BLS LLB 5 Years Sem 1 Logic 1 2017-18 Question Paper with Solutions

A word is the smallest independently meaningful unit of a language. Example: "of", "very", "man".

A term is a word or group of words which can stand as the subject or the predicate of a proposition. Example: "man", "the present Chief Justice of India".

A name is a word or group of words used to designate an individual or a class. Example: "Rama", "man".

A singular term denotes a single definite individual, and only that individual. Examples: Rama; the Ganga; the present Chief Justice of India; this book.

A general term denotes each of an indefinite number of individuals and connotes the attributes they share. Examples: man, table, advocate, contract. It applies distributively, one member at a time.

A third kind, the collective term, denotes a group taken as a whole and not its members individually: army, jury, Parliament.

A term is said to be DISTRIBUTED when the proposition speaks of every member of the class which that term names, and UNDISTRIBUTED when it speaks of only part of that class.

The rule: universals distribute the subject; negatives distribute the predicate.

A class-membership proposition asserts that a named individual belongs to a class. Example: "Socrates is a man."

The symbols:

• An individual is written with a lower-case letter, an individual constant: a, b, c, or s for Socrates.
• A class is written with a capital letter, a predicate or class letter: M for the class of men.

The proposition is therefore written Ms, or in set notation s ∈ M, where the sign ∈ is read "is a member of".

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

Example: from "All advocates are graduates" it follows immediately that "Some advocates are graduates" (subalternation), and that "Some advocates are not graduates" is false (contradiction).

Its two branches are opposition, where the terms stay unchanged and only the quantity or quality differs, and eduction, where the terms change place or are replaced by their contradictories: conversion, obversion, contraposition and inversion.

For full marks, cover: two claims, each stated, supported and qualified; and a conclusion that says how they fit together.

1. Logic is the science of all sciences

Every science reasons: it observes, frames hypotheses, draws consequences and tests them. Logic is the science that examines reasoning itself, so it studies the instrument every other science uses. It stands to the sciences as grammar stands to the languages.

Four supports:

1. It supplies the method. Definition, division, classification, hypothesis and proof are laid down by logic and used everywhere.
2. It is presupposed by all of them. A science can be pursued without knowing logic, not without using it.

All three are the same argument, and the third shows what is left when the content is removed. Modern logic carries the method to its limit by replacing the content with symbols, after which the argument can be tested by a truth table.

⚠️ The qualification. Form settles validity and cannot settle truth. What anyone wants is soundness, which is validity plus true premises, and the truth of the premises is a matter of content, not form.

How the two claims fit together

They are the same fact stated twice. Logic can be the science of all the sciences precisely because it is formal: only a study that abstracts from every subject matter can apply to every subject matter. And the price of that generality is exactly the qualification both claims need: logic reaches everywhere and settles nothing about the world.

The rule

Every component is a constituent; not every constituent is a component.

Why the distinction exists

Only a component can be replaced by a statement letter. A compound proposition is truth-functional when its truth value is determined by the truth values of its components, so a truth table cannot be drawn until the components have been identified.

It is therefore the test for whether a sentence is compound at all:

The objective connotation of "gold" includes every property gold has, including those chemistry has not yet discovered.

⚠️ Unusable. Nobody can state it, because part of it is by definition unknown; and it would change with every scientific discovery, though the meaning of the word had not changed at all.

3. Conventional connotation

The attributes fixed by the usage of the language community, that is, the attributes competent speakers agree a thing must have before the term applies to it.

The conventional connotation of "man" is animality together with rationality.

This is the only workable sense, and it is the one logic uses: it is public, it is fixed, and it can be stated, which is exactly what a definition does.

Why the threefold division matters

What a singular proposition is

A singular proposition is one whose subject is a single definite individual, named or otherwise picked out. Examples: "Socrates is wise"; "Dronacharya was a great teacher"; "This contract is void."

