Ancient Platonists and Aristotelians considered the heuristic method of reasoning to first principles as “analysis.” It was derived from Greek geometrical practice. Plato’s theory of first principles, as we reconstruct it following Aristotle, postulated such an “analytic system.” In this system both sensible things and mathematical objects, ideas and eidetic numbers are gradually reduced to the same principles (ἕν – μέγα – μιχρόν). In the reversal order, from the principles are genetically elicited eidetic numbers and through them numbers, mathematical objects, and sensible things. This is a great analytical system that in fact has a mathematical structure. It transcends the physical explanation of the Timaios and is a broad translation of the nature of things. Our considerations concern a reconstruction and debatable issues, and they follow the following topics: 1. Testimonia Platonica, 2. Analytic theory of principles and agrapha dogmata, 3. Contextual problem and the field of agrapha dogmata, 4. The construction of a system: a procedure from and toward the principles, 5. The alleged paradox: “Good – One.” Ethics or mathematics? 6. Written and unwritten dogmata: dialogue or system?

The article deals with the Greek idea of circular thought and especially with the question of its presence and meaning in the philosophy of Parmenides of Elea. A new interpretation of the fragment DK 28 B 5, which is crucial to this issue, is proposed. It is suggested that the circularity of thought refers to the deductive mode of the arguments in the “Aletheia” and to the proleptic character of some of the Parmenidean statements. Both fragment B 5 (to be placed probably at the beginning of the deduction of the “Aletheia”) and B 8.50-51 (the end of the “Aletheia”) may be successfully interpreted on the basis of this idea. The proposed interpretation makes clear why the circularity of thought does not oppose the linearity of the reasoning and why the logical character of cognition does not contradict its immediacy for Parmenides.

Hildegard of Bingen and her spiritual writings are an interesting example of female thought in the Middle Ages. She was not only the abbess of a convent who had her visions, but also a politically active woman that took an important part in the social life of the twelfth century. Hildegard spoke about controversial problems. It remains true that while preaching she expressed her opinions, described her revelations and proclaimed the will of God. It is no doubt that not only Hildegard herself grew in fame but also her convent, things that we may attribute to her writings. Commonly, Hildegard of Bingen was remembered as a Benedictine nun and as a person who revealed the spiritual knowledge. Her visions were well known. The writings and authority of Hildegard as a prophet intensified so much that in the thirteen century it was used against the Dominican and the Franciscan Order. In this century some false visions were written and attributed to Hildegard herself. Later on one of them was also published against Jesuits. The copy of this print is in the Library of the Jagiellonian University in Cracow.