Welcome to the list, Karl. Please don't expect any philosophy out of me. I abjure philosophy. It's the Devil's workshop. Never think twice, I say, and seldom once. "Let your needs be your guide." I think Kant said that. Or maybe it was me. Who knows? Who cares? Here's a hint on how to play it right on Lit-Id: call Mr. Speranza "Say hey, Jorge!" He loves that.
Good luck, guy. Mike Geary Memphis----- Original Message ----- From: <Jlsperanza@xxxxxxx>
To: <lit-ideas@xxxxxxxxxxxxx> Sent: Thursday, June 11, 2009 7:15 AM Subject: [lit-ideas] Re: Pons Asinorum In a message dated 6/11/2009 6:47:58 A.M. Eastern Daylight Time, karltrogge@xxxxxxxx writes:
Thank you Mr Paul - this is more in line with what I thought I was remembering about 'pons asinorum'. This is why I was wondering why Mr Speranza
Karl, feel free to call me just "Speranza". My first name is Jorge-Luis, as per Borges, but NOBODY, never, even my mother who bore me, calls me "Jorge Luis". They call me "JL" But more to the point, nodoby called BORGES,Jorge-Luis. Or "Mr. Borges", or "Senor Borges". He ALWAYS made the point, "Call
me BORGES". If I may, I will call you Trogge. R. Paul called you Karle, but I think it's just Karl, right? TROGGE seems a fascinating German name. I suppose the etymon is related to English, 'tray' (whatever that means?). My surnamemeans HOFFEN, but it's formed in vulgar Latin by the spero- plus 'things to be
hoped for', sper-A-NT-IA. It's apparently Provencal, though I claim Ligurian roots, only. --- (The Jorge-Luis was my mother's joke on her liking Borges -- She was going to call me "Mike" -- just joking).
was associating it with 'Euclid's famous proof' (sic) of the shortest distance between two points being a straight line.
Right. But did you acknowledge MY TWO Long posts --- one citing directlyfrom M. Keleny on the 'ass' that Epicurus mentions as _knowing_ how to do the
isosceles. There is a basis for relating the pons asinorum to theProposition 5. I mentioned the thing about the straight line because, in essence,
that's the ass's reasoning. I don't think he _cares_ it's an isoscelestriangle. The site R. Paul mentions the thing may be called a 'bridge' because
of its shape which is one of the silliest things I've ever heard.
From what little I remember of Euclidean geometry this is not proven but is AXIOMATIC (and this was why I asked Mr Speranza to tell us where in Euclid the PROOF of which he speaks is to be found).
Euclid was a bit, if you ask me, crazy. I never understood him, nor did my mother. His talk is Aristotelian with a vengeance, Axioma, corollary,theorem, -- who cares! His word for 'point', as I recall, is 'sign' (semeion) so
there! He was confused in large parts. People laughed at him -- Epicureans notably. People were having good healthy fun in those Hellenistic days,and Euclid was, with his typical pale skin, enclosed in his bathroom, playing
with diagrams -- It's odd how little different from current professors of mathematics.
Rushing in perhaps where angels fear to tread, I will go further. In (some?)non-Euclidean geometries IT IS NOT THE CASE THAT the shortest distance between two points is a straight line. If I remember correctly, (some of?) these geometries arise from rejecting Euclid's postulate concerning parallel lines.
Yes, that's true. And a little history here. This list origianted asPhil-Lit by D. G. Myers, then there was a big split: one part of it remained now
as THEORIA, tamu.edu, run by L. J. Kramer, and this which is left to itsown devices (while we love Andreas and Taamu). I'm in touch with Kramer, and
he has a blog and one of the entries there is called, "The FifthPostulate". Kramer uses that metaphorically, to mean, 'anything', almost -- but we've
discussed that to tears. In fact, Geary's mother is non-Euclidean. --- In my reply to M. Keleny in CHORA, publicly available, I made exactly your point about proof and postulate and theorem and axiom -- all confusing talk -- cfr. wff -- well-formed formula --. I was even considering the factthat 'prove' is ambiguous. And an _ass_ may be said to _prove_ this or that.
My analogy was indeed The Cynic (Diogenes). Zeno of Elea has demonstrated that movement is impossible. Diogenes stood up and said, "There, you see; I have refuted Zeno". Cfr. Johnson refuting Berkeley by kicking a stone. Kramer says that the fifth postulate enjoins us to be _real_, but then, parts of the universe, I am told, are non-Euclidean, which gives a twist to the fifth-postulate.
My parenthetical queries (some? some of?) indicate my ignorance and I would be grateful for advice about the relationship between the AXIOMATIC shortest-distance- straight-line (which given or assumed) and the POSTULATE (which is proved).
Yes. I'll mention Grice, because he is the expert here. In "Logic and
Conversation", first and second page. He mentions 14 criteria to tell an
'axiomatic' system alla Peano.
