of modalities that play the crucial role in formative operation, i.e. in shaping narrative worlds into orders that have the potential to produce stories. Based on the theories of modal logic
, Dolezel introduces a set of modal systems that are appropriated for fictional semantics
, expanding on the table used by Georg Henrik von Wright
(1968).
:
alethic
, deontic, axiological and epistemic.
modal operators (M-operators) determine the fundamental conditions of fictional worlds, especially causality
, time-space parameters, and the action capacity of persons. They indicate the possibility, impossibility and necessity of actions, states of affairs, events, people, and qualities in the fictional worlds. Alethic modal operators play an important role in distinguishing a natural fictional world from the supernatural and intermediate ones. “The natural world generates stories of human condition” and such stories tend to be tragic from the very beginning, for example J.W. Goethe's The Sorrows of Young Werther
. The structure of the supernatural worlds is usually revealed by the alethic modal operators (a) when they show the presence of physically impossible beings in the fictional world (gods, spirits, monsters); (b) when selected natural-world persons are granted properties and action capacities that are not available to ordinary persons of that world: becoming invisible, flying on a carpet, etc.; (c) when inanimate objects are anthropomorphized (for example the legend of Don Juan in Alexander Pushkin's The Stone Guest.) The intermediate worlds are usually represented in dreams within a fictional world.
modal operators (P-operators) influence the construction of fictional worlds as proscriptive or prescriptive norms, i.e. they indicate what is prohibited, obligatory, or permitted in the fictional world. The deontic marking of actions is the richest source of narrativity; it generates the famous triad of the fall (violations of a norm – punishment), the test (obligation fulfilled – reward), and the predicament (conflict of obligations) stories. An example in literature of a story of the fall would be Mme. De Renal, in Stendhal
’s Le Rouge et le Noir
(1830). An example of a deontic alien in literature, a person who “exempts himself from the world’s codex and follows his own principles” is Raskolnikov, the protagonist of F.M. Dostoevsky’s Crime and Punishment
(1866).
and the axiological rebel. A nihilist negates the axiological order of the world and replaces it with a subjective axiology with a single operator: indifference. An example of the nihilist axiological alien in literature is Pechorin, the protagonist of Mikhail Lermontov
’s A Hero of Our Time
(1839).
. Epistemic code can also be perceived at the core of the Bildungsroman
, where the protagonist undergoes a transformation from ignorance (of self) to knowledge (of self). An example of such transformation in German literature would be J.W. Goethe’s Wilhelm Meister's Apprenticeship
(1795).
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...
, a modal operator is an operator
Operation (mathematics)
The general operation as explained on this page should not be confused with the more specific operators on vector spaces. For a notion in elementary mathematics, see arithmetic operation....
which forms proposition
Proposition
In logic and philosophy, the term proposition refers to either the "content" or "meaning" of a meaningful declarative sentence or the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence...
s from propositions. In general, a modal operator has the "formal" property of being non-truth-functional, and is "intuitively" characterised by expressing a modal attitude (such as necessity
Necessity
In U.S. criminal law, necessity may be either a possible justification or an exculpation for breaking the law. Defendants seeking to rely on this defense argue that they should not be held liable for their actions as a crime because their conduct was necessary to prevent some greater harm and when...
, possibility
Possibility
Possibility is the condition or fact of being possible. The Latin origins of the word hint at ability. Possibility also refers to something that "could happen", that is not precluded by the facts, but usually not probable...
, belief
Belief
Belief is the psychological state in which an individual holds a proposition or premise to be true.-Belief, knowledge and epistemology:The terms belief and knowledge are used differently in philosophy....
, or knowledge
Knowledge
Knowledge is a familiarity with someone or something unknown, which can include information, facts, descriptions, or skills acquired through experience or education. It can refer to the theoretical or practical understanding of a subject...
) about the proposition to which the operator is applied. The concrete examples in this entry relate modality to literary theory
Literary theory
Literary theory in a strict sense is the systematic study of the nature of literature and of the methods for analyzing literature. However, literary scholarship since the 19th century often includes—in addition to, or even instead of literary theory in the strict sense—considerations of...
.
Literary theory
In literary and fiction theory, the concept of modal operators has been explored by Lubomir DolezelLubomir Dolezel
Lubomír Doležel is a Czech literary theorist and one of the founders of the so-called fictional worlds theory.- Life, Work, and Academic Career :...
in Heterocosmica (1998), a book that articulates a complete theory of literary fiction based on the idea of possible worlds
Possible Worlds
Possible Worlds may refer to:* Possible worlds, a concept in philosophy* Possible Worlds , by John Mighton** Possible Worlds , by Robert Lepage, based on the Mighton play* Possible Worlds , by Peter Porter...
