On Interpretation
Encyclopedia
Aristotle
's De Interpretatione (the Latin
title by which it is usually known) or On Interpretation (Greek
Περὶ Ἑρμηνείας or Peri Hermeneias) is one of the earliest surviving philosophical works in the Western tradition
to deal with the relationship between language and logic in a comprehensive, explicit, and formal way.
The work begins by analyzing simple categoric propositions, and draws a series of basic conclusions on the routine issues of classifying and defining basic linguistic forms, such as simple terms and propositions, nouns and verbs, negation
, the quantity of simple propositions (primitive roots of the quantifiers in modern symbolic logic), investigations on the excluded middle (what to Aristotle isn't applicable to future tense propositions — the Problem of future contingents), and on modal proposition
s.
The first five chapters deal with the terms that form propositions. Chapters 6 and 7 deal with the relationship between affirmative, negative, universal and particular propositions. These relationships are the basis of the well-known Square of opposition
. The distinction between universal and particular propositions is the basis of modern quantification theory. The last three chapters deal with modalities
. Chapter 9 is famous for the discussion of the sea-battle. (If it is true that there will be a sea-battle tomorrow, then it is true today that there will be a sea-battle. Thus a sea-battle is apparently unavoidable, and thus necessary. Another interpretation would be: that we can not know that which has not yet come to pass. In other words: if there is a sea battle tomorrow then it is true today that tomorrow there will be a sea battle. So, only if we can know whether or not there will be a sea battle tomorrow then can we know if there will be a sea battle).
De Interpretatione is (the second) part of the Organon
, Aristotle's collected works on logic
.
Chapter 2. A noun signifies the subject by convention, but without reference to time (i.e. 'Caesar' signifies the same now, two thousand years after his death, as it did in Roman times).
Chapter 3. A verb carries with it the notion of time. 'He was healthy' and 'he will be healthy' are tenses of a verb. An untensed verb indicates the present, the tenses of a verb indicate times outside the present.
Chapter 4. The sentence is an expression whose parts have meaning. The word 'man' signifies something, but is not a sentence. Only when words are added to it do we have affirmation and negation.
Chapter 5. Every simple proposition contains a verb. A simple proposition indicates a single fact, and the conjunction of its parts gives a unity. A complex proposition is several propositions compounded together.
Chapter 6. An affirmation is an assertion of something of something, a denial an assertion denying something of something. (For example, 'a man is an animal' asserts 'animal' of 'man'. 'A stone is not an animal' denies 'animal' of stone').
Chapter 7. Terms. Some terms are universal. A universal term is capable of being asserted of several subjects (for example 'moon' - even though the Earth has one moon, it may have had more, and the noun 'moon' could have been said of them in exactly the same sense). Other terms are individual. An individual or singular term ('Plato') is not predicated (in the same) sense of more than one individual.
A universal affirmative proposition, such as, 'Every man is white' and a universal negative proposition having the same subject and predicate, such as, 'No man is white,' are called contrary. A universal affirmative proposition ("Every man is white") and the non-universal denial of that proposition in a way ("Some man is not white") are called contradictories. Of contradictories, one must be true, the other false. Contraries cannot both be true, although they can both be false, and hence their contradictories are both true (for example, both, 'Every man is honest,' and 'No man is honest,' are false. But their contradictories, 'Some men are not honest,' and, 'Some men are honest,' are both true.
Chapter 8. An affirmation is single, if it expresses a single fact. For example 'every man is white'. However, if a word has two meanings, for example if the word 'garment' meant 'a man and a horse', then 'garment is white' would not be a single affirmation, for it would mean 'a man and a horse are white', which is equivalent to the two simple propositions 'a man is white and a horse is white'.
Chapter 9. Of contradictory propositions about the past, one must be true, the other false. But when the subject is individual, and the proposition is future, this is not the case. For if so, nothing takes place by chance. For either the future proposition such as, 'A sea battle will take place,' corresponds with future reality, or its negation does, in which case the sea battle will take place with necessity, or not take place with necessity. But in reality, such an event might just as easily not happen as happen; the meaning of the word 'by chance' with regard to future events is that reality is so constituted that it may issue in either of two opposite possibilities. This is known as the problem of future contingents.
