G. Spencer-Brown wrote in his book Laws of Form from 1969, that (as you can see in Chapters 9 and 10) his LoF is complete and independent. In fact this proves, that LoF can't deduce paradoxes of the form $ p \wedge \neg p $. So my question is the following:
As we know by Gödels Incompleteness Theorems, every System, which contains Peano Arithmetic is incomplete. Now Spencer-Brown deduced in the Appendix 4 & 5 of my german edition the PA with his LoF. What does that mean? Is PA now complete in the interpretation of LoF or is LoF in fact incomplete instead of complete?
Am I missing here something? Also I did not find any information on this subject. I hope some of you can explain this.