LOGIC 1 - BLS LLB NOTES SEM 1

LOGIC 1

CHAPTER - 1

NATURE OF LOGIC

SUBJECT AND PREDICATE

            EXAMPLES :-

1)     Katrina is not drinking maaza

Subject : Katrina

Predicate : is not drinking maaza

2)     Munna bhai was eating vada pav

Subject : munna bhai

Predicate : was eating vada pav

3)     Amitabh loves chocolate.

Subject : Amitabh

Predicate : loves chocolate

4)     Jaya like flower.

Subject : Jaya

Predicate : like flower

5)     Aishwarya purchase a nappy

Subject : Aishwarya

Predicate : purchase a nappy

6)     Abhishek bought few toys.

Subject : Abhishek

Predicate : bought few toys

7)     Lalu asked bipasha if she will come for a movie.

Subject : Lalu asked bipasha

Predicate : if she will come for a movie.

8)     Sharukh is one of the famous heroes in India

Subject : Sharukh

Predicate : is one of the famous heroes in India

9)     Ram loves Sita.

Subject :  Ram

Predicate : loves sita.

10) I have done my work.

Subject :  I

Predicate : have done my work.

PREMISES

                  Statement which includes :

1)     Major premises

2)     Minor premises

3)     Conclusion

Eg :-

1)     Shahid love kareena

2)     Saif likes Shahid

v  Saif loves Kareena

(Common – Middel Term is Shahid)

v Major term : - Predicate of the conclusion

v Minor term : - subject of the conclusion.

EXAMPLES :

·        All girls are beautiful

·        Sheela is a girl.

v Sheela is beautiful

·        All boys are handsome

·        Rnbir is a boy

v Ranbir is handsome

                            

·        Rabridevi have 11 childrens

·        Lalu Prasad loves Rabri devi

v Lalu have 11 childrens

·        All students are clever

·        I am a student

v I am clever

·        All politicians are corrupt.

·        I am a politician

v I am a corrupt

1)     WHAT IS LOGIC ?

ANS :-

Men sometime reason well, and sometime badly. We use various expressions to indicate this. The word ‘correct’ , ‘valid’ , & ‘logical’ stands for good reasoning, the words ‘incorrect’, ‘invalid’ , & ‘illogical’ stands for bad reasoning. The science which enables us to draw these distinctions is logic. Logic furnish principals and methods for distinguishing between correct & incorrect reasoning.

2)     DEFINE LOGIC & STATE THE TYPES OF DEFINATION ? OR DEFINATION OF LOGIC ?

ANS :-

·        TRADITIONAL DEFINATION :-

Traditionally, logic was defined as the science, which investigates the general principal of valid thaught.

·        MODERN DEFINATION :-

Logic is a science of implication or of valid inference.

Eg :-     All hindus are men.

            All Brahmins are hindus.

v All Brahmins are men.

3)     DEDUCTIVE ARGUMENT :-

A deductive argument is one, in which the premises imply the conclusion. As such, the conclusion cannot be false, if the premises are true. A deductive argument is certain.

      Eg :-     All birds have feathers

                  All crow are birds.

v All crow have feathers.

4)     INDUCTIVE ARGUMENT : -

An inductive argument is one, in which the premises do not provide sufficient evidence for the conclusion. An inductive argument is probable.

      Eg :-     A, B and C are intelligent.

                  A, B, and C are men.

v Men are intelligent.

5)     INFERENCE AND IMPLICATION :-

INFERENCE :

An inference is the act or process of deriving logical conclusion from premises know or assumed to be true.

TYPES OF INFERENCE:

IMMEDIATE INFERENCE:

Immediate inference is one, which is derived from single proposition.

Eg:-     dogs are animals

v Some animals are dogs

                                   MEDIATE INFERENCE :

                                   A mediate inference is one which is derived from two proposition co-jointly.

                                   Eg :-      every animal is mortal

                                                Every dog is an animal

v Every dog is mortal

6)     DEFINATION IMPLICATION :- (5 MARKS)

IMPLICATION :

In an inference the thinker proceeds from the premises to the conclusion. He does so, because he believes that there is a certain relationship between the premises and the conclusion. This relation is that of implication.

