BLS LLB 5 Years Sem 1 Logic 1 2024-25 - ATKT Set 2 60/40 Question Paper with Solutions

A proposition is a statement in which something is affirmed or denied of something else, and which is therefore necessarily either true or false.

Example: "All men are mortal."

It has three parts: the subject ("men"), the predicate ("mortal") and the copula ("are"), which joins the two and asserts the relation between them.

Connotation is of three kinds, and the subjective connotation of a term is the set of attributes which a particular individual actually associates with that term in their own mind.

It varies from person to person and with each person's knowledge and experience. To a chemist the subjective connotation of "water" includes its molecular composition; to a child it is a clear liquid that quenches thirst.

The other two kinds are:

1. Objective connotation: the whole set of attributes actually possessed by the things the term denotes, known and unknown alike.
2. Conventional connotation: the attributes fixed by the usage of the language community, which is what a definition states and what logic works with.

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

Its two branches are:

1. Opposition, in which the subject and predicate stay unchanged and only the quantity or the quality differs: from "All advocates are graduates" being true it follows at once that "Some advocates are not graduates" is false.
2. Eduction, in which the terms change place or are replaced by their contradictories: conversion, obversion, contraposition and inversion.

The Law of Identity is the first of the three laws of thought. It states that whatever is, is: everything is identical with itself.

Symbolically: A is A, or p ⊃ p.

Its practical force is that a term must keep the same meaning throughout an argument. A word that shifts its sense between premise and conclusion breaks the law, and the resulting mistake is the fallacy of equivocation.

A relational proposition is one which asserts a relation between two or more terms, instead of attributing a predicate to a single subject.

Examples: "Shyam is taller than Ravi"; "Bombay is west of Nagpur"; "A owes money to B".

Traditional logic could not handle them, because it had to force every proposition into subject, copula and predicate. Modern logic symbolises them with a many-place predicate: "Shyam is taller than Ravi" is written Tsr, where T is the two-place relation "... is taller than ...", s is Shyam and r is Ravi.

For full marks, cover: what a term is; each kind defined with examples; the third kind, collective; the table of differences; connotation and denotation applied to each; and the legal application.

What a term is

A term is a word or group of words which can stand as the subject or the predicate of a proposition. Terms are classified in several ways, and one of them is by how many individuals the term applies to.

Singular term

A singular term is one which denotes a single definite individual, and only that individual.

Its kinds:

1. Proper names: Rama, the Ganga, the Taj Mahal.
2. Descriptive phrases that pick out one individual: the present Chief Justice of India, the author of Hind Swaraj.
3. Demonstratives with a common noun: this book, that man.

Why a singular term is said to have no connotation

A proper name identifies without describing. "Rama" tells you which individual is meant and nothing about what he is like, and it would go on naming the same person if every one of his attributes changed. J.S. Mill put it that a proper name is a mark set on an individual, not a description of him. It follows that a proper name cannot be defined per genus et differentiam, since it has no differentia within a species, and can only be explained by describing the individual.

For full marks, cover: what a disjunctive proposition is and what a disjunct is; both senses with symbol, meaning and truth table; the test that tells them apart; why logic takes the weak sense as basic; the disjunctive syllogism and the fallacy it invites; and the legal application.

The disjunctive proposition

A disjunctive or alternative proposition asserts an alternation between two or more propositions, joined by "either ... or". Each component is called a disjunct or an alternative.

Example: "Either the accused confesses or the prosecution proves the charge."

The words "either ... or" carry two different meanings in ordinary English, and the two disjuncts are accordingly called weak or strong.

The weak, or inclusive, sense

A weak disjunction asserts that at least one of the disjuncts is true, and leaves open the possibility that both are.

Example: "The accused is either guilty or innocent." He cannot be both.

How to tell which is meant

Ask whether the two disjuncts can both hold. Where they are contradictories, or are otherwise mutually exclusive by their nature, the sense is strong. Where they can coexist, the sense is weak. English gives no reliable sign, which is why the symbol is fixed by definition.

Why logic takes the weak sense as basic

Because the weak sense is the weaker of the two and is common to both uses. Whatever the strong sense asserts, the weak sense asserts as well, with the extra denial ~(p · q) added. So logic takes the weaker as the primitive connective and builds the stronger out of it when it is wanted, rather than the other way round.

The disjunctive syllogism, and the fallacy it invites

From a disjunction and the denial of one disjunct, the other follows, and this holds in both senses:

Either p or q. Not p. Therefore q.

But arguing from the affirmation of one disjunct to the denial of the other,

For full marks, cover: the statute; both definitions with their section numbers; the fourfold classification with the two bases it uses; the deeming provisions and the Schedule; how compensation follows; and, because this is a logic paper, what the classification illustrates about definition and division.

The statute

Disablement is defined by the Employee's Compensation Act 1923, formerly the Workmen's Compensation Act, which makes an employer liable to pay compensation for personal injury caused to an employee by accident arising out of and in the course of employment.

Disablement in this sense is the loss or reduction of earning capacity resulting from such an injury. Note that the Act measures it by earning capacity, not by physical injury as such: two people with the same wound may suffer different disablement.

