Problem of change & permanence in antiquity
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What is the problem of change?
One of the most striking and mysterious of all the appearances in the world about us is that of change. The problem early arose as to how things can change and yet remain themselves, be infinitely diverse and yet stem from a single or a few basic elements. This is what is known as the problem of change and permanence, and it was destined to dominate greek philosophy for a century and a half.
Heraclitus
Heraclitus is still known as the philosopher of change. Change for him was the key to the universe. Nothing is so universal as the fact of change, from the movement of the heavenly bodies to the rhythm of growth and decline among terrestrial bodies. “All things are in a state of flux” declared heraclitus. Reality is a torrent of change and just as “you can never step into the same river twice” so too the world is never the same at successive instants. Heraclitus use the example of a burning candle to illustrate his point. The flame of the candle seems constant, yet we know that the solid body of the candle is slowly melting and being taken up into the flame of the candle where its changed into smoke. Heraclitus chose fire as the ground of all things because it was the element that seemed most alive. Things are always changing into and out of fire. Imagine the smoke from the burning candle turning back into wax and you are fairly close to heraclitus’ idea of the rhythm of change. The four elements are the various forms of fire: earth, the lowest and heaviest form of matter, melts into water; water changes into air, and air into fire. This is what heraclitus called the upward path. The reverse changes of fire into air, water, and earth constitute the downward path. What happens in the great world happens also in the little world of man. (Heraclitus too adopted the comparison of man and the world which is expressed by the notions of the microcosm and the macrocosm). As far as the appearances of things are concerned, then, it seemed to heraclitus and his followers that we cannot name a single thing in the world around us which isnt undergoing change. As heraclitus furthermore stressed, if a thing is changing its not the same from one moment to the next. In the very act of naming it, it is becoming something else.
Parmenides
Parmenides set up the opposite extreme to heraclitus' position. According to parmenides the change of which heraclitus made so much is an illusion and there is no such thing, really, as change. He said as philosophers we should try to get behind the appearances of things to their reality. Now the true reality of all things isnt fire, air, water, earth. The one thing we can say about all things in common is that they exist, they are being. Being, not change or becoming is the key to reality. Everything that is = being everything that isnt = non being change can only come about only through a mixture of being with something else (nothing) aka change = impossible. }<===== argument =====>If each thing is a being then each thing is what everything else is. A tree for example is a being and a horse is a being. They are therefore the same thing (being). There is no real difference between the tree and the horse or as a matter of fact between any things. All being then is one. Reality is just being, one single solitary unchanging being. Reality is the one.All differences including all changes, are just appearances. Naturally, things seem different things seem to change, but reason proves that this appearance of change and diversity is simply the deception of the senses.
Paradoxes of zeno
<==== First Paradox ====>The first paradox uses the fable of the race between achilles and the tortoise. The Tortoise is given a head start on Áchilles. Before Achilles can catch the Tortoise he must cover the distance between himself and the point from which the Tortoise started. But when he reaches the point from which the Tortoise started, the Tortoise has in the meantime advanced part of the way toward the goal. Before Achilles can catch the Tortoise he must advance to that new point. But when he reaches the new point, the Tortoise will have again advanced toward the goal. Since the Tortoise is always moving toward the goal, Achilles is always faced with a prior task of crossing the distance between his starting point and the Tortoise’s ever shifting starting point. Therefore, appearances to the contraty, the fleet-footed Achilles will never catch the Tortoise. As a matter of fact, we can prove that Achilles never gets off his mark. Before Achilles can catch the Tortoise, he must cover ,half the distance between himself and the Tortoise. But before he can reach the halfway point of that distance, he has to cover half the first half. But half that distance has to be covered first, and so on and so on. It may be infinitesimally small, but there is always a first half of some distance to be covered before any of the further points can be reached. Achilles, then, cannot even get going, let alone catch the Tortoise.
<==== Second Paradox ====>Another paradox offered by Zeno was that of an arrow in flight. If anything seems to be in motion, it is an arrow flying swiftly through the air. But here again appearances are deceiving and reason tells us differently. Consider the arrow in mid-flight. At the exact moment when we consider it, it is displacing the air to the extent of its own volume at one certain place and no other place. To displace its own volume of the atmosphere it has to be there, where the displacement is taking place—in that place and no other place. It is, therefore, in one precise geographical position, which could be accurately calculated— and while it is in one place it cannot be in any other place at the same time. For that exact moment, then, the arrow is here, and no place else. In other words, at that precise moment, while it is in that place and before it goes on to the place in front of it, it is not moving.
Conclusion for the ancients
Common sense is, naturally, shocked to hear from the disciples of Parmenides that all change and all differences are illusion, and that everything is an undifferentiated oneness-just as common sense is also shocked to hear from the disciples of Heraclitus that the things we call constant and stable are really in a state of endless flux and that stability, sameness, permanence, are all illusion. Heraclitus represents the climactic extreme of the sensist position-the doctrine that the only reality is what falls immediately under our senses. Parmenides, working in the tradition of Pythagoras, represents another extreme-the stress of reason to the point of excluding the testimony of our senses. (This will later be called rationalism.) The reconciliation of these extremes is destined to be henceforth one of the permanent problems of philosophy. On the solution of all these problems Greek philosophers divided into two camps. Since each side seemed to have unanswerable arguments in favor of completely opposite positions, many men came to feel that the search for truth was a hopeless one: a despair of truth which was to lead quickly into an era of skepticism.

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