BLS LLB 5 Years Sem 1 Logic 1 2023-24 - ATKT 75/25 Question Paper with Solutions

Logic is the science and the art of reasoning: the study of the methods and principles by which correct reasoning is distinguished from incorrect reasoning.

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

Two standard definitions: Whately, logic is the science, and also the art, of reasoning; Copi, logic is the study of the methods and principles used to distinguish correct from incorrect reasoning.

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: the conclusion is only probable; it rests on uncontradicted experience and not on causation; one negative instance destroys it; and its probability rises with the number and the variety of the instances. Bacon dismissed it as childish.

Nuisance is an unlawful interference with a person's use or enjoyment of land, or of some right over or in connection with it.

Private nuisance is 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. Instances: noise, smoke, smell, dust, vibration.

Public nuisance is 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 may sue in tort only on proof of special damage.

Conversion is a form of eduction, that is, of immediate inference, in which the subject and the predicate of a proposition change places, the quality remaining the same and the meaning unchanged. The original is the convertend, the inferred proposition the converse.

Its rule: no term may be distributed in the converse unless it was distributed in the convertend.

3. To make disputes soluble. Many disputes are merely verbal: the parties agree on the facts and use a word differently. Defining the word ends the quarrel 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 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 merely naming it does not.

The modern classification, by purpose

1. Stipulative: assigns a meaning by declaration. Cannot be true or false, only useful or useless.
2. Lexical: reports the meaning a word already has. Can be true or false.
3. Precising: reduces vagueness at the borderline, as when a statute fixes an age of majority.

For full marks, cover: both definitions with examples; the point that the test is meaning and not spelling; privative terms; the difference between negative and contrary terms; infinite terms; the place of negative terms in obversion; and a legal application.

The two kinds

A positive term connotes the presence of a quality or attribute in the thing it denotes: man, honest, brave, legal, competent, present.

A negative term connotes the absence of that quality, and is usually formed by prefixing not, non, un, in or dis: not-man, dishonest, non-Indian, illegal, incompetent, absent.

The two are contradictory: between them they exhaust the universe of discourse, so everything is either a man or a not-man.

The test is the meaning, not the spelling

This is where the marks are, and three groups matter.

Infinite terms

A negative term such as "not-man" is sometimes called an infinite or indefinite term, because its denotation is unlimited: it takes in stones, ideas, numbers and everything else in the universe that is not a man. That is why negative terms are of little use as the subject of a proposition and are chiefly useful as predicates.

Where negative terms are needed: obversion

Obversion changes the quality of a proposition and replaces the predicate by its contradictory, so it cannot be performed at all without negative terms. "All men are mortal" obverts to "No men are non-mortal"; "Some men are not wise" obverts to "Some men are non-wise".

⚠️ The replacement must be the contradictory and never the contrary. The obverse of "All swans are white" is "No swans are non-white"; writing "No swans are black" would assert far less.

For full marks, cover: Section 13 with the maxim; Section 14 and free consent; each of the five vitiating factors with its section and effect; the table of consequences; the difference between no consent and unfree consent; and the logical point, since this is a logic paper.

Section 13: what consent is

"Two or more persons are said to consent when they agree upon the same thing in the same sense."

This identity of mind is called consensus ad idem. Where it is absent there is no consent at all, and therefore no agreement: the parties have not met.

Section 14: when consent is free

Consent is said to be free when it is not caused by:

1. Coercion (s.15): committing or threatening to commit any act forbidden by the Penal Code, or unlawfully detaining or threatening to detain any property, to the prejudice of any person, with the intention of causing a person to enter into an agreement.

Why Section 10 matters

Section 10 makes free consent one of the essentials of a valid contract, along with competence of the parties, lawful consideration, lawful object and the agreement not being expressly declared void. Free consent is therefore not an optional refinement: without it the agreement is at best voidable and at worst no contract at all.

For full marks, cover: what division is and its three elements; the two rules chosen, each stated, explained, and shown breached with a worked example and a correction; the other three listed for completeness; and the general test. The question asks for any two, so two are taken in full.

What division is

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.

Its three elements are the totum divisum, the class divided; the membra dividentia, the dividing members; and the fundamentum divisionis, the single attribute on which the division rests. Division sets out the denotation of a term, as definition sets out its connotation.

Rule 1 chosen: there must be only one fundamentum divisionis at each step

Statement. A division must proceed on one basis at a time. Every member of the genus must give exactly one answer to the single question the basis asks.

The fallacy on breach: cross-division.

Worked breach. "Vertebrates into fishes, birds and mammals." Amphibians and reptiles are vertebrates and appear nowhere, so the species fall short of the genus and the division sorts only part of what it claims to sort.

The opposite breach. "Coins into gold, silver, bronze and bank notes." A bank note is not a coin, so a member has been admitted which is not a species of the genus divided.