1)   IMPLICANS :-

Implicans is the statement or (statements) which implies some other statements.

2)   IMPLICATE :-

Implicate is the statement which follows from the implicants.

            EG: -    A  is red ---- implicans

v A is coloured ---- implicate.

7)     WHAT IS IMPLICANS OR WHAT IS IMPLICATE ?        (2 MARKS)

ANS:

                  EG:-     Mahendra is a father

v Mahendra is a man.

     In the relation of implication, if the implicans is true, the implicate must be true. If the relation between the premises and the conclusion were not that of implication the conclusion cannot be drawn from the premises.

                  EG:-     A is the brother of B

v B is the brother of A

In this inference the premises does not imply the conclusion. The conclusion may be false even if the premises is true. Infect, the premises implies that

“B is either the brother or the sister of A”. Since it may be the case that B is the sister of A, the above conclusion cannot be drawn.

8)     TRUTH AND VALIDITY :              (5 – MARKS)

A)   TRUTH :

Truth is the property of a proposition. A true proposition represent facts, while a false proposition does not.

            EG:-     The earth is round.

                        Gold is heavier then silver.

                        There are golden mountain in India

                        Man can live without oxygen.

The first two proposition are true, while the last two are false. This is because the first two proposition represent the fact, but the last two do not.

B)   VALIDITY :

Validity of an argument depends upon the nature of relationship between it premises and its conclusion. An argument is valid when its conclusion is a logic consequence of its premises. When the premises of an argument imply its conclusion the argument is valid.

            EG:-     Kareena love dogs

                        Shahid love kareena

v Shahid love dogs.

9)     FORM AND CONTENT :-             (SHORT NOTE) (5 – MARKS)

Each inference is about a certain subject matter this is called its contents. Apart from its constant it has certain other characteristics.

The contents of an inference is the thaught, idea, opinion, expressed either in spoken or in written language, while the form of an inference consists of logical characteristics which are independent of the specified content.

           

            EG:-     All politicians are corrupt

                        Lalu Prasad is a politician

v Lalu Prasad is corrupt.

                                   

            EG:-     All actors are artists.

                        Sharukh is an actor

v Sharukh is an actor.

It is obvious that these two inference differ in their content. How ever they are vary similar. In both of them an individual (Lalu Prasan and Sharukh) is stated to be the member of a class. These class is a member of wider class. In both the inference there is a certain relation between individual and a class.

                       

CHAPTER - 2

PROPOSITION

1)     PROPOSITION : -                        (2 MARKS)

Proposition is a statement which is either true or false. A proposition is true when it represents a fact, it is false when it does not.

                  EG :-    Tagore was great poet.

                              Dogs do not dance.

2)     CHARACTERISTIC OF PROPOSITION :

Every proposition is either true or false it cannot be both true and false.

The proposition “India has congress government” appears to be true for some years, and false some other years. However, wrong impression is created, because the proposition has not been fully expressed. A proposition is asserted with the reference to a given date and with reference to that date it cannot be both true and false. “ India has congress government in the year 2013” it is so expressed, that it cannot be both true and false.

The truth or falsity of a proposition is definite. The truth or falsity of a proposition is always remain the same, it cannot be change of course we cannot know a given statement is true or false. For EG:- today we cannot say whether the statement “ there are living being on the planet Mars” is true. Further, we may even hold wrong believe about it truth or falsity. But neither absence of knowledge nor wrong believes affects the truth or falsity of a statement.

3)     PROPOSITION AND FACTS :-                 (2 MARKS)

Facts determines the truth or falsity of a proposition. If a proposition represents the facts as they are it is true. If it does not it is false.

“Butter melts in heat” is a true proposition. While “the has to legs” is a false proposition. A proposition claims to represents facts. This claim may or may not be justified. If it is justified, the proposition is true, otherwise it is false.

4)     PROPOSITION AND SENTENCE  :-         (5 MARKS)

Is closely related, as a proposition is expressed in the form of a sentence. But it is not same as a sentence. The same proposition may be expressed by different sentence.

