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I am reading Gödel's proof book. But there is sentences that i cannot understand.

"One of them "From a fixed set of axioms and a fixed set of typographical rules, one could shunt symbols around and produce new strings of symbols, called “theorems.”. "

Other is

"A couple of decades later, Gödel began to doubt this noble vision, and one day, while studying the extremely austere patterns of symbols in these volumes, he had a flash that those patterns were so much like number patterns that he could in fact replace each symbol by a number and reperceive all of Principia Mathematica not as symbol shunting but as number crunching (to borrow a modern term)."

I could not understand what the word "shunt" means. Also "number chrunching". Could you explain these phrases for me?

  • shunt probably means derivate (not the analytic operation of differentiate) and number crunching a mathematical work which is executed by people or computers that it takes time but easy to do. – Alejandro Dec 19 '15 at 22:12
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    one could push symbols around – Kreiri Dec 19 '15 at 23:02
  • I am guessing this is more of a math question than a language one, given the context. Maybe ask on math SE? – user3169 Dec 19 '15 at 23:26
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shunt

In that context I think it means what its dictionary definition is. From Merriam-Webster:

to move (someone or something) to a different and usually less important or noticeable place or position

So that is, to move symbols around; rearrange; shuffle; etc. I don't think the "usually less important or noticeable" part of that definition applies here.

"Number crunching" is an idiom that basically means doing a lot of relatively basic but highly tedious math, or doing a lot of boring mathematical work. It generally refers to more concrete, arithmetic work, rather than conceptual or abstract mathematical actions.

In that second sentence you quoted, Gödel is talking about the difference between the more abstract manipulation of symbols vs. the more concrete arithmetic manipulation of numbers.

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