Types of definitions in logic | Logical Reasoning Study Notes UGC NET

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Topics Based on UGC NET Syllabus of Logical Reasoning

• Understanding the structure of arguments: argument forms, the structure of categorical propositions, Mood and Figure, Formal and Informal fallacies, Uses of language, Connotations and denotations of terms, Classical square of opposition.
• Evaluating and distinguishing deductive and inductive reasoning.
• Analogies.
• Venn diagram: Simple and multiple uses for establishing the validity of arguments.
• Indian Logic: Means of knowledge.
• Pramanas: Pratyaksha (Perception), Anumana (Inference), Upamana(Comparison), Shabda (Verbal testimony), Arthapatti (Implication) and Anupalabddhi (Non-apprehension).
• Structure and kinds of Anumana (inference), Vyapti (invariable relation), Hetvabhasas (fallacies of inference).

Types of definitions 

What is a definition?

• A definition is a statement of the meaning of a term.
• When writers are trying to explain an unfamiliar idea, they rely on definitions.
• All definitions attempt to explain or clarify a term.
• In mathematics, a definition is used to give a precise meaning to a new term, by describing a condition that unambiguously qualifies what a mathematical term is and is not.
• Definitions and axioms form the basis on which all of modern mathematics is to be constructed.

What is axiom ?

a statement or proposition which is regarded as being established, accepted, or self-evidently true .

So, A definition is made up of two parts :

DEFINIENDUM- term which is to be defined.

A word, phrase, or symbol which is the subject of a definition, especially in a dictionary entry, or which is introduced into a logical system by being defined .

DEFINIEN–  words used to define a term. 

The different types of definitions are given below –

Different Types of definition 

#1. Formal definition-

It is the definition which we generally see in the dictionary for a book, describing some particular characteristics of a concept things, or phenomenon. Such characteristics are used to familiarise reader with unknown terms.

A formal definition is based upon a concise, logical pattern that includes as much information as it can within a minimum amount of space .

Formal sentences components are the term being defined, the class it belongs to, and its distinguishing characteristics.

#2. Informal definition –

sometime a  known word in the form of antonyms and synonyms can be used for explaining something unknown.

Such definitions are introduced by “ like “ “also known as” or “in other words” extra these are used to familiarise a lesson on term with any other well-known related term. 

Having a relaxed, friendly, or unofficial style, manner, or nature.

Informal language is more casual and spontaneous. It is used when communicating with friends or family either in writing or in conversation.

#3. Extended definition –

An extended definition is a one or more paragraphs that attempt to explain a complex term. Some terms may be so important in your report, there may be so much confusion about them, or they may be so difficult to understand that an extended discussion is vital for the success of your report.

The extended definition can be formal or informal. As the name suggest these are used for explanation by including examples of listing familiar points, explaining concepts, historical references etc .

When you write reports, you may often discover that you need to explain certain basics before you can discuss the main subject matter.

For example:

• In a report on new treatments for sickle cell anemia, you’d need a section defining the disease.
• In a report on the benefits of drip irrigation, you’d need to write an extended definition of drip irrigation, explaining how it works and what equipment is used.
• In a report showing small businesses how to weather economic recessions, an extended definition of the term economic recession would be needed first.

One of the first things to do when you write an extended definition is to compose the formal sentence definition of the term you are writing about. Place it toward the beginning of the extended definition.

It establishes the focus for the rest of the discussion. It is “formal” because it uses a certain form .

#4. Lexical definition  –

Its relating to the words or vocabulary of a language. 

