1. There is a commonly held endoxon that idealism did not exist and could not exist before Plato, since the «Presocratics» did not yet distinguish between the material and the ideal etc. This preconception is based on the misleading conception of «Presocratics» as physicalists and the simplistic evolutionist scheme of Aristotle’s Metaph. A. In fact, religious and idealist metaphysics are attested in different archaic traditions before Plato, whereas «simple» physical theories of elements of the Milesian type did not exist before (...) the 6th century B.C. scientific revolution. 2. Those who deny the existence of idealism in Greek philosophy commonly refer to Myles F. Burnyeat. We will argue against this article on the following grounds: a) it is based on a selective and incomplete data from early Greek philosophy, b) Burnyeat understands by «idealism» subjective idealism and anti-realism. But Greek idealism as a rule is a form of objective idealism and has nothing to do with anti-realism. The two basic forms are: dualstic idealism and monistic idealism. 3. We will argue against modern naturalist interpretations of the Pythagorean first principles by Huffmann and others. Both in the table of opposites and in Philolaus πέρας καὶ ἄπειρον denote self-subsistent mathematical essences, ‘out of which’ physical bodies are composed. It is impossible to interpret “the limit and the unlimited” as physical bodies themselves or as properties of physical bodies. 4. We will argue for the Pythagorean origin of the 5th centu-ry graffiti on bones’ plates from Olbia. According to this early table of oppo-site, the body is ψεῦδος, i.e., an illusion. 5. The Zeller-Burnet interpretation of Parmenides B3 is grammatically impossible. The fragment states the identity of νοεῖν καὶ εἶναι, i.e., affirms mental nature of Being.6.The basic opposition of Parmenides’ Aletheia exactly corresponds to the basic opposition of doxa. Light is the active and thinking element, night is the «heavy», dense, corporeal substance. Sine light corresponds to Being, night corresponds to non-Being. The philosophy of Parmenides is a radical form of immaterialism and idealistic monism. (shrink)