6.1271 It is clear that the number of “logical basic laws” is arbitrary, since one could indeed derive logic from a single basic law, by simply, e.g., forming the logical product of Frege’s basic laws [Grundgesetzen]. (Frege would perhaps say that this basic law is now no longer immediately self-evident. But it is remarkable that so exact a thinker as Frege appealed to the degree of self-evidence as the criterion of a logical proposition.)

Yes, what is self-evident in this sense, or degree of self-evidence at any rate, is a psychological matter, not a logical one. The anti-psychologism Frege, of all people, should have seen that.