• The  lexical definition also known as the dictionary definition, is the closely matching the meaning of the term in common usage.
• It is also known as reporting definition. 
• According to Oxford English dictionary, lexical means relating to the words or vocabulary of a language. Does the lexical definition related to a words dictionary meaning of the meaning in the common vocabulary of language. It shows how the term is used in a language. It is difficult to change.
• Lexical meanings are denotative meanings . 
• Lexical meanings can’t be changed.
• It is used to avoid ambiguity. 
• It should be universal, never supporting any positive or negative aspects. 
• As its other name implies, this is the sort of definition , one is likely to find in the dictionary. A lexical definition is usually the type expected from a request for definition, and it is generally expected that such a definition will be stated as simply as possible in order to convey information to the widest audience . 
• The definition which reports the meaning of a word or a phrase as it is actually used by people is called a lexical definition. Meanings of words given in a dictionary are lexical definitions. As a word may have more than one meaning, it may also have more than one lexical definition.
• Lexical definitions are either true or false. If the definition is the same as the actual use of the word then it is true, otherwise it is false . 

#5 Stipulative definition  –  

A stipulative definition is a type of definition in which a new or currently existing term is given a new specific meaning for the purposes of argument or discussion in a given context . 

• When the term already exists, this definition may, but does not necessarily, contradict the dictionary definition of the term.
• It is the new meaning giving to an already existing term on meaning assigned to a new term.
• It is arbitrary in nature .
• A term can have different stipulative meaning at different places or among different people. 
• For example some people use “LOL” for “lots of love” and some use it for “laughing out loud”. 
• Idioms and slangs have stipulative meanings .
•  The terms to prove stipulative definition is sometimes used to make a deliberately misleading definition.
•  It is easy to change as it has a meaning in local language. 
• When the stability of definition of a term that popular former y my get included in the dictionary and becomes a lexical definition.

For example:

• Suppose we say that to love someone is to be willing to die for that person.
• Take “human” to mean any member of the species Homo sapiens.
• For the purposes of argument, we will define a “student” to be “a person under 18 enrolled in a local school”

#6 Persuasive definition  –

• Such definitions favour  a particular view or an favour any view, but are presented in a neutral form. In such definitions ,  emotional, positive or derogatory meaning is attached to the term.
• The term “persuasive definition” was introduced by philosopher Charles Stevenson as part of his emotive theory of meaning . 
• It is usually used in discussions,  debates ,  etc to favour or unfavour particular  views.  For example  –  there can be different views on death penalty ,  those who are in favour will define it as Harsh punishment which will help in preventing heinous crimes and those who are not in its favour will define it as “legalized murder”. 

A persuasive definition is a form of stipulativedefinition which supports to describe the true or commonly accepted meaning of a term, while in reality stipulating an uncommon or altered use, usually to support an argument for some view, or to create or alter rights, duties or crimes.

Examples of persuasive definitions (definist fallacies) include:

• Democrat – “a leftist who desires to overtax the corporations and abolish freedom in the economic sphere”.

• Persuasive definitions commonly appear in controversial topics such as politics, sex, and religion, as participants in emotionally charged exchanges will sometimes become more concerned about swaying people to one side or another than expressing the unbiased facts.

#7 Parenthetical definition – 

Sometimes, for the sake of explanation we write the meanings of some words in parentheses in a sentence. Meaning of a difficult word mentioned in a few words in parentheses ( brackets) is known as parenthetical definition. 

Some times to understand better difficult words we write easy words or meaning  in brackets are called parenthetical meaning.

For example  – to understand meanings of arbitrariness we write in brackets to choose randomly or by chance . what ever we write in bracket for own understanding are called parenthetical definition.

Parenthetical phrase is an explanatory or qualifying word, clause, or sentence inserted into a passage. The parenthesis could be left out and still form grammatically correct text.

• Parentheses are usually marked off by round or square brackets, dashes, or commas.
• Billy-bob, a great singer, was not a good dancer. The phrase a great singer, set off by commas, is both an appositive and a parenthesis.
• A dog (not a cat) is an animal that barks. The phrase not a cat is a parenthesis.
• My umbrella (which is somewhat broken) can still shield the two of us from the rain. The phrase which is somewhat broken is a parenthesis.

