4. LANGUAGE AND LOGIC

Outline

 

James Fieser, UT Martin

updated 9/1/2023

 

This chapter explores some of the logical aspects of statements in natural languages such as English.

 

A. FOUR GRAMMATICAL FORMS OF LANGUAGE

 

We express ourselves in sentences, where a sentence is an utterance that conveys a complete thought. Grammarians commonly designate four types of forms that our sentences take: declarative, interrogative, imperative, and exclamatory.

 

1. Declaratives: such and such is the case

e.g., "the time now is 2:00"

e.g., "you are standing on my foot"

e.g., "I have a headache"

 

2. Interrogatives: questions

e.g., "what time is it?"

e.g., "is there a reason why you are standing on my foot?"

e.g., "can you give me something for this headache?"

 

3. Imperatives: commands, do X

e.g., "get that done by 2:00"

e.g., "get off my foot"

e.g., "please give me something for this headache."

 

4. Exclamatories: exclamations

e.g., "2:00!"

e.g., "my foot!"

e.g., "oh, my aching head!"

 

B. FOUR FUNCTIONS OF LANGUAGE

 

Aside from the form of language, there is also the function, which is how we use sentences to accomplish different purposes, and there are four such functions: to inform, to express, to direct, and to perform. The four above forms of sentences are not identical to these four functions, and, each of the four forms can be used for several different functions. Imagine, for example, that the waiter at a restaurant was a robot which was programmed to understand the four forms of sentences, but not their functions. You then say "I’d like a cup of coffee." This is in the declarative form and, for all the robot knows, you are just informing it of some fact, that is, the fact that you would like a cup of coffee. So the robot would just stand there. But behind the declarative form of that sentence is a directive for the robot to perform some action, namely, to get you a cup of coffee. Central to the function of language is the implied meaning, regardless of what form an uttered sentence might take.

 

1. Informative (assertions): to communicate information, affirm or deny propositions, present arguments.

Often in the form of declarative sentences.

e.g., "I have a headache" (declarative form)

e.g., "Did you know that I have a headache?" (interrogatory form)

e.g., "Oh, my aching head!" (exclamatory form)

 

2. Expressive (emotion): to vent or arouse feelings.

Often in the form of exclamatories.

e.g., "O my Love’s like a red, red rose" (exclamatory form)

e.g., "That’s too bad" (declarative form)

e.g., "It’s nice to meet you" (declarative form)

e.g., "Go to the devil" (imperative form)

 

3. Directive (command): to cause or prevent overt action.

Often in the form of imperatives or interrogatories.

e.g., "Get off my foot" (imperative form)

e.g., "You are on my foot" (declarative form)

e.g., "Is there a reason why you are standing on my foot?" (interrogative form)

e.g., "My foot!" (exclamatory form)

 

4. Performative: to perform something through words (speech acts, illocutionary acts).

Technically, all three of the above functions are performative in that the utterances in and of themselves do something (e.g., I hereby inform you that the door is brown, I hereby request that you tell me what time it is). But, performative utterances are more overtly about the words, such as "with these words I hereby x", such as to make something, start something, or claim something. Often in the form of declarative sentences (e.g., "I hereby sentence you to 1 day in the county jail). However, they can also be in the imperative or exclamatory form.

e.g., "I promise to return this" (declarative form)

e.g., "I now pronounce you husband and wife" (declarative form)

e.g., "You have the right to remain silent" (declarative form)

e.g., I claim this continent in the name of Lord Keg-Chugger (declarative form)

e.g., I confer on you all the rights and benefits thereof (declarative form)

e.g., I call firsties! (declarative form)

e.g., "Satan be gone!" (imperative form)

e.g., Let the games begin! (imperative form)

e.g., Bingo! (exclamatory form)

 

5. Historical Note: Logical Positivism and ethical emotivism

A movement in twentieth-century ethical theory called emotivism draws on the critical distinction between the form and function of language. It maintains that declarative ethical statements such as "John is good" in fact have no informative function, but instead have merely expressive and directive functions. That is, "John is good" merely expresses the speaker’s emotional approval of John, essentially meaning "hooray for John", and it also directs others to approve of John’s conduct, essentially meaning "you too should approve of John". Similarly, the declarative statement "Abortion is wrong" means "boo for abortion" (expressive) and "you should disapprove of abortion" (directive).

