BLS LLB 5 Years Sem 1 Logic 1 2019-20 Question Paper with Solutions

A term is a word or a group of words which can stand as the subject or the predicate of a proposition.

Example: in "All men are mortal", both "men" and "mortal" are terms.

A term is not the same as a word. "The present Chief Justice of India" is four words and one term; and a word such as "and", "of" or "very" is not a term at all, because it cannot occupy the subject or predicate place on its own.

Two terms are contradictory when one is the simple negative of the other, so that between them they exhaust the universe of discourse: nothing falls under both and nothing falls outside both. Examples: man and not-man; legal and illegal.

Two terms are contrary when they are the two extremes of the same series, so that they exclude each other but do not exhaust the field. Examples: white and black; rich and poor. A thing may be neither white nor black, but everything must be either white or not-white.

The Law of Excluded Middle is the third of the three laws of thought. It states that everything must either be or not be: between a proposition and its denial there is no third possibility.

p v ~p

Example: an agreement either is void or is not void. There is no middle state.

An extensive definition, also called a definition by denotation, defines a term by enumerating the individuals or the species which it denotes, instead of stating the attributes which it implies.

Example: "By a metal is meant a substance such as gold, silver, copper, iron and aluminium."

It is a verbal or nominal definition, not a real one: it shows what the word covers without saying what makes those things what they are.

Division by dichotomy is the division of a class into two members by a pair of contradictory terms, one positive and one negative.

Examples: people into introverts and non-introverts; books into fiction and non-fiction; Indians into Hindus and not-Hindus.

Its merit is that it can never break the rules: because the members are contradictories, the division is necessarily exhaustive, by the Law of Excluded Middle, and necessarily mutually exclusive, by the Law of Contradiction. It is the only formally guaranteed division.

Its defect is that the negative member is wholly indeterminate: "non-introvert" says only what its members are not.

For full marks, cover: both definitions with a worked table; the three kinds of connotation; the law of inverse variation with its limits; the terms that have one and not the other; the link to definition and division; and the legal application.

The two aspects

The connotation, or intension, of a term is the sum of the essential attributes which the term implies, that is, the qualities a thing must possess before the term can be applied to it.

The denotation, or extension, of a term is the range of individuals or classes to which the term applies.

Terms with only one of the two

Proper names denote an individual and connote nothing, because they identify without describing; abstract terms connote a quality and denote no class of individuals; general terms have both.

The link to definition and division

Definition sets out the connotation, by naming genus and differentia. Division sets out the denotation, by breaking the class into species. Every step down a division is a step up in connotation, which is the inverse law stated as a procedure.

Legal application

A definition clause fixes the connotation and the court decides the denotation. When a bench asks whether an e-rickshaw is a "motor vehicle", it is testing an object against a connotation the legislature has fixed. Ejusdem generis is a rule about genus and species, and therefore about connotation.

Fixing a universe of discourse makes the negative term determinate. Inside the universe of "living creatures", "not-man" means the other animals; inside the universe of "the members of this club", it means the other members.

Its two effects

1. On negative terms, and therefore on eduction. Obversion replaces the predicate by its contradictory, so it cannot be performed without negative terms, and contraposition and inversion are built on obversion. The obverse of "All members are graduates" is "No members are non-graduates", and the phrase is intelligible only because the universe is the membership and not the cosmos.

2. On the truth value of a proposition. The same words may be true in one universe and false in another. "Everything is a whole number" is true within arithmetic and false at large; "all the members are present" is true of a committee and false of the electorate. A proposition is not fully stated until its universe is fixed.

The modern counterpart

In modern logic the same idea is the domain of quantification: the set of things over which the variable ranges. "(x)(Sx ⊃ Px)" reads "for every x", and the domain says what the x's are.

For full marks, cover: the statutory definition; the leading case and its triple test; what is included and what excluded; the dominant nature test; the fate of the 1982 amendment; and, because this is a logic paper, what the definition illustrates.

The statutory definition

Section 2(j) of the Industrial Disputes Act 1947 defines "industry" as any business, trade, undertaking, manufacture or calling of employers, and includes any calling, service, employment, handicraft, or industrial occupation or avocation of workmen.

The definition has two limbs, one looking at the employer and one at the workmen, and the words "undertaking" and "service" are wide enough to have generated fifty years of litigation.

The leading case: the triple test

Bangalore Water Supply and Sewerage Board v A. Rajappa (1978) 2 SCC 213, a seven-judge Bench, laid down the triple test. An activity is an industry where there is:

1. systematic activity;

2. Activities where there is no employer-employee relationship, such as a purely individual professional practice with no organised co-operation.
3. Institutions run on a purely spiritual or religious basis, though the Court noted that even there an activity such as making and selling prasad on an organised footing may qualify.

The dominant nature test

Where an undertaking carries on several activities, some of which would be industry and some not, the Court applied a dominant nature test: look at the predominant activity of the whole and characterise the undertaking by it, rather than dissecting each department.