The following are examples of types of parenthetical phrases:

1. Introductory phrase: Once upon a time, my father ate a muffin.  
2. Interjection: My father ate the muffin, gosh damn it!
3. Aside: My father, if you don’t mind me telling you this, ate the muffin.
4. Appositive: My father, a jaded and bitter man, ate the muffin.
5. Absolute phrase: My father, his eyes flashing with rage, ate the muffin.
6. Free modifier: My father, chewing with unbridled fury, ate the muffin.
7. Resumptive modifier: My father ate the muffin, a muffin which no man had yet chewed.
8. Summative modifier: My father ate the muffin, a feat which no man had attempted.

While a parenthesis need not be written enclosed by the curved brackets called parentheses, their use, principally around rhetorical parentheses, has made the punctuation marks the only common use for the term in most contexts.

#8. Sentence definition-

such definitions are given in sentence forms , like ‘ computer is an electronic machine used to store , process and retrieve data. 

• Here is the first part of definition  is ‘ computer the term itself , the next part- electronic machine , shows what it is , and the last part depicts the function of computer. 
•  Sentence  is a set of words that is complete in itself, typically containing a subject and predicate, conveying a statement, question, exclamation, or command, and consisting of a main clause and sometimes one or more subordinate clauses.
• The sentence is generally defined as a word or a group of words that expresses a thorough idea by giving a sentence or order.

#9. Intention definition –

Such definitions specifiy the properties, features, meanings , and the necessary and sufficient conditions of a term.

For example – even numbers are the numbers divisible by two.

#10. Ostensive definition – 

literal meaning of ostensive is denoting a way of defining by direct demonstration, e.g. pointing .

• In this type of definition, a term is described by showing the real objects; for example, showing banana, tulips, mangos, etc, to describe the yellow colour . 
• An ostensive definition conveys the meaning of a term by pointing out examples.
• This type of definition is often used where the term is difficult to define verbally, either because the words will not be understood (as with children and new speakers of a language) or because of the nature of the term (such as colors or sensations).
•  It is usually accompanied with a gesture pointing to the object serving as an example, and for this reason is also often referred to as “definition by pointing”.
• An ostensive definition assumes the questioner has sufficient understanding to recognize the type of information being given . 

SOLVED MCQ Question for practice 

Question 1 – Determine the nature of the following definition “abortion” means the ruthless murdering of innocent beings.

1. Lexical
2. Persuasive 
3. Stipulative 
4. Theoretical 

Answer- Persuasive

Solution – A persuasive definition is a form of stipulative definition which supports to describe the true or commonly accepted meaning  of a term, while in reality stipulating an uncommon or altered use, usually to support an argument for some view, or to create or alter rights, duties or crimes. 

Question 2 – when the conclusion of an argument follows from its premise conclusively, the argument is called

1. Circular argument
2. Inductive argument 
3. Deductive argument 
4. Analogical argument

Answer- Deductive argument

Solution– Deductive argument, also deductive logic, is the process of reasoning from one or more statements to reach a logical conclusion. Deductive reasoning goes in the same direction as that of the conditionals, and links premises with conclusions. 

Question 3- A stipulative definition may be said to be 

1. Always true
2. Always false
3. Sometime true, Sometime false
4. Neither true Neither false.

Answer-Sometime true, Sometime false

Solution- Stipulative definition is a type of definition in which a new or currently existing term is given a new specific meaning for the purposes of argument or discussion in a given context . When the term already exists, this definition may, but does not necessarily, contradict the dictionary definition of the term.

Question 4. A definition put forward to resolve a dispute by influencing attitudes or stirring emotions is called

1. Lexical
2. Persuasive
3. Stipulative 
4. Precision 

Answer– Persuasive [See Above Notes]

Question 5 – A definition that has a meaning that is deliberately assigned to some symbol is called : 

1. Lexical 
2. Pressing
3. Stipulative 
4. Persuasive 

Answer– Stipulative [See Above Notes]

Solution already given in one of the  above question.