The difficulty

The square of opposition rests on quantity, universal against particular. A singular proposition has no quantity in that sense: its subject is not a class of which some members are spoken of and others not, but one individual, spoken of entirely.

Contrariety, sub-contrariety and subalternation all depend on a difference of quantity, so none of them is available.

The answer

A singular proposition has exactly ONE opposite: its contradictory, formed by changing the quality alone.

Socrates is wise. Socrates is not wise.

⚠️ The subject must be the same individual in both. "Socrates is wise" and "Plato is not wise" are not opposed at all.

All S is P converts to Some P is S

Also called conversio per accidens.

Example: "All advocates are graduates" gives "Some graduates are advocates", and not "All graduates are advocates", which would be a different and false proposition.

Two exceptions

⚠️ An A proposition does convert simply in two cases, and in both the predicate turns out to be distributed after all.

1. Where the predicate is a singular term. "Everest is the highest mountain" converts to "The highest mountain is Everest", because a singular term names one thing and so is necessarily distributed.
2. Where the proposition is a definition, so that the two terms are co-extensive. "All men are rational animals" also yields "All rational animals are men", because the predicate class has no members outside the subject class.

⚠️ Both exceptions follow from the matter of the particular proposition, not from its form, and an answer should say which is which.

The other three forms, for comparison

The definition

Section 15 of the Indian Contract Act 1872: "Coercion" is

1. the committing, or threatening to commit, any act forbidden by the Indian Penal Code, or
2. the unlawful detaining, or threatening to detain, any property,

to the prejudice of any person whatever, with the intention of causing any person to enter into an agreement.

Explanation: it is immaterial whether the Indian Penal Code is or is not in force in the place where the coercion is employed.

The elements

1. An act forbidden by the Penal Code, or the unlawful detention of property, committed or threatened.
2. To the prejudice of any person whatever, so the threat need not be directed at the other contracting party.
3. With the intention of causing a person to enter into the agreement.

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 love the circus", so it says that not many children fail to love it, which is to say that most of them do. The two negations cancel and an affirmative particular is left.

(2) Human nature never changes.

No instances of human nature are things that change. (E proposition)

Distributed: both terms.

Reason: "never" is a universal sign of time, and what is denied at all times of the subject is denied of the whole of it, so the proposition is universal and negative. An E proposition distributes its subject because the whole of it is spoken of, and its predicate because to shut the subject out of a class is to shut it out of every member.

A note on the subject: "human nature" is an abstract term, and strictly an abstract term denotes no class of individuals. Reducing it to "instances of human nature" turns it into a class term so that the proposition can be handled at all, which is a step worth showing rather than performing silently.

(1) "If Radha was the wife of Krishna, Krishna was a male"

Identification: a compound proposition; the connective is the conditional, signalled by "if ... then", the "then" being understood.

• Let p = Radha was the wife of Krishna.
• Let q = Krishna was a male.

Symbolic form: p ⊃ q

p is the antecedent and q the consequent.

Truth table

(∃x)(Ix · Bx), an I proposition. "Most" is a particular sign: logic recognises only two quantities, so most, many and several all reduce to "some".

(2) Arjun was a warrior.

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

Wa, where W = "... was a warrior" and a = Arjun.

Logic has no tense: the past tense is carried inside the predicate, not into the symbolism.

(3) It rains.

A simple, atomic proposition with no internal subject-predicate structure of the ordinary kind.

p, a single statement letter.

Reason: this is an impersonal proposition. The word "it" refers to nothing; it is a grammatical placeholder that English requires and logic does not. There is no individual for a predicate to attach to and no class to quantify over, so the proposition cannot be broken down any further, and a statement letter is the whole of its symbolisation.

For full marks, cover: both definitions with an illustration; the distinction in a table; then, at greater length because that is what the question is about, the ways in which each depends on the other; scientific method and legal reasoning as cases of the partnership; and a conclusion that answers the proposition as put.

The two forms

Deduction is inference in which the conclusion follows necessarily from the premises, so that it can never be wider than they are.

