tweakabelle
Posts: 7522
Joined: 10/16/2007 From: Sydney Australia Status: offline
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quote:
ORIGINAL: UllrsIshtar quote:
ORIGINAL: tweakabelle quote:
ORIGINAL: tweakabelle The idea that there is no objective notion of truth is utterly consistent with science, where all 'truth' is provisional, a hypothesis that works until a superior hypothesis is formulated and advanced. Godel's findings are considered proven - there is no dispute about the validity of his 'Incompleteness Theorem', though there is some disagreement about the extent of the implications of this work. If there is no objective notion of fact, then it's impossible that Godel's findings are proven. Any interpretation indicating that they are true isn't nothing but a subjective interpretation. From wiki: "Gödel's incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system containing basic arithmetic.[1] These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics (ie a Theory of Everything or a totalising theory) is impossible. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of the natural numbers. For any such formal system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency. Employing a diagonal argument, Gödel's incompleteness theorems were the first of several closely related theorems on the limitations of formal systems. They were followed by Tarski's undefinability theorem on the formal undefinability of truth, Church's proof that Hilbert's Entscheidungsproblem is unsolvable, and Turing's theorem that there is no algorithm to solve the halting problem. https://en.wikipedia.org/wiki/Main_Page Thus, within the principles of mathematics, paradox is part of the structure of maths and cannot be removed without violating its principles. As maths is the most rigourous and accurate language we possess, this is valid for all closed knowledge systems - all have insoluble paradoxes built into their structure. The effect of this is that for any knowledge system, we can have a consistent but incomplete description of the data (ie theory) or we can have a complete but inconsistent explanation. Therefore all knowledge systems are partial - objective truth cannot be arrived at through a rational knowledge process. A Theory of Everything or totalising theory is impossible. Anything that describes itself as an objective fact, or as a complete and consistent description of the data developed through a scientific/mathematic method cannot be valid - it is impossible.
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