Liberty vs Valley

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Broadly speaking, liberty is the ability to do as one pleases. It is a synonym for the word freedom. In modern politics, liberty is the state of being free within society from control or oppressive restrictions imposed by authority on one's way of life, behaviour, or political views. In philosophy, liberty involves free will as contrasted with determinism. In theology, liberty is freedom from the effects of "sin, spiritual servitude, [or] worldly ties". Sometimes liberty is differentiated from freedom by using the word "freedom" primarily, if not exclusively, to mean the ability to do as one wills and what one has the power to do; and using the word "liberty" to mean the absence of arbitrary restraints, taking into account the rights of all involved. In this sense, the exercise of liberty is subject to capability and limited by the rights of others. Thus liberty entails the responsible use of freedom under the rule of law without depriving anyone else of their freedom.

Freedom is more broad in that it represents a total lack of restraint or the unrestrained ability to fulfill one's desires. For example, a person can have the freedom to murder, but not have the liberty to murder, as the latter example deprives others of their right not to be harmed. Liberty can be taken away as a form of punishment. In many countries, people can be deprived of their liberty if they are convicted of criminal acts. The word "liberty" is often used in slogans, such as "life, liberty, and the pursuit of happiness" or "Liberty, Equality, Fraternity".Liberty originates from the Latin word libertas, derived from the name of the goddess Libertas, who, along with the Goddess of Liberty, usually portrays the concept, and the archaic Roman god Liber.

Source: Wikipedia

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A valley is an elongated low area often running between hills or mountains which will typically contain a river or stream running from one end to the other. Most valleys are formed by erosion of the land surface by rivers or streams over a very long period of time. Some valleys are formed through erosion by glacial ice. These glaciers may remain present in valleys in high mountain or polar areas. At lower latitudes and latitudes, these glacially-formed valleys may have been created or enlarged during ice ages but now be ice-free and occupied by streams or rivers.

In desert areas, valleys may be entirely dry or carry a watercourse only rarely. In areas of limestone bedrock, dry valleys may also result from drainage taking place underground rather than at the surface. Rift valleys arise principally from earth movements, rather than erosion. Many different types of valley are described by geographers, using terms that may be global in use or else applied only locally.

Source: Wikipedia