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== '''[[Human rights]]''' ==
== '''[[Set theory]]''' ==
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A '''set''', in [[mathematics]], is a collection of distinct entities, called its elements, considered as a whole. The early study of sets led to a family of [[paradox]]es and apparent contradictions. It therefore became necessary to abandon "naïve" conceptions of sets, and a precise definition that avoids the paradoxes turns out to be a tricky matter. However, some unproblematic examples from naïve set theory will make the concept clearer. These examples will be used throughout this article:


The concept of '''human rights''' as the innate entitlement of all human beings found early expression during  the American and French revolutionary movements of the late 18th century,  but received  little further development until the conclusion of World War II. It then  acquired the current connotation of a body of entitlements whose realisation  is considered to be a universal obligation. This article is about the implementation of that concept of human rights. Doubts have been expressed about its ethical foundations, and about its philosophical consistency, but its emotional impact upon worldwide consciousness is beyond doubt. As a result, it has acquired considerable political importance, and  has been embodied in a wide range of generally-accepted international  treaty obligations.  There have been numerous breaches of those undertakings, and there is widespread disagreement concerning the appropriate international response to such  breaches.
* A = the set of the numbers 1, 2 and 3.
* B = the set of primary light colors -- red, green and blue.
* C = the empty set (the set with no elements).
* D = the set of all books in the British Library.
* E = the set of all positive integers, 1, 2, 3, 4, and so on.


===The nature of the concept===
Note that the last of these sets is infinite.
As an ethical concept, the term  human rights is not susceptible to precise definition concerning either its content or its scope. The generally-held  judgement that torture is wrong does not depend upon agreement concerning the degree of pain or discomfort that it involves; and the ethical purpose of banning it is served if the ban puts an end to what most people consider to be torture. There is widespread agreement  concerning many of the practices that are considered to be breaches of human rights, but the disagreements that exist -  concerning, for example, abortion, the death penalty and blasphemy - are  not held to justify  a wholesale rejection of the concept. And, although human rights are generally considered to be innate to their possessors, the fact  they can be given effect only by the assent of others,  makes them difficult to distinguish from community-granted rights.


===The historical background===
A set is the collection of its elements considered as a single, abstract entity. Note that this is different from the elements themselves, and may have different properties. For example, the elements of D are flammable (they are books), but D itself is not flammable, since [[abstract objects]] cannot be burnt.
The  1948 [[/Addendum#The Universal Declaration of Human Rights (1948)|Universal Declaration of Human Rights]] is generally held to have been inspired by revulsion at the treatment or the victims of the [[holocaust]] and by  wartime aspirations for a better post-war world. Although much of its  content was  new, there were precedents for its concept of  universally innate human entitlements in the [[/Addendum#TheAmerican Declaration of Independence|American Declaration of Independence]] and the [[/Addendum#The French Declaration of the Rights of Man|French Declaration of the Rights of Man]]. Its unprecedented feature was its claim to be doubly universal - to invoke the universal acceptance of agreed obligations, as well as the recognition of what were agreed to be universal entitlements. It was an overstated claim, however, in view of the absence among it signatories of many of the  countries that are now members of the United Nations, and the fact that many of its signatories  were themselves in breach of its proposed obligations<ref>[http://tannerlectures.utah.edu/lectures/documents/Ignatieff_01.pdf  Ignatieff, Michael: '' Human Rights as Politics'' and '' Human Rights as Idolatry'']  (lectures delivered at Princeton University April 4–7, 2000)</ref>. The actual content of the declaration was, as Justice Michael Kirby recalls
''[[Set theory|.... (read more)]]''
<ref>[http://www.lawfoundation.net.au/ljf/app/&id=1A826DB973993289CA2571A700012832 Michael Kirby: ''The Universal Declaration of Human Rights - Fifty Years On''] (Speech at an UNESCO dinner at Sydney on 5 December 1998)</ref>  a political compromise, and rights were included that apparently stood little chance of unqualified implementation.
 
''[[Acute coronary syndrome|.... (read more)]]''


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Revision as of 03:26, 24 September 2012

Set theory

A set, in mathematics, is a collection of distinct entities, called its elements, considered as a whole. The early study of sets led to a family of paradoxes and apparent contradictions. It therefore became necessary to abandon "naïve" conceptions of sets, and a precise definition that avoids the paradoxes turns out to be a tricky matter. However, some unproblematic examples from naïve set theory will make the concept clearer. These examples will be used throughout this article:

  • A = the set of the numbers 1, 2 and 3.
  • B = the set of primary light colors -- red, green and blue.
  • C = the empty set (the set with no elements).
  • D = the set of all books in the British Library.
  • E = the set of all positive integers, 1, 2, 3, 4, and so on.

Note that the last of these sets is infinite.

A set is the collection of its elements considered as a single, abstract entity. Note that this is different from the elements themselves, and may have different properties. For example, the elements of D are flammable (they are books), but D itself is not flammable, since abstract objects cannot be burnt. .... (read more)

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