Crescent vs Liberty

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A crescent shape (, British English also ) is a symbol or emblem used to represent the lunar phase in the first quarter (the "sickle moon"), or by extension a symbol representing the Moon itself. In Hinduism, Lord Shiva is often shown wearing a crescent moon on his head symbolising that the lord is the master of time and is himself timeless. It is used as the astrological symbol for the Moon, and hence as the alchemical symbol for silver.

It was also the emblem of Diana/Artemis, and hence represented virginity. In Roman Catholic Marian veneration, it is associated with the Virgin Mary. From its use as roof finial in Ottoman era mosques, it has also become associated with Islam, and the crescent was introduced as chaplain badge for Muslim chaplains in the US military in 1993.

Source: Wikipedia

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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