How to guarantee it. A dichotomy, dividing by a pair of contradictory terms, is exhaustive of necessity, because by the Law of Excluded Middle everything must be either S or not-S. That is why dichotomy is used as a first step where completeness matters.

Corrected: vertebrates into fishes, amphibians, reptiles, birds and mammals.

The other three rules, in brief

1. The members must be mutually exclusive; breach is overlapping division.
2. The division must proceed step by step to the proximate species; breach is the saltus in dividendo.
3. Every member must be a species of the genus divided; breach confuses division with partition, as in "umbrella into rod, handle, spokes and cloth".

Strict logical form and the distribution rule

A proposition is in strict logical form when it reads

quantity sign + subject term + copula (is or are, present tense) + predicate term

Universals distribute the subject; negatives distribute the predicate.

Reason: "Few" is not "a few". "Few S are P" carries a negative force, meaning not many, that is, that most are not. Here the sentence is "Few men are not in need of money", so it says that not many men lack the need, which is to say that most of them have it. The two negatives cancel and an affirmative particular is left.

(iii) Not all who try succeed.

Some persons who try are not persons who succeed.

Kind: O proposition, particular negative. Distributed: the predicate, "persons who succeed", only.

Reason: "not all" is the sign of a particular negative: it denies the universal without denying the whole. It does not say that nobody who tries succeeds, which would be E; it says only that they do not all succeed.

The biconditional is the conjunction of two conditionals, so it may equally be written (p ⊃ q) · (q ⊃ p). The table is built showing both, so the equivalence can be seen rather than asserted.

Truth table

Reading of the table: the biconditional is true when both components have the same truth value and false when they differ. It is contingent, and the identity of the last two columns proves the two forms equivalent.

What the proposition claims. Because it is a biconditional, taking the medicine is asserted to be both a sufficient and a necessary condition of the cure: not only will the medicine cure you, but nothing else will.

(ii) Symbolise the following propositions

1. All scientists are hardworkers. (Sx, Hx)

The rules a definition must satisfy

1. It must state the essential attributes, per genus et differentiam, and the genus must be the proximate one.
2. It must not be circular.
3. It must be co-extensive with the term defined, neither too wide nor too narrow.
4. It must not be in obscure or figurative language.
5. It must not be negative where it can be affirmative.

(i) Law is the backbone of order.

Fallacy: the definition is expressed in figurative or metaphorical language. It breaks rule 4.

Corrected: food is any substance taken into the body by mouth which nourishes it by supplying energy and building tissue. Naming the manner of taking supplies the differentia the original lacks.

(iii) A politician is a member of parliament.

Fallacy: the definition is too narrow. It breaks rule 3.

Reasons: very many politicians are not members of Parliament. A member of a State legislature, a municipal councillor, a party office-bearer and a defeated candidate are all politicians, and the definition shuts every one of them out. It therefore fails convertibility in one direction, and a single counter-instance proves it.

It is arguably too wide as well, since a person nominated to a House for distinction in the arts or sciences is a member of Parliament without being a politician. A definition can be too wide and too narrow at once, and where it is, say both.

Corrected: a politician is a person engaged in the activity of governing or of seeking public office.

Reasons: three bases are used at one step. Aryans and Mongolians divide mankind by race; "Asiatics" divides by geography; "Buddhists" by religion. Rule 1 is broken twice over, and rule 2 falls with it, because a Mongolian is very likely an Asiatic and may well be a Buddhist, so one man belongs to three members at once. The list is not exhaustive on any of the three bases either.

(ii) Wars into civil, aggressive and naval.

Fallacy: cross-division, and the members overlap.

Reasons: three bases again. "Civil" divides wars by who the parties are, that is, whether the fighting is within one State; "aggressive" divides them by the character or cause of the war, aggressive as against defensive; "naval" by the theatre in which they are fought, as against land and air. A war can be aggressive and naval at the same time, and a civil war can be fought at sea, so the members are far from exclusive.

A sound division on each basis: wars into civil and international; or into aggressive and defensive; or into land, naval and aerial.

(iii) Hindus into rich, tall, learned and Brahmans.

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

Logic is a NORMATIVE science, not a positive one. A positive science, such as physics or psychology, describes what is: how bodies actually move, how minds actually work, mistakes included. A normative science sets up a standard and judges by it: it says what ought to be. Logic tells us how we ought to reason if our conclusions are to follow, which is why it is grouped with ethics, the science of what we ought to do, and aesthetics, the science of what ought to please, and not with the natural sciences.

Logic is also an ART. A science states principles; an art lays down rules for practice. Logic does both, which is why Whately defined it as the science and the art of reasoning. The relation is that of anatomy to surgery.