Chapter 10. Aristotle enumerates the affirmations and denials that can be assigned when 'indefinite' terms such as 'unjust' are included. He makes a distinction that was to become important later, between the use of the verb 'is' as a mere copula or 'third element', as in the sentence 'a man is wise', and as a predicate signifying existence, as in 'a man is [i.e. exists]'.
" or "square of Apuleius" has its origin in the four marked sentences to be employed in syllogistic reasoning, as follows:
Robert Blanché
published with Vrin his Structures intellectuelles in 1966, and since then, many scholars think that the logical square representing four values should be replaced by the logical hexagon
which by representing six values is a more potent figure because it has the power to explain more things about logic and natural language. The study of the four propositions constituting the square is found in Chapter 7 and its appendix, Chapter 8. Most important also is the immediately following Chapter 9, dealing with the problem of future contingents. This chapter and the subsequent ones are at the origin of modal logic
. Perhaps Blanché's hexagon is particularly useful in the domain of modal logic, in so far as it explains clearly the nature and importance of the bilateral possible. The notion of "bilateral possible" is crucially important to understand both logic and natural language when applied to modal values.
Another translation was completed by Boethius in the 5th century, c.510/512.
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
's De Interpretatione (the Latin
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...
title by which it is usually known) or On Interpretation (Greek
Ancient Greek
Ancient Greek is the stage of the Greek language in the periods spanning the times c. 9th–6th centuries BC, , c. 5th–4th centuries BC , and the c. 3rd century BC – 6th century AD of ancient Greece and the ancient world; being predated in the 2nd millennium BC by Mycenaean Greek...
Περὶ Ἑρμηνείας or Peri Hermeneias) is one of the earliest surviving philosophical works in the Western tradition
Western philosophy
Western philosophy is the philosophical thought and work of the Western or Occidental world, as distinct from Eastern or Oriental philosophies and the varieties of indigenous philosophies....
to deal with the relationship between language and logic in a comprehensive, explicit, and formal way.
The work begins by analyzing simple categoric propositions, and draws a series of basic conclusions on the routine issues of classifying and defining basic linguistic forms, such as simple terms and propositions, nouns and verbs, negation
Negation
In logic and mathematics, negation, also called logical complement, is an operation on propositions, truth values, or semantic values more generally. Intuitively, the negation of a proposition is true when that proposition is false, and vice versa. In classical logic negation is normally identified...
, the quantity of simple propositions (primitive roots of the quantifiers in modern symbolic logic), investigations on the excluded middle (what to Aristotle isn't applicable to future tense propositions — the Problem of future contingents), and on modal proposition
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...
s.
The first five chapters deal with the terms that form propositions. Chapters 6 and 7 deal with the relationship between affirmative, negative, universal and particular propositions. These relationships are the basis of the well-known Square of opposition
Square of opposition
In the system of Aristotelian logic, the square of opposition is a diagram representing the different ways in which each of the four propositions of the system are logically related to each of the others...
. The distinction between universal and particular propositions is the basis of modern quantification theory. The last three chapters deal with modalities
Linguistic modality
In linguistics, modality is what allows speakers to evaluate a proposition relative to a set of other propositions.In standard formal approaches to modality, an utterance expressing modality can always roughly be paraphrased to fit the following template:...
. Chapter 9 is famous for the discussion of the sea-battle. (If it is true that there will be a sea-battle tomorrow, then it is true today that there will be a sea-battle. Thus a sea-battle is apparently unavoidable, and thus necessary. Another interpretation would be: that we can not know that which has not yet come to pass. In other words: if there is a sea battle tomorrow then it is true today that tomorrow there will be a sea battle. So, only if we can know whether or not there will be a sea battle tomorrow then can we know if there will be a sea battle).
