This paper intends to make some remarks on the philosophy of the ancient Greek. It is divideded into 6 parts. 1. Distinction between nomos and physis. 2. Intuition in knowledge. 3. Intuition, operation, persuasion, and demonstration. 4. Division of knowledge by the method of demonstration. 5. Ontology as an apodeictic knowledge. 6. Conclusion. a. Greek philosophy was born when the distinction between nomos and physis was aware of, and this distinction had an constant effect on the development of the Greek philosophy. b. Intuition which is instantaneous wants to be supplemented by operation. Intuition rejects anything to be infused into the mind. Demonstration means to bring any knowledge into intuition by means of its grounds. c. Knowledge is divided by the method of demonstration. The most strict demonstration consists in the apodeictic knowledge. Ontology is one of the apodeictic knowledge. d. Greek ontology intends to provide the most strict philosophical knowledge. Furthermore, it serves to solve the most important problems of the hard reality at the downfall of the ancient Greek culture.