Alice laughed. "There's no use trying," she said: "one can't believe impossible things."
"I daresay you haven't had much practice," said the Queen. "When I was your age, I always did it for halfanhour a day. Why, sometimes I've believed as many as six impossible things before breakfast."
Through the LookingGlass, and What Alice Found There (1871)
by Lewis Carroll (nom de plume for mathematician and logician Charles Lutwidge Dodgson).
"If I had some ham I could have ham and eggs if I had some eggs."
Anonymous Logician
From a Student of Set Theory
Might not a mouse
in iron grip of owl, review
his forest world
in wonder 'midst his fear?And see his meadow home below,
and tree and stream as new,
and think
"How beautiful from here?"
I have written some notes, placed them in PDF format and collected links to them from this page.
In fact the notion of truth a la Tarski avoids complete triviality by the use of the magical expression "meta." We presuppose the existence of a metaworld, in which logical operations already make sense. The world of discourse can therefore be interpreted in the metaworld. The truth value of "A" is determined by "metaA," and we can in turn explain "metaA" by "metametaA" ... 
paraphrased from a note of JeanYves Girard

I was looking something up in Ronald Brown's "Topology and Groupoids" and he quoted the character Theseus in Shakespeare's "A Midsummer Night's Dream" commenting on the role of Poets:
The Poet's Eye in a Fine Frenzy Rolling
Doth Glance From Heaven to Earth, From Earth to Heaven,
And as Imagination Bodies Forth the Forms of Things Unknown
The Poet's Pen Turns Them to Shapes, and Gives to Airy Nothing
A Local Habitation and a Name.
Brown remarks that the verse could apply to mathematicians and their creations as well as to poets.
And now, of course, I'm quoting Brown.
The Axiom of Choice (google it, if you wish) is a foundational mathematical assumption used explicitly or implicitly by most modern mathematicians. Many of the most intricate triumphs of recent mathematics depend upon it: in some cases the standard proofs fail without the axiom. In (many) other cases the result is known to be unprovable without AC. It has numerous surprising consequences and alternative formulations. The WellOrdering Principle and Zorn's Lemma are two of these. The following is a joke, and most mathematicians think it is really funny. The "dry humor" type of funny, but still quite good. It is a quote from mathematician Jerry Boma.
The Axiom of Choice is obviously true, the WellOrdering Principle obviously false, and who can tell about Zorn's Lemma?
Here is another joke on more or less the same topic containing a hint of irony. Or perhaps that's not quite right. Anyway Frechet, Tarski and Lebesgue are titans of early 20th century mathematics. PolishAmerican mathematician Jan Mycielski relates this anecdote in a 2006 article in the Notices of the AMS.
Tarski tried to publish his theorem (the equivalence between AC and "every infinite set A has the same cardinality as AxA") in Comptes Rendus, but Frechet and Lebesgue refused to present it. Frechet wrote that an implication between two well known (true) propositions is not a new result, and Lebesgue wrote that an implication between two false propositions is of no interest.
Meditating upon the ancient Latin truism "Audentes fortuna adiuvat," and the excerpt from a Jack Vance novel found below, I have decided to set up a bucket at the back of class each day. After five minutes I will examine the contents of this bucket, and proceed with the remainder of the discussion as prompted by the relevant muse, and the goddess Fortuna."What are your fees?" inquired Guyal cautiously."I respond to three questions," stated the augur.
"For twenty terces I phrase the answer in clear and actionable language;
for ten I use the language of cant, which occasionally admits of ambiguity;
for five, I speak a parable which you must interpret as you will;
and for one terce, I babble in an unknown tongue."
Jack Vance, Tales of the Dying Earth
Link to my Bellevue College Page
I can be contacted by phone at Bellevue College at (425) 5642484 or by email at lsusanka@bellevuecollege.edu . My PGP public key can be found on the public keyservers and also here.
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