This work will help us re-understand the essences of the three schools and have a better understanding of “what mathematics is”-----to improve our fundamental researches especially in the infinite related area.
From many arguments between and among three schools of intuitionism, formalism and logicism, we understand that they three are all important in the foundation of mathematics.
But the cutting apart of the three produces some negative effects (such as placing particular emphasis on one aspect but negate the others,…) which deeply influence our clear understanding of “what mathematics is”, especially in the infinite related area.
Human intuition is important in our researches as any science branches are all our “human science”, but form and logic are with the same importance because we need to behave scientifically and communicate with people clearly.
For me intuition has to come first, without it we are not human. From intuition it is possible to make a form and present it as logic. Starting from logic is wrong as then the connection with nature is lost. And form can be the connection between intuition and logic. The logic can also be subjective, one order is not the other.
Strange is that intuition is leading to the same way, and is objective at the end. In Zen the Way seems absurd but becomes a logic on its own. If we look through the form we see it more clearly. The purest ideas are archetypes.
I cannot agree with you more Ms. Rita De Vuyst: science is ours, without intuition we are not human.
But I think if we take science as a whole process, intuition, form and logic each play important role in different scientific stage.
Yours, Geng
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