1) Eine Bildung muss der Mensch haben.

2) Alle Bildung ist Einbildung.

3) Für Dedekinds psychische Verfassung ist besagend dass er nie heiratete,
dass er sich nie von seinem Bruder und seiner Schwester, von seines Vaters
Familie trennte.

4) All mein Wissen entspringt meinem Gemüt.
All my knowledge issues from my mind.
By definition, all that issues from my mind is intuition. 
All my knowledge issues from intuition.

5) Intuition has degrees of objective validity

6) A subsequent intuition may confirm, repudiate, converge on, diverge from, 
contradict or extinguish its predecessors.

7) Intuition has degrees of subjective validty. Some intuition is 
compelling; other intuition is fleeting and evanescent.

8) The criterion of correctness of objective intuition is diverse congruity 
as well as social concurrence and confirmation.

9) The criterion of correctness of subjective intuition is persistence
and/or autologous congruity.

10) All mathematical knowledge is intuitive.

11) All knowledge or intuition is inherently mathematical or is, in any event,
indistinguishable from non-mathematical knowledge. Note the paradox that two
things which are different should be indistinguishable. If they were 
indistinguishable how would I ever know that they were different.

12) Some intuition (knowledge) is immediate, such as perceptions of points
(of light), of lines as boundaries, of planes and solids, of temperature,
sound, pressure, flow.

13) Other intuition is contingent on words as identifiers, 
e.g. names of persons, places, animals, plants, etc.

14) The understanding of symbols, be they mathematical or verbal, is also
intuition. I recognize a circle, a pattern as circular, 
as soon as it appears so me, sobald es mir als solches auffällt. 
I define a circle as that line which is everywhere equidistant from a point.
Equidistance everywhere is likewise a topic, an item, "a thing" the 
meaning of which entails intuition. Mathematical proofs are translations
and concatenations of single intuitions into elaborate patterns which
corroborate the validity of the primary intuition that was subject to proof.

15) In Dedekinds book, Was sind und was sollen die Zahlen? (What are numbers, 
and what are numbers about?) I was struck by his assertion that all matters
of mathematical knowledge subject to proof, should be proved even if they
are "self-evident". Self-evidence is subjective. I can point out to you an
object (a thing, an appearance) which is "self-evident" to me, but I cannot
conclude that you also will find it self-evident.

16) I contemplate processes of mathematical proof as social expansions of
primary private, subjective individual intuition. What especially strikes me
is that each term, each link in the chain of proof requires its own 
demonstration, requires to be apprehended by a separate intuition.
The mathematical proof therefore becomes a series of exercises in common,
or more accurately, in coincidence of intuition, reminiscent of a childrens
game we used to play: "I see something you don't see." (Ich sehe was, was du 
nicht siehst.) By constructing a staging of series of cognitive hurdles, each 
of which requires to be surmounted by intuition, mathematical proof coerces a 
serial coincidence of intuitions and appears as the ultimate secular epiphany.