 

C. THREE TYPES OF DISPUTES

 

Disputes, or disagreements among people, are common in all walks of life. With trivial matters, such as whether a movie was a good or a bad one, we argue for the sake of arguing, and don’t particularly care whether the matter gets settled. With more serious matters, such as how to stop global warming, we might hope to find some resolution or consensus. Often we don’t, though, and part of the cause is failing to distinguish between different types of disputes. Some involve facts, others are merely verbal, and yet others rest on deeply held values.

 

1. Factual dispute: disagreeing about whether some event happened, or something is true. These can be resolved by determining the facts, such as through scientific inquiry, unless the facts aren’t known, such as with past events lost in history.

e.g., (a) "Illinois is east of Indiana"; (b) "no it is west of Indiana"

e.g., (a) "We were told to be there at 3:00"; (b) "no, it was 4:00"

e.g., (a) "Mom cooked chicken last night; (b) "no, she cooked snake"

e.g., (a) "Oswald acted alone when killing JFK"; (b) "no he was part of a conspiracy" (disagreement over facts that are inaccessible)

 

2. Verbal (terminological) dispute: disagreement about the use of an ambiguous term; the dispute can be resolved by clarifying the ambiguous term.

e.g., (a) "Bob lives far away; it took two hours to walk to his home"; (b) "no, Bob lives close; it took ten minutes to drive there" (verbal disagreement over the term "far away" regarding walking vs. driving)

e.g., (a) "Joe is an excellent student; he takes a lively interest in everything and asks intelligent questions in class"; (b) "no, Joe is not an excellent student; he never gets his assignments in on time" (verbal disagreement over the term "excellent student" and its criteria)

e.g., (a) "All humans are created equal"; (b) "no, we all have unique DNA" (verbal disagreement over the term "equal" and its political vs. biological meanings)

e.g., (a) "I bought a new house"; (b) "no, it was built 20 years ago" (verbal disagreement over the term "new" regarding time of acquisition vs. time of construction)

e.g., From William James: a hunter chases a squirrel around a tree, but the two are always on opposite sides: they both go around the tree, but does the hunter go around the squirrel? James’s answer: "If by ‘going around’ you mean ‘going east, south, west, north, east, etc.,’ then the man certainly goes around the squirrel. But if by 'going around' you mean ‘going from side to back to side to belly to side, etc.’ then the man does not go around the squirrel."

e.g. (a) "Joe is tall, much more so than his father;" (b) "no, Joe is not tall; his father is exceptionally short" (verbal disagreement over the term "tall" and whether it is relative to his Joe's father or an average person)

 

3. Value dispute: disagreement about major value assumptions and fundamental world-life outlooks that are largely unprovable, such as in religion, ethics, aesthetics, political ideology, economic ideology, metaphysics. These typically cannot be resolved by establishing empirical facts or clarifying terminology. The school of Logical Positivism (discussed above) describes value statements as pseudo-propositions, which do not involve actual facts about the world. On this view, while such disputes may appear to involve factual matters, they actually do not, and thus constitute a value dispute rather than a factual dispute.

