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An Inconsistency

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Posted by Richard Ruquist on August 27, 2002 19:07:00 UTC


The two statements below, which followed each other seem to be contradictory, one saying that Peano Axioms are assumptions, and the other implying that they are math tools and not assumptions. Stafford and I have gone round and round about his assumptions- particularly the shift symmetry assumption. I do not see how shift symmetry follows from a communicable universe. Could you explain that one for me.

Paul:I agree, those assumptions being at least the Peano Axioms which deliver numbers.

Paul: You mistake the tools of mathematics for the objects of mathematics. Dick used the
tool kit provided by the English language, the rules of logic, the mathematical system of arithmetic with
its numbers, and the theorems of analysis including calculus and matrix algebra. Using these tools, he
proved that any universe which is communicable must adhere to his constraint. He made no assumption
on the universe except that it be communicable.

Me: I do not see any evidence of shift symmetry in the above statement.



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