[lit-ideas] Re: Pons Asinorum
- From: Jlsperanza@xxxxxxx
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Thu, 11 Jun 2009 08:15:04 EDT
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 surname
means 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 directly
from 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 the
Proposition 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 isosceles
triangle. 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 as
Phil-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 its
own 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 Fifth
Postulate". 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 fact
that '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's
syllogistic, 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 not
really 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
Other related posts:
