What are the similarities and differences between Empedocles', Epicurus's, and Aristotle's views on the possibility and nature of change?
As we are limited in space, the following are a few ideas to help get you started. Empedocles' theories concerning the nature of change stem from his theories of nature in general. Empedocles argued that the cosmos is made of four different elements, "fire, air, earth, and water." These four elements are constantly being moved by "two opposing forces," the forces of "Love and Strife" (Stanford Encyclopedia of Philosophy, "Empedocles: On Nature"). He further describes the coming into being and ceasing to be, especially the birth and death of "mortal things," as a dual process of the forces of Love and Strife. Love brings together the elements to create being and then come apart, or die, through Strife ("Empedocles: On Nature"). Scholars have interpreted Empedocles as referring to a vortex in which Strife controls and separates the elements in order to form all of the different parts of the cosmos, "land-masses, oceans, rivers, winds, sun, moon, seasons, planets, stars, etc." ("Empedocles: On Nature"). Once the different parts of the cosmos are formed, Love mixes together different elements until different animal lives are formed ("Empedocles: On Nature"). Hence, according to Empedocles the forces of Love and Strife are constantly changing the elements to either separate them or to join them into different beings. Therefore, nature changes as a direct result of Love and Strife.
In contrast to Empedocles, Epicurus defined nature in accordance with other atomists, like Democritus. Rather than identifying nature by the elements of air, wind, fire, and water, Epicurus defined it as being made up of "solid, indivisible particles" that cannot be seen and which we now identify as atoms. He goes on further to identify different motions of atoms, such as moving non-uniformly and moving in vectors ("Epicurus: Physical Theory"). Scholar Peter Gibson cites Epicurus as explaining in a letter to Herodutus that motion wholly stems from atoms and not from any help from divine beings, as we see in Gibson's following passage:
Movements, turnings, rising, settings, and related phenomena occur without any god helping out and ordaining or being about to ordain things, and at the same time have complete blessedness and indestructibility. (PhilosophyIdeas.com, "Single Idea 14048: Existence/Theories of Existence/Physicalism")
Hence, we see that for Epicurus the nature of change stems from motion of atoms.
Empedocles' and Epicurus's concepts concerning the nature of change are similar in that both attribute change to elements of nature rather than to any divine being; Empedocles attributes change to elements of nature, while Epicurus attributes change to the motion of atoms. One difference lies in the fact that Empedocles also attributes change as a result of forces acting upon the elements of nature, while Epicurus only attributes atoms as having the ability to move themselves.