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

Induction is inference in which, from 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. Neither can be established inductively without circularity, so both are assumed and used as major premises, 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 particular instances exactly as a major premise is applied to a minor. At the point where induction becomes rigorous, it borrows the shape of deduction.

4. Scientific method runs both in one cycle. Observation gathers particulars; induction frames a hypothesis; deduction draws out what must follow if it 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.

For full marks, cover: the definition and the form; its place among the forms of inference; the tests of strength; then, because the question names them, the value and the limitations in sections of their own; the use in law; and a conclusion.

Definition

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.

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.

2. It is the only reasoning available where experiment is impossible, as in history, archaeology, astronomy and much of medicine, where the investigator cannot vary the conditions at will.

3. It is indispensable in practical life. We buy the same make of car, consult the same doctor and avoid the same road, all on analogies, and we could not act at all if we waited for a causal law.

4. It is the engine of the common law. Precedent is analogical reasoning, and a legal system that must decide new cases with old rules has no other way of moving from what has been decided to what has not.

5. It explains as well as proves. Even where nothing is inferred, an analogy makes an unfamiliar thing intelligible by setting a familiar one beside it.

The LIMITATIONS of analogical reasoning

1. The conclusion is never certain. No number of resemblances makes it necessary, and an analogy can be strong and still false.

2. Number without relevance proves nothing. Two things may agree in a hundred respects and differ in the one that matters, which is why the fallacy of false analogy is so easy to commit and so hard to see.

Conclusion

Analogy is the weakest form of inference in logic and among the most used everywhere else. Its value is that it supplies hypotheses, serves where experiment cannot, and carries the common law from case to case; its limitation is that it never proves, and that its strength rests entirely on a judgement of relevance which the form itself cannot guarantee.

All three are the same argument, and the third shows what is left when the content is removed.

Demonstrated in reverse: same content, different form

All men are mortal. Socrates is a man. So Socrates is mortal. (valid)
All men are mortal. Socrates is mortal. So Socrates is a man. (invalid)

The terms are identical; only the arrangement differs, and the second commits the undistributed middle. Content cannot decide validity; only form can.

What is wrong.

1. Deduction is not purely formal in use, because soundness needs true premises, and where those premises come from is induction's business.
2. Induction is not purely material, because it has a form of its own: Mill's methods are general rules applied to instances, and an induction that misapplies the Method of Difference fails for a formal reason.
3. Induction rests on premises of its own, the uniformity of nature and the law of causation, and uses them deductively.
4. The difference is one of degree, not of kind: each attends more to one aspect and neither can dispense with the other.

Verdict: it is correct that deductive logic is primarily formal and inductive logic primarily material. It is not correct that either is purely so.

For full marks, cover: two distinctions, given roughly equal space, each defined, illustrated and set out in a table, with the consequences of each; and a closing paragraph on what the two have in common.

(1) Singular and general terms

The two defined

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

Its kinds: proper names (Rama, the Ganga); descriptive phrases picking out one individual (the present Chief Justice of India); demonstratives with a common noun (this book, that man).

A general term denotes each of an indefinite number of individuals, and connotes the attributes they share. Examples: man, table, advocate, contract. It applies distributively, one member at a time.

A third kind, the collective term, denotes a group taken as a whole and not its members: army, jury, Parliament. A soldier is not an army, whereas a man is a man.

It follows that a proper name cannot be defined per genus et differentiam, since an individual has no differentia within a species, and can only be explained by describing the individual.

The consequences

1. In opposition: a general proposition has four opposites on the square; a singular proposition has only its contradictory, because it has no quantity for anything else to differ in.
2. In the syllogism: traditional logic must treat a singular proposition as universal to use it at all.
3. In the fallacies: treating a collective term as general produces the fallacy of composition (every juror is fallible, so the jury is) or of division (the committee was unanimous, so each member was).

(2) Contrary and contradictory terms

The two defined

Two terms are CONTRADICTORY when one is the simple negative of the other, so that between them they exhaust the universe of discourse: nothing falls under both and nothing falls outside both.