Why the definitions are drawn as they are

The difference between the two limbs of Section 2(1)(g) is deliberate and is where the cases are fought. Temporary partial disablement is measured against the employment he was in; permanent partial disablement is measured against every employment he could then have undertaken. A clerk who loses a finger may be unable to do his own job for a month and yet remain able to do it permanently, so the two limbs give different answers on the same facts.

Compensation

Section 4 fixes the amount, and it follows the classification: death and permanent total disablement are compensated by a percentage of monthly wages multiplied by a relevant factor, permanent partial disablement by the percentage of loss of earning capacity given in Schedule I, and temporary disablement by a half-monthly payment.

Its classical form is per genus et differentiam: state the proximate genus and the differentia. "Man is a rational animal": animal is the genus, rational the differentia.

Its rules, in brief: state the essential attributes; be co-extensive, neither too wide nor too narrow; do not be circular; do not use obscure or figurative language; do not be negative where an affirmative is possible.

Division

Division is the process of separating a class 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.

Its rules, in brief: use only one fundamentum divisionis at each step; the members must be mutually exclusive; the division must be exhaustive; it must proceed step by step; and every member must be a species of the genus divided.

The comparison

Division fails at two: an individual cannot be divided into kinds, only partitioned into parts; and an infima species, the lowest species, has no species under it to divide into.

They are two halves of one operation

Each depends on the other. To define a term you must name its genus, which is to place it in a division already made. To divide a class you must know which attribute is essential, which is what a definition states. The two are performed together, and the tree of Porphyry, running from substance down to man, is a division at every step and a definition at every node.

Legal application

The definition clause of a statute is a definition; the Schedule or the list of categories is a division. Section 2(h) of the Indian Contract Act 1872 defines a contract as an agreement enforceable by law, which is genus plus differentia. The division of nuisance into public and private is a division on a single basis, and it satisfies every rule. Where a taxing schedule mixes bases, its entries overlap and an assessee falls under two at once, which is why cross-division is a drafting fault before it is a logical one.

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.

(iii) Rarely drums are buckets.

Some drums are not buckets. (O proposition)

Distributed: the predicate, "buckets", only.

Reason: "rarely" belongs with "seldom" and "few": it means not often, and the negative force is part of its meaning. A proposition of the form "Rarely S are P" therefore asserts that most S are not P, which is a particular negative. Being negative, it distributes its predicate; being particular, it leaves its subject undistributed.

Reading of the table: the conditional is false in one case only, where the antecedent is true and the consequent false. The promise is broken only by someone who studies hard and does not achieve success. It is contingent, neither a tautology nor a contradiction.

(ii) Identify and symbolise the following simple propositions

1. Sachin Tendulkar is a great cricketer.

A singular proposition, that is, a class-membership proposition: a predicate is attributed to a named individual, so no quantifier is used.

Gs, where G = "... is a great cricketer" and s = Sachin Tendulkar.

2. Shyam is taller than Ravi.

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

Tsr, where T = "... is taller than ...", s = Shyam and r = Ravi.

The kinds of definition to choose from

Denotative or extensional techniques: by example, by enumeration, ostensive. Connotative or intensional techniques: synonymous (biverbal), operational, genus and difference. By purpose: stipulative, lexical, precising, theoretical, persuasive.

(i) Furniture means table, chair, cupboard etc.

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

Reasons: the term is defined by listing the species it denotes rather than by stating the attributes it connotes. The word "etc." is the definition's own admission that the list is incomplete, which is the standing weakness of the extensive form wherever the class is open: beds, desks, almirahs and sofas are furniture too.

Reasons: the meaning is conveyed by pointing at an instance. The words "what you see in the water now" do no defining at all; they only direct attention to a specimen.

Its limits are the ones the sentence itself shows. It depends entirely on the situation, so it fails the moment the water is empty or holds something else, and the words "now" make it useless a minute later. It also cannot show which feature the term picks out: a listener shown a fish might take "aquatic animal" to mean anything with fins, anything silver, or that particular fish.

Reasons: one fundamentum divisionis is used, the relation of the animal to man, that is, whether it has been tamed and kept. "Wild" here does the work of "not domestic", so the two members are contradictories and the division is necessarily exhaustive and mutually exclusive. Every rule is satisfied.

The qualification worth adding: a feral animal, once domesticated and now living wild, sits awkwardly, and so does a captive wild animal. That does not break the division, because the members remain exclusive in the same respect and at the same time; it means only that the attribute is one an animal can acquire and lose.

(ii) Books into fiction, non-fiction.

Sound. This is a division by dichotomy and it is formally faultless.

Reasons: one fundamentum divisionis is used, whether the content is invented or not. The two members are contradictories, so the division is necessarily exhaustive, since every book must be one or the other, and mutually exclusive, since no book can be both.

The uses of logic in everyday life

1. It makes our own thinking consistent. The three laws of thought are the minimum conditions of coherent belief. A person who holds two contradictory opinions at once, or who uses a word in one sense in a premise and another in a conclusion, cannot be argued with and cannot decide anything. Logic supplies the discipline of holding one meaning at a time.

