How does Heraclitus' statement "You cannot step into the same river twice..." illustrate his belief that "all is change"?

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This statement is an analogy for his belief that everything is constantly changing. This idea, that the water and life within a river are always changing, even if the river looks the same, can be applied to life in general. People are never the same, changing in some way from our day-to-day experiences, and same with society. 

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Heraclitus was not only spare in his explanations, but his only known work exists merely in fragments. The piecemeal verses we still have of his writing render it difficult to tell if he was being unintentionally vague, or if he thought his statements were self-explanatory.

While his thoughts regarding "flow" are translated with varying degrees of difference, they usually share the same general sentiment, and complexity, as the "you can't step in the same river twice" adage. This is typically interpreted in both a literal and metaphorical manner. The river physically changes always. The very fact that this change is present, and yet often escapes our notice, brings attention to the fact that similar changes take place in everything. Therefore, everything is changing, or is capable of change.

A more nuanced view might analyze the concept in comparison to Plato's Theory of Forms. A carpenter, for example, might never be capable of creating the "perfect" chair; yet the idea of the perfect chair informs the carpenter's work. The perfect chair is an idea, and always will be; does the fact that it can never exist make it less "real" than the chair that actually exists before us?

In his meditation on change, Heraclitus might be seen as agreeing with Plato's premise of constant change and improvement. The "real" manifestation of an idea—the river—is always changing, both in the manner in which it manifests and in its composition. So while the physical manifestation is physically more "real" than an idea, we rely on the idea to describe and judge the object. That judgment may be inherently flawed if it fails to take into account the impossibility for the real object to surpass the very changes that separate it from the infallible idea and render it subject to judgment in the first place.

Heraclitus might go a step further and say the idea is also changing, just as we might not even agree on what name to call a river. This implies that even the things we might consider to be immutable facts are, in the long term, impermanent. Based on that theory, change is not problematic and should be included in how we evaluate the forms that our ideas take.

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This statement from the Greek philosopher Heraclitus means that the world constantly changes and that no two situations are exactly the same. Just as water flows in a river, one cannot touch the exact same water twice when one steps into a river. The water one touched previously will be downstream while one steps in water from up the stream. This water may or may not have been touched by someone else. By stepping into the river, one puts oneself into its environment, thus changing it for someone else downstream.

Streams are also noted for their changes especially in times of either heavy rains or a lack of precipitation. A shallow gravel bar may be in deep water or vice versa from one season to the next.

Heraclitus noted that society is similar to a river in that it constantly changes. This is also true of interpersonal relationships as these change based on the history between two people. Just as no two situations are exactly the same, each situation is different based on what happened before. Heraclitus wants others to know that each interaction one has in society has implications for the future.

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According to Heraclitus, who reasoned that everything is always changing and that this fact is fundamental to the functioning of the universe, it is not possible to step in the "same river" twice because the river is ever-changing.  Although we may look at this river and see that it looks, generally speaking, the same as it did the last time we stepped in it, it is, in fact, different. Setting aside any potential movement of the riverbed, rocks, branches, fish, and the like, the water itself is always going to be different between any one moment and any other moment. It may flow from the same source; it may taste the same and look the same and be the same temperature, but it is different water than the water we touched the last time. Because the water is always moving, the river is never the same, even if we perceive it as being the same.

Something similar can be said for many other things: individuals, communities, countries, planets, universes.  Even if change is slow—so slow that we cannot perceive it with our naked eyes—it still exists, always.

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Heraclitus is famous for his argument that change is constant; that everything in the world is always changing.  The saying that you quote shows this perfectly because it illustrates how even things that seem constant to us are actually undergoing change.

When we look at a river, we see a single entity that has always been there and always will, seemingly, be there.  Therefore, a river seems to be almost the epitome of something that does not change.  But, as Heraclitus says, it really is not possible to say that the river remains the same.  The river is constantly changing and is, in effect, not the same river.

If you step in a river, you are stepping in a specific bit of water.  If you withdraw your foot and step in it again, you are stepping in a different bit of water.  Moreover, just by stepping in the river, you have changed it.  You have altered the course of the water a little bit.  You have eroded the river bed a little bit.  The river is always changing and therefore it is never the same.

We can look at human beings and societies in the same way.  We may seem to be the same person today that we were last week, but we have been changed in some way by our experiences.  Society has been changed by all the things that happen.  Human life is like the river that seems to stay constant yet is actually continually changing.

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