[FOM] Frege on self-evidence, etc. (comments by Dean Buckner)

[Martin Davis]

As a courtesy to Dean Buckner, a former FOM subscriber, I am posting
his comments in the following. -Martin
***************************************************************************************
"I have never disguised from myself its lack of the self-evidence that
belongs to the other axioms and that must properly be demanded of a
logical law. Frege 1903, 253". If Frege did not disguise this from
himself, why did
he disguise it from his readers by alleging that he had succeeded in
basing arithmetic on logic? Why did he not tell them that he had more
work to do on it? (Frango Nabrasa)
 >>>>>>>>
He did not entirely diguise it from his readers. Frege's next sentence
(in the appendix to the 2nd vol of Grundgesetze which he included after
hearing of the paradox from Russell) reads "And so in fact I indicated
this weak point in the preface to Vol 1. I should gladly have dispensed
with this foundation if I had known of any substitute for it."
The passage in Vol 1 he refers appears to be "A dispute can break out
here, so far as I can see, only with regard to my fundamental law
concerning value ranges (V), which has not yet perhaps been expressly
formulated by logicians, although one has it in mind, for example, when
speaking of extensions of concepts. I hold it to be purely logical. At
any rate, the place is hereby indicated where the decision must be
made."
In his view of self evidence, he write earlier in the preface: "It
cannot be required that everything be proved, because that is
impossible; but we can demand that all propositions used without proof
be expressly declared as such, so that we can clearly see upon what the
whole construction is based."
On Frege's insincerity: he was genuinely amazed at the paradox, and says
he has been left "thunderstruck" by Russell's letter (letter to Russell,
Jena 22 June 1902). "I must give further thought to the matter. It is
all the more serious as the collapse of my Law V seems to undermine not
only the foundations of my arithmetic but the only possible foundations
of arithmetic as such."
"The second volume of my Grundgesetze is to appear shortly. I shall
have to give it an appendix where I will do justice to your discovery".
Seems honest enough to me.
Dean