                  EG:.     I am an Indian

The three sentences are from different languages, yet they convey the same proposition this is because a proposition is what a sentence and not the word in which the statement is made.

                  EG:.     Thief!

What thief would trust a thief!. Truth or Falsity of above sentences are not possible to determine, so these sentences do not express propositions. So, we can say that every sentence does not express a proposition. But every proposition is in the form of a proposition.

KIND OF SENTENCES

1)     Assertive sentences / Declarative sentences

A sentence which asserts or declare something

                  Eg.:      Sun rises in the east.

2)     Indicative sentences :

Which indicate something.

                  Eg.:      This is my collage.

3)     Imperative sentences :

Any order, command, request or suggestion.

                  Eg.:      Don’t touch the flame of the candle.

4)     Interrogative sentences :

(?) question is asked.

a)      WH – QUESTION

Eg.:      What is the time ?

b)     YES / NO – QUESTION

Eg.:      Lalu Prasad asked Bipasha whether you will come for a movie ?

5)     Exclamatory sentences :

Expressing sudden feelings or motions.

                  Eg.:      What a giant he is !

                              Or Oh! How sad it is.

  

6)     DISTINCTION BETWEEN A SENTENCE AND PROPOSITION   (12 MARKS)

In common mans language proposition is equal to sentence. But technically speaking “ sentence that is either true or false”. So it is clear that all propositions can be said to be a sentence, but all sentences are not proposition. Grammatical sentence can be distinguished by proposition in following ways :

1)     Grammatical sentences are of four types :-

a)      Imperative b) Interrogative c) Exclamatory d) assertive or Indicative, while proposition is only assertive or indicative types of sentences.

2)     As language changes, sentences is grammatically is said to be different, while on change of language make no difference in proposition.

3)     Grammatical sense of subject – predicate understanding is different from logical one. ‘also in grammatical sentence subject – predicate can change its position, but in proposition first subject and then predicate’.

4)     Grammatical sentence has two divisions only which is Viz. subject and Predicate, while proposition has one more part Viz. Copula – (helping verb)

5)     Grammatical sentence can have multiple subject. As ‘ Time & Tide waits for no Man’. But proposition has only one subject.

6)     Grammatical sentence can be in past, present and future tense, but logical proposition must be in present tense only.

7)     Grammatical can be with or without any quantity or quality, but proposition must have one quality & one quantity.

8)     Grammatical sentence can be true today and false tomorrow, but propositions truth and falsity must be universal, that is, if it is true then it must be true in all time and places.

9)     Lastly grammatical sentence can be expressed incompletely, while proposition has to be complete and definite to maintain its condition of true or false of universality.

Eg.:      ‘India has congress government’

(It can be true now, but in the past it can be false, so it is not proposition in real sense) to be proposition it must be ‘India has congress government in 2013’.

7)     CONSTITUENTS AND COMPONENTS :             (5 MARKS)

Though proposition is a basic unit of logic, it can be analyz its elements. However, the elements into which a proposition is analyzed have no existence apart from the proposition these are called constituents. So, constituents can be defined as “The elements into which a proposition can be analyzed are called its constituents.

                  Eg.:      Bipasha is bold and beautiful

In above proposition, Bipasha is bold and beautiful are constituents of given proposition.

A constituents is any element of a proposition; it can be a subject, object, copula.

In every proposition there is a one element which combines the other elements. This combining element is called as component.

                  Eg.:      John loved Bipasha.

In the above proposition love is combining element i.e. component, so without combining element there would be no proposition.

8)     DIFFERENCE BETWEEN COMPONENTS AND CONSTITUENTS

1)     A component is universal; while the constituents it combines can be particular.

This is the reason, constituents and components combined may be changed, yet the proposition would be meaningful.

We will change individuals combine by the component ‘Loved’ and still proposition would be meaningful.

                        Eg.:      Mother loved children

                                    Romio loved Juliet.

In this, the component (combining element) ‘Loved’ cannot be replaced by individual.