e.g., (a) "Lou Reed was a musical visionary"; (b) "no, he was just an untalented rebel" (disagreement in value over musical aesthetics)

e.g., (a) "The pay for this job is reasonable"; (b) "no, the pay for this job is exploitive" (disagreement in value over economic fairness)

e.g., (a) "My parents are in heaven"; (b) "no they’re not because there is no heaven" (disagreement in value about the existence of heaven)

e.g., (a) "Beth and Jill just got married;" (b) "no they didn’t, marriage is only between a man and a woman." (disagreement in value about the nature of true marriage)

e.g., (a) "The President’s welfare policies will reduce poverty;" (b) "no, they will destroy our capitalist economy and ultimately put us all in poverty" (disagreement in value about welfare and capitalism)

e.g., (a) "I freely chose to major in business"; (b) "no, your parents nagged you into it, and that’s not a free choice" (disagreement in value about free will)

e.g., (a) "My dog is demon possessed" (b) "dude, you watch too many horror movies; everyone knows that demons only possess people" (disagreement in value about demon possession)

 

4. Combination disputes: disputes that have some mixture of factual, verbal, and value disagreement.

e.g., (a) "You were fired because of your poor work performance"; (b) "no, my work performance was fine, I was fired because my supervisor didn’t like me" (disagreement in terminology over "work performance", and disagreement in fact over why he was fired)

e.g., (a) "I went to the God Boy concert last night and it was heaven!" (b) "as I’ve argued with you before, heaven doesn’t exist, so it follows that you didn’t go to the concert, which is just as well since those religious bands are awful" (factual disagreement over whether he went to the concert, verbal disagreement over the word "heaven", and value disagreement over the quality of religious bands)

 

D. DEFINITIONS

 

Many arguments or disputes rest on the definitions of key terms, and whether a given definition is a good or bad one. The task of defining a word is a complex one and involves differing purposes and techniques.

 

1. Parts of definitions

Definiendum (di-fin-ee-EN-dum): the term to be defined

Definiens (di-fin-ee-ENS): the definition

e.g., "triangle (defiendum) means three sides (definiens)]

 

2. Purposes of Definitions

a. Lexical: designates meaning by showing how English-speaking people use a word as based on statistical usage.

e.g., "mountain" means a large mass of earth or rock rising to a considerable height above the surrounding country

e.g., "robot" means a machine capable of carrying out a complex series of actions automatically, especially one programmable by a computer.

e.g., "cat" means a small domesticated carnivorous mammal with soft fur, a short snout, and retractile claws.

e.g., "microphone" is an instrument for converting sound waves into electrical energy variations, which may then be amplified, transmitted, or recorded

b. Precising: designates meaning by clarifying vague ordinary usage with a more precise meaning.

e.g., "moral right" is a justified constraint upon how others may act

e.g., "poor" means earning less than $15,000 a year

e.g., "crime" is an action or omission that constitutes an offense that may be prosecuted by the state and is punishable by law

c. Theoretical: designates meaning by indicating how a word is used in some presupposed theory; these are even narrower than precising definitions, and often refer to a single theory

e.g., "heat" is a form of energy in a body involving the irregular motion of its molecules

e.g., "Bourgeoisie" for Marx means the capitalist class who own most of society's wealth and means of production

d. Stipulative: designates meaning by proposing a new meaning of a term; these typically indicate that the new definition is for a specific or limited purpose.

e.g., "G factor" for the purposes of this experiment means intelligence

e.g., by "guest" I mean anyone who I formally invite to my exclusive party

e.g., the word "sinner", for our cult, means anyone who has not recited the Sacred Creed of Credulity

e. Persuasive definition: designates meaning with the purpose of influencing attitudes.

e.g., "abortion" is the murdering of the innocent unborn children.

e.g., "Politics" is derived from the words "poly" meaning "many", and "tics" meaning "blood-sucking parasites."

e.g., "faith" means believing something that you know is not true.

e.g., "blonde jokes" refer to jokes that are easy enough for men to understand.

e.g., "committee" means a body that keeps minutes and wastes hours.

e.g., "student loan" refers to a mystical transaction in which students subject themselves to life-long financial slavery.

 

3. Techniques of Definition

a. Extensional (denotative): designates meaning by indicating members that belong to a class of objects.

