The excerpt is: 1."Rigorous reasoning is crucial in mathematics, and insight plays an important secondary role these days. In the natural sciences, I would say that the order of these two virtues is reversed. Rigor is, of course, very important. But the most important value is insight--insight into the workings of the world. It may be because there is another guarantor of correctness in the sciences, namely, the empirical evidence from observation and experiments."
"Thoughts without content are empty, intuitions without concepts are blind." where the words of Immanuel Kant. From these words I understood that in order for the world to make sense, we need to combine our two faculties; our senses and our mind.
For example, if we see a stick in the water our visionary sense might mislead us into believing it is bent. But once we take it out we can see it is not deformed. Therefore it is hard to come to a conclusion by just relying on our senses. Instead I believe that, we need to allow some explanation to be given in order to understand the concept of the bent stick. The reason behind it is simple. That is, the refraction of light has allowed us to see the stick bent while it was in the water.
In mathematics, reasoning is crucial. For the years that I have been debating on how to believe the theories that I have been taught. The science lessons where easy to understand because, I could prove them with my senses, but in mathematics, especially with trigonometry, it was hard to relate them and prove them with my senses. Over the years, I have related the theories that I have picked up into everyday situation. This helped me prove that mathematics was something that I could take out of the classroom and use in practical every day circumstances. But now that I have come out of that "I need to see to believe" mentality, I now depend more on the reasoning in than insight.
Hence, I believe that weather it is in mathematics or natural science the importance of being rationalist or empirical may be reverse. But in the end, they are both necessary in the conclusion to convince the hardest judges (human beings), but I would agree more with reasoning as it is the key to the world around us, because after all, "We are because we think".
What do u guys think of my response ? =S
"Thoughts without content are empty, intuitions without concepts are blind." where the words of Immanuel Kant. From these words I understood that in order for the world to make sense, we need to combine our two faculties; our senses and our mind.
For example, if we see a stick in the water our visionary sense might mislead us into believing it is bent. But once we take it out we can see it is not deformed. Therefore it is hard to come to a conclusion by just relying on our senses. Instead I believe that, we need to allow some explanation to be given in order to understand the concept of the bent stick. The reason behind it is simple. That is, the refraction of light has allowed us to see the stick bent while it was in the water.
In mathematics, reasoning is crucial. For the years that I have been debating on how to believe the theories that I have been taught. The science lessons where easy to understand because, I could prove them with my senses, but in mathematics, especially with trigonometry, it was hard to relate them and prove them with my senses. Over the years, I have related the theories that I have picked up into everyday situation. This helped me prove that mathematics was something that I could take out of the classroom and use in practical every day circumstances. But now that I have come out of that "I need to see to believe" mentality, I now depend more on the reasoning in than insight.
Hence, I believe that weather it is in mathematics or natural science the importance of being rationalist or empirical may be reverse. But in the end, they are both necessary in the conclusion to convince the hardest judges (human beings), but I would agree more with reasoning as it is the key to the world around us, because after all, "We are because we think".
What do u guys think of my response ? =S