De Interpretatione is (the second) part of the Organon
Organon
The Organon is the name given by Aristotle's followers, the Peripatetics, to the standard collection of his six works on logic:* Categories* On Interpretation* Prior Analytics* Posterior Analytics...
, Aristotle's collected works on logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
.
Contents
Chapter 1. Aristotle defines words as symbols of 'affections of the soul' or mental experiences. Spoken and written symbols differ between languages, but the mental experiences are the same for all (so that the English word 'cat' and the French word 'chat' are different symbols, but the mental experience they stand for - the concept of a cat - is the same for English speakers and French speakers). Nouns and verbs on their own do not involve truth or falsity.Chapter 2. A noun signifies the subject by convention, but without reference to time (i.e. 'Caesar' signifies the same now, two thousand years after his death, as it did in Roman times).
Chapter 3. A verb carries with it the notion of time. 'He was healthy' and 'he will be healthy' are tenses of a verb. An untensed verb indicates the present, the tenses of a verb indicate times outside the present.
Chapter 4. The sentence is an expression whose parts have meaning. The word 'man' signifies something, but is not a sentence. Only when words are added to it do we have affirmation and negation.
Chapter 5. Every simple proposition contains a verb. A simple proposition indicates a single fact, and the conjunction of its parts gives a unity. A complex proposition is several propositions compounded together.
Chapter 6. An affirmation is an assertion of something of something, a denial an assertion denying something of something. (For example, 'a man is an animal' asserts 'animal' of 'man'. 'A stone is not an animal' denies 'animal' of stone').
Chapter 7. Terms. Some terms are universal. A universal term is capable of being asserted of several subjects (for example 'moon' - even though the Earth has one moon, it may have had more, and the noun 'moon' could have been said of them in exactly the same sense). Other terms are individual. An individual or singular term ('Plato') is not predicated (in the same) sense of more than one individual.
A universal affirmative proposition, such as, 'Every man is white' and a universal negative proposition having the same subject and predicate, such as, 'No man is white,' are called contrary. A universal affirmative proposition ("Every man is white") and the non-universal denial of that proposition in a way ("Some man is not white") are called contradictories. Of contradictories, one must be true, the other false. Contraries cannot both be true, although they can both be false, and hence their contradictories are both true (for example, both, 'Every man is honest,' and 'No man is honest,' are false. But their contradictories, 'Some men are not honest,' and, 'Some men are honest,' are both true.
Chapter 8. An affirmation is single, if it expresses a single fact. For example 'every man is white'. However, if a word has two meanings, for example if the word 'garment' meant 'a man and a horse', then 'garment is white' would not be a single affirmation, for it would mean 'a man and a horse are white', which is equivalent to the two simple propositions 'a man is white and a horse is white'.
Chapter 9. Of contradictory propositions about the past, one must be true, the other false. But when the subject is individual, and the proposition is future, this is not the case. For if so, nothing takes place by chance. For either the future proposition such as, 'A sea battle will take place,' corresponds with future reality, or its negation does, in which case the sea battle will take place with necessity, or not take place with necessity. But in reality, such an event might just as easily not happen as happen; the meaning of the word 'by chance' with regard to future events is that reality is so constituted that it may issue in either of two opposite possibilities. This is known as the problem of future contingents.
Chapter 10. Aristotle enumerates the affirmations and denials that can be assigned when 'indefinite' terms such as 'unjust' are included. He makes a distinction that was to become important later, between the use of the verb 'is' as a mere copula or 'third element', as in the sentence 'a man is wise', and as a predicate signifying existence, as in 'a man is [i.e. exists]'.
The square of opposition
The logical square, also called "square of oppositionSquare of opposition
In the system of Aristotelian logic, the square of opposition is a diagram representing the different ways in which each of the four propositions of the system are logically related to each of the others...