Ostensive (demonstrative): designates meaning by demonstrating an object, such as by pointing to something.

e.g., that object over there is a desk

e.g., look at where I’m pointing, that object is a computer chip

e.g., look directly at me, what you see is an eyeball

Limitations: cannot tell what exactly is referred to

Enumerative: designates meaning by listing objects that belong to a class.

e.g., "planet" means Mercury, Venus, Earth, Mars, etc.

e.g., "romance language" means Spanish, Portuguese, French, Italian, Romanian, etc.

e.g., "robot" means things like R2-D2, C-3PO, Optimus Prime, etc.

Limitations: lists may be incomplete, two lists might be identical

b. Intensional (connotative): designates meaning by indicating a set of characteristics agreed to be common to all objects being defined.

Synonymous: designates meaning by indicating how two words have the same meaning.

e.g., "voracious" means insatiable

e.g., "hat" means headwear

e.g., "boast" means brag

Genus and difference: designates meaning by first indicating a class that an object belongs to, and second a distinguishing feature of that object.

e.g., "triangle" means polygon with three sides

e.g., "planet" means a celestial body moving in an elliptical orbit around a star

e.g., "beauty" means a combination of qualities, such as shape, color, or form, that pleases the aesthetic senses, especially the sight

Etymological: designates meaning by explaining the historical origin of a word.

e.g., "philosophy" means love of wisdom in the original Greek

e.g., "robot" comes from the Czech word "robota" meaning forced labor

e.g., "psychology" means study of the soul in the original Greek

Functional: designates meaning by indicating the purpose of an object; these are often genus and difference definitions, with the function indicated in the difference.

e.g., "hammer" is an instrument made for pounding nails into a solid surface

e.g., "telescope" is an instrument made for making distant objects appear closer

e.g., "picture frame" is an instrument made to hold and display photographs and other two-dimensional representations

Operational: designates meaning by specifying a repeatable procedure, often through some test.

e.g., "genius" means a score above 140 on the Stanford Binet intelligence scale

e.g., "profound hearing loss" means the inability to hear sounds lower than 95 dB

e.g., "antique" means over 100 years old

 

4. Five Rules of Good Lexical Definitions

a. Should state the essential attributes of the object, not accidental attributes.

Good examples (have essential attributes)

e.g., "man" is a rational animal

e.g., "wealth" is the measure of the value of all of the assets of worth owned by a person or entity

e.g., "triangle" is a three-sided rectilinear figure

e.g., "school" is an institution for education

Bad examples (have only accidental attributes)

e.g., "man" is a cooking animal

e.g., "wealth" is the power to purchase fine clothing

e.g., "magnesium" is a metal capable of ignition

e.g., "Tree" is a vegetable organism, having roots, branches, leaves, etc.

b. Must not be circular.

e.g., "man" is the sole occupier of the class of human beings

e.g., "wealth" is that which makes one wealthy

e.g., "bed" means an object suitable for bedding

e.g., "sleep deprivation" is the condition of not having enough sleep

e.g., "virtue" means acting virtuously

c. Must be neither too broad nor too narrow.

Too broad

e.g., "man" is a featherless biped (includes plucked chickens)

e.g., "wealth" is that which has value to an individual (includes non-economic goods like sleep)

e.g., "spelt" is a kind of food (includes all food)

e.g., "eloquence" is the power of influencing the feelings by speech or writing (includes threats or profanity)

Too narrow

e.g., "man" is a civilized rational animal (excludes uncivilized and irrational humans)

e.g., "wealth" consists of money (excludes non-monetary economic value)

e.g., "shoe" is a leather covering for the foot (excludes canvass shoes)

e.g., "logic" is a machine for combating fallacy (excludes formal symbolic logic)

d. Must not be ambiguous or figurative.

