Thus something as simple as a newspaper might be specified to six levels, as in Douglas Hofstadter's illustration of that ambiguity, with a progression from abstract to concrete in Gödel, Escher, Bach ( 1979 ):

Within philosophy familiar names include Daniel Dennett who writes from a computational systems perspective, John Searle known for his controversial Chinese room, Jerry Fodor who advocates functionalism, and Douglas Hofstadter, famous for writing Gödel, Escher, Bach, which questions the nature of words and thought.

He is best known for his book Gödel, Escher, Bach: an Eternal Golden Braid, first published in 1979.

Hofstadter's thesis about consciousness, first expressed in Gödel, Escher, Bach ( GEB ) but also present in several of his later books, is that it is an emergent consequence of seething lower-level activity in the brain.

* Gödel, Escher, Bach: an Eternal Golden Braid ( ISBN 0-465-02656-7 ) ( 1979 )

A typical description of the problem is given in the book Gödel, Escher, Bach, by Douglas Hofstadter

Typical of these references is Gödel, Escher, Bach by Douglas Hofstadter, which accords the paradox a prominent place in a discussion of self-reference.

* MU puzzle, a puzzle in Gödel, Escher, Bach

The name " quine " was coined by Douglas Hofstadter, in his popular science book Gödel, Escher, Bach: An Eternal Golden Braid, in the honor of philosopher Willard Van Orman Quine ( 1908 – 2000 ), who made an extensive study of indirect self-reference, and in particular for the following paradox-producing expression, known as Quine's paradox:

* Gödel, Escher, Bach by Douglas Hofstadter ( detailed discussion and many examples )

* In Gödel, Escher, Bach by Douglas Hofstadter, the various chapters are separated by dialogues between Achilles and the tortoise, inspired by Lewis Carroll ’ s works.

Author Douglas Hofstadter, in Gödel, Escher, Bach, characterizes the distinction in this way.

The concept of a strange loop was proposed and extensively discussed by Douglas Hofstadter in Gödel, Escher, Bach, and is further elaborated in Hofstadter's book I Am a Strange Loop, published in 2007.

Gödel, Escher, Bach: An Eternal Golden Braid ( commonly GEB ) is a 1979 book by Douglas Hofstadter, described by his publishing company as " a metaphorical fugue on minds and machines in the spirit of Lewis Carroll ".

On its surface, GEB examines logician Kurt Gödel, artist M. C. Escher and composer Johann Sebastian Bach, discussing common themes in their work and lives.

Gödel, Escher, Bach won the Pulitzer Prize for general non-fiction

ca: Gödel, Escher, Bach

cs: Gödel, Escher, Bach

de: Gödel, Escher, Bach

et: Gödel, Escher, Bach

es: Gödel, Escher, Bach: un Eterno y Grácil Bucle

fr: Gödel, Escher, Bach: Les Brins d ' une Guirlande Éternelle

is: Gödel, Escher, Bach

Assuming ZF is consistent, Kurt Gödel showed that the negation of the axiom of choice is not a theorem of ZF by constructing an inner model ( the constructible universe ) which satisfies ZFC and thus showing that ZFC is consistent.

Eventually, he would suggest his ( primitive ) recursion, modified by Herbrand's suggestion, that Gödel had detailed in his 1934 lectures in Princeton NJ ( Kleene and another student J.

For example, the view that numbers are Platonic objects was revived by Kurt Gödel as a result of certain puzzles that he took to arise from the phenomenological accounts.

Gödel demonstrated that any non-contradictory formal system, which was comprehensive enough to include at least arithmetic, cannot demonstrate its completeness by way of its own axioms.

For example, if we can enumerate all such definable numbers by the Gödel numbers of their defining formulas then we can use Cantor's diagonal argument to find a particular real that is not first-order definable in the same language.

The work of both authors was heavily influenced by Kurt Gödel's earlier work on his incompleteness theorem, especially by the method of assigning numbers ( a Gödel numbering ) to logical formulas in order to reduce logic to arithmetic.

Gödel's ontological proof is a formal argument for God's existence by the mathematician Kurt Gödel.

" A more elaborate version was given by Gottfried Leibniz ( 1646 CE to 1716 CE ); this is the version that Gödel studied and attempted to clarify with his ontological argument.

From these hypotheses, it is also possible to prove that there is only one God in each world by Leibniz's law, the identity of indiscernibles: two or more objects are identical ( are one and the same ) if they have all their properties in common, and so, there would only be one object in each world that possesses property G. Gödel did not attempt to do so however, as he purposely limited his proof to the issue of existence, rather than uniqueness.

It was first proved by Kurt Gödel in 1929.

* Stanford Encyclopedia of Philosophy: " Kurt Gödel " -- by Juliette Kennedy.

The proof of Gödel's completeness theorem given by Kurt Gödel in his doctoral dissertation of 1929 ( and a rewritten version of the dissertation, published as an article in 1930 ) is not easy to read today ; it uses concepts and formalism that are outdated and terminology that is often obscure.

Gödel then studied number theory, but when he took part in a seminar run by Moritz Schlick which studied Bertrand Russell's book Introduction to Mathematical Philosophy, he became interested in mathematical logic.

This was the topic chosen by Gödel for his doctorate work.

The theorems were proven by Kurt Gödel in 1931, and are important in the philosophy of mathematics.

To prove the first incompleteness theorem, Gödel represented statements by numbers.

This result, known as Tarski's undefinability theorem, was discovered independently by Gödel ( when he was working on the proof of the incompleteness theorem ) and by Alfred Tarski.

Another approach is taken by the von Neumann – Bernays – Gödel axioms ( NBG ); classes are the basic objects in this theory, and a set is then defined to be a class that is an element of some other class.

The term has been used by modern philosophers such as Kurt Gödel and has entered the English language.