. Dolezel works with the concept of modalities that play the crucial role in formative operation, i.e. in shaping narrative worlds into orders that have the potential to produce stories. Based on the theories 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...
, Dolezel introduces a set of modal systems that are appropriated for fictional semantics
Semantics
Semantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....
, expanding on the table used by Georg Henrik von Wright
Georg Henrik von Wright
Georg Henrik von Wright was a Finnish philosopher, who succeeded Ludwig Wittgenstein as professor at the University of Cambridge. He published in English, Finnish, German, and in Swedish. Belonging to the Swedish-speaking minority of Finland, von Wright also had Finnish and 17th-century Scottish...
(1968).
Modality interpreted
There are four established interpretations of the modal operator of modal modal logicModal 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...
:
alethic
Alethic
The adjective alethic refers to the various modalities of truth, such as necessity, possibility or impossibility, as in:* Alethic modality, a modality in linguistics* Subjunctive or alethic possibility, a form of modality studied in modal logic...
, deontic, axiological and epistemic.
Alethic
AlethicAlethic modality
Alethic modality is a linguistic modality which indicates logical necessity, possibility or impossibility.Alethic modality is often associated with epistemic modality in research. However, it has been questioned whether this modality should be considered distinct from epistemic modality which...
modal operators (M-operators) determine the fundamental conditions of fictional worlds, especially 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....
, time-space parameters, and the action capacity of persons. They indicate the possibility, impossibility and necessity of actions, states of affairs, events, people, and qualities in the fictional worlds. Alethic modal operators play an important role in distinguishing a natural fictional world from the supernatural and intermediate ones. “The natural world generates stories of human condition” and such stories tend to be tragic from the very beginning, for example J.W. Goethe's The Sorrows of Young Werther
The Sorrows of Young Werther
The Sorrows of Young Werther is an epistolary and loosely autobiographical novel by Johann Wolfgang von Goethe, first published in 1774; a revised edition of the novel was published in 1787...
. The structure of the supernatural worlds is usually revealed by the alethic modal operators (a) when they show the presence of physically impossible beings in the fictional world (gods, spirits, monsters); (b) when selected natural-world persons are granted properties and action capacities that are not available to ordinary persons of that world: becoming invisible, flying on a carpet, etc.; (c) when inanimate objects are anthropomorphized (for example the legend of Don Juan in Alexander Pushkin's The Stone Guest.) The intermediate worlds are usually represented in dreams within a fictional world.
Deontic
DeonticDeontic logic
Deontic logic is the field of logic that is concerned with obligation, permission, and related concepts. Alternatively, a deontic logic is a formal system that attempts to capture the essential logical features of these concepts...
modal operators (P-operators) influence the construction of fictional worlds as proscriptive or prescriptive norms, i.e. they indicate what is prohibited, obligatory, or permitted in the fictional world. The deontic marking of actions is the richest source of narrativity; it generates the famous triad of the fall (violations of a norm – punishment), the test (obligation fulfilled – reward), and the predicament (conflict of obligations) stories. An example in literature of a story of the fall would be Mme. De Renal, in Stendhal
Stendhal
Marie-Henri Beyle , better known by his pen name Stendhal, was a 19th-century French writer. Known for his acute analysis of his characters' psychology, he is considered one of the earliest and foremost practitioners of realism in his two novels Le Rouge et le Noir and La Chartreuse de Parme...
’s Le Rouge et le Noir
The Red and the Black
Le Rouge et le Noir , 1830, by Stendhal, is a historical psychological novel in two volumes, chronicling a provincial young man’s attempts to socially rise beyond his plebeian upbringing with a combination of talent and hard work, deception and hypocrisy — yet who ultimately allows his passions to...
(1830). An example of a deontic alien in literature, a person who “exempts himself from the world’s codex and follows his own principles” is Raskolnikov, the protagonist of F.M. Dostoevsky’s Crime and Punishment
Crime and Punishment
Crime and Punishment is a novel by the Russian author Fyodor Dostoyevsky. It was first published in the literary journal The Russian Messenger in twelve monthly installments during 1866. It was later published in a single volume. This is the second of Dostoyevsky's full-length novels following his...
(1866).