2)     Every proposition is about certain contents (subject matters) A constituents indicate the contents of a proposition. Since the contents of proposition differ, their constituents too differ, however even though proposition differ in their constituents they may have sense from

Eg.:      Ram is honest

            Rahul is handsome

            Raman is clever.

All these above proposition assert that an individual possessive a quality, thus the above proposition have different constituent, but the relation between the constituent is same.

3)     The form of a proposition depends upon the why he constituents are combine.

That is to say, form of a proposition, depends upon a component, however a component, is not to be identified with the words, through which is expressed, the following proposition have different component, though in all of them the component is expressed by the same word “is”.

                        Eg.:      Sharukh is hulk

                                    Sonunigam is singer

                                    Crow is bird

In the first proposition, the component Is predication, the attribute of hulk is affirm to sharukh.

In the second proposition, the component is membership of a class. Sonunigam is a member of the class of a singer.

In the last proposition, the component is class enclosure. The class of crow is included in the class of birds.

9)     COPULA :-

Copula is a word which act as a connector between subject and predicate

                              Eg.:      The house is on the top of hill.

CHAPTER 3

TERMS

1)     TERM :                                          ( 2 MARKS )

The term is a word or group of word which stand as a subject and predicate of a logical proposition

                              Eg.:      India is a rich country with poor people.

In the above proposition the subject term ‘India’ is single word, but the predicate term ‘is a rich country with poor people’ is a group of word.

2)     WORD :                                        ( 2 MARKS )

A sentence consists of words, as such, the subject and predicate of a proposition are words.

Though every term is a word (or combination of words) every word is not a term. A word becomes a term when it stand as subject or predicate in a proposition.

TYPES OF WORDS :-

There are three types of words :-

A)     CATEGROMATIC :

These word stand as term without any support of other words like, Himalaya, Ram, Goa, etc.

B)     SYNCATEGROMATIC :

This words are dependent on categromatic words and cannot become term itself.

                  Eg.:      a, an, the, is, etc.

C)     ACATEGROMATIC :

This words are expressive feelings, emotion, or exclamation. They never become term.

                  Eg.:      Oh!, Oops!, etc.

3)     DISTINCTION BETWEEN A TERM AND WORD            ( 2 MARKS )

1)     The meaning of a term depends upon its being as element in a proposition.  But when a word is the subject or the predicate of the proposition its meaning become definite.

Word have an independent meaning however, when words are considered by themselves they may have more then one meaning.

                         Eg.:     The word sound ‘sound’ have more then one meaning, sound may mean ‘that which is heard, or it may mean ‘free from defect’.

2)     Terms can express only information, thought or reasoning’s. They cannot express feeling, question, wishes, request, commands, etc. on the other hand, words may express not only information, thoughts, or reasoning, but also question, wishes, request, command, etc. terms are concerned with informative use of languages, words are not restricted so informative use.

4)     GENERAL AND SINGULAR TERM                      ( 2 MARKS )

1)     GENERAL TERM :-

General term is that which can be applied in the same sense, to each of an indefinite number of objects, having certain comman quality.

                        Eg.:      All hindus are Indian.

In the above proposition the subject term ‘Hindus’ applies to every hindus, and the predicate term ‘Indians’ applies to every Indian.

2)     SINGULAR TERM :-

Is that which can be applied to one definite object.

                        Eg.:      Lalu Prasad is a politician

Singular terms are of two kinds these are proper names and designation.

Proper name (term) :-

Proper name term is a mark which distinguishes a individual person or thing

It does not indicate the possession of any attribute, such name are mostly those of persons, places and pet animals.

                        Eg.:      Ram, Mumbai, Tajmahal.

DESIGNATION :-

Designation indicate one definite object by stating an attribute which only that object possess.

                        Eg.:      This man, That author, Those books.

5)     POSITIVE AND NEGATIVE TERM :

1)     POSITIVE TERM :

Positive term implies the presence of attribute.

                        Eg.:      Living, Present, Equal.

2)     NEGATIVE TERM :

Negative term is one which implies the absence of attribute.

