BLS LLB 5 Years Sem 1 Logic 1 2024-25 - ATKT 75/25 Question Paper with Solutions

Inference is the mental process by which the mind passes from one or more propositions, called the premises, to another proposition, called the conclusion, which is asserted on the strength of them.

Example:

All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.

Its three marks are: there must be two or more propositions; there must be a relation of implication between them; and the conclusion must be asserted because of the premises, not merely after them.

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

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

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

Section 13 of the Indian Contract Act 1872: "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.

Section 14 adds that consent is free when it is not caused by coercion (s.15), undue influence (s.16), fraud (s.17), misrepresentation (s.18) or mistake (ss.20 to 22).

Section 10 makes free consent an essential of a valid contract. Consent caused by coercion, undue influence, fraud or misrepresentation makes the agreement voidable at the option of the party whose consent was so caused (ss.19 and 19A); a bilateral mistake of fact makes it void (s.20).

Both are denotative techniques: they show what a term covers instead of stating what it means.

An ostensive, or demonstrative, definition defines a term by pointing at an instance of it. Example: "This is a pen", said while holding one up. It is how a child learns a first language, and how colours and tastes are taught.

An extensive definition, or definition by denotation, defines a term by enumerating the individuals or the species it denotes. Example: "By a metal is meant a substance such as gold, silver, copper, iron and aluminium."

For full marks, cover: both definitions; the kinds of sentence that are not propositions; the table of differences; the two directions of the many-to-one relation; the third term, judgement; and why logic reduces sentences to logical form.

Sentence

A sentence is a grammatical unit: a group of words which is complete in itself as an expression of thought. Grammar divides sentences into assertive, interrogative, imperative, optative and exclamatory.

Proposition

A proposition is a statement in which something is affirmed or denied of something else, and which is therefore either true or false. It has three parts: subject, predicate and copula.

Only one kind of sentence expresses a proposition

An assertive sentence asserts something and so is true or false. The others do not:

The relation runs both ways

One proposition may be expressed by many sentences. "Rama killed Ravana" and "Ravana was killed by Rama" are two sentences and one proposition, and a translation into Marathi would be a third sentence and still the same proposition.

One sentence may express different propositions on different occasions, because of ambiguity or because it contains a word such as "I", "here" or "now" whose reference changes with the speaker.

The third term: judgement

A judgement is the mental act of affirming or denying. The proposition is that act expressed; the sentence is the grammatical clothing the expression wears. Judgement belongs to psychology, proposition to logic, sentence to grammar.

• Radhey Shyam v Gur Prasad AIR 1978 All 86: a flour mill causing continuous noise in a residential area was restrained.
• Ram Raj Singh v Babulal AIR 1982 All 285: dust from a brick grinding machine entering a doctor's consulting room was actionable.

Public nuisance

Section 268 of the Indian Penal Code 1860, now Section 270 of the Bharatiya Nyaya Sanhita 2023: an act or illegal omission causing common injury, danger or annoyance to the public, or to people in general who dwell or occupy property in the vicinity.

It is a crime, punishable under Section 290 IPC (Section 292 BNS). An individual may sue in tort only on proof of special damage (Campbell v Paddington Corporation [1911] 1 KB 869). Public remedies: Section 91 of the Code of Civil Procedure 1908, and Section 133 of the Code of Criminal Procedure 1973, now Section 152 of the Bharatiya Nagarik Suraksha Sanhita 2023.

The differences

For full marks, cover: the statement of the theory; its history; its merits; the three standard objections; the two rival theories; and its place in the law of evidence.

The theory stated

The correspondence theory holds that a proposition is true if, and only if, it corresponds to a fact, and false if it does not. Truth is a relation between what is asserted and what is the case; it is not a property a proposition has by itself.

The oldest statement is Aristotle's: to say of what is that it is, and of what is not that it is not, is true. In modern philosophy it was developed by G.E. Moore, Bertrand Russell and, in the Tractatus, by Ludwig Wittgenstein, whose picture theory treats a true proposition as a picture whose structure matches that of a fact.

Its merits

1. It matches ordinary usage: to ask whether a statement is true is to look for the fact it reports.

Its place in law

Judicial fact-finding is correspondence-based. Section 3 of the Indian Evidence Act 1872, now Section 2(1) of the Bharatiya Sakshya Adhiniyam 2023, defines a fact as "proved" when the court believes it to exist, and the whole law of relevancy is machinery for testing an assertion against what happened.

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.

(i) Many citizens are present at the meeting.

Some citizens are persons present at the meeting.

(i) "If and only if laws are just will they be obeyed"

Identification: a compound proposition; the connective is the biconditional, or material equivalence, signalled by "if and only if".

• Let p = Laws are obeyed.
• Let q = Laws are just.

Symbolic form: p ≡ q

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

Truth table

It is not the case that every subject is difficult, that is, some subject is not difficult. An O proposition.

