BLS LLB 5 Years Sem 1 Logic 1 2022-23 Question Paper with Solutions

Logic is the study of the methods and principles used to distinguish correct from incorrect reasoning. (Irving Copi)

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

Two other standard definitions: Whately, logic is the science, and also the art, of reasoning; and the oldest, logic is the science of the laws of thought.

Definition per genus et differentiam is the classical form of real definition: a term is defined by stating the proximate genus to which the thing belongs, together with the differentia which marks it off from every other species of that genus.

Definition = proximate genus + differentia

Examples:

• Man is a rational (differentia) animal (genus).
• A triangle is a plane figure bounded by three straight lines.
• A contract is an agreement enforceable by law (Section 2(h), Indian Contract Act 1872).

The Law of Contradiction is the second of the three laws of thought. It states that nothing can both be and not be at the same time and in the same respect; two contradictory propositions cannot both be true.

~(p · ~p), or "A is not not-A"

Example: "This agreement is void" and "This agreement is not void" cannot both be true of the same agreement at the same time.

⚠️ The qualification "at the same time and in the same respect" is part of the law, not decoration. A man may be tall beside one person and short beside another, and a contract may be valid as to one party and voidable as to the other; neither is a contradiction, because the respect differs.

A propositional function is an expression which contains one or more variables and which becomes a proposition when the variable is given a value or is bound by a quantifier. By itself it is neither true nor false.

Example: "x is a lawyer", written Lx. It becomes a proposition in two ways:

1. By instantiation, substituting a constant: "Ambedkar is a lawyer", La, which is true.
2. By generalisation, prefixing a quantifier: (x)Lx, everything is a lawyer, which is false; (∃x)Lx, something is a lawyer, which is true.

The idea belongs to modern symbolic logic and is due to Bertrand Russell.

For full marks, cover: the distinction; why logic is called formal; the demonstration by two arguments of the same form and different content; the reverse demonstration; symbolisation as the extreme of the method; the limits of formality, that is, validity against soundness; formal against material fallacies; and the legal application.

The distinction

The content, or matter, of an argument is what it is about: the particular terms and propositions that appear in it. The form is its structure: the arrangement of those terms and propositions, considered apart from what they mean.

Logic is a formal science, which means that validity is a property of the form alone. An argument is valid in virtue of its structure, so every argument with the same structure is valid too, whatever it happens to be about.

The demonstration: same form, different content

Symbolisation

Modern logic carries the method to its limit by replacing the content with symbols: statement letters p, q, r for whole propositions, predicate letters and variables for their parts. Once an argument is written as p ⊃ q, p, therefore q, nothing of the subject matter remains and the argument can be tested mechanically by a truth table.

The limits of formality

⚠️ Form settles validity and cannot settle truth. A valid argument with false premises proves nothing: "All birds are mammals; all crows are birds; therefore all crows are mammals" is perfectly valid and worthless.

What is wanted is soundness, which is validity plus true premises, and the truth of the premises is a matter of content. Logic can certify the form and no more; the content belongs to whoever knows the facts.

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.

1. Proper names denote an individual and connote nothing, because they identify without describing.
2. Abstract terms connote a quality and denote no class of individuals.
3. General terms have both, and are what logic ordinarily works with.

The link to definition and division

Definition sets out the connotation of a term, by naming the proximate genus and the differentia. Division sets out the denotation, by breaking the class into its species. That is why the three topics are always examined together, and it is why the inverse law matters: every step down a division is a step up in connotation.

Legal application

A definition clause fixes the connotation of a word and the court decides what falls within its 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.

What "coherence" means

More than consistency, which is merely the absence of contradiction. A coherent system is one whose members support one another, so that each helps to explain the rest and would be missed if it were removed. On the strongest version, held by the British idealists, the only completely true proposition is the whole system, and each single proposition is true only in degree, according to how much of the system it captures.

Its home

The theory belongs to the idealist tradition: Hegel, and in England F.H. Bradley and Bernard Bosanquet, and later Brand Blanshard. It has also been defended by philosophers of science who observe that a scientific claim is never tested against a bare fact but always against a body of theory.