" or "square of Apuleius" has its origin in the four marked sentences to be employed in syllogistic reasoning, as follows:
- "Every man is white" - the universal affirmative;
- "Not every man is white" - negation, or "Some men are not white" - the particular negative on the one hand;
- "Some men are white" - the particular affirmative; and
- "No man is white" - the universal negative on the other.
Robert Blanché
Robert Blanché
Robert Blanché was an associate professor of philosophy at the University of Toulouse. He wrote many books addressing the philosophy of mathematics.-Works :...
published with Vrin his Structures intellectuelles in 1966, and since then, many scholars think that the logical square representing four values should be replaced by the logical hexagon
Logical hexagon
The logical hexagon is a conceptual model of the relationships between the truth values of six statements. It is an extension of Aristotle's square of opposition. It was discovered independently by both Augustin Sesmat and Robert Blanché.This extension consists in introducing two statements Y and U...
which by representing six values is a more potent figure because it has the power to explain more things about logic and natural language. The study of the four propositions constituting the square is found in Chapter 7 and its appendix, Chapter 8. Most important also is the immediately following Chapter 9, dealing with the problem of future contingents. This chapter and the subsequent ones are at the origin 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...
. Perhaps Blanché's hexagon is particularly useful in the domain of modal logic, in so far as it explains clearly the nature and importance of the bilateral possible. The notion of "bilateral possible" is crucially important to understand both logic and natural language when applied to modal values.
Translations
Aristotle's original Greek text, Περὶ Ἑρμηνείας (Peri Hermeneias) was translated into the Latin "De Interpretatione" by Marius Victorinus, at Rome, in the 4th century.Another translation was completed by Boethius in the 5th century, c.510/512.
See also
- Hermeneutics
- InterpretationInterpretation (logic)An interpretation is an assignment of meaning to the symbols of a formal language. Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation...
- SemeioticSemeioticSemeiotic is a spelling variant of a word used by Charles Sanders Peirce, likewise as "Semiotic," "Semiotics", and "Semeotic", to refer to his philosophical logic, which he cast as the study of signs, or semiotic. Some, not all, Peircean scholars have used "semeiotic" to refer to distinctly...
- SemiosisSemiosisSemiosis is any form of activity, conduct, or process that involves signs, including the production of meaning. Briefly – semiosis is sign process...
- SemioticsSemioticsSemiotics, also called semiotic studies or semiology, is the study of signs and sign processes , indication, designation, likeness, analogy, metaphor, symbolism, signification, and communication...
- SignSign (semiotics)A sign is understood as a discrete unit of meaning in semiotics. It is defined as "something that stands for something, to someone in some capacity" It includes words, images, gestures, scents, tastes, textures, sounds – essentially all of the ways in which information can be...
- Sign relationSign relationA sign relation is the basic construct in the theory of signs, also known as semeiotic or semiotics, as developed by Charles Sanders Peirce.-Anthesis:...
External links
- Text of On Interpretation, as translated by E. M. EdghillElla Mary EdghillElla Mary Edghill M.A. was a British translator known primarily for her translation of Categories which appeared in Volume 1 of the The Works of Aristotle series, edited by W. D. Ross and J. A. Smith. She was the daughter of Rev...
- Aristotle's De Interpretatione: Semantics and Philosophy of Language with an extensive bibliography of recent studies
- The Master Argument: The Sea Battle in De Intepretatione 9, Diodorus Cronus, Philo the Dialectician with a bibliography on Diodorus and the problem of future contingents
- Sea Battle Hub, a tutorial introduction to the discussion of the truth status of future events from De Interpretatione 9.
- Audiobook of On Interpretation, as translated by Octavius Owen (Public Domain).
- Jules VuilleminJules VuilleminJules Vuillemin was a French philosopher, succeeding to Maurice Merleau-Ponty at the Collège de France from 1962 to his death. A friend of Michel Foucault, he supported his election at the College, and was also close to Michel Serres...
, "Le chapitre IX du De Interpretatione d'Aristote - Vers une réhabilitation de l'opinion comme connaissance probable des choses contingentes, in Philosophiques, vol. X, n°1, April 1983