Po mnoha dopisů mezi dva, Frege upravila jednu z jeho axiomy a vysvětluje, v dodatek ke knize, že tomu tak bylo obnovit konzistenci systému. Nicméně se tento pozměněný axiom, mnohé z vět na Svazek 1 nešla projít a Frege musí vědět to.
After many letters between the two, Frege modified one of his axioms and explains in an appendix to the book that this was done to restore the consistency of the system. However with this modified axiom, many of the theorems of Volume 1 do not go through and Frege must have known this.