BLS LLB 5 Years Sem 1 Logic 1 2024-25 - ATKT 60/40 Question Paper with Solutions

The Law of Identity is the first of the three laws of thought. It states that whatever is, is: everything is identical with itself, and a term must keep the same meaning throughout an argument.

Symbolically: A is A, or p ⊃ p.

Example: "A contract is a contract." In use, the law requires that if "bank" means a financial institution in the premise, it must mean the same in the conclusion. A word that shifts its sense between the two produces the fallacy of equivocation:

All banks are beside rivers.
The State Bank of India is a bank.
Therefore the State Bank of India is beside a river.

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

Examples: the denotation of "man" is Rama, Shyam, Fatima and every other human being, past, present and future; the denotation of "triangle" is equilateral, isosceles and scalene triangles; the denotation of "contract" is sale, lease, agency and bailment.

It is contrasted with the connotation, or intension, which is the sum of the essential attributes the term implies: the connotation of "man" is animality together with rationality.

Logical division is the process of separating a class, called the genus, into the sub-classes or species contained under it, on the basis of a single attribute.

It has three elements: the totum divisum, the class divided; the membra dividentia, the dividing members or species; and the fundamentum divisionis, the single attribute on which the division rests.

Example: triangle, divided on the basis of the length of the sides, gives equilateral, isosceles and scalene triangles.

Analogy is that form of inference in which, from the resemblance of two things in certain respects, we conclude that they resemble each other in some further respect.

Its form is: A and B resemble each other in the properties p, q and r; A has the further property s; therefore B probably has s.

Example: Mars resembles the Earth in having an atmosphere, water and seasons; the Earth is inhabited; therefore Mars is probably inhabited.

Its conclusion is probable only, and it moves from particular to particular.

Nuisance is an unlawful interference with a person's use or enjoyment of land, or of some right over or in connection with it. The word comes from the French nuire, to hurt.

Its kinds are two:

1. Public nuisance, an act or illegal omission causing common injury, danger or annoyance to the public or to people in general in the vicinity. Section 268 of the Indian Penal Code 1860, now Section 270 of the Bharatiya Nyaya Sanhita 2023. It is a crime, and an individual can sue in tort only on proof of special damage.
2. Private nuisance, an unreasonable interference with a particular person's use or enjoyment of land. It is a tort, and only the occupier of the affected land may sue.

Some writers add a third, statutory nuisance, created and defined by particular statutes.

For full marks, cover: each of the two separately, with its divisions and its sign words; the combined A, E, I, O scheme; the distribution table that follows from the pair; the treatment of singular propositions; and why the pair matters to the square of opposition and to the syllogism.

Quantity

The quantity of a proposition is settled by how much of the subject the proposition is about.

1. Universal: the predicate is affirmed or denied of the whole of the subject. Sign words: all, every, any, no, none, whoever, always, never.

Example: All advocates are graduates.

1. Particular: the predicate is affirmed or denied of a part of the subject. Sign words: some, a few, certain, many, most, sometimes.

Example: Some advocates are graduates.

The letters come from the Latin AffIrmo, I affirm, and nEgO, I deny: the first two vowels of each word give the two affirmative and the two negative forms.

What follows: distribution

A term is distributed when the proposition speaks of every member of the class it names. Distribution follows directly from quantity and quality:

For full marks, cover: the rule broken; what "too narrow" means, with the test; three or four worked examples with the counter-instance for each; the contrast with "too wide"; how the fault arises; and a legal illustration.

The rule broken

A definition must be co-extensive with the term defined: neither too wide nor too narrow. Definition and definiendum must be interchangeable, which is the test of convertibility.

A definition is too narrow when it applies to less than the term applies to, that is, when there are things covered by the term which the definition shuts out.

The test

Read the definition backwards and forwards.

1. Is everything that satisfies the definition an instance of the term? If not, the definition is too wide.
2. Is every instance of the term covered by the definition? If not, the definition is too narrow.

A definition too narrow therefore fails the second direction, and a single excluded instance proves it.