2. It teaches us to define our terms. Most everyday disputes are verbal, not real: the parties agree on the facts and use a word differently. A quarrel about whether a film is "art" or whether a colleague was "rude" ends the moment the word is defined, and logic supplies the rules for defining it neither too widely nor too narrowly.

3. It sharpens our reading of what other people assert. Everyday speech hides the quantity of a proposition. "Politicians are corrupt", "Young people don't read", "This medicine never fails" are universal claims made without evidence, and reducing a sentence to strict logical form exposes how much is being claimed. A single counter-instance answers a universal, and knowing that is a practical skill.

8. It is the ground of the sciences and of law, both of which everyone meets as a citizen: reading a news report of a study, or a notice from an authority, is easier for someone who can see the argument inside it.

The fallacies of everyday life

Naming them is half of resisting them, and each is met daily:

1. Argumentum ad hominem: attacking the person instead of the argument.
2. Ad populum: this is what everybody thinks, so it is true.
3. Ad verecundiam: an appeal to an authority outside their field, which is what a celebrity endorsement is.
4. Ad misericordiam: an appeal to pity in place of a reason.
5. Petitio principii: assuming in the premise what the conclusion has to prove.
6. Hasty generalisation: one bad experience of a place or a group taken as a rule.
7. False cause, post hoc ergo propter hoc: the recovery followed the remedy, so the remedy caused it.
8. False analogy: running a country is just like running a household.

Conclusion

Logic matters in everyday life because ordinary life is full of arguments, most of them unexamined. It makes belief consistent, disputes soluble, claims measurable and fallacies nameable. It does not make anyone wise, and it does not decide what is worth pursuing; it ensures only that the way from what a person accepts to what they conclude is sound, which is the smallest thing that can honestly be asked of any piece of thinking.

2. Particular: the predicate is affirmed or denied of a part. Signs: some, a few, many, most, certain, sometimes.

Quality

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 four forms, illustrated

The propositions that do not fit, and how they are forced in

Since the question says "illustrate", these matter, because they are what a reduction question actually puts in front of a student.

1. Singular: "Socrates is wise." No quantity in the ordinary sense; traditional logic treats it as universal, so that it can be used in a syllogism.
2. Indefinite: "Dogs are faithful." No quantity sign printed; read as universal when it states a general truth, particular when it reports a fact about some.
3. Exclusive: "Only citizens may vote." Becomes an A proposition with the terms interchanged: "All voters are citizens".
4. Exceptive: "All but minors are competent." Becomes two propositions: "All non-minors are competent" and "No minors are competent".
5. Propositions with a hidden verb: "Birds fly" becomes "All birds are creatures that fly", because the copula must be the bare verb "to be".
6. Words of time as quantity signs: always and never are universal; sometimes is particular; rarely and seldom are particular and negative.

The uses of the classification

Conclusion

The fourfold classification is quantity and quality taken together, and it is the smallest scheme that will carry the traditional machinery of inference. Two questions, each with two answers, give four forms; the four forms give the distribution table; and the distribution table gives most of the rules of traditional logic.

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, and it is the heart of the classification.

The connectives

1. Negation (~p), "not p". Reverses the truth value.

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

3. Disjunction (p v q), "p or q". The components are disjuncts. Inclusive: false only when both are false. The exclusive sense is (p v q) · ~(p · q).

1. Singular, attributing a predicate to a named individual, needing no quantifier: "Sachin is a great cricketer", Gs. A class-membership proposition.
2. Relational, asserting a relation between individuals: "Shyam is taller than Ravi", Tsr. The order matters, and traditional logic could not express this at all.
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.

The four traditional forms reappear as (x)(Sx ⊃ Px), (x)(Sx ⊃ ~Px), (∃x)(Sx · Px) and (∃x)(Sx · ~Px).

Statement forms by their truth tables

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.

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

• Contrary: an O proposition has no contrary. Contrariety holds only between two universal propositions, A and E, which is why they occupy the top of the square. What an O proposition has at the foot of the square is a sub-contrary, the I proposition "Some solids are crystals".
• Contradictory (A): All solids are crystals.

Write both: give the contradictory, name the sub-contrary, and say why there is no contrary. That is what the item is testing.

(ii) Every diamond is a hard jewel. (Give Subaltern and contradictory) (2 marks)

An A proposition: "All diamonds are hard jewels."

• Subaltern (I): Some diamonds are hard jewels. Truth descends from the universal to the particular.
• Contradictory (O): Some diamonds are not hard jewels.

(iii) No coaches are lenient. (Give contradictory and subaltern) (2 marks)

An E proposition.

• Contradictory (I): Some coaches are lenient.
• Subaltern (O): Some coaches are not lenient.

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

Reason: the attempted converse would be "Some atheists are not scientists". In the original, "scientists" is the subject of a particular proposition and is undistributed; in the attempted converse it has become the predicate of a negative proposition and is therefore distributed. A term distributed in the converse but undistributed in the convertend breaks the rule of conversion, so the inference is invalid.