Parmenides is one of Plato's most important dialogues, according to both ancient and modern scholars, and focuses on the critique of the theory of forms, based on the influence of pre-Socratic thinkers such as Pythagoras, Parmenides, and Heraclitus. The theory of Forms is founded on the assumption that a higher, spiritual realm of Forms, or Ideas, exists beyond the world of physical things.
The realm of Forms has a hierarchical order, the highest level being that of the Form of Good. The physical world, as perceived by the senses is in constant flux, therefore making knowledge derived from it variable and restricted. The realm of Forms, however, is only apprehensible by the mind and is eternal and changeless. Each Form is actually a pattern of a certain category of things in the physical world -- things which are only an imperfect copy of the perfect Forms.
Although in the Phaedo dialogue, Socrates seems to describe the theory of Forms as a very familiar concept that he has applied for a long time without any difficulties, Parmenides, which is a dialogue of the second period, contains a set of criticisms of this theory. Therefore, scholars have asked themselves whether Plato had two distinct philosophies, an earlier and a later, or whether the main objective that Plato was trying to achieve by writing the first dialogues was to conserve the memory of Socrates, by presenting his ideas, although from a Platonic perspective, while the later dialogues contain Plato's own distinctive ideas.
Plato's Parmenides has influenced many of the thinkers of the Western World: Plotinus, Proclus, Dionysius the Areopagite, Nicholas Cusanus and GWF Hegel. Still, in order to understand how Plato has arrived to the conclusions presented in this dialogue, an analysis of the work of Parmenides, Pythagoras and Heraclitus is required.
Heraclitus remains famous for his panta rei doctrine, ("all flows"). The flux of all things imagined by Heraclitus is actually the perpetual becoming of life and death, which are unified by this process. The general concept taught by Heraclitus is that there is a dynamic unity of all opposites and that the main characteristic of this flux of existing things is the constant transformation between pairs of contrary principles. An apparent contrast with the static separation of substantial entities is unavoidable, because the dynamic transformation of opposites into each other seems irreconcilable with a fixed structure. However, Heraclitus builds his flux related ideas on the foundation of the Logos, the supporting structure of the world and the mind.
He argues that it is not his arguments but the logos itself that makes the hearer acquiesce to the idea that all things are one. Heraclitus says that only the ignorant do not understand how a thing agrees with itself in differing and illustrates his theory by making a connection between the bow and the lyre.
The conclusion is that Heraclitus perceived the world as a perpetual transformation of things into their opposites. The rule according to which these transformations are performed is that of the logos, which can only be expressed in contradictions.
Pythagoras, the earliest of the philosophers who have influenced Plato's ideas on being and becoming, believed that all things are in number and that the universe is created and ruled by certain numerical principles. According to Pythagoras, there is an inherent connection between the derivation of all numbers from the single unit -- one, and the derivation of all existent things from an original entity.
Pythagoras proves this point by illustrating the mathematical order of the cosmos -- geometrical principles or mathematical scales are all examples of mathematical ratios, which dominate space. Pythagoreans manifested the belief that all things are a combination of certain eternal principles, such as One and Many, Limit and Unlimited or At Rest and In Motion. The conception according to which the material world of becoming imitates the mathematical world of being has deeply influenced ancient thinkers such as Parmenides and Heraclitus, and helps explain the apparent controversy between the two.
Just like Heraclitus, Parmenides built his philosophical structure around the concept of One. Still, the latter had different idea on what 'One' means. While Heraclitus stated that One is a union of opposites, Parmenides believed that no opposites can be accepted by One. Heraclitus had a dynamic philosophy, focused around becoming, while Parmenides concentrated on being, on the static aspect. Ironically, Parmenides also founded his ideas on the concept of logos. In his interpretation, no real change can take place, since that would be contrary to the logos. The consequence is that there is no possibility for One to become many.
As long as the unity and being of the One are accepted, the reality cannot make the One become something that it is not -- therefore, nothing can proceed out of the One and transform into the opposite. Dynamicity, manifested in plurality, change, becoming, motion or flux do not actually exist, although man's senses indicate that they do. Parmenides though that Being is ungenerated and indestructible, whole and complete. There is no past, present or future, since admitting such notions would mean admitting the existence of change. The One was not born, now will it perish.
There is an apparent contrast between the doctrines of Parmenides and Heraclitus. One says that everything is motionless, the other that everything is motion. However, the common point of the two ideas on the world is that the reality is actually a unity and not a plurality of static entities. Parmenides thought that the One is the only true reality and that its various manifestations do not change simply because they do not exist. Heraclitus thought that these manifestations are not independent of each other and that they turn into one another, without denying the unity of the One.
However, neither one has managed to provide an adequate solution to the philosophical problem of the relation between being and becoming. Neither one explained in a satisfactory manner how the One relates to the Many or what was the nature of the diverse manifestations of the One. Since all was flux for the Heracliteans, there was no more analysis to be performed, and a similar statement may be made about the Eleatics, since all there was never changed.
Plato's reaction to these schools of though was of partial rejection; he managed to find a solution to the problem of the relationship between being and becoming in his Parmenides and Sophist dialogues. Although this paradox was considered very difficult to solve by pre-Socratic philosophers, Plato provide a very interesting solution, which is based on the idea that certain degrees of intensity define the Being. The world of Forms, as changeless Beings, is the most intense, while the degree of intensity decreases in the world of appearances. Although both realms are "real," the degree of intensity defines the actual quality of the world.
Plato presents the relationship between the intelligible forms and sensible objects as a relation from a general concept - the form -- to a particular one - various objects modeled after the form. The physical object acquires intelligible properties participating in the forms corresponding to those properties. A triangle made out of wood or stone is an object from the sensible world, and the shadows that the sun casts on the ground is an image of this sensible object. In an analogous manner, the wooden or stone triangles are a physical representation of the mathematical form of a triangle. The fact that man recognizes this object to be a triangle is caused by the fact that the senses perceive the properties of the form of triangle. However, it is the mind, the reason, who leads to the mathematical form of the triangle, and not the sensible perceptions.
There are no two things in the physical world perfectly equal, just as there are no things perfectly good or beautiful. Still, equality is considered one of the most important characteristics of things, not only in mathematics, but also in everyday life, since it is the foundation of all measurement. Therefore, just like the notions of good and beautiful, equality seems to come from a different world, which is located beyond our senses. Plato called this realm the world of Ideas. Men appear to prefer what is perfect, what is true to what is false, a logical conclusion to a fallacy, and even an elegant scientific demonstration to a lousy one. Therefore, all things perceivable by the senses are imperfect copies of the eternal ideas, the most important one being the Idea of Good.
The theory of a sensible world conceived as an imperfect copy of the world of ideas solves the Eleatic paradox (the relation between being and becoming). The idea of an object survives the destruction of that particular object, so the idea may be considered more powerful than the thing, as it escapes the accidents and contingencies of the sensible world.
A moral perception of the world can also be founded on the theory of Ideas. Goodness…
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