Reddit mentions of Incompleteness: The Proof and Paradox of Kurt Godel (Great Discoveries)

GEB is a neat book, but it is more one man's digressions on those three subjects rather than a coherent scientific explanation of much of anything. Try reading Rebecca Goldstein's Incompleteness.

Am currently reading the book "Incompleteness: the Proof and Paradox of Kurt Godel":

http://www.amazon.com/Incompleteness-Proof-Paradox-Godel-Discoveries/dp/0393051692

One of the suggestions the author makes is that, according to a Platonist like Godel, mathematics is as empirical as any other science form. This contrasts with the logical positivist perspective of asserting that mathematics and logic are language games and thus mathematical truths are simply bound by the nature of the syntax of mathematical language (and thus do not actually say anything verifiable or otherwise true).

Godel's position is a bit more complex than I've described above, per the book. According to the author, one of Godel's assertions was that reality was a priori. That is, all of reality is bound by the nature of mathematical truth (and therefore, if you accept the Platonist position, then nothing is ever inherently empirical, or everything is inherently empirical).

Not knowing enough about the fundamentals of mathematics, I cannot give a suitable position either way, but just saying that there are some who claim that mathematics is as empirical as any other real science.

Well, "as far as you know" happens to be dead wrong. Gödel never recognized that at all. His final paper in the Einstein tribute book was Gödel's attempt at a proof for physical platonic theory by proving time to be ideal.

Gödel loved him some Plato and Leibniz.

Check out "The Disappearance of Time: Kurt Godel and the Idealistic Tradition in Philosophy."
http://www.findarticles.com/p/articles/mi_m2346/is_n409_v103/ai_14916956

But I do love the GEB!

Here's another book pointing out this Gödel-platonic link...
http://www.amazon.com/Incompleteness-Proof-Paradox-Godel-Discoveries/dp/0393051692

Sorry to burst your bubble. But I hope this helps you understand Gödel's view of his theory better!

>Godel's incompleteness theorem is solved if the assumption of infinite is dropped

Point of order, Godel's incompleteness theorem does not at all rely on the concept of infinity. In fact, Godel wrote the proof as an objection to people who think that infinity is an "unnecessary" assumption. I suggest you read this book for an understanding of the background of the proof, and for the proof itself.