Typographical Number Theory
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High Quality Content by WIKIPEDIA articles! Typographical Number Theory (TNT) is a formal axiomatic system describing the natural numbers that appears in Douglas Hofstadter's book Gödel, Escher, Bach. It is an implementation of Peano arithmetic that Hofstadter uses to help explain Gödel's incompleteness theorems.Like any system implementing the Peano axioms, TNT is capable of referring to itself (it is self-referential).The symbol S can be interpreted as "the successor of", or "the number after". Since this is, however, a number theory, such interpretations are useful, but not strict. We can...
High Quality Content by WIKIPEDIA articles! Typographical Number Theory (TNT) is a formal axiomatic system describing the natural numbers that appears in Douglas Hofstadter's book Gödel, Escher, Bach. It is an implementation of Peano arithmetic that Hofstadter uses to help explain Gödel's incompleteness theorems.Like any system implementing the Peano axioms, TNT is capable of referring to itself (it is self-referential).The symbol S can be interpreted as "the successor of", or "the number after". Since this is, however, a number theory, such interpretations are useful, but not strict. We cannot say that because four is the successor of three that four is SSSS0, but rather that since three is the successor of two, which is the successor of one, which is the successor of zero, which we have described as 0, four can be "proved" to be SSSS0. TNT is designed such that everything must be proven before it can be said to be true. This is its true power, and to undermine it would be to undermine its very usefulness.
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