(b) A few men are ambitious. (Mx, Ax)

(∃x)(Mx · Ax)

There is at least one x which is a man and is ambitious. An I proposition. Note "a few", with the article, is affirmative.

(c) All great poets are creative. (Px, Cx)

(x)(Px ⊃ Cx)

For every x, if x is a great poet then x is creative. An A proposition.

Reasons: one word is offered as equivalent to another. No genus and no differentia are stated, so nothing is analysed. It helps only a reader who already knows "courage", and because the two words are near enough to identical in English, the definition comes very close to explaining a thing by itself, which is the fault of circularity. A real definition would name the genus: valour is a quality of mind which enables a person to face danger without fear.

(ii) Ocean means Arctic, Antarctica, Atlantic, Indian and Pacific.

Kind: an extensive definition, that is, a definition by enumeration. A denotative technique.

Reasons: the term is defined by listing the members it denotes rather than by stating the attributes it connotes.

Worth noticing, because it is unusual: the enumeration here is complete, since there are exactly five oceans, so the definition does not suffer from the ordinary weakness of the extensive form, which is that an open class can never be exhausted. It is still not a real definition: it tells the reader which bodies of water are oceans and nothing at all about what makes them oceans, so a newly named sixth ocean could not be recognised from it.

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.

Two of the three divisions below are sound, and saying so is part of the answer.

(i) Educational institutions into schools and colleges.

Fallacy: the division is incomplete.

The one qualification: some events have both a natural trigger and a human cause, a flood worsened by bad drainage being the standing example. That does not break the division, because the members remain exclusive in the same respect; it means only that a single event may be classified twice over on two different aspects.

(iii) Hindus into those who are religious minded and those who are not.

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

Reasons: one fundamentum divisionis is used, the presence or absence of religious-mindedness. Because the two members are contradictories, the division is necessarily exhaustive, since everyone must be one or the other, and necessarily mutually exclusive, since nobody 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: it says only what its members are not. Dichotomy is therefore used as a first step, the negative member being broken into positive species at the next.

For full marks, cover: both definitions with an illustration of each; the points of distinction in a table; then, because the question asks for it "precisely", the connection under numbered heads; the place of both in scientific method and in legal reasoning; and a conclusion.

The two branches

Deductive logic studies inference in which the conclusion follows necessarily from the premises, so that it can never be wider than they are. If the premises are true the conclusion must be true.

All men are mortal. Socrates is a man. Therefore Socrates is mortal.

Inductive logic studies inference in which, from a number of observed particular instances, a general conclusion is drawn which goes beyond the evidence and is therefore only probable.

This crow is black, and that one, and that one. Therefore all crows are black.

2. Deduction supplies premises induction needs. Every induction rests on the uniformity of nature and the law of universal causation. Those cannot be established inductively without circularity, so they are assumed and used as a major premise, which is a deductive use.

3. Mill's methods are deductive in form. The Method of Agreement, the Method of Difference and the rest are general rules applied to instances exactly as a major premise is applied to a minor. At the point where induction becomes rigorous, it borrows the form of deduction.

4. Scientific method runs both in one cycle. Observation gathers particulars; induction frames a hypothesis; deduction draws out what must follow if the hypothesis holds; observation and experiment test those consequences. This is the hypothetico-deductive method, and neither half can be removed.

5. They divide the labour, not the subject. Deduction is concerned with validity, induction with truth, and an argument needs both to be sound. They are two requirements on one process rather than two rival processes.

For full marks, cover: what the fourfold classification is and the two bases it rests on; quantity with its signs; quality with the rule about the copula; the four forms in a table with examples; the letters and where they come from; distribution, which follows from the pair; singular and other awkward propositions; the uses of the classification in opposition, eduction and the syllogism; the modern re-expression; and a conclusion.

What the fourfold classification is

The fourfold classification divides categorical propositions into A, E, I and O, by combining the two divisions of quantity with the two divisions of quality. It is the foundation of the whole of traditional deductive logic, because opposition, eduction and the syllogism are all stated in terms of these four forms.

Quantity

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

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.

2. Eduction. Conversion and obversion are stated form by form, and the rules follow from distribution: A cannot be converted simply, O cannot be converted at all.
3. The syllogism. Its rules are rules about distribution: the middle term must be distributed at least once, and no term distributed in the conclusion may be undistributed in its premise.

The modern re-expression

Modern logic keeps the four forms and rewrites them with quantifiers: (x)(Sx ⊃ Px), (x)(Sx ⊃ ~Px), (∃x)(Sx · Px), (∃x)(Sx · ~Px). The change is not cosmetic. On the modern reading a universal asserts nothing to exist, so A no longer implies I and E no longer implies O, and with subalternation gone, contrariety and sub-contrariety go too.

For full marks, cover: why the traditional scheme was replaced; simple against compound; the five truth-functional connectives with symbol, meaning and truth table; compounds that are not truth-functional; singular, relational and general propositions, with class membership against class inclusion; tautologous, contradictory and contingent forms; and a legal illustration.

