A summary from my essay
This is the short summary section form my essay on systems of notation, our minds, and Gödel. In this essay I treat the subject of how the notation influences our fundamental thinking, and how it puts boundaries on us. I first tackle the problem from a very easy point of view, that is, so that everyone can understand the problem and possibilities. I therefore use our language as the object of study. Then I go further into the details with the help of mathematics, and its notation. Here Gödel’s theorem comes in in it’s pure and most powerful form.
Now here’s the summary, translated to English by myself:
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SUMMARY
Many questions asked, few answered. This is an abstract and difficult subject, certainly not easy to grasp, especially not when reading it like this. A book I would like to recommend is Gödel, Escher, Bach - an eternal golden braid by Douglas R. Hofstadter. It discusses this a lot, at different levels of abstraction. Gödel’s theorem is itself interesting in this particular case. Those who are familiar with Gödel’s proof should start wondering if one can apply that knowledge in this particular case that I have described. It is in fact, partially at least, formal typographical systems we’re dealing with. My main point here is to lay importance on the fact that the notation often puts us inside boundaries of what we’re able to accomplish. This is by no means neither a trivial nor an intuitivly obvious fact. Think of Gödels theorem… “To reach outside the system.”. This, is what we need to be able to do more.
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Someday I might translate the whole thing.