How the fault arises

1. An accident is mistaken for the essence: colour, age or occupation is written into the definition.
2. One species is mistaken for the genus: sale is treated as though it were contract.
3. The definition is drawn from the most familiar instance, which is the commonest cause of all.

For full marks, cover: what quantification is; the propositional function it operates on; the two quantifiers with the connective each requires; the four traditional forms in quantified dress; the equivalences of quantifier negation; and, because the word carries a second meaning in a logic syllabus, Hamilton's quantification of the predicate and why it was rejected.

What quantification is

Quantification is the operation of prefixing a quantifier to a propositional function so as to turn it into a proposition. It is the device on which the whole of modern predicate logic rests.

A propositional function is an expression containing a variable which is neither true nor false as it stands: "x is a lawyer", written Lx. It becomes a proposition in two ways: by instantiation, putting a constant for the variable, La; or by quantification.

The two quantifiers

The universal quantifier, written (x) or ∀x, read "for every x". The existential quantifier, written (∃x), read "there is at least one x such that".

So "not every subject is difficult" becomes "some subject is not difficult", which is why the contradictory of A is O.

What quantification gained

1. Relations can be expressed: "Suresh is taller than Shyam" is Tsh, and "everybody loves somebody" is (x)(∃y)Lxy, neither of which the syllogism could state.
2. The order of quantifiers matters, and the difference is real: (x)(∃y)Lxy, everybody loves somebody, is not (∃y)(x)Lxy, there is somebody whom everybody loves.
3. Existential import is made explicit. A universal is read as a denial and asserts nothing to exist, which is why subalternation fails in the modern square and only the contradictories survive.

The other meaning: Hamilton's quantification of the predicate

In traditional logic the phrase also names Sir William Hamilton's proposal to attach a quantity sign to the predicate as well as to the subject, so that "All men are mortal" would be written "All men are some mortals". Combining two quantities for the subject with two for the predicate and two qualities yields eight propositional forms in place of four.

(i) Diamonds are not always shiny.

Some diamonds are not shiny things. (O proposition)

Distributed: the predicate, "shiny things", only.

Reason: "not always" denies universality without denying the whole. It does not say that no diamond is shiny; it says that they are not all shiny, which is a particular negative. Read "always" as the universal sign and the "not" as detaching it, and the O form follows.

(ii) Few males are househusbands.

Some males are not househusbands. (O proposition)

Distributed: the predicate, "househusbands", only.

Reason: "Few" is not "a few". "A few S are P" is affirmative and means that some are; "Few S are P" carries a negative force, meaning not many, that is, that most are not. The proposition is therefore a particular negative.

(iii) Politicians are never corrupt.

No politicians are corrupt persons. (E proposition)

(i) "Unless you strive for perfection, success is difficult"

Identification: a compound proposition. "Unless" means "if not", so the connective is the conditional with a negated antecedent.

• Let p = You strive for perfection.
• Let q = Success is difficult.

Symbolic form: ~p ⊃ q

Read: if you do not strive for perfection, then success is difficult.

Truth table

"Run!" is an imperative. It affirms nothing and denies nothing, so it is neither true nor false, and only what can be true or false is a proposition. Commands, questions, requests, prayers and exclamations are all sentences without being propositions. Logic has no symbol for it in the propositional or predicate calculus, and that is the answer the question is looking for.

3. Suresh is taller than Shyam.

A relational proposition: it does not attribute a quality to a subject but states a relation between two individuals.

Tsh, where T = "... is taller than ...", s = Suresh and h = Shyam.

Note that the order matters: Tsh and Ths say opposite things. Note also that traditional logic could not symbolise this at all, because it had to force everything into subject-copula-predicate; expressing relations is one of the gains of the modern classification.

Corrected: a spinster is an unmarried adult woman.

(ii) Water is a medicine for thirst.

Kind: a figurative definition, and in modern terms a persuasive one rather than a lexical one. It is defective on two counts.