Why a new classification was needed

Traditional logic classified propositions by quantity, quality, relation and modality, reducing everything to A, E, I and O. Three limits made that insufficient: it forces every proposition into the subject-predicate mould; it cannot express relations such as "Suresh is taller than Shyam"; and it cannot express multiple generality such as "every advocate has a client". It also offered no mechanical test of validity.

Modern logic, developed by Boole, Frege, Peano, Russell and Whitehead, classifies propositions by what determines their truth value.

4. Implication (p ⊃ q), "if p then q". The first component is the antecedent, the second the consequent. False only when the antecedent is true and the consequent false. This is material implication and asserts no real connection between the two.

5. Equivalence (p ≡ q), "p if and only if q". True when both components have the same truth value. It is the conjunction of the two conditionals.

The four binary connectives are best set out in one table, because the whole of the propositional calculus is contained in these four columns:

Read down the columns: conjunction is true on one row, disjunction false on one row, implication false on one row, equivalence true on two.

1. Tautologous, true on every row: p v ~p.
2. Contradictory, false on every row: p · ~p.
3. Contingent, true on some rows and false on others: p ⊃ q.

Legal illustration

Statutes are written in these connectives and the choice decides cases. Conjunction makes conditions cumulative: Section 10 of the Contract Act requires free consent and competence and lawful consideration and lawful object. Disjunction makes them alternative. Implication is the form of every proviso and deeming clause. Equivalence is what a definition clause asserts.

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.

Its place among the forms of inference

Analogy is neither deduction nor complete induction. Not deduction, because the conclusion can be false while the premises are true; not a full induction, because it does not generalise to a class but moves from particular to particular. Its conclusion is always probable, which is why the question of soundness arises at all: there is no valid or invalid here, only stronger and weaker.

The soundness of an analogical argument: six tests

1. The number of respects in which the two things resemble each other. The more the better, because every further agreement makes coincidence less likely. But number alone is worth little; see the second test.

2. The relevance of the resemblances to the property inferred. This is the decisive test, and every other one is subordinate to it. A resemblance strengthens the argument only if it is causally connected with the property inferred. Two cars of the same colour tell us nothing about their engines; two cars of the same make and model tell us a great deal. Ten irrelevant resemblances are worth less than one relevant one.

The fault is never that the two things are unlike, since no two things are alike in everything. It is that the likeness relied on has nothing to do with the conclusion drawn. The stock example is the argument that a State should be run like a household, which treats a political community as though it were a family.

Analogy in law, and its limits

Precedent is analogical reasoning. To follow a case is to argue that its material facts resemble the present ones in the respects that produced the earlier result; to distinguish it is to argue that they do not. That is test 2 in daily use. Analogy also fills gaps where no rule covers a case, as when the duty of care in Donoghue v Stevenson [1932] AC 562 was extended from a manufacturer of ginger beer to manufacturers generally, and the interpretive maxims ejusdem generis and noscitur a sociis are rules for reasoning from likeness.

Its limits are firm. In criminal law analogy is forbidden, because no act is an offence unless the law makes it one and Article 20(1) would be defeated. It cannot override an express provision. And it proves nothing by itself: the conclusion is probable, and a court that reasons only by analogy has given a reason, not a demonstration.

For full marks, cover: each item with the given proposition's form named, the answer written out in full, and the rule that produces it. The last two items carry three and four marks, so they need their steps shown.

Contraries are the two universals differing in quality. They cannot both be true, though they may both be false. Here the original is true, so the contrary is false.

(iii) "No dishonest person is brave." (State Subaltern) (1 mark)

An E proposition.

Subaltern (O): Some dishonest persons are not brave.

The subaltern is the particular of the same quality. Truth descends from the universal to it.

(iv) "Some Scientists are mathematicians." (State Contradictory) (1 mark)

An I proposition.

Contradictory (E): No scientists are mathematicians.

The contradictory differs in both quantity and quality. The two cannot both be true and cannot both be false.

(v) "All lecturers are voters." (State Obverse) (1 mark)

An A proposition.

Obverse (E): No lecturers are non-voters.

The quality changes from affirmative to negative and the predicate is replaced by its contradictory.

(viii) "All irrelevant talk is useless." (State Inverse) (4 marks)

An A proposition. Inversion infers a proposition whose subject is the contradictory of the original subject.

Step 1, obvert: No irrelevant talk is non-useless. (E) Step 2, convert: No non-useless talk is irrelevant talk. (E) Step 3, obvert: All non-useless talk is non-irrelevant talk. (A) Step 4, convert by limitation: Some non-irrelevant talk is non-useless talk. (I), the partial inverse. Step 5, obvert: Some non-irrelevant talk is not useless talk. (O), the full inverse.

Answer: partial inverse, "Some talk that is not irrelevant is not-useless"; full inverse, "Some talk that is not irrelevant is not useless".

The results for the four forms are: A gives the inverse "Some non-S is not P"; E gives "Some non-S is P"; I and O have no inverse at all, because neither can begin the chain.