⚠️ It is therefore misleading to say without qualification that logic is a science. It is a normative science and an art together, and the word in the old definition carries only the first half.

2. What 'law' means here

A law of thought is not a law in either of the two ordinary senses, and saying which two is what earns the marks.

They are also axioms, in that they cannot be proved without being assumed: any proof offered would already use them.

3. What 'thought' means here

"Thought" in this definition does not mean everything that passes through the mind. Memory, imagination, daydreaming, association of ideas and emotion are all mental processes and logic examines none of them; they belong to psychology.

Thought here means reasoning, that is, the process of passing from what is already accepted to something further on the strength of it.

Traditional logic recognises three grades of thought, and logic studies each in its expressed form, because only an expression can be examined by another person:

That is why the definition was replaced. Whately: logic is the science, and also the art, of reasoning. Copi: logic is the study of the methods and principles used to distinguish correct from incorrect reasoning. Copi's is the most exact of the three, because it names reasoning rather than thought, and because "distinguish correct from incorrect" states the normative character without needing the word "law" at all.

Conclusion

In the old definition, "science" means a systematic body of general truths, and must be read as a normative science that is also an art; "law" means neither a law of nature nor a law of the State but a principle stating a condition of valid thinking; and "thought" means not every mental process but reasoning, studied in its expressed form and in respect of its form alone. Read that way the definition is defensible; read in the ordinary senses of its words it is far too wide, and that is why later logicians preferred to define the subject by reasoning rather than by thought.

1. Universal: the predicate is affirmed or denied of the whole of the subject. Signs: all, every, any, no, none, whoever, always, never.
2. Particular: of a part only. Signs: some, a few, many, most, certain, sometimes.
3. Singular: the subject is one named individual. Treated as universal, so that it can be used in a syllogism.

Classification by quality

Quality is settled by whether the copula joins or separates.

1. Affirmative: the predicate is affirmed of the subject.
2. Negative: the predicate is denied of the subject.

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

The fourfold scheme

The mnemonic: universals distribute the subject; negatives distribute the predicate. Quantity governs the subject; quality governs the predicate.

Illustrating every cell

A: "All men are mortal." The proposition speaks of every man, so the subject is distributed. It does not speak of every mortal; it says only that the men are somewhere among the mortals, and leaves the rest of the mortals entirely out of account. So the predicate is undistributed.

E: "No men are angels." It speaks of every man, so the subject is distributed. It also shuts men out of the whole class of angels, because to exclude a thing from a class is to exclude it from every member of that class. So the predicate is distributed too.

What distribution is for

1. Eduction. The rule of conversion is that no term may be distributed in the converse unless it was distributed in the convertend, and the whole conversion table follows: A converts by limitation, E and I simply, and O not at all.
2. The syllogism. Two of its rules are rules about distribution: the middle term must be distributed at least once, breach of which is the fallacy of the undistributed middle; and no term distributed in the conclusion may be undistributed in its premise, breach of which is illicit major or illicit minor.

The modern re-expression

Modern logic keeps the four forms and writes them with quantifiers: (x)(Sx ⊃ Px), (x)(Sx ⊃ ~Px), (∃x)(Sx · Px), (∃x)(Sx · ~Px). It reads a universal as a denial that asserts nothing to exist, so A no longer implies I and E no longer implies O, and it has no need of distribution at all, because the rules that used it belonged to the syllogism.

For full marks, cover: the definition of opposition with its strict conditions; the four forms with one set of examples used throughout; the drawn square; each of the four relations with its rule and a worked illustration; the complete table of inferences from truth and from falsity, worked rather than merely printed; the modern square and existential import; and a legal illustration.

Opposition

Opposition is the relation between two propositions which have the same subject and the same predicate, but which differ in quantity, or in quality, or in both.

Three conditions are strict: the subject term must be the same, the predicate term must be the same, and both must be taken in the same sense and at the same time. Opposition is a form of immediate inference, drawn from a single premise with no middle term.

The four forms

Taking S as advocates and P as graduates:

2. Contraries: A with E. Both universal, differing in quality. They cannot both be true, but they may both be false.

Illustration: "All students are honest" and "No students are honest" cannot both hold; but in the ordinary case, where some are honest and some are not, both are false. That is why the falsity of one leaves the other doubtful.

3. Sub-contraries: I with O. Both particular, differing in quality. They cannot both be false, but they may both be true.

Illustration: if it is false that some advocates are graduates, then every advocate must be without a degree, so it is true that some are not. In the ordinary mixed case both are true together, which is why the truth of one leaves the other doubtful.

4. Subalterns: A with I, and E with O. Same quality, differing in quantity. The universal is the subalternant and the particular the subalternate. Truth descends and falsity ascends.

