59-05-032 Proceeding

21 Proceedings of the Princess Maha Chakri Sirindhorn Congress Intuition By induction through intuition, we establish a law. We are convinced of the law by proving through deduction. Deduction Analysis and Synthesis: go together in - Science - Geometry: synthetical in the Theorems; analytical in the proofs of Theorems - Psychology - Logic N.B. Analysis emphasizes the details, synthesis emphasizes the whole and creates the system. Nowadays human mind is critical enough to create a system with a sound method, though the critical methodology may be improved in some details, but globally we can rely on the capacity of human mind in creating system. However the evaluation of systems is other problem than the validity of system, and is still a topic for serious discussions. A system has a consistency in some aspect. - System of content (Modernism) - System of methodology (Postmodernism) Content of Logic Processes and Laws of thoughts Content of Arithmetic - Laws of numbers and their relations. - Numbers and their relations are conventional for practical purposes. By a long experiences of Mankind in using Arithmetic, we believe that the actual system is effective. We need only to add more and more details to what we had found along history. 2 × 3 = 6 cannot be otherwise rational. We are 100% certain by our rational mind. But that is only the Form of our Rationality without any content. “2 cows + 3 bulls = 5 cattle” is formally 100% certain, but the content has to be checked and may be doubtful at any degree. Content of Geometry - Geometrical study may be analytical or synthetical. You can analyze a triangle to know its characters and prove them. You analyze to see the details and synthesize to be convinced of the truth of its content.