The 1982 amendment

Parliament tried to overturn parts of the decision by substituting a new definition of "industry" through the Industrial Disputes (Amendment) Act 1982, which expressly excluded hospitals, educational institutions and some others. That amendment has never been brought into force, so the definition in Section 2(j) as interpreted in Bangalore Water Supply continues to govern.

Rule 2. The dividing members must be mutually exclusive. Fallacy: overlapping division. Breach: "Human beings into men, women and doctors."

Rule 3. The division must be exhaustive. Fallacy: incomplete division. Breach: "Triangles into equilateral and isosceles", which omits the scalene.

Rule 4. The division must proceed step by step, to the proximate species. Fallacy: saltus in dividendo. Breach: "Literature into poetry, drama and the novel."

Rule 5. Every dividing member must be a species of the genus divided. Fallacy: partition mistaken for division. Breach: "Umbrella into rod, handle, spokes and cloth."

Division against partition

Division separates a class into kinds; partition separates an individual object into its parts. The test is to predicate the name of the whole of each member: "an epic is a poem" passes, "a handle is an umbrella" fails. Partition is not a fault in itself, only when offered as a logical division.

Reason: this is an exclusive proposition, marked by "alone", and the rule is that "Only S is P" becomes "All P is S": the terms change places when the exclusive sign is removed. The sentence asserts that nobody outside the class of graduates is eligible; it does not assert that every graduate is eligible, and writing "All graduates are eligible" would be a different and stronger proposition.

(ii) Few Indian wrestlers are long-lived.

Some Indian wrestlers are not long-lived persons. (O proposition)

Distributed: the predicate, "long-lived persons", only.

Reason: "Few" is not "a few". "Few S are P" carries a negative force, meaning not many, that is, that most are not, so the proposition is a particular negative. A negative distributes its predicate.

(iii) Only ignorant persons hold such opinions.

All persons who hold such opinions are ignorant persons. (A proposition)

Distributed: the subject, "persons who hold such opinions", only.

(i) "You will catch the plane if and only if you reach in time"

Identification: a compound proposition; the connective is the biconditional, or material equivalence.

• Let p = You will catch the plane.
• Let q = You reach in time.

Symbolic form: p ≡ q

Equivalently (p ⊃ q) · (q ⊃ p), since the biconditional is the conjunction of the two conditionals.

Truth table

(3) All that glitters is not gold. (Gx, Ax)

The sentence has two readings and both should be given.

Taken word for word it is "All glittering things are not gold", an E proposition: (x)(Gx ⊃ ~Ax).

Taken in its proverbial sense it is "Not everything that glitters is gold", an O proposition: ~(x)(Gx ⊃ Ax), equivalently (∃x)(Gx · ~Ax).

The idiomatic reading is the intended one, because gold does glitter, so the E reading is false and the proverb is not asserting a falsehood.

A note on the key: the paper gives Ax for "is gold", where Gx would be the natural letter and Gx has been used for "glitters". The answer follows the key as printed, because a symbolisation is judged by consistency and not by whether the letters are mnemonic.

Reasons: alcohol is not a species of medicine. It is a chemical compound which is sometimes used medicinally, and a use is not a genus: sugar is used as a preservative and is not a kind of preservative. Because the genus is misassigned there is no differentia at all, and the definition tells a reader nothing that would let him recognise alcohol.

It is too narrow, because alcohol used as a fuel or a solvent is no less alcohol; and too wide, because a great many things are kinds of medicine and are not alcohol.

Corrected: alcohol is a colourless volatile liquid formed by the fermentation of sugars, and the intoxicating constituent of wine, beer and spirits.

(ii) Man is a civilized rational animal.

Fallacy: the definition is too narrow, and the added word is an accident, not part of the differentia. It breaks rules 3 and 1.

Reasons: the classical definition is "man is a rational animal", with animal as the proximate genus and rational as the differentia, and it is exactly co-extensive. Adding "civilized" shuts out every human being who is not civilised, which is a counter-instance and proves the definition too narrow.

The rules of logical division

1. Only one fundamentum divisionis at each step; breach is cross-division.
2. The members must be mutually exclusive.
3. The division must be exhaustive.
4. It must proceed step by step; breach is the saltus in dividendo.
5. Every member must be a species of the genus divided.

(i) Man into Indians, Chinese and educated.

Fallacy: cross-division, and the members are not mutually exclusive.

(iii) Metals into white, heavy, ductile and precious.

Fallacy: cross-division of the worst kind, and the members overlap completely.

Reasons: four bases are used at one step: colour, weight, malleability and value. Every member answers a different question, and silver is white, heavy, ductile and precious all at once, so it belongs to all four members. Nothing has been sorted. The list is also not exhaustive on any of the four bases.

For full marks, cover: the question in the order it is asked. First the science-and-art question, answered as "both" with the sense of each; then the nature under its remaining heads; then the scope; then the significance in law courts, which is the specific tail; then the limits and a conclusion.

In what sense logic is a science

A science is a systematic body of general truths about some subject matter, arranged so that the later truths follow from the earlier. Logic is one: its truths about terms, propositions and inference are general, systematic and connected, and the whole of the syllogism follows from the distribution table.

