Mimicry and The Goedel Number
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From: John Jones on 7 May 2010 20:28 The Goedel Number isn't a number, because it has no base. The Goedel Number only mimics numbers. A Goedel Number is an arbitrary mark on paper that imitates the marks and shapes we use for depicting numbers. Mimicry of purpose establishes a law or a mathematical axiom. The mimicry of form, such as we see in the Goedel Number and moths, can have uses in camouflage and deception (mothematics), but not in mathematics.
From: bigfletch8 on 7 May 2010 21:11 On May 8, 8:28 am, John Jones <jonescard...(a)btinternet.com> wrote: > The Goedel Number isn't a number, because it has no base. The Goedel > Number only mimics numbers. A Goedel Number is an arbitrary mark on > paper that imitates the marks and shapes we use for depicting numbers. > > Mimicry of purpose establishes a law or a mathematical axiom. The > mimicry of form, such as we see in the Goedel Number and moths, can have > uses in camouflage and deception (mothematics), but not in mathematics. Just another variation of mythmatics. BOfL
From: Immortalist on 7 May 2010 22:02 On May 7, 5:28 pm, John Jones <jonescard...(a)btinternet.com> wrote: > The Goedel Number isn't a number, because it has no base. The Goedel > Number only mimics numbers. A Goedel Number is an arbitrary mark on > paper that imitates the marks and shapes we use for depicting numbers. > > Mimicry of purpose establishes a law or a mathematical axiom. The > mimicry of form, such as we see in the Goedel Number and moths, can have > uses in camouflage and deception (mothematics), but not in mathematics. If Godel's Incompleteness theorem is that no consistent system of axioms whose theorems can be listed by an "effective procedure" (essentially, a computer program) is capable of proving all facts about the natural numbers; because there will always be statements about the natural numbers that are true, but that are unprovable within the system and secondly that if such a system is also capable of proving certain basic facts about the natural numbers, then one particular arithmetic truth the system cannot prove is the consistency of the system itself, then doesn't it sound very much like Russel's Paradox or the impossibility of a set of all sets since the former must be contained in the later, or that; Russell's paradox represents either of two interrelated logical antinomies. The most commonly discussed form is a contradiction arising in the logic of sets or classes. Some classes (or sets) seem to be members of themselves, while some do not. The class of all classes is itself a class, and so it seems to be in itself. The null or empty class, however, must not be a member of itself. However, suppose that we can form a class of all classes (or sets) that, like the null class, are not included in themselves. The paradox arises from asking the question of whether this class is in itself. It is if and only if it is not. The other form is a contradiction involving properties. Some properties seem to apply to themselves, while others do not. The property of being a property is itself a property, while the property of being a cat is not itself a cat. Consider the property that something has just in case it is a property (like that of being a cat) that does not apply to itself. Does this property apply to itself? Once again, from either assumption, the opposite follows. The paradox was named after Bertrand Russell, who discovered it in 1901. http://www.iep.utm.edu/p/par-russ.htm http://plato.stanford.edu/entries/russell-paradox/ http://en.wikipedia.org/wiki/Russell's_paradox
From: Sam Wormley on 7 May 2010 22:21 On 5/7/10 7:28 PM, John Jones wrote: > Goedel Number G�del Number http://mathworld.wolfram.com/GoedelNumber.html
From: John Jones on 8 May 2010 11:03
Sam Wormley wrote: > On 5/7/10 7:28 PM, John Jones wrote: >> Goedel Number > > > G�del Number > http://mathworld.wolfram.com/GoedelNumber.html Phrases such as - "Let the states and tape cell colors be numbered and represented by quadruples of ordinal numbers" demonstrate my point. My point is that such a representation is not a mathematical, numbered representation. You can number each member of a list but that doesn't make the list numerically ordered. |