Sunday, September 19, 2010

Opposition of Propositions and Venn Diagrams

Opposition of Propositions and Venn Diagrams


Traditional logicians classified propositions into two types, namely, singular and general.

When the subject of a proposition represents one single individual, it is a singular proposition.

When the subject of a proposition represents a group of individuals, it is a general proposition.

General propositions are further classified into Universal and Particular.

When the subject tells something about the whole group represented by it, the proposition is known to be universal.

When the subject tells something about some members of the group represented by it, the proposition is known to be particular.

The propositions are also classified using another criteria of quality and this makes them affirmative or negative.

So, both the singular as well as general propositions are either affirmative or negative.

As a result, we have four types of general propositions, as the general propositions have both the quality as well as quantity.

The four types of general propositions are:

A, E, I, & O.

The quantity and quality of these are as follows:

A = Universal affirmative
E = Universal negative
I = Particular affirmative
O = Particular negative

Relation of opposition between these propositions is as follows:

When two universal propositions differ in quality, they are known as CONTRARY.

When two particular propositions differ in quality, they are known as SUB-CONTRARY.

When two propositions with same quality, differ in quantity, they are known as SUB-ALTERN.

When two propositions differ both in quality and quantity, they are known as CONTRADICTORY.

The relation of truth values between these opposite propositions is as follows:

If a universal proposition is true, its contrary is false, its sub-altern is true and its contradictory is false.

If a universal proposition is false, its contrary is uncertain, its sub-altern is uncertain and its contradictory is true.

If a particular proposition is true, its sub-contrary is uncertain, its sub-altern is uncertain and its contradictory is false.

If a particular proposition is false, its sub-contrary is true, its sub-altern is false and its contradictory is true.

The general propositions represent the relation of two groups indicated by the subject and predicate, and so, they can be represented symbolically using the venn diagram method used in mathematics.

To do this, we use two intersecting circles.

The circle on the left represents the subject, and the one on the right, represents the predicate.

To represent "A" proposition, we shade the part of the circle of subject, that is outside that of predicate. This shows that the set of subject outside the predicate is empty.

To represent "E" proposition, we shade the part of the circle of subject, that is inside predicate. This shows that the set of subject inside the predicate is empty.

To represent "I" proposition, we put a cross in the part of the circle of subject, that is inside that of predicate. This shows that the set of subject inside the predicate is not empty.

To represent "O" proposition, we put a cross in the part of the circle of subject, that is outside that of predicate. This shows that the set of subject outside the predicate is not empty.

Pl check the images for venn diagrams and opposition of proposition.

When these propositions are symbolized, we change them in a specific format so that we can show the class membership of the subject and the predicate terms. This method is known as the method of Quantification and the symbols used to indicate the quantity of the subject are known as quantifiers.

Let us see how this is done:

Singular propositions:

Affirmative:

Ramu is a boy.

is symbolized as:
Br

Negative:

Sita is not a boy.

is symbolized as:
~Bs

General propositions:

These are of four kinds as we have seen earlier. They are symbolized as follows:

"A"
proposition:

Subject-less:

Everything perishes.

will be written as:
Given any x, x is Perishable.

This is symbolized as follows:
(x)(Px)

With subject:

All S is P.

will be written as:
Given any x, if x is S, then x is P

This is symbolized as follows:
(x)(Sx>Px)

[Since the implication sign cannot be put due to font limits of the portal, so, a similar sign is put here]

"E"
proposition:

Subject-less:

Nothing is Permanent.

will be written as:
Given any x, x is not Permanent.

This is symbolized as follows:
(x)(~Px)

With subject:

No S is P.

will be written as:
Given any x, if x is S, then x is not P

This is symbolized as follows:
(x)(Sx>~Px)

[Since the implication sign cannot be put due to font limits of the portal, so, a similar sign is put here]

"I"
proposition:

Subject-less:

Lions exist

will be written as:
There is an x, such that, x is a Lion.

This is symbolized as follows:
(Ex)(Lx)

[Since the Existential quantifier sign that is actually reverse as a mirror image as actual E, cannot be put due to font limits of the portal, so, E is put here]

With subject:

Some S is P.

will be written as:
There is an x, such that, x is S and x is P.