e.g., "man" is the only animal who blushes—or needs to

e.g., "wealth" consists of having few wants

e.g., "net" refers to a reticulated fabric made with interstitial vacuities

e.g., "soul" is the first entelechy of the natural body

e.g., "bread" is the staff of life

e.g., "life" is a continuous adjustment of internal relations to external relations

e.g., "architecture" is frozen music

e.g., "body" is the visible garment of the soul.

e. Should not be negative where it can be affirmative.

e.g., "man" is neither angel nor beast but stands between the two

e.g., "wealth" is the lack of poverty

e.g., "couch" is not a bed and not a chair

e.g., "Turanian language" is one which is neither Aryan nor Semitic

 

E. PHILOSOPHY OF LANGUAGE (bonus material, not included on test)

 

Philosophers since ancient Greece had theorized about the nature of language, but the subject of "the philosophy of language" as we know it today emerged in the early twentieth-century. Much of this is intertwined with concepts in contemporary logic.

 

1. Theories of Meaning: A central issue within the philosophy of language is the relationship between language and meaning: how it is that verbal utterances or scribbles on paper convey meaning that we understand. Now, "meaning" is not the same as "truth": something is true when it reflects reality as it is, whereas something is meaningful when it is simply understandable. Take the sentence, "the Statue of Liberty is in New York City": this is both meaningful and true. However, the sentence "the Statue of Liberty is in Washington DC" is meaningful, yet is false. Meaningfulness, then, is the broader concept, and an adequate theory of meaning will need to account for both true and false statements. We will look at eight such theories of meaning.

 

a. Referential theory of meaning (Mill): the meaning of a linguistic utterance is how it stands for things in the world.

e.g., "the cat is on the table" stands for an actual cat being on an actual table.

Map: utterance > the world

Criticism: some meaningful words do not denote actual objects, e.g., "Easter Bunny", "The present King of France".

b. Ideational theory of meaning (Locke): the meaning of a linguistic utterance resides in the ideas within the speaker's mind.

e.g., "the cat is on the table" reflects the mental image I have of a particular cat being on a particular table.

Map: utterance > mental image

Criticism: Some meaningful words have no particular mental image or content associated with them, e.g., "is", "of", "and".

c. Proposition theory of meaning (Russell): the meaning of a linguistic utterance are propositions (i.e., abstract objects that are independent of human language and mental states, and are either true or false expressions of affairs).

e.g., "the cat is on the table" expresses a proposition about a specific cat being on a specific table.

Map: utterance > unambiguous logical paraphrase > propositions

Criticism: propositions are strange metaphysical objects, since they are eternal and existed before the creation of the world (a requirement if they are universally graspable by any rational creature).

d. Language use (game) theory of meaning (Wittgenstein): the meaning of a linguistic utterance is established within the context of its use or social practice (like rules of a game that we learn, i.e., a language game).

e.g., "the cat is on the table" is understood within specific contexts where we where someone might ask "where is the cat", or "what is on the table".

Map: utterance > social practice

Criticism: we could know the rules of the language game without understanding what it means, e.g., I might know the rules of a religious ritual or liturgy, without understanding what it means.

e. Communicative intention theory of meaning (Grice): the meaning of a linguistic utterance is the psychological intention of the speaker ("speaker-meaning"; by uttering x, S meant that P).

e.g., "the cat is on the table" expresses the speaker's intention that the hearer form a belief that the cat is on the table.

Map: utterance > speaker's psychological intention

Criticism: Sentences are often used to express meanings that aren't literal, e.g., figurative speech, sarcasm, subtext, secret codes.

f. Verification theory of meaning (logical positivism): the meaning of a linguistic utterance is the future experience that shows its truth (verification condition; epistemic account of meaning).

e.g., "the cat is on the table" is meaningful since we can verify it by petting the cat on the table.

e.g., "Everything, including all measuring devices, has just doubled in size" is meaningless since its truth cannot be verified.