1. There are indeed considerations of vocabulary.
2. Considerations of wff well formed formulae (syntax)
3. AXIOMS. This is Aristotle's term.
4. RULES OF INFERENCE alla Getzen. You cannot do ANYTHING without them, but
R. Paul disagrees, since Principia Mathematica notably does without them.
But that means that some metalogical considerations of Getzen are turned
_axiomatic_.
5. THEOREMS. An axiom is not a theorem, although it looks like one. It's
like some snarks are not boojums. A theorem is still true in all possible
worlds, like an axiom.
6. COROLLARY. This is a neologism by Geary, almost. The etymology is fun.
-----
So
a proof -- as per proof theory (and Aristotle calls 'semeion', a proof --
to confuse Euclid).
is a chain of propositions of the form
premise
____________
conclusion
Q. E. D. is used, quod erat demonstrandum.
It would be otiose to prove an axiom alla what Grice calls 'woman's reason'
("I like him because I like him")
p v - p
__________
p v - p
but it's _not_ illegal.
(Some people consider that because something or someone is otiose, it or
she is _false_ -- cfr. Richards's quote in thread, "Otiose").
The people who rejected Euclid's things were right.
The problem there is that the _universe_ of discourse is not, as in systems
philosophers are used to, _vacuous_, but interpreted in the arithmetic
domain, making the thing doubly silly for us philosophers who can think
_higher_ than numbers.
Peano is slightly better, and he had recursion which Euclid never
forethought. This is the closure postulate, and the 'mathematical induction'
thing.
Very clever of this Italian. The bridge of ass stuck, but it was also used to relate to Aristotle'ssyllogistic, as my quotes in the OED notes. It's also even related to Buridan's
ass. But the EARLIEST origin of the 'ass' reference is indeed to this Ep icurean who brought in the idea of an ass who would get to the fodder in a_straight_ line -- hence my misleading, but true, reference that the ass and
the bridge _were_ connected -- via Proclus (and Kemeny)
Further to 'pons asinorum': in German an ESELSBRÜCKE (donkey's bridge) is an aid to remembering some formula or series - a mnemonic. For example, in German, to remember the tuning of violin strings from low to high: Geh Du Alter Esel - GDAE; in English, to remember the lines of the treble staff: Every Good Boy Deserves Fun - EGBDF. It seems that the meaning has 'wandered' from 'any intellectual difficulty which separates the inept from the ept' to 'an aid which helps the inept overcome some such intellectual difficulty'.
Right. The problem here is _bridge_. The Greeks didn't have _bridges_. It's
a Roman invention. 'pontifex', and then there's the Catholic religion,
which I don't support. People can _swim_; they don't need bridges. In fact,
I'd go as far as to say that the 'cause' (i.e. telos) of a bridge is to
_avoid_ the swimmer to swim. Which is silly.
Indeed, considering a bridge and the brain of an ass, I would imagine the
scenario
BRIDGE
fodder
river
ass
Some asses are so ignorant that they will take the bridge to get to the
fodder, even while they would possibly swim using the shortest line, to get
to
the fodder. Humans are like that, in parts. In fact, I love bridges, in cities, which have nothing else. E.g. ROMA.People spend hours studying those barroco statues, which one loves, but I find
tacky in parts, and the surroundings don't help. I would rather spend my time on the bridges, or more likely, under the bridges of Rome. They are beautiful and the Tiber flows so majestic. Or consider Cambridge, Mass. -- that stone bridge on the Charles is just... BEAUTIFUL. it's only a pedestrian bridge which is what all bridges should
be. The bridges of Paris have been destroyed by NOT making them pedestrian. And recall that the University of Paris started on a bridge. In London, I studied ALL the Bridges, starting, alas, from Lambeth -- to Tower Bridge, of course, which people hate, but I don't. The old London bridge, in between, is no longer. In Oxford, the best bridge is next to Magdalen College -- and that little thing is indeed the best landscape in Oxford I've seen. There is another bridge in the centre of town. Some bridges can be too monumental: San Francisco Golden Gate, is notreally a bridge, but a monstrosity. It makes for the walking so difficult. I was
reading that being such a typical place for suicide, they were placing nets below to block the success of the usual suicides.Grice lived next to the Bay Bridge, which connects Oakland with S. F. -- this is slightly nicer, and the Bay looks better there. Grice's main studio
overlooked the Bay Bridge. NYC has one bridge too many. Yost should speak about them, because he rides the bike around the whole town. Brooklyn bridge of course, but the area is too harboury for my taste. But my favourite bridge would be the one near the Cloisters, since I on the whole preferred the riverside drive.
Hamburg, Germany
I'm not too familiar with the area. But isn't that Georg Handel country? In any case, what I do love is Angeln-Schls. -- Angeln being the mother country of the English, no less. Cheers, J. L. Speranza Buenos Aires, Argentina **************Download the AOL Classifieds Toolbar for local deals at your fingertips. (http://toolbar.aol.com/aolclassifieds/download.html?ncid=eml cntusdown00000004) ------------------------------------------------------------------ To change your Lit-Ideas settings (subscribe/unsub, vacation on/off,digest on/off), visit www.andreas.com/faq-lit-ideas.html
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