Axiological
Axiological modal operators (G-operators) transform the world’s entities into values and disvalues as seen by a social group, a culture, or a historical period. Axiological modalities are highly subjective categories: what is good for one person may be considered as bad by another one. “Subjective abnegation of the world’s axiological order generates the story of the axiological alien” of which there are two kinds – the nihilistNihilist movement
The Nihilist movement was a Russian movement in the 1860s which rejected all authorities. It is derived from the Latin word "nihil", which means "nothing"...
and the axiological rebel. A nihilist negates the axiological order of the world and replaces it with a subjective axiology with a single operator: indifference. An example of the nihilist axiological alien in literature is Pechorin, the protagonist of Mikhail Lermontov
Mikhail Lermontov
Mikhail Yuryevich Lermontov , a Russian Romantic writer, poet and painter, sometimes called "the poet of the Caucasus", became the most important Russian poet after Alexander Pushkin's death in 1837. Lermontov is considered the supreme poet of Russian literature alongside Pushkin and the greatest...
’s A Hero of Our Time
A Hero of Our Time
A Hero of Our Time is a novel by Mikhail Lermontov, written in 1839 and revised in 1841. It is an example of the superfluous man novel, noted for its compelling Byronic hero Pechorin and for the beautiful descriptions of the Caucasus...
(1839).
Epistemic
Epistemic modal operators (K-operators) reflect the level of knowledge, ignorance and belief in the fictional world. The epistemic imbalance in the fictional world of a story produces a “mystery story,” which is usually the basic model of detective fictionDetective fiction
Detective fiction is a sub-genre of crime fiction and mystery fiction in which an investigator , either professional or amateur, investigates a crime, often murder.-In ancient literature:...
. Epistemic code can also be perceived at the core of the Bildungsroman
Bildungsroman
In literary criticism, bildungsroman or coming-of-age story is a literary genre which focuses on the psychological and moral growth of the protagonist from youth to adulthood , and in which character change is thus extremely important...
, where the protagonist undergoes a transformation from ignorance (of self) to knowledge (of self). An example of such transformation in German literature would be J.W. Goethe’s Wilhelm Meister's Apprenticeship
Wilhelm Meister's Apprenticeship
Wilhelm Meister's Apprenticeship is the second novel by Johann Wolfgang von Goethe, published in 1795-96. While his first novel, The Sorrows of Young Werther, featured a hero driven to suicide by despair, the eponymous hero of this novel undergoes a journey of self-realization...
(1795).
Examples
- In the alethic modal logicModal logicModal 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...
of C.I. LewisClarence Irving LewisClarence Irving Lewis , usually cited as C. I. Lewis, was an American academic philosopher and the founder of conceptual pragmatism. First a noted logician, he later branched into epistemology, and during the last 20 years of his life, he wrote much on ethics.-Early years:Lewis was born in...
, the modal operator
expresses necessity: if the proposition A is read as "it is true that A holds", the proposition 
A is read as "it is necessarily true that A holds". - In the tense logic (more commonly now called temporal logicTemporal logicIn logic, the term temporal logic is used to describe any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time. In a temporal logic we can then express statements like "I am always hungry", "I will eventually be hungry", or "I will be hungry...
) of A.N. PriorArthur PriorArthur Norman Prior was a noted logician and philosopher. Prior founded tense logic, now also known as temporal logic, and made important contributions to intensional logic, particularly in Prior .-Biography:Prior was entirely educated in New Zealand, where he was fortunate to have come under the...
, the proposition A is read as "A is true at the present time"; F A, as "A will be true at some time in the future"; and G A, as "A is true now and will always be true". - The previous two examples are of unaryUnary* Unary numeral system, the simplest numeral system to represent natural numbers* Unary operation, a kind of mathematical operator that has only one operand* Unary coding, an entropy encoding that represents a number n with n − 1 ones followed by a zero...
or monadicMonad (category theory)In category theory, a branch of mathematics, a monad, Kleisli triple, or triple is an functor, together with two natural transformations...
modal operators. As an example of a dyadicDyadicDyadic may refer to:*Adicity of a mathematical relation or function *Dyadic communication* Dyadic counterpoint, the voice-against-voice conception of polyphony...
modal operator—which produces a new proposition from two old propositions—is the operator P in the dyadic deontic logicDeontic logicDeontic logic is the field of logic that is concerned with obligation, permission, and related concepts. Alternatively, a deontic logic is a formal system that attempts to capture the essential logical features of these concepts...
of G.H. von WrightGeorg Henrik von WrightGeorg Henrik von Wright was a Finnish philosopher, who succeeded Ludwig Wittgenstein as professor at the University of Cambridge. He published in English, Finnish, German, and in Swedish. Belonging to the Swedish-speaking minority of Finland, von Wright also had Finnish and 17th-century Scottish...
. P(A,B) expresses that "A is obligatory under the circumstances B".