Map: utterance > future verifying experience

Criticism: the theory applies only to propositional utterances (expressions that state facts), not non-propositional utterances like questions, commands, expressions of feelings, jokes, ceremonial language.

g. Truth-condition theory of meaning (Davidson): the meaning of a linguistic utterance is based on the truth-value of a representative logical proposition insofar as it corresponds to the factual world.

e.g., "the cat is on the table" (in English) means that the cat is on the table in the factual world (with its truth value indicated in propositional logic).

Map: utterance > unambiguous logical paraphrase > the world

Criticism: many meaningful sentences don't have truth conditions, e.g., questions, commands, expressions of feelings.

h. Possible world theory of meaning (Kripke): the meaning of a linguistic utterance is its relation to the truth values they take in all possible worlds ("possible world semantics").

e.g., "the cat is on the table" means the cat is on the table in one set of possible worlds, but not in another set.

Map: utterance > unambiguous logical paraphrase > possible worlds

Criticism: possible worlds are strange metaphysical objects, similar to the strangeness of propositions. They are not simply metaphors, but seem to be actual alternative worlds that do not actually exist.

 

2. Other Concepts and Terms in the Philosophy of Language.

 

a. Linguistic utterances/expressions/sentences: verbal marks or noises, e.g., "asdfjkl" (gibberish), "car chair cat" (meaningful words), "the cat is on the table" (meaningful sentences).

b. Singular vs. general terms: two ways utterances designate objects.

• Singular terms: utterances that designate particular individual people, places, or other objects; e.g. "Joe" (proper name), "the man with three eyes" (definite description).

• General terms: utterances that can designate more than one thing; e.g., "car", "chair".

c. Syntax vs. semantics: two ways of examining expressions.

• Syntax: the rules of grammar in languages like English or propositional logic for combining expressions into well-formed sentences, such as the rule prohibiting sentence fragments.

• Semantics: the meaning of those expressions.

d. Lexical meaning vs. sentence meaning: two types of meaningful expressions.

• Lexical meaning: the meaning of a word or short phrase.

• Sentence meaning: the meaning of a full sentence.

e. Sense vs. reference (Frege): two different ways expressions might have meaning.

• Sense: the thought expressed by a sentence; e.g., "Batman" is the superhero in Gotham City who dresses like a bat.

• Reference: the object indicated by the expression; e.g., "Batman" is the person Bruce Wayne.

e.g., "Hesperus" and "Phosphorus". In Greek mythology, these were names given respectively to "the morning star" and "the evening star" (i.e., the first and last stars to appear in the night sky). Later it was discovered that they were both the planet Venus. Thus, the sense of "Hesperus" is the "morning star" (and "Phosphorus" the "evening star"), but the reference is the planet Venus. So too with the statement "Jane believes that Hesperus is currently shining, but Phosphorus is not shining." This sentence is about Jane's belief regarding the sense of the two stars, not the reference.

f. The principle of substitutivity (salva veritate, Leibniz's law): two expressions may be interchanged if they do not alter the truth-value of statements in which the expressions occur (non-intensional propositions might be substitutable, but intensional propositions are not)

g. Propositional attitude: a mental state held by an agent toward a proposition P; e.g., Jane believes P, disbelieves P, likes P, dislikes P, hopes P, fears P.

h. Rigid vs. non-rigid designator (Kripke): two ways singular terms designate objects in possible worlds

• Rigid designator: a term that designates the same object in all possible worlds in which that object exists; e.g., "water" and "H2O".

• Non-rigid designator: a term that designates different objects in different possible worlds; e.g., the forty-fifth president of the U.S., which in some possible world was Hillary Clinton.

i. Linguistic pragmatics: the semantic study of how linguistic expressions are used in social contexts.

• Semantic pragmatics: the content of expressions varies in different contexts because of pronouns and tense; e.g., "I am happy now" changes depending on who "I" is and when "now" is.

• Pragmatic pragmatics: assumes the semantic content of an expression; e.g., "I am happy now", but examines wider questions about context, such as what "happy" means in different social contexts.

j. Speech acts (illocutions): a linguistic expression that accomplishes some action, e.g., requests, warnings, invitations, promises, apologies, predictions.