                        Eg.:      Non living, Non present, Non equal.

3)     UNIVERSE OF DISCOURSE :

Universe of discourse, the limits to the application of a term constitute its universe of discourse.

                        Eg.:      Not white.

6)     CONTRADICTORY AND CONTRARY :

1)     CONTRADICTORY TERMS :

Terms that are mutually exclusive and collectively exhaustive are contradictory.

                        Eg.:      White & Non white.

2)     CONTRARY TERMS :

Contrary terms are those which expressed greatest degree in the same universe if discourse. They are mutually exclusive.

                        Eg.:      Black & white, Good & bad, Happy & sad, Dead & alive.

7)     DENOTATION & CONNOTATION :

1)     DENOTATION :

It consist of all individual object to which it can be applied.

                        Eg.:      City, Man.

2)     CONNOTATION :

It consist of the common attribute posses by all the objects to which the term is applied.

                        Eg.:      Rationality, Animality, Humanity.

CHAPTER 4

TRADITIONAL  CLASSIFICATION OF PROPOSITION

1)     SIMPLE AND COMPOUND PROPOSITION :

a)      Simple proposition :

A simple proposition is one which affirms or derive a predicate of a subject.

                        Eg.:      All girls are beautiful.

                                    All politicians are not corrupt.

b)     Compound proposition :

When a proposition makes an assertion under certain conditions it is called a compound proposition.

                        Eg.:      If John ride bike, then Bipasha will love him.

                                    Either Abhishek is a Ra-one or Bluffmaster.

2)     CATEGORICAL & CONDITIONAL PROPOSITION :

a)      Categorical proposition :

A categorical proposition which affirms or denies a predicate of a subject.

                        Eg.:      All girls are beautiful.

                                    All politicians are not corrupt.

b)     Conditional proposition :

When a proposition makes an assertion under certain conditions it is called a conditional proposition.

                        Eg.:      If John ride bike, then Bipasha will love him.

                                    Either Abhishek is a Ra-one or Bluffmaster.

Conditional propositions are of two kinds & these are hypothetical and disjunctive proposition.

1)     Hypothetical proposition :

Hypothetical proposition is one which presence a condition together with some consequence which follows from it.

                  Eg.:      if Ranbir proposes  Katrina, then Salman will beat him.

2)     Disjunctive proposition :

Disjunctive proposition is one which state alternatives.

                  Eg.:      Either salman will marry, or he will remain bachelor

CLASSIFICATION OF PROPOSITION

                        SIMPLE                                                                                               COMPOUND

                        CATEGORICAL                                                                                   CONDITIONAL

                                                                        HYPOTHETICAL                                 DISJUNCTION

                                                                        IF …. THEN                                         EITHER ….. OR

3)     FOUR FOLD CLASSIFICATION OF PROPOSITION :

a)      UNIVERSAL AFFIRMATIVE (A) :-

In this kind of proposition the predicate is affirm of the whole subject.

                  Eg.:      All boys are handsome

b)     UNIVERSAL AFFIRMATIVE (E) :-

In this kind of proposition the predicate is denied of the whole subject.

                  Eg.:      No politician are moral.

c)      PARTICULAR AFFIRMATIVE (I) :-

In this kind of proposition the predicate is affirm of the part of subject.

                  Eg.:      Some actors are singers.

d)     PARTICULAR NEGATIVE (O) :-

In this kind of proposition, the predicate is denied of the part of the subject.

                  Eg.:      Some wives are not dominating.

A	All S is P
E	No S is P
I	Some S is P
O	Some S is Not P

4)     REDUCTION OF STATEMENT TO LOGICAL FORM :

A	Affirmative sentence with all, every, each, any, always, whether,   invariably, necessarily, absolutely.
E	Sentence with No, never, none, not at all, not a single, not even one.
I	Affirmative sentence with, most, many a few, certain, all most all, all but one several, mostly, generally, frequently, often, perhaps, nearly, sometimes, occasionally.
O	When ‘A’ is denied we got ‘O’; when affirmative sentence which contain words indicating ‘I’ are denied we got ‘O’

            EXAMPLE :-

1)     Every man is responsible for his actions.

