LANGUAGE AND LOGIC

 

LANGUAGE FORM AND FUNCTION

 

Four grammatical forms of language

We express ourselves in sentences, where a sentence is an utterance that convey complete thought. Grammarians commonly designated 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!”

Four functions of language

Aside from the form of language, there is also the function, which is how we 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 a 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 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): communicates information, affirms or denies propositions, presents 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: illocutionary acts where the words perform something

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 make something, start something, or claim something

Often in the form of declarative sentences

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)

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).

 

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 the 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”

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” (disagreement in terminology over the word “excellent student”)

e.g., (a) “All humans are created equal”; (b) “no, we all have unique DNA

e.g., (a) “I bought a new house”; (b) “no, it was built 20 years ago”

e.g., From William James: a hunter chases a squirrel around a tree, but the two 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 a midget”

3. Value dispute: disagreement about major value assumption 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 ascertaining empirical facts or clarifying terminology. A twentieth-century philosophical movement called “logical positivism’ describes value statements as pseudo-propositions, which do not involve actual facts about the world. Thus, while such disputes may appear to be over factual matters, they are not, and thus they constitute a separate type of value 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 whether he should have been 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” (disagreement in fact, terminology, and value)

 

DEFINITIONS

 

Parts of definitions

Defiendum: the term to be defined

Definiens: the definition

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

Purposes of Definitions

Lexical: designates meaning by showing how English speaking people use a word as based 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

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

Stipulative: designates meaning by proposing a new meaning of a term

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

Theoretical: designates meaning by indicating how a word is used in presuppose some 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

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 short 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 life-long financial slavery.

Techniques

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

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 first 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 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

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

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

e.g., “profound hearing loss” means the inability to hear sound lower than 95 dB

e.g., “antique” means over 100 years old

Five Rules of Good Lexical Definitions

1. 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.

2. Must not be circular

e.g., “man” is the sole occupier of 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

3. 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

e.g., “spelt” is a kind of food

e.g., “eloquence” is the power of influencing the feelings by speech or writing

Too narrow

e.g., “man” is a civilized rational animal

e.g., “wealth” consists of money

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

e.g., “logic” is a machine for combating fallacy

4. 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.

5. 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

 

LINGUISTIC CONCEPTS IN OLD LOGIC BOOKS (not included on test)

Aristotelean concepts

Laws of Thought (Aristotle)

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)

Others:

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

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

Predicables (Aristotle, 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)

Meaning of terms (Aristotle)

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

Kinds of terms (Mill)

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

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,

Absolute-relative

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

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

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

Connotative and non-connotative words (Mill)

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”

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