• Performatives: speech acts that are in the first person, present tense, e.g., "I pronounce you husband and wife"

• Three forces of speech acts: the locutionary force is the utterance ("I'm warning you"), the illocutionary force is the implied action (to stop doing something), and the  perlocutionary force is the effect  (to persuade or scare).

 

F. LINGUISTIC CONCEPTS IN OLD LOGIC BOOKS (bonus material, not included on test)

 

The above issues concerning language and logic are of comparatively recent interest to logicians, and commonly appear in introductory logic books today. However, for much of logic's 2,000-plus year history, Aristotle's system dominated, and older discussions of language and logic drew on this. During the nineteenth-century, a new set of linguistic concepts was introduced into logic, most notably in John Stuart Mill's A System of Logic (1843), and these began appearing in introductory logic books of the time along with the Aristotelean concepts. Both Aristotle's and Mill's discussions are obsolete from the perspective of recent logic, but they remain important in the history of philosophy.

 

1. Aristotelean concepts

a. Laws of Thought (from Aristotle's Metaphysics)

The Law of Identity: A is A (e.g., Bob is Bob)

The Law of Contradiction: A is not not-A (e.g., it is not the case that Bob is not-Bob)

The Law of Excluded Middle: Everything is either A or not-A (e.g., everything is either Bob or not-Bob)

Later additions:

The Law Causation (or sufficient reason): every event must have a cause

The Law of the Uniformity of Nature: the same antecedents are invariably followed by the same consequents

b. Predicables (from Aristotle's Categories, modified in middle ages)

Predicable: ways that predicates stand in relation to subjects (that which can be predicated)

Five predicables

Genus: a term which refers to two or more subordinate classes, e.g., "man"

Species: an attribute that represents one of the subordinate classes in a genus, e.g., English man, French man

Differentia: an attribute that distinguishes one species from another,

Property: an attribute that helps make a term what it is

Accident: an attribute that does not help make a term what it is

Examples

This trigon (species) is a polygon (genus) of three sides (differentia) and three angles (property) the sum of the angles being equal to two right angles (accident)

A moonbeam (species) is a ray of light (genus) from the moon (differentia)

A dwelling (species) is a building (genus) where people live (differentia)

c. Meaning of terms (from Aristotle's Categories)

Univocal words: have only one meaning, often technical terms, e.g., molecule, angle, vertebrate

Equivocal words: have more than one meaning, e.g., "bit" means morsel or part of a horse’s harness

Analogical: meanings are partly, but not wholly the same, e.g., "love" where king loves subjects as parent loves children

 

2. Kinds of terms (from John Stuart Mill's System of Logic)

a. Abstract-concrete

Abstract: quality or relation taken apart from its setting, e.g., sweetness, equality

Concrete: person or thing or group of them, e.g., man, animal

b. Singular-general

Singular: applies to only one thing, e.g., large dictionary in this room,

General: applies to any number of things, e.g., dog, holidays, member of congress,

Collective: lose sight of individual members, e.g., Army, family, tribe,

c. Absolute-relative

Absolute: object considered by itself, e.g., stone, building,

Relative: meaning in relation to something else, e.g., shepherd, patient,

d. Positive-negative

Positive: implies the presence of a quality, e.g., heavy, efficient,

Negative: implies the absence of a quality, e.g., light, inefficient,

Privative: absence of a quality usually present, e.g., maimed, blind, orphaned

e. Connotative and non-connotative words

Connotative: a term that denotes a subject and implies an attribute, e.g., "man" denotes subjects and implies the attribute of rationality

Non-connotative: a term that denotes a subject but does not imply an attribute e.g., "blueness"

f. Extension and intention of terms

Extension: refers to objects that the term stands for, e.g., isosceles triangle, scalene triangle

Intension: refers to the attributes that the term stands for, e.g., three-sided and three-angled