⚠️ But it is a normative science, not a positive one. Physics and psychology describe what is; logic sets up a standard and judges by it, saying what ought to be. It belongs with ethics and aesthetics.

General. Every discipline reasons; logic examines reasoning itself, and is called the science of sciences, though it is the science of their method and not their master.

The scope

Deductive logic: terms, propositions, immediate inference (opposition and eduction), mediate inference (the syllogism), and modern symbolic logic. Inductive logic: observation and experiment, causation, hypothesis, Mill's methods, analogy, simple enumeration, probability. Applied logic: definition, division, classification, scientific method and the fallacies.

Its significance in law courts

1. The judgment is a syllogism. Rule of law as major premise, facts as found as minor, order as conclusion. Because the form is a syllogism, the distinction between an appeal on law and an appeal on fact is the distinction between attacking the major and attacking the minor.

2. Refuting a rule needs only its contradictory. To answer "all agreements of this kind are void", counsel need not prove "none is void"; "some are not void" suffices, and one instance proves it. That is what a distinguishing case does.

Conclusion

Logic is a science because it is a systematic body of truths about valid inference, and an art because it lays down rules for using them; it is normative, formal and general besides. In a court it is not an ornament: the judgment is cast in its form, refutation depends on its rules of opposition, and the appreciation of circumstantial evidence follows its inductive canons.

2. Particular: of a part only. Signs: some, a few, many, most, certain, sometimes.
3. Singular: the subject is one individual, and is treated as universal.

Quality

Settled by whether the copula joins or separates. Affirmative or negative.

⚠️ The quality is carried by the copula and nothing else. "All men are not-honest" is affirmative with a negative predicate.

The four forms

The uses

1. Opposition: the square is built on quantity and quality.
2. Eduction: the rules of conversion and obversion follow from distribution.
3. The syllogism: its rules are rules about distribution, and the undistributed middle and illicit process are breaches of them.

For full marks, cover: both definitions, since the question asks for two; the two branches of immediate inference; the strict conditions of opposition; the four forms; the drawn square; each relation with its rule and an illustration; the complete table of inferences; the modern square; and a legal illustration.

Immediate inference

Immediate inference is an inference drawn from a single premise, without the help of a middle term: the conclusion follows directly from one proposition.

It has two branches:

1. Opposition, in which the subject and predicate stay unchanged and only the quantity or the quality differs.
2. Eduction, in which the terms change place or are replaced by their contradictories: conversion, obversion, contraposition and inversion.

The contrast is with mediate inference, which needs two or more premises and a middle term, as the syllogism does.

The square of opposition

Diagram: draw a square with A at the top left, E at the top right, I at the bottom left and O at the bottom right. The top edge is contraries, the bottom edge sub-contraries, the two sides subalterns, and the two diagonals contradictories. The drawing is reproduced at the end of this answer.

The four relations, illustrated

1. Contradictories: A with O, E with I. Differing in both quantity and quality. Neither both true nor both false.

Illustration: if all advocates are graduates then it is false that some are not, and a single advocate without a degree settles both at once.

2. Contraries: A with E. Both universal, differing in quality. Not both true, but possibly both false.

Illustration: "All students are honest" and "No students are honest" both fail wherever the class is mixed, which is why the falsity of one leaves the other doubtful.

3. Sub-contraries: I with O. Both particular, differing in quality. Not both false, but possibly both true.

The modern square

The traditional square assumes the subject class has members. Modern logic reads a universal as a denial, so A no longer implies I nor E O, subalternation fails, and contrariety and sub-contrariety fail with it. Only the two diagonals survive.

Legal illustration

Take S as agreements with a minor, P as void agreements. A is the law after Mohori Bibee v Dharmodas Ghose (1903) 30 IA 114; O is its contradictory and false; E is its contrary and false; I is its subaltern and true.

The practical use: to defeat a rule stated as "all X are Y", establish its contradictory, which one instance proves.

For full marks, cover: each item with the form of the given proposition named, both answers written out where they exist, and the rule that produces each; and the two items where what is asked cannot be given, answered with the reason and with the relation that does exist.

The tables the answers depend on

Opposition: contradictories are A with O and E with I; contraries are A with E; sub-contraries are I with O; subalterns are A with I and E with O.

• Sub-contrary: an E proposition has no sub-contrary. Sub-contrariety holds only between the two particulars, I and O, at the foot of the square. An E proposition is universal; what it has at the top is a contrary, the A proposition "All animals with horns are carnivores".
• Contradictory (I): Some animals with horns are carnivores.

(iii) Some uranium isotopes are highly unstable substances. (Sub-contrary and subaltern)

An I proposition.

• Sub-contrary (O): Some uranium isotopes are not highly unstable substances.
• Subaltern: an I proposition has no subaltern. Subalternation runs downward from the universal to the particular, so only a universal has a subaltern beneath it. What stands above an I proposition is its subalternant, the A proposition "All uranium isotopes are highly unstable substances".

(iv) Some men are wise. (Converse and obverse)

An I proposition.