·        All men are those who are responsible for his actions.

2)     Any men can lift this weight.

·        All men are those who can lift this weight.

3)     All that glitters is not gold.

·        Something are those who glitters is not gold.

4)     Every military general does not have a sound plan for defense.

·        Some military general are those who does not have a sound plan for defense.

5)     What ever goes up must come down.

·        All things are those who goes up must come down.

6)     Men are not necessarily bad.

·        Some men are those who are not necessarily bad.

7)     Not a single members of the crew was saved.

·        No single member are those of the crew was saved.

8)     Not even one mango in the basket was rotten.

·        No mango are those in the basket was rotten.

9)     Judges are not at all partial.

·        No judges are those who are partial.

10) Most houses in japan are build of light material.

·        Some houses in japan are those who are build of light material.

11) All most all the passenger were injured.

·        Some passenger are those who were injured.

12) A few donors did not help the victims of famine in Bihar.

·        Some donors are those who did not help the victims of famine in Bihar.

13) All but one member of the picnic party did not return safe.

·        Some but one member of the picnic are those who did not return safe.

14) Central railway trains frequently run late.

·        Some central railway train are those who run frequently run late.

15) Perhaps modern men do not care for religion.

·        Some modern men are those who do not care for religion.

16) Few men are free from vanity.

·        Some men are not those who are not free from vanity.

17) Few have peace of mind who prosper by cheating.

·        Some men do not have peace of mind who prosper by cheating.

18) Few nation do not wish to avoid third world war.

·        Some nation are those who wish to avoid third world war.

19) Few great men are not considerate.

·        Some great men are those who considerate.

20) A few thieves are kind hearted.

·        Some thieves are those who are kind hearted.

5)     INDEFINITE PROPOSITION :

Indefinite proposition is one in which quantity is not definite.

                  Eg.:      1)         Planet revolve round the sun

·        All planet revolve round the sun                (A)

Muslims are not idol worshipers

·        No muslims are idol worshipers                 (E)

South Indians are black

·        Some south Indians are black                     (I)

·         

6)     MULTIPLE QUALIFICATION :

Sometimes the predicate is affirm or denied of the subject under certain limitations. This limitation is by reference to time or place. This limitation leads to secondary quantification of the proposition.

                  Eg.:      Men sometimes lose their temper

·        All men lose their temper sometimes.       (A)

                              He always order the expensive item in the menu.

·        He is a person who order the expensive item in the menu always.       (A)

7)     EXCLUSIVE PROPOSITION :

Exclusive proposition is one which limits the application of the predicate to the subject only. These proposition are indicated by the expression like, only, alone, none but, & nothing else but. These are to be reduced to A & E propositions.

                  Eg.:      Only experts can judge scientific matters

·        All experts can judge scientific matters                             (A)

·        No non-experts can judge scientific matters.                    (E)

                  Eg.:      None but, graduate can vote.

·        All graduate can vote                                   (A)

·        No non-graduate can vote.                          (E)

EXERCISE:

1)     Brother sometimes quarrel with each other.

All brother quarrel with each other sometimes.                    (MQ)

2)     A few distinguished men have undistinguished son.

Some distinguished men have undistinguished son.             (I)

3)     Grapes come from nasik           

Some grapes come from nasik.                                                 (I)

4)     Hardly any men is tolerant.      

Some men are those who are not tolerant.                            (I)

5)     Women are jealous.

Some women are jealous.

6)     No one like to be wrong.

No person are those who likes to be wrong.

7)     Only those who are registered are permitted to vote.

All those who are registered are permitted to vote.                          (A)

No person who are non – registered are permitted to vote.            (E)

8)     People who like sheela also like munni.

All people who like sheela also like munni.

9)     Few children do not like circus.

Some children are those who love circus.                               (E)

10) Only human being are intelligent.

All human being are intelligent.                                                (A)

No non human being are intelligent                                         (E)

11) None but gold will silence her.

All golden thing will silence her.                                               (A)

No non golden will silence her.                                     (E)