The consequences

1. In eduction: the predicate must be replaced by its contradictory and never its contrary. The obverse of "All swans are white" is "No swans are non-white"; writing "No swans are black" asserts far less.
2. In opposition: contradictory propositions can neither both be true nor both be false; contrary propositions cannot both be true but may both be false, which is the same difference one level up.
3. In pleading: denying that a person is a citizen is contradictory and puts the other side to proof; asserting that he is a foreigner is contrary and must itself be proved.

For full marks, cover: the definition of opposition with its strict conditions; the four forms with the square; each with its rule; then, because that is what the question turns on, an argument about which of the four deserve the name, taken in stages; and a conclusion that gives a verdict.

When propositions are said to be opposed

Two propositions are opposed when they have the same subject and the same predicate but 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 differing in their terms are not opposed at all; they are merely different.

Which of them deserve the name

The test is conflict. To be opposed is to be in conflict, so a relation deserves the name only in so far as the two propositions cannot stand together as they are.

Subalternation does not deserve the name at all.

A and I do not conflict in any degree. If "All advocates are graduates" is true, "Some advocates are graduates" is also true, and the truth of the one guarantees the truth of the other. Two propositions which can both be true, and one of which follows from the other, are not opposed; they are subordinate. Traditional logic itself calls the universal the subalternant and the particular the subalternate, and the very words say subordination rather than conflict. It is placed on the square because the inference from one to the other is immediate, and that is a reason of convenience, not of opposition.

Contrariety and sub-contrariety deserve the name only in part.

Contraries genuinely conflict: they cannot both be true. But they may both be false, so the conflict is incomplete. Knowing that one is false tells you nothing at all about the other.

The modern verdict confirms it

Modern logic reads a universal proposition as a denial, asserting nothing to exist. On that reading A no longer implies I and E no longer implies O, so subalternation fails, and contrariety and sub-contrariety, which depend on it, fail with it. Only the two diagonals survive. The square becomes an X, and the one relation modern logic keeps is precisely the one traditional logic could already see was the strongest.

Conclusion

Propositions are opposed when they share a subject and a predicate and differ in quantity, in quality, or in both. Of the four relations placed on the square, contradiction alone fully deserves the name, because only there is the conflict complete in both directions. Contrariety and sub-contrariety are partial oppositions, each settling one direction and leaving the other open. Subalternation is not opposition at all but subordination, and modern logic, for quite independent reasons, has arrived at the same conclusion.

For full marks, cover: each item with the given proposition reduced and its form named, the answers written out, and the rule that produces each; the two items where what is asked cannot be given; and the last item, which asks for an inference to be identified rather than performed.

(2) All irrelevant talk is useless. (Obverse and converse) (2 marks)

An A proposition.

• Obverse (E): No irrelevant talk is useful, that is, no irrelevant talk is non-useless.
• Converse (I): Some useless talk is irrelevant talk. This is conversion by limitation: the predicate of an A proposition is undistributed, so it may not become the distributed subject of a universal converse.

(3) All logic books contain misprints. (Contrary and contradictory) (2 marks)

Reduced: "All logic books are books which contain misprints." An A proposition.

• Contrary (E): No logic books are books which contain misprints.
• Contradictory (O): Some logic books are not books which contain misprints.

Contraries cannot both be true but may both be false; contradictories can be neither both true nor both false.

• Obverse (I): Some tales are unbelievable tales, that is, some tales are non-believable.
• Converse: an O proposition cannot be converted. It has no converse.

Reason: the attempted converse would be "Some believable things are not tales". In the original, "tales" 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.

(6) "A politician is a man. Therefore a good politician is a good man." Identify the inference and give reason. (2 marks)

This is an immediate inference by ADDED DETERMINANT, and as it stands it is INVALID.

What added determinant is: the same qualifying word is added to both the subject and the predicate of a proposition. It is valid only where the added word means exactly the same in both places.