Dear Nikola,

Is it naughty of me to compose a document pretending to myself that
I am writing to you, while at the same reassuring myself, that just as 
you are not obligated to reply, or even to read my script, so I 
reserve the opportunity to retain my letter with the caption NOT SENT,
perhaps committing it to nothing more the entanglement of my computer 
files? My first reaction on rereading yesterday's letter to you,
was embarrassment that in my frenzy to assert myself in the arena
of metamathematics, I had been careless in criticising
Kleene's report of Galileo as remarking in 1638 "that the squares of
the positive integers can be placed in a 1-1 correspondence with the
positive integers themselves, despite the ancient axiom that the whole
is greater than any of its parts." 

In Euclid Book 1, Common Notion No. 8, I 
find: "καὶ τὸ ὅλον τοῦ μέρους μεῖζον ἐστιν." which I translate:
"and the whole is greater than its part." 
I do not wish to argue that the difference between
"and the whole is greater than its part," and
"the whole is greater than any of its parts," 
is worth quibbling about. My question to Kleene and to Galileo (and to you)
with respect to the set of positive integers on the one hand, 
and the set of positive integers squared on the other hand, 
which is the whole and which of the parts of this whole 
might be deemed greater than this whole, remains unanswered.
Implicit in Keene's report of Galileo's remark is an assertion that
"the positive integers themselves" are the whole,
and that the squares of the positive integers are part of that whole.
Such an assertion would not be intuitive persuasive to me.

Continuing to read Keene's treatise, I stumble over his statement (p. 3)
"Cantor, between 1874 and 1897, first undertook systematically
to compare infinite sets in terms of the possibility of establishing
correspondences." If my inference that Cantor proceeded to calibrate 
diverse other series as infinite using the series of natural numbers
as a standard, I must learn to understand the logic by which Cantor
identified the natural numbers to be an infinite set and as such to
enumerable or denumerable or countable. I acknowledge that the natural
numbers as an infinite set is established mathematical doctrine. What right
do I have to question established wisdom? What right have I to a critical
review of the concept, of the experience of infinity. What does it mean
"to experience infinity"? Is it possible to "experience" infinity,
and if so, how do I proceed? Ist es möglich die Unendlichkeit zu erleben?