Its merits

1. It states a test we actually use. We accept or reject a report by seeing whether it fits what we already know, and that is how a court weighs evidence.

The rivals

The correspondence theory: a proposition is true if it corresponds to a fact. Aristotle, Russell, Moore. Objection: the two sides cannot be compared as two objects can.

The pragmatic theory: a proposition is true if acting on it works. James, Dewey. Objection: a useful belief may be false, and an inconvenient truth is still true.

Legal application

A court applies coherence as a test while holding correspondence as the definition. 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 way a judge reaches that belief is by asking whether an account hangs together with the documents, the medical evidence and the other testimony. The standard direction on circumstantial evidence, that the circumstances must form a complete chain, is a demand for coherence in so many words.

3. Fraud (s.17): a false suggestion, active concealment, or a promise made without intention of performing it, done with intent to deceive.
4. Misrepresentation (s.18): a false statement made innocently, believing it true.
5. Mistake (ss.20 to 22).

The effects

Kind: I proposition, particular affirmative. Distributed: neither term.

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 children do not like chocolates", so it says that not many children dislike them, which is to say that most do like them. The two negatives cancel and an affirmative particular is left.

(ii) Plants grow towards the sun.

All plants are things that grow towards the sun.

Kind: A proposition, universal affirmative. Distributed: the subject, "plants", only.

Reason: the sentence prints no quantity sign, and an indefinite proposition stating a general truth of its kind is read as universal. The finite verb "grow" is split into the copula "are" and a predicate term, because in strict logical form the copula must be the bare verb "to be" in the present tense.

(iii) Certain men are atheists.

Some men are atheists.

(i) "He is clever and he is rich"

Identification: a compound proposition; the connective is conjunction, signalled by "and".

• Let p = He is clever.
• Let q = He is rich.

Symbolic form: p · q

The components are called conjuncts.

Truth table

An E proposition. Equivalently ~(∃x)(Sx · Ax): there is nothing that is both.

(c) Lions do not exist. (Lx)

~(∃x)Lx, equivalently (x)~Lx

This one is different in kind from the other two, and saying so is the point of it. It is not a proposition about the relation between two classes; it is an existence proposition, denying that the class of lions has any members at all. It therefore needs only one predicate letter, and no second predicate appears in the formula.

Traditional logic cannot express it. There is no subject-copula-predicate form for "lions do not exist" that is not misleading: "No lions are existent things" treats existence as a predicate, and Kant's objection is that existence is not a predicate. Modern logic writes the denial of existence directly with the quantifier, and that is one of the limitations discussed at Q18 of this paper.

Reasons: a ship is not a prison. The word is a metaphor, chosen to attach an unfavourable attitude to the thing defined while wearing the appearance of a plain report of meaning, which is exactly what a persuasive definition does. The sentence states no genus and no differentia, and it is not co-extensive in either direction, since prisons are not ships and a ship in dock offers no chance of drowning.

Corrected: a ship is a large sea-going vessel built to carry persons or goods over water.

(ii) A moral man is one who does not lie or steal or live intemperately.

Fallacy: the definition is negative where an affirmative is possible, and the enumeration of negatives is incomplete. It breaks rule 5, and rule 3 with it.

Reasons: morality is a positive quality of character and can be defined affirmatively, so the negative form is not forced on the definer as it is with a privative term such as "orphan". Worse, a list of things not done can never be complete: a man who tells no lie, steals nothing and drinks nothing may still be cruel, dishonest in other ways or indifferent to every duty, and the definition would still call him moral. It is therefore too wide.

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) Wars into civil, aggressive and naval.

Fallacy: cross-division, and the members overlap.

(iii) Sugar into whiteners and sweetness.

Fallacy: this is not a division at all. The members are not species of the genus, and one of them is an abstract term.

Reasons: two separate faults, and both should be named.

"Whiteners" is a use, not a kind. Whiteners are things used to whiten, and the class takes in chalk and titanium dioxide as well as sugar. Sugar may be used as a whitener; a whitener is not a species of sugar. Rule 5 is broken.

