Word: theoremhood
(lookup in dictionary)
(lookup stats)
Dates: all
Sort By: most recent first
(reverse)
...mathematics was that it eliminated all need for thought or judgment. As long as the axioms were true statements and as long as the rules of inference were truth preserving, mathematics could not be derailed; falsehoods simply could never creep in. Truth was an automatic hereditary property of theoremhood...
...thinking of theorems as patterns of symbols, Godel discovered that it is possible for a statement in a formal system not only to talk about itself, but also to deny its own theoremhood. The consequences of this unexpected tangle lurking inside mathematics were rich, mind-boggling and--rather oddly--very sad for the Martians. Why sad? Because the Martians--like Russell and Whitehead--had hoped with all their hearts that their formal system would capture all true statements of mathematics. If Godel's statement is true, it is not a theorem in their textbooks and will never, ever show...
| 1 |