This is symbolized as follows:
(Ex)(Sx.Px)

[Since the Existential quantifier sign that is actually reverse as a mirror image as actual E, cannot be put due to font limits of the portal, so, E is put here]

"O"
proposition:

Subject-less:

Ghosts do not exist

will be written as:
There is an x, such that, x is not a Ghost.

This is symbolized as follows:
(Ex)(~Gx)

[Since the Existential quantifier sign that is actually reverse as a mirror image as actual E, cannot be put due to font limits of the portal, so, E is put here]

With subject:

Some S is not P.

will be written as:
There is an x, such that, x is S and x is not P.

This is symbolized as follows:
(Ex)(Sx.~Px)

[Since the Existential quantifier sign that is actually reverse as a mirror image as actual E, cannot be put due to font limits of the portal, so, E is put here]

When we symbolize, the first letter of the subject term is taken as a capital letter and small x is written after it to indicate the singular variable that is quantified in the beginning.

This is how we symbolize the general propositions in traditional classification.

Saturday, September 18, 2010

DISABLEMENT

Disablement is something that reduces the earning capacity of a workman in any employment in which he was engaged at the time of the accident resulting in the disablement,where the disablement is of a permanent nature, such disablement as reduces his earning capacity in every employment which he was capable of undertaking at that time.

Workmen's Compensation Act, 1923


2. DEFINITIONS. - (1) (g) "partial disablement" means, where the disablement is of a temporary nature, such disablement as reduces the earning capacity of a workman in any employment in which he was engaged at the time of the accident resulting in the disablement, and, where the disablement is of a permanent nature, such disablement as reduces his earning capacity in every employment which he was capable of undertaking at that time :
Provided that every injury specified in Part II of Schedule I shall be deemed to result in permanent partial disablement;

2. DEFINITIONS. - (1) (l) "total disablement" means such disablement, whether of a temporary or permanent nature, as incapacitates a workman for all work which he was capable of performing at the time of the accident resulting in such disablement :
Provided that permanent total disablement shall be deemed to result from every injury specified in Part I of Schedule I or from any combination of injuries specified in Part II thereof where the aggregate percentage of the loss of earning capacity, as specified in the said Part II against those injuries, amounts to one hundred per cent or more;


SCHEDULE I
[See sections 2(1) and (4)]


PART I = LIST OF INJURIES DEEMED TO RESULT IN PERMANENT TOTAL DISABLEMENT

1 Loss of both hands or amputation at higher sites Percentage of loss of earning capacity = 100

2 Loss of a hand and foot Percentage of loss of earning capacity = 100

3 Double amputation through leg or thigh, or amputation through leg or thigh on one side and loss of other foot Percentage of loss of earning capacity = 100

4 Loss of sight to such an extent as to render the claimant unable to perform any work for which eye sight is essential Percentage of loss of earning capacity = 100

5 Very severe facial disfigurement Percentage of loss of earning capacity = 100

6 Absolute deafness Percentage of loss of earning capacity = not mentioned but to be taken as 100 as it is in permanent disablement list


PART II = LIST OF INJURIES DEEMED TO RESULT IN PERMANENT PARTIAL DISABLEMENT

Amputation Cases - Upper limbs - Either arm

1 Amputation through shoulder joint
Percentage of loss of earning capacity = 90

2 Amputation below shoulder with stump less than 20.32 cms. from tip of acromion
Percentage of loss of earning capacity = 80

3 Amputation from 20.32 cms. from tip of acromion to less than 4" below tip of olecranon
Percentage of loss of earning capacity = 70

4 Loss of a hand or of the thumb and four fingers of one hand or amputation from 11.43 cms. below tip of olecranon
Percentage of loss of earning capacity = 60

5 Loss of thumb
Percentage of loss of earning capacity = 30

6 Loss of thumb and its metacarpal bone
Percentage of loss of earning capacity = 40

7 Loss of four fingers of one hand
Percentage of loss of earning capacity = 50

8 Loss of three fingers of one hand
Percentage of loss of earning capacity = 30

9 Loss of two fingers of one hand
Percentage of loss of earning capacity = 20

10 Loss of terminal phalanx of thumb
Percentage of loss of earning capacity = 20

Amputation cases - Lower limbs

10A Guillotine amputation of tip of thumb without loss of bone
Percentage of loss of earning capacity = 10