"Sweetness" is an abstract term, and worse. It names a quality, not a kind of thing at all. Sugar has sweetness; sugar is not divided into sweetness. A division separates a class into sub-classes, and an attribute is not a sub-class of the things that possess it, so what has been offered is not a division of sugar but a confusion of the substance with one of its properties.

A sound division of the genus: sugar into cane sugar, beet sugar and palm sugar, on the basis of its source; or into raw, refined and brown, on the basis of processing.

For full marks, cover: the etymology and three definitions with the criticism of the oldest; then the features under numbered heads, which is what this question asks for and what distinguishes it from a plain "nature and scope" question; the scope briefly; the utility; the limits; and a conclusion.

Definition

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

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.

The first is too wide, because thought includes memory and imagination, which logic does not examine. The later two narrow the subject to reasoning, and Copi's adds that logic discriminates rather than describes.

6. It is concerned with inference, not with the discovery of truth. It takes the premises as given and asks only whether the conclusion follows.

7. It deals with thought as EXPRESSED. A mental act cannot be examined by anyone but the thinker, so logic works on the term, the proposition and the argument, which are the expressions of the concept, the judgement and the inference.

8. Its conclusions are certain in deduction and probable in induction, and it keeps the two apart rather than treating one as a defective form of the other.

The scope, in brief

Deductive logic: terms, propositions, immediate inference, the syllogism, symbolic logic. Inductive logic: observation and experiment, causation, hypothesis, Mill's methods, analogy, probability. Applied logic: definition, division, classification, scientific method and the fallacies.

Conclusion

Logic is the science and the art of reasoning: normative because it sets a standard, formal because validity belongs to structure, general because every subject reasons, and concerned throughout with the form of inference rather than the truth of what is inferred from. It is necessary to good thinking and not sufficient for it, and knowing that boundary is part of using it.

2. It cannot express RELATIONS. "Shyam is taller than Ravi" states a relation between two individuals. Traditional logic must read it as attributing the quality "taller-than-Ravi" to Shyam, which hides the fact that Ravi is a second term and makes the obvious inference from "Shyam is taller than Ravi" and "Ravi is taller than Mohan" impossible to draw formally.

3. It cannot express MULTIPLE GENERALITY. "Every advocate has a client" contains two quantities, one over advocates and one over clients, and the subject-predicate form has room for only one. The difference between "everybody loves somebody" and "there is somebody whom everybody loves" cannot even be stated.

4. It cannot express EXISTENCE propositions. "Lions do not exist" is not a statement about the relation between two classes. Rendering it "No lions are existent things" treats existence as a predicate, which Kant's famous objection denies. Modern logic writes ~(∃x)Lx and the difficulty vanishes. (This paper sets exactly that proposition at Q14.)

8. It treats COMPOUND propositions only by reduction. Hypotheticals and disjunctives are dealt with by turning them into categoricals, which loses their structure. The relation between "if p then q" and "not q, therefore not p" is invisible in the categorical form and obvious in the truth-functional one.

9. It leaves MODALITY unanalysed. Assertoric, problematic and apodeictic are named and no rules of inference are given for them, and modal logic had to be built separately in the twentieth century.

10. It does not remove the AMBIGUITY of ordinary language. The classification works on English sentences, and "or", "if" and "all... not" are ambiguous. Symbolisation fixes each connective by definition, so nothing turns on how a sentence happens to be phrased.

What modern logic does instead

It classifies propositions by what determines their truth value: simple or compound, and among the simple, singular, relational or general. It keeps the four traditional forms and rewrites them with quantifiers, (x)(Sx ⊃ Px), (x)(Sx ⊃ ~Px), (∃x)(Sx · Px), (∃x)(Sx · ~Px), which makes the existential-import question explicit instead of hidden.

For full marks, cover: the definition with its three strict conditions; the four forms with one set of examples used throughout; the drawn square; each kind of opposition explained and illustrated, since the question asks for both; the complete table of inferences; the modern square; and a legal illustration.