Reasons: first, it is figurative: water is not a medicine, and calling it one is a metaphor. A definition must be plainer than the term defined, and this one substitutes a picture for an analysis. Second, it defines by effect rather than by essence, and the effect is not co-extensive with the term: buttermilk and lemon juice also relieve thirst, so the definition is too wide, while water used for washing is still water, so it is too narrow as well.

Corrected: water is a transparent, odourless liquid compound of hydrogen and oxygen, which names a genus and a differentia.

(iii) A genius is one who cannot earn his own living.

Kind: a persuasive definition.

The rules of logical division

1. Only one fundamentum divisionis at each step; breach is cross-division.
2. The members must be mutually exclusive; breach is overlapping division.
3. The division must be exhaustive; breach is incomplete division.
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) Vehicles into public vehicles, private vehicles, motor-cars and lorries.

Faulty: cross-division, and the members overlap.

(iii) Religion into hindu and non-hindu.

No fallacy. This is a division by dichotomy and it is formally faultless.

Reasons: one fundamentum divisionis is used, and because the two members are contradictories the division is necessarily exhaustive, since every religion must be one or the other, and necessarily mutually exclusive, since none can be both. Every rule is satisfied.

The criticism that may fairly be made is of usefulness, not validity. The negative member is wholly indeterminate: "non-hindu" tells us nothing about what its members are, and it lumps Islam, Christianity, Buddhism, Jainism, Sikhism and Zoroastrianism into one undifferentiated remainder. Dichotomy is therefore a first step only, and at the next step the negative member must be broken into positive species.

For full marks, cover: the definitions of logic with the etymology; the nature of the subject in brief, since a definition question expects it; then, at length, the uses in a court, which is what this question asks about and a general "utility in law" answer does not; the limits; and a conclusion.

Definition

The word logic comes from the Greek logos, meaning word, thought or reason. The subject was founded by Aristotle, whose logical works are collected as the Organon, the instrument.

1. The traditional definition: logic is the science of the laws of thought.
2. Whately: logic is the science, and also the art, of reasoning.
3. Copi: logic is the study of the methods and principles used to distinguish correct from incorrect reasoning.

2. Refuting a proposition requires only its contradictory. To answer "all agreements of this kind are void", counsel does not have to establish "no such agreement is void". The contradictory, "some such agreements are not void", is enough, and a single instance proves it. That is precisely what a distinguishing case does to a rule stated too widely.

3. Circumstantial evidence is applied induction. The five conditions in Sharad Birdhichand Sarda v State of Maharashtra AIR 1984 SC 1622, that the circumstances be fully established, consistent only with guilt, of a conclusive nature, excluding every other hypothesis, and forming a complete chain, are Mill's method of elimination in judicial dress.

4. Precedent is argued by analogy. To follow a case is to argue relevant resemblance between its material facts and the present ones; to distinguish it is to deny that the resemblance is the one that mattered. The relevance test of a good analogy is the whole technique of distinguishing.

5. Interpretation applies connotation and denotation. A definition clause fixes the connotation of a word and the court decides what falls within its denotation. Ejusdem generis and noscitur a sociis are rules about genus and species.

The limits

Logic tests the validity of reasoning; it does not supply the premises. Choosing the rule, finding the facts and weighing competing values are not logical operations. As Holmes wrote in The Common Law (1881), the life of the law has not been logic but experience. Logic is therefore necessary and not sufficient: an illogical judgment is certainly wrong, but a perfectly logical judgment may still be unjust.

Conclusion

Logic is the science and the art of reasoning, normative in character and formal in method. In a court it is not an ornament: the judgment is cast in its form, the advocate's refutation depends on its rules of opposition, the appreciation of circumstantial evidence follows its inductive canons, and the detection of a fallacy is often the whole of an answer. What it cannot do is decide what the law ought to be, and a lawyer who knows the difference is using it correctly.

First division: simple and compound

A simple proposition contains no other proposition as a component. Example: "Rama is honest."

A compound proposition contains at least one other proposition as a component, joined by a connective. Example: "Rama is honest and Shyam is diligent."

A compound is truth-functional when its truth value is completely determined by the truth values of its components and the connective. That property is what makes the truth table possible.