11 Amputation of both feet resulting in end bearing stumps
Percentage of loss of earning capacity = 90

12 Amputation through both feet proximal to the metatarso-phalangeal joint Percentage of loss of earning capacity = 80

13 Loss of all toes of both feet through the metatarso-phalangeal joint
Percentage of loss of earning capacity = 40

14 Loss of all toes of both feet proximal to the proximal inter-phalangeal joint Percentage of loss of earning capacity = 30

15 Loss of all toes of both feet distal to the proximal inter-phalangeal joint
Percentage of loss of earning capacity = 20

16 Amputation at hip
Percentage of loss of earning capacity = 90

17 Amputation below hip with stump not exceeding 12.70 cms. in length measured from tip of great trenchanter but not beyond middle thigh
Percentage of loss of earning capacity = 80

18 Amputation below hip with stump exceeding 12.70 cms. in length measured from tip of great trenchanter but not beyond middle thigh
Percentage of loss of earning capacity = 70

19 Amputation below middle thigh to 8.89 cms. below knee
Percentage of loss of earning capacity = 60

20 Amputation below knee with stump exceeding 8.89 cms. but not exceeding 12.70 cms.
Percentage of loss of earning capacity = 50

21 Amputation below knee with stump exceeding 12.70 cms.
Percentage of loss of earning capacity = 50

22 Amputation of one foot resulting in end bearing
Percentage of loss of earning capacity = 50

23 Amputation through on foot proximal to the metatarso-phalangeal joint
Percentage of loss of earning capacity = 50

24 Loss of all toes of one foot through the metatarso-phalangeal joint
Percentage of loss of earning capacity = 20

Other injuries
25 Loss of one eye, without complications, the other being normal
Percentage of loss of earning capacity = 40

26 Loss of vision of one eye, without complications or disfigurement of eyeball, the other being normal
Percentage of loss of earning capacity = 30

26A Loss of partial vision of one eye
Percentage of loss of earning capacity = 10

Loss of -

A - Fingers of right or left hand

Index finger

27 Whole
Percentage of loss of earning capacity = 14

28 Two phalanges
Percentage of loss of earning capacity = 11
29 One phalanx
Percentage of loss of earning capacity = 9
30 Guillotine amputation of time without loss of bone
Percentage of loss of earning capacity = 5

Middle finger

31 Whole
Percentage of loss of earning capacity = 12

32 Two phalanges
Percentage of loss of earning capacity = 9

33 One Phalanx
Percentage of loss of earning capacity = 7

34 Guillotine amputation of tip without loss of bone
Percentage of loss of earning capacity = 4

Ring or little finger

35 Whole
Percentage of loss of earning capacity = 7

36 Two phalanges
Percentage of loss of earning capacity = 6

37 One Phalanx
Percentage of loss of earning capacity = 5

38 Guillotine amputation of tip without loss of bone
Percentage of loss of earning capacity = 2

B - Toes of right or left foot

Great toe

39 Through metatarso-phalangeal joint
Percentage of loss of earning capacity = 14

40 Part, with some loss of bone
Percentage of loss of earning capacity = 3

Any other toe

41 Through metatarso-phalangeal joint
Percentage of loss of earning capacity = 3

42 Part with some loss of bone
Percentage of loss of earning capacity = 1

Two toes of one foot, excluding great toe
43 Through metatarso-phalangeal joint
Percentage of loss of earning capacity = 5

44 Part, with some loss of bone
Percentage of loss of earning capacity = 2

Three toes of one foot, excluding great toe
45 Through metatarso-phalangeal joint
Percentage of loss of earning capacity = 6

46 Part, with some loss of bone
Percentage of loss of earning capacity = 3

Four toes of one foot, excluding great toe

47 Through metatarso-phalangeal joint
Percentage of loss of earning capacity = 9

48 Part-with some loss of bone
Percentage of loss of earning capacity = 3

Note - Complete and permanent loss of the use of any limb or member referred to in this Schedule shall be deemed to be equivalent to the loss of that limb or member.

Sunday, September 5, 2010

CONCEPTS FROM LAW:

INDIAN CONTRACT ACT:

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

14. "Free consent" defined.- Consent is said to be free when it is not caused by –
(1) coercion, as defined in section 15, or
(2) undue influence, as defined in section 16, or
(3) fraud, as defined in section 17, or
(4) misrepresentation, as defined in section 18, or
(5) mistake, subject to the provisions of sections 20, 21 and 22.
Consent is said to be so caused when it would not have been given but for the existence of such coercion, undue influence, fraud, misrepresentation or mistake.

