Change

Change refers to a difference in a state of affairs at different points in <a href="https://en.wikipedia.org/wiki/Time" title="Time">time</a>. Although it is a familiar experience, an analysis of change provides subtle problems which have occupied <a href="https://en.wikipedia.org/wiki/Philosopher" title="Philosopher">philosophers</a> since the <a href="https://en.wikipedia.org/wiki/Presocratics" class="mw-redirect" title="Presocratics">Presocratics</a>.<a href="https://en.wikipedia.org/wiki/Change_%28philosophy%29#cite_note-1">[1]</a> <a href="https://en.wikipedia.org/wiki/Heraclitus" title="Heraclitus">Heraclitus</a> is the first philosopher known to have directly raised such issues, with <a href="https://en.wikipedia.org/wiki/Aphorism" title="Aphorism">aphorisms</a> such as "one cannot step into the same river twice". The <a href="https://en.wikipedia.org/wiki/Eleatics" title="Eleatics">Eleatics</a> were particularly concerned with change and raised a number of problems, including <a href="https://en.wikipedia.org/wiki/Zeno_of_Elea" title="Zeno of Elea">Zeno's</a> <a href="https://en.wikipedia.org/wiki/Zeno%27s_paradoxes" title="Zeno's paradoxes">paradoxes</a>, 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 <a href="https://en.wikipedia.org/wiki/Atomism" title="Atomism">atomism</a> in attempts to circumvent the Eleatic problems. In the <a href="https://en.wikipedia.org/wiki/Modernity" title="Modernity">modern era</a>, some of these problems would enter the domain of <a href="https://en.wikipedia.org/wiki/Mathematics" title="Mathematics">mathematics</a>, with the development of <a href="https://en.wikipedia.org/wiki/Calculus" title="Calculus">calculus</a> and <a href="https://en.wikipedia.org/wiki/Mathematical_analysis" title="Mathematical analysis">analysis</a>. These developments were regarded by some as solving problems of change, but others maintain that philosophical issues persist.

<a href="https://en.wikipedia.org/wiki/Heraclitus" title="Heraclitus">Heraclitus</a> is the first philosopher for whom there exists an extant written account of an enquiry into change. Writing in an <a href="https://en.wikipedia.org/wiki/Aphorism" title="Aphorism">aphoristic</a> 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 the river "the same", while knowing that the material constituents of the 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 <a href="https://en.wikipedia.org/wiki/Predicate_%28grammar%29" title="Predicate (grammar)">predicates</a> 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 <a href="https://en.wikipedia.org/wiki/Eleatic" class="mw-redirect" title="Eleatic">Eleatic</a> school of thought founded by <a href="https://en.wikipedia.org/wiki/Parmenides" title="Parmenides">Parmenides</a>. 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 <a href="https://en.wikipedia.org/wiki/Melissus_of_Samos" title="Melissus of Samos">Melissus</a> and <a href="https://en.wikipedia.org/wiki/Zeno_of_Elea" title="Zeno of Elea">Zeno</a>, who provided additional arguments, specifically for the impossibility of <a href="https://en.wikipedia.org/wiki/Motion_%28physics%29" title="Motion (physics)">motion</a>. 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 <a href="https://en.wikipedia.org/wiki/Achilles" title="Achilles">Achilles</a> and a <a href="https://en.wikipedia.org/wiki/Tortoise" title="Tortoise">tortoise</a>. 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 <a href="https://en.wikipedia.org/wiki/Arrow" title="Arrow">arrow</a>. 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.

Modern mathematics has developed a rigorous approach to dealing with change, which addresses Zeno's paradoxes of motion in particular. <a href="https://en.wikipedia.org/wiki/Infinite_series" class="mw-redirect" title="Infinite series">Infinite series</a> with finite sums have been given a rigorous treatment in the subject of <a href="https://en.wikipedia.org/wiki/Mathematical_analysis" title="Mathematical analysis">mathematical analysis</a>, and the concepts of motion and <a href="https://en.wikipedia.org/wiki/Infinitesimal" title="Infinitesimal">infinitesimal</a> quantities of time and space are understood through the <a href="https://en.wikipedia.org/wiki/Calculus" title="Calculus">calculus</a>.

In physics, although a number of <a href="https://en.wikipedia.org/wiki/Conservation_laws" class="mw-redirect" title="Conservation laws">conservation laws</a> such as the <a href="https://en.wikipedia.org/wiki/Conservation_of_energy" title="Conservation of energy">conservation of energy</a> have been discovered, phenomena such as the <a href="https://en.wikipedia.org/wiki/Matter_creation" title="Matter creation">creation</a> and <a href="https://en.wikipedia.org/wiki/Annihilation" title="Annihilation">destruction</a> of matter cast <a href="https://en.wikipedia.org/wiki/Empiricism" title="Empiricism">empirical</a> doubt upon Parmenides' claim that something cannot come from or become nothing.[<a href="https://en.wikipedia.org/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed">citation needed</a>]

<ul>

<li><a href="https://en.wikipedia.org/wiki/Identity_and_change" title="Identity and change">Identity and change</a></li>

<li><a href="https://en.wikipedia.org/wiki/Process_philosophy" title="Process philosophy">Process philosophy</a></li>

<li><a href="https://en.wikipedia.org/wiki/Eternalism_%28philosophy_of_time%29" title="Eternalism (philosophy of time)">Eternalism (philosophy of time)</a></li>

</ul>

<h2>References</h2>

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<cite class="citation web"><a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/change/#intro">"Change and Inconsistency"</a>. Stanford Encyclopedia of Philosophy.</cite>

Change

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