Unity of being" in Parmenides as indistinguishability noema's constituents

This paper attempts to interpret to eon in Parmenides' poem not as a real object, but as a noema or intentional object of thinking. So, we succeed to J. Barrington's and G. E. L. Owen's approach. We have shown that there is a possible interpretation of Parmenides, in which his proof of "indivisibility (indistin-guishability) to eon" is very convincing one: this proof is based on the assumptions that are difficult to discard without a peep; moreover, this proof allows for the formalization, in which it is logically correct. We have demonstrated that Parmenides's noema is fully determinated by each act of thinking, thanks to which it is thought about. Then we have interpret Parmenides' thesis on "indivisibility (indistinguishability) to eon" as the averment that the intentional objects, which can be determinated only simultaneously, are indistin-guishable.The formalization of this proof was carried out in two ways. In both cases, it is proved that if a act thinking, which is directed to noema as some intentional composite (whole) object, is possible in principle, then the constituents of this whole object are indistinguishable from each other. In the first case the constituents are propositions that determine a intentional composite (whole) object, and in the second case - intentional individuals. In our formalization of Parmenides' argument is used the Operator of Thinking from Epistemic Logic. Furthermore, our notation is based on the notation in B. Linsky and E. Zalta's Theory of abstract objects. The most controversial assumption in constructed formal proofs is the assertion that states that internal objects of thinking are identical, if they cannot be thought independently. We can say that the criterion for distinction of intentional objects of thinking is here their ability to independent existence - i.e. the possibility for one object of thinking to be thought about, when the other object of thinking is not thought about. Discussion of these problems can lead to the discussion of the nature of identity and deep epistemological problems.

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