Definition

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. Two propositions with different terms are not opposed at all; they are merely different.

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:

Illustration: if it is true that all advocates are graduates, then it is false that some advocates are not; and if that is false, the first is true. One advocate without a degree settles both at once. This is why, to defeat a rule stated as "all X are Y", a single counter-instance is enough.

2. Contrary opposition: 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. In the ordinary case, where some are honest and some are not, both are false, which is precisely why the falsity of one leaves the other doubtful.

3. Sub-contrary opposition: 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 no advocate is one, so it must be 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.

"Doubtful" is a result, not an evasion: it means the truth value is not settled by the premise.

The modern square

The traditional square assumes the subject class has members. Modern logic reads a universal as a denial, so it asserts nothing to exist, and A no longer implies I nor E O. Subalternation fails, and contrariety and sub-contrariety with it. Only the two diagonals survive.

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: induction and the inductive leap; the definition with examples; the characteristics as numbered points; the grounds it rests on; Bacon's criticism and Mill's qualified defence; the conditions under which it grows strong; the comparison with perfect and scientific induction; and, since the question names it, the value of the method, given its own section.

Induction and the inductive leap

Induction is the process of inferring a general proposition from the observation of particular instances. Because the conclusion asserts more than the premises, there is a gap between the evidence and what is concluded, and that gap is the inductive leap.

The definition

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.

The grounds it rests on

Like every induction it assumes the uniformity of nature. Unlike scientific induction it does not rest on the law of universal causation, because it discovers no cause: it records that A and B have gone together and infers that they always will. That is its weakness, because a run of agreeing instances is consistent with a causal connection and equally consistent with coincidence.

Bacon's criticism

Bacon, in the Novum Organum, dismissed it: inductio per enumerationem simplicem ... res puerilis est, induction by simple enumeration is a childish thing.

His three objections: it counts instances instead of weighing them; it is passive, waiting on nature instead of questioning her by experiment; and it does not search for the negative instance, which is the one thing that would test it.

Its value

The question asks for it separately, so it gets its own heads.

1. It is the foundation of ordinary life. Almost every practical belief rests on it: that the sun will rise, that bread nourishes, that a familiar road leads where it always has. Nobody establishes a cause before acting.

Conclusion

Simple enumeration is the weakest form of induction and the most used. It generalises on a run of agreeing instances without discovering why they agree, so its conclusion is probable and one exception destroys it. Bacon was right that it is not the method of science; Mill was right that it cannot be done without. Its value lies at the beginning of enquiry, where it supplies the hypothesis, and in the whole of ordinary life, where nothing better is available.

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.

Conversion, subject to the rule that no term may be distributed in the converse unless it was distributed in the convertend: A converts by limitation to I; E and I convert simply; O cannot be converted.

Obversion, which changes the quality and replaces the predicate by its contradictory, works for every form: A gives E, E gives A, I gives O, O gives I.

(i) Girls always obey their parents. (State contrary) (1 mark)

Reduced: "All girls are persons who obey their parents." An A proposition, since "always" is a universal sign.

Contrary (E): No girls are persons who obey their parents.

(ii) A few writers are teachers. (State Contradictory) (1 mark)

An I proposition. "A few", with the article, is affirmative.

Contradictory (E): No writers are teachers.

This is conversion by limitation, or per accidens. The subject of an A proposition is distributed but the predicate is not, so when the predicate becomes the subject of the converse it must stay undistributed, and only a particular proposition leaves its subject undistributed.

(vii) Some men are not wise. (State Contrapositive) (3 marks)

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

Step 1, obvert: Some men are non-wise. (I) Step 2, convert (simple): Some non-wise beings are men. (I), the partial contrapositive. Step 3, obvert again: Some non-wise beings are not non-men. (O), the full contrapositive.

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

Note that an O proposition can be contraposed although it cannot be converted, because obversion turns it into an I proposition first, and an I proposition converts simply.

(viii) No men are angels. (State Inverse) (4 marks)

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