15. "Coercion" defined .– "Coercion" is the committing, or threatening to commit, any act forbidden by the Indian Penal Code, or 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. (45 of 1860.)
Explanation.-It is immaterial whether the Indian Penal Code is or is not in force in the place where the coercion is employed. (45 of 1860.)
Illustration
A, on board an English ship on the high seas, causes B to enter into an agreement by an act amounting to criminal intimidation under the Indian Penal Code. (45 of 1860.) A after wards sues B for breach of contract at Calcutta.
A has employed coercion, although his act is not an offense by the law of England, and although section 506 of the Indian Penal Code was not in force at the time when or place where the act was done.(45 of 1860.)

16. "Undue influence" defined. defined .- (1) A contract is said to be induced by "undue influence” where the relations subsisting between the parties are such that one of the parties is in a position to dominate the will of the other and uses that position to obtain an unfair advantage over the other.
(2) In particular and without prejudice to the generality of the foregoing principle, a person is deemed to be in a position to dominate the will of another-
(a) where he holds a real or apparent authority over the other or where he stands in a fiduciary relation to the other; or
(b) where he makes a contract with a person whose mental capacity is temporarily or permanently affected by reason of age, illness, or mental or bodily distress.
(3) Where a person who is in a position to dominate the will of another, enters into a contract with him, and the transaction appears, on the face of it or on the evidence adduced, to be unconscionable, the burden of proving that such contract was not induced by undue influence shall lie upon the person in a position to dominate the will of the other.
Nothing in this sub-section shall affect the provisions of section Ill of the Indian Evidence Act, 1872. (1of 1872.)
Illustrations
(a) A having advanced money to his son, B during his minority, upon B's coming of age obtains, by misuse of parental influence, a bond from B for a greater amount than the sum due in respect of the advance. A employs undue influence.
(b) A, a man enfeebled by disease or age, is induced, by B's influence over him as his medical attendant, to agree to pay B an unreasonable sum for his professional services. B employs undue influence.
(c) A, being in debt to B, the money-lender of his village, contracts a fresh loan on terms which appear to be unconscionable. It lies on B to prove that the contract was not induced by undue influence.
(d) A applies to a banker for a loan at a time when there is stringency in the money market. The banker declines to make the loan except at an unusually high rate of interest. A accepts the loan on these terms. This is a transaction in the ordinary course of business, and the contract is not induced by undue influence.

17. "Fraud" defined .- "Fraud" means and includes any of the following acts committed by a party to a contract, or with his connivance, or by his agent, with intent to deceive another party thereto of his agent, or to induce him to enter into the contract:-
(1) the suggestion, as a fact, of that which is not true, by one who does not believe it to be true;
(2) the active concealment of a fact by one having knowledge or belief of the fact;
(3) a promise made without any intention of performing it
(4) any other act fitted to deceive;
(5) any such act or omission as the law specially declares to be fraudulent.
Explanation.- Mere silence as to facts likely to affect the willingness of a person to enter into a contract is not fraud, unless the circumstances of the case are such that, regard being had to them, it is the duty of the person keeping silence to speak, or unless his silence is, in itself, equivalent to speech.
Illustrations
(a) A sells, by auction, to B, a horse; which; A knows to be unsound. A says nothing to B about the horse's unsoundness. This is not fraud in A.
(b) B is A's daughter and has just come of age. Here, the relation between the parties would make it A's duty to tell B if the horse, is unsound.
(c) B says to A - "If you do not deny it, I shall assume that the horse is sound." A says nothing. Here, A's silence is equivalent to speech.
(d) A and B, being traders, enter upon a contract. A has private information of a change in prices which would affect B's willingness to proceed with the contract. A is not bound to inform B.

18. "Misrepresentation" defined. – "Misrepresentation" means and includes –
(1) The positive assertion, in a manner not warranted by the information of the person making it, of that which is not true, though he believes it to be true
(2) any breach, of duty which, without an intent to deceive, gains an advantage to the person committing it, or any one claiming under him, by misleading another to his prejudice or to the prejudice of any one claiming under him;
(3) Causing, however innocently, a party to an agreement to make a mistake as to the substance of the thing which is the subject of the agreement.