The five connectives

1. Negation (~p), "not p".

2. Conjunction (p · q), "p and q". True only when both conjuncts are true.

Compounds that are not truth-functional

A compound whose truth value is not settled by its components falls outside the scheme: "Rama believes that the earth is flat", "It is necessary that two and two are four", "He died because he was poisoned". Belief, modality and causation are handled by separate branches for exactly that reason.

Among the simple propositions: singular and general

1. Singular, attributing a predicate to a named individual, needing no quantifier: "Sachin is a cricketer", written Cs. This is a class-membership proposition.
2. Relational, stating a relation between individuals: "Suresh is taller than Shyam", written Tsh.
3. General, formed by quantifying a propositional function: universal, (x)(Sx ⊃ Px), or existential, (∃x)(Sx · Px). A universal affirmative is a class-inclusion proposition.

Conclusion

The modern classification groups propositions by what settles their truth value: simple or compound, and among the simple, singular, relational or general. It gains a mechanical test of validity, a symbolism free of the ambiguities of English, and the power to express relations and multiple generality. It does not discard the four traditional forms; it re-expresses them and shows what they always meant.

2. To mark the term off from every other. A good definition tells you not only what a thing is but what it is not, by naming the differentia that separates it from the other species of its genus.

3. To make disputes soluble. Many disputes are verbal, that is, the parties agree on the facts and use a word differently. Defining the word ends the dispute or shows that it was real after all.

4. To supply the major premise of an argument. "A contract is an agreement enforceable by law" is a definition, and it is also the premise from which it follows that an unenforceable agreement is no contract.

5. To introduce or fix a technical vocabulary. Every science and every statute defines its own terms, so that the reader is not left with the ordinary meanings.

6. To increase knowledge of the thing itself. A real definition, per genus et differentiam, states what the thing essentially is, and framing one forces an analysis that a mere name does not.

The kinds of definition, by purpose

1. Stipulative: assigns a meaning to a new word, or a new meaning to an old one, by declaration. It cannot be true or false, only useful or useless.

What it is

Induction by simple enumeration is that form of induction in which a general conclusion is drawn merely from the fact that all the observed instances agree and no contrary instance has been observed. It infers from "some" to "all" without discovering any causal connection.

Example: "All the crows I have seen are black; therefore all crows are black."

Its features

1. The conclusion is only probable, never certain.
2. It rests on uncontradicted experience, not on the law of causation.
3. A single negative instance destroys it: one white crow ends the generalisation.
4. Its probability increases with the number and, more importantly, the variety of the instances observed.

Its value and its weakness

Francis Bacon dismissed the method as childish, inductio per enumerationem simplicem ... res puerilis est, because it counts instances instead of looking for the cause, and because a run of agreeing cases may be a coincidence.

In law

Its legal cousin is the argument from an unbroken line of precedent, and it carries the same risk. A rule that has never been challenged is not thereby proved right; it may only be that the contrary instance has not yet come to court, and the first case that raises it may overturn a century of practice. The same caution applies to the appreciation of evidence: a witness who has always been truthful is probably truthful now, which is a reason and not a proof.

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. Only universals have contraries; only particulars have sub-contraries.

Conversion, subject to the rule that no term may be distributed in the converse unless it was distributed in the convertend:

Obversion, which changes the quality and replaces the predicate by its contradictory, and which works for every form:

The contradictory differs in both quantity and quality; the subaltern is the particular of the same quality, and truth descends to it from the universal.

(iii) All birds have wings. (Give Contrary and Subaltern) (2 marks)

Reduced: "All birds are winged creatures." An A proposition.

• Contrary (E): No birds are winged creatures.
• Subaltern (I): Some birds are winged creatures.

Contraries cannot both be true, though they may both be false. The subaltern follows from the truth of the universal.

(iv) Some politicians are not good orators. (Give Converse and Obverse) (2 marks)

An O proposition.

• Converse: an O proposition cannot be converted. It has no converse.

• Converse (I): Some naughty persons are babies. An I proposition converts simply, because it distributes neither term and so nothing can go wrong.