There have been many definitions of free will proposed over the years, but in essence it is the ability to act as one wills without being constrained; constraints can be physical, logical, metaphysical, social, etc. Though subtle nuances can make a large difference in the way an argument for or against it can develop. Thomas Hobbes' definition makes clear that free will is not only that a person is able to perform an action that he desires to do, but also that he would have had the power to do otherwise should he have chosen to. In fact, defining the idea of free will has become just as much a topic of discussion as its existence. The definition of free will is often linked to the mind-body problem.
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On the other hand, we have the idea of physical determinism, which states that all events can be explained by natural laws, and cause and effect. Therefore the future is determined. Imagine an omniscient being such as God or Laplace's demon; this being theoretically knows the precise characteristics of every atom of the universe and so through careful calculation and application of the natural laws of the world, all the effects can be determined. The world, right up to infinity, can be calculated. If it can be determined, then it must exist in some way, which would mean that free will cannot exist. This is an example of incompatibilist thought – free will and determinism cannot go hand in hand.
Opposed to incompatibilism would be compatibilism: the idea that free will and determinism can co-exist. Compatibilists are often charged with re-defining free will to fit their needs. The typical argument is that free will is simply the ability to act in accordance with one's own desires. There is no metaphysical conception of free will here (i.e. Incompatibilists often define free will to be only present if the actions that one made were ultimately caused by oneself). This is only a simple outline of some ideas; there are many variations and different lines of thought including hard determinism, hard incompatibilism, metaphysiical libertarianism, predeterminism, etc.
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