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Change refers to a difference in a state of affairs at different points in time. Although it is a familiar experience, an analysis of change provides subtle problems which have occupied philosophers since the Presocratics. Heraclitus is the first philosopher known to have directly raised such issues, with aphorisms such as "one cannot step into the same river twice". The Eleatics were particularly concerned with change and raised a number of problems, including Zeno's paradoxes, which caused them to go as far as insisting that change was impossible, and that reality was one and unchanging. Later philosophers would reject this conclusion, instead developing systems such as atomism in attempts to circumvent the Eleatic problems. In the modern era, some of these problems would enter the domain of mathematics, with the development of calculus and analysis. These developments were regarded by some as solving problems of change, but others maintain that philosophical issues persist.
In Chinese philosophyEdit
The Chinese philosophy of change was described in centuries of commentary on the I Ching, the Book of Changes.
In Greek philosophyEdit
Heraclitus is the first philosopher for whom there exists an extant written account of an enquiry into change. Writing in an aphoristic and esoteric style, Heraclitus remarked that, "On those stepping into rivers staying the same other and other waters flow". Or, more popularly: "One cannot step into the same river twice." This is generally taken to refer to the seeming contradiction between our calling a river "the same", while knowing that the material constituents of a river, the "waters", have completely changed. (A later follower amended the final word in the saying from "twice" to "once".)
It is unclear what reaction Heraclitus intends to induce by this statement, and he provides no exposition. It is however but one of many examples of a more general theme which Heraclitus termed the "unity of opposites" - the fact that opposing predicates could be asserted of the same thing, another example being, "the road up and the road down is one and the same".
Change was one of the chief concerns of the Eleatic school of thought founded by Parmenides. Parmenides considered non-existence to be absurd, and thus asserted that it was impossible for something to come into existence out of nothing, or for something to pass out of existence into nothing. By "something", he was referring not just to material, but to any general predicate; rejecting, for instance, changes of colour, as they involved the new colour arising from nothing and the old colour passing into nothing. He therefore rejected all change as impossible, and claimed that reality was an undifferentiated and unchanging whole.
These ideas were taken up by various followers of Parmenides, most notably Melissus and Zeno, who provided additional arguments, specifically for the impossibility of motion. Melissus claimed that reality was "full" (nonexistence being impossible), and that therefore nothing could move. Zeno gave a series of arguments which were particularly influential. Among the simplest was his observation that to move from A to B, one must first reach the halfway point between A and B; but then in order to do this, one must get halfway from A to this halfway point; and so on. Thus all motion involves an infinite number of steps, which Zeno held to be impossible. A similar argument involved a footrace between Achilles and a tortoise. The tortoise is given a headstart. Achilles quickly reaches the point where the tortoise stood, but by this time the tortoise has moved on a little, so Achilles must now reach this new point, and so on. A different argument involved the flight of an arrow. Zeno observed that if one considers a single moment of time, the arrow is not moving in that moment. He then claimed it was impossible that an arrow in motion could arise as the result of a sequence of motionless arrows.
Responses to the EleaticsEdit
The atomism of Democritus and Leucippus can be seen as a response to the Eleatic denial of change. The atomists conceded that something coming from or becoming nothing was impossible, but only with respect to material substance, not to general qualities. They hypothesised that every visible object was in fact a composite of unseen indivisible particles of different shapes and sizes. These particles were held to be eternal and unchanging, but by rearranging themselves, the composite objects which they formed could come into and go out of being. These composite objects and their properties were not taken as truly real; in the words of Democritus, "by convention sweet, by convention bitter; by convention hot, by convention cold; by convention colour: but in reality atoms and void." Any perceived change in an object's properties was therefore illusory and not susceptible to the objections of Parmenides.
Anaxagoras provided a similar response, but instead of atoms, he hypothesised a number of eternal, primal "ingredients" which were mixed together in a continuum. No material object was made of a pure ingredient; rather, it had its material character due to a preponderance of various ingredients over every other. In this way, Anaxagoras could assert that nowhere did any ingredient ever fully come into or go out of being.
Modern mathematics and scienceEdit
Modern mathematics has developed a rigorous approach to dealing with change, which addresses Zeno's paradoxes of motion in particular. Infinite series with finite sums have been given a rigorous treatment in the subject of mathematical analysis, and the concepts of motion and infinitesimal quantities of time and space are understood through the calculus.
In physics, although a number of conservation laws such as the conservation of energy have been discovered, phenomena such as the creation and destruction of matter cast empirical doubt upon Parmenides' claim that something cannot come from or become nothing.
Never disproven theory of relativity by Albert Einstein explains how time is a result of change, in contradiction to the idea that change occurs in time. This point of view makes it easier to understand direction of time, as in reality time is a perception of the order of change seen from a point of view. In other words it is a relation between objects rather than an object.[user-generated source?]