Existential import and the modern square

The traditional square assumes the subject class has at least one member. Modern logic reads a universal as a denial, so "All advocates are graduates" asserts only that there is no advocate who is not a graduate, and it stays true even if there are no advocates at all. On that reading A no longer implies I and E no longer implies O, so subalternation fails, and contrariety and sub-contrariety fail with it. Only the two diagonals survive: the modern square is an X.

Legal illustration

Take S as agreements with a minor, P as void agreements.

• A: All agreements with a minor are void, the law after Mohori Bibee v Dharmodas Ghose (1903) 30 IA 114.
• O: Some agreements with a minor are not void. Contradictory, therefore false.
• E: No agreements with a minor are void. Contrary, therefore false.
• I: Some agreements with a minor are void. Subaltern, therefore true.

For full marks, cover: two parts, and both must be there. Part one: what a definition is, its two elements, the classical form, the rules and the limits. Part two: the significance of logic in law, under numbered heads with a section or a case behind each. Divide the space roughly evenly, with a little more to the second part, which is the larger question.

Part one: what is definition?

The definition of definition

A definition is a statement which sets out the connotation of a term, that is, the attributes a thing must possess before the term can be applied to it. The term to be defined is the definiendum; the expression which defines it is the definiens.

Definition sets out the connotation of a term, as division sets out its denotation.

The classical form: per genus et differentiam

State the proximate genus and the differentia.

4. It must not be in obscure or figurative language.
5. It must not be negative where an affirmative is possible.

The working test of all of them is convertibility: read the definition backwards, and it must still hold.

What cannot be defined

The summum genus, because there is no wider class to serve as genus; individuals, because they have no differentia within a species; and simple unanalysable qualities, because there is nothing in them to take apart.

Part two: the significance of logic in law

1. Interpretation is applied connotation and denotation. A definition clause fixes the connotation of a word; the court decides what falls within its denotation. Ejusdem generis, by which general words following an enumeration are confined to the same kind, and noscitur a sociis, are rules about genus and species.

2. Drafting is applied definition and division. A definition clause too wide catches conduct the legislature never meant to reach; one too narrow leaves a gap only an amendment can fill; a circular one defines nothing. A schedule of categories must use one basis of division, or its entries overlap and every claim is litigable.

7. Pleadings and cross-examination rest on the laws of thought. Issues under Order XIV of the Code of Civil Procedure are framed on contradictory pairs; a written statement that admits and denies the same fact offends the Law of Contradiction; and cross-examination is a search for two propositions from one witness that cannot both be true.

8. Naming a fallacy answers it. Ad hominem, ad misericordiam, petitio principii, ignoratio elenchi and the undistributed middle are met in court constantly.

The limits

Logic tests validity; it does not supply the premises, and it cannot say what the law ought to be. As Holmes wrote in The Common Law (1881), the life of the law has not been logic but experience. Logic is necessary and not sufficient.

For full marks, cover: each item with the form named and the rule stated. Items (i) to (vii) carry one mark each and want one line; items (viii) and (ix) carry three each and want the steps written out. Two of the items are exceptions to the ordinary rule of conversion, and saying so is what they are set for.

(iii) "Some diamonds are precious stones." (Give Subcontrary) (1 mark)

An I proposition. Sub-contrary (O): Some diamonds are not precious stones.

Sub-contraries cannot both be false, though they may both be true.

(iv) "Everest is the highest mountain." (Give Converse) (1 mark)

Converse: "The highest mountain is Everest."

This is a singular proposition of identity: both its terms are singular, and it asserts that the two name the same thing. It therefore converts simply, and the reason is worth one line.

Reason: the ordinary bar on simple conversion of an affirmative proposition is that its predicate is undistributed. Here the predicate, "the highest mountain", is a singular term, and a singular term is necessarily distributed, because there is only one of it and the whole of it is spoken of. Nothing is therefore distributed in the converse that was not distributed in the original, and simple conversion is allowed.

(viii) "No man is perfect." (Give Contrapositive) (3 marks)

An E proposition. Contraposition is obversion followed by conversion; the full form adds a second obversion.

Step 1, obvert: All men are non-perfect. (A) Step 2, convert by limitation: Some non-perfect beings are men. (I), the partial contrapositive. Step 3, obvert again: Some non-perfect beings are not non-men. (O), the full contrapositive.

Answer: partial, "Some non-perfect beings are men"; full, "Some non-perfect beings are not non-men".

(ix) "All men are naturally good." (Give Contrapositive) (3 marks)

An A proposition.

Step 1, obvert: No men are non-(naturally good). (E) Step 2, convert (simple): No non-(naturally good) beings are men. (E), the partial contrapositive. Step 3, obvert again: All non-(naturally good) beings are non-men. (A), the full contrapositive.

Answer: partial, "No beings that are not naturally good are men"; full, "All beings that are not naturally good are non-men".