LAW OF TORTS:

NUISANCE

Substantial interference with the right to use and enjoy land, which may be intentional, negligent or ultrahazardous in origin, and must be a result of defendant's activity.

This word means literally annoyance; in law, it signifies, according to Blackstone, " anything that worketh hurt, inconvenience or damage."

Nuisances are either public or common, or private nuisances.

A public or common nuisance is such an inconvenience or troublesome offence, as annoys the whole community in general, and not merely some particular person. To constitute a Public nuisance, there must be such 'a number of persons annoyed, that the offense can no longer be considered a private nuisance: this is a fact to be judged of by the jury. It is difficult to define what degree of annoyance is necessary to constitute a nuisance. In relation to offensive trades, it seems that when such a trade renders the enjoyment of life and property uncomfortable, it is a nuisance for the neighborhood have a right to pure and fresh air.

A thing may be a nuisance in one place, which-is not so in another; therefore the situation or locality of the nuisance must be considered. A tallow chandler seeing up his baseness among other tallow chandlers, and increasing the noxious smells of the neighborhood, is not guilty of setting up a nuisance, unless the annoyance is much increased by the new manufactory. Such an establishment might be a nuisance-in a thickly populated town of merchants and mechanics where no such business was carried on.

Public nuisances arise in consequence of following particular trades by which the air is rendered offensive and noxious. From acts of public indecency; as bathing in a public river in sight of the neighboring houses or for acts tending to a breach of the public peace, as for drawing a number of persons into a field for the purpose of pigeon-shooting, to the disturbance of the neighborhood or keeping a disorderly house or a gaming house or a bawdy house or a dangerous animal, known to be such and suffering him to go at large, as a large bull-dog accustomed to bite people or exposing a person having a contagious disease, as the smallpox, in public and the like.

A private nuisance is anything done to the hurt or annoyance of the lands, tenements, or hereditaments of another.

These are such as are injurious to corporeal inheritances; as, for example, if a man should build his house so as to throw the rain water which fell on it, on my land or erect his building, without right, so as to obstruct my ancient lights; keep hogs or other animals so as to incommode his neighbor and render the air unwholesome.
Private nuisances may also be injurious to incorporeal hereditaments. If, for example, I have a way annexed to my estate, across another man's land, and he obstruct me in the use of it, by plowing it up or laying logs across it and the like.

The remedies for a public nuisance are by indicting the party.
Labor Law:

LABOUR LAW

Definition of Industry

As per Section 2(j) of Industrial Disputes Act, 1947 “Industry” means any systematic activity carried on by co-operation between an employer and his workmen(whether such workmen are employed by such employer directly or by or through any agency, including a contractor) for the production ,supply or distribution of goods or services with a view to satisfy human wants or wishes (not being wants or wishes which are merely spiritual or religious in nature), whether or not,-

(i) any capital has been invested for the purpose of carrying on such activity; or
(ii) such activity is carried on with a motive to make any gain or profit, and includes-
(a) any activity of the Dock Labour Board established under section 5-A of the Dock Workers ( Regulation of Employment)Act,1948( 9 of 1948);
(b) any activity relating to the promotion of sales or business or both carried on by an establishment,
but does not include-
1) any agricultural operation except where such agricultural operation is carried on in an integrated manner with any other activity (being any such activity as is referred to in the foregoing provisions of this clause) and such other activity is the predominant one.
Explanation:- For the purposes of this sub-clause ,” agricultural operation” does not include any activity carried on in a plantation as defined in clause (f) of section 2 of the Plantation Labour Act,1951; or

2) hospitals or dispensaries; or
3) educational, scientific, research to training institutions ; or
4) institutions owned or managed by organizations wholly or substantially engaged in any charitable ,social or philanthropic service; or
5) khadi or village industries ; or
6) any activity of the Government relatable to the sovereign functions of the Government including all the activities carried on by the departments of the Central Governments dealing with defence research , atomic energy and space ; or
7) any domestic service ;or
8) any activity ,being a profession practiced by an individual or body of individuals ,if the number of persons employed by the individuals or body of individuals in relation to such profession is less than ten; or
9) any activity , being an activity carried on by a co-operative society or a club or any other like body of individuals , if the number of persons employed by the co-operative society ,club or other like body of individuals in relation to such activity is less than ten;