These results of Gödel, the manner of their proof, and the abstractions they rest on – as familiar to mathematical logicians as Einstein’s work is to physicists – are what the book stalks, exposes, celebrates, explains, and en-goldens.īut all is not so simple. In the same paper Gödel also indicated how the consistency of elementary arithmetic itself – its freedom from contradictions – could not be established by reasoning expressible within the system. And that, however many of these truths were listed as fresh axioms, there would always remain others that lay outside the net of possible proofs available in the system. Put another way: all the truths of elementary arithmetic can never be obtained as consequences from a single list – finite or finitely specifiable – of axioms for whole numbers. The main theorem of this remarkable work demonstrated the existence of true statements about whole numbers expressible in the language of a simple arithmetical system that could never be proved within the system. In 1931 the Austrian mathematician Kurt Gödel published a long difficult mathematical paper whose techniques and results revolutionized mathematical notions of proof and philosophical discussions of formal reasoning. We haven’t got past the cover but it is clear that the book is claiming for itself a message that is large, important, exciting and out of the ordinary. Is this perhaps an icon for the whole book? Shoot to the second subtitle and the tone is pretentious and pompous undercut by the suggestion of playfulness Carroll’s name always invokes.
![godel escher bach godel escher bach](https://images-na.ssl-images-amazon.com/images/I/51KJcmqUXsL._AC_UL160_SR160,160_.jpg)
It casts the letters E, G, B as light is shone through it from three perpendicular directions. Shoot to the book’s cover picture: a cleverly hollowed out shape is depicted. Braid? Less poetically fanciful in translation (American Braid = British Plait) it conjures a triple spiral of the book’s heroes, a kind of higher conceptual protein chain whose DNA constituents are the ideas of E, G and B.
![godel escher bach godel escher bach](https://coctes.files.wordpress.com/2016/08/0422_m_douglas-r-hofstadter_godel-escher-bach-an-eternal-golden-braid.jpg)
Ethernal and Golden suggest everlasting truth.
![godel escher bach godel escher bach](https://i.pinimg.com/originals/39/d8/51/39d851388f8f7b992bdfc985d2420ceb.jpg)
Immediately intrigued by the punchy juxtaposition of these names in the title, they will read the subtitle. Most readers will be familiar with Bach’s music, perhaps have seen some of Escher’s prints, and might (just) have heard – as a distant incomprehensible mystery of higher mathematics – of Gödel’s theorem.