[hist-analytic] The Polyhedron: From Plato to Euler -- and Back

Jlsperanza at aol.com Jlsperanza at aol.com
Sat Feb 7 11:15:33 EST 2009


I love polyhedra. Came to love them by reading Thomas (Loeb Library -- two  
volumes).
Indeed, the triangle is the first plane figure, but the prism is the first  
_corpse_ (to use Danny Frederick's phrase -- corpus).
Apparently, Plato's Timmaeus is full of them, and my teachers always told  
me, "Avoid that -- hardly philosophical, and slightly _crazy_. Ah, tutors are  
the least type of person who should be allowed to have tuttees. 
Anyway, apparently Euler, topologically and characteristically, thought  
otherwise.
So perhaps Lakatos, a star in our little mathematical firmament -- see  below 
for his claim to fame in the EOD -- is echoing what Whitehead said of  
metaphysics,
 
      "footnotes to Plato".
 
Ditto -- mathematics? Think so!
 
"A Star in the Mathematical Firmament": a tribute to Imre Lakatos
 
In a message dated 2/7/2009 10:30:19 A.M. Eastern Standard Time,  
danny.frederick at tiscali.co.uk writes in "Re: Quine's Holism"
For a discussion  see
Lakatos, ‘Infinite Regress and the Foundations of Mathematics.’

I  have seen that JL has just sent a post which covers part of what I have
said  about Lakatos. But I must say that some of that wiki stuff sounds
suspect to  me.



---

or unclear for a non-native English speaker.  Consider the passage:

"It was Agassi  who first introduced 
Lakatos to  Popper  under the rubric of 
his applying a fallibilist methodology of  
conjectures and refutations to  mathematics 
in his Cambridge PhD  thesis."

I see it's Lakatos's own PhD Cantab, "Essays in the Logic of  Mathematical 
Discovery" as D. Frederick quotes it. -- and I'm glad D. Frederick  can quote 
from other stuff by Lakatos which looks interesting, like the above  item, 
"Infinite regress...".

I was confused by Agassi (born Jerusalem,  1927 -- lives in Boston, or 
Canada, or Tel Aviv). 

What confused me was  the 'rubric' bit.

If it was Agassi, I would assume he was his  thesis-advisor, so-called. 

Glad to hear of 'metaphysical research programmes' from the lips of Popper.  
Apparently, this saw published light with Bartley (1983) in "Poscript to the  
Logic of Scientific Discovery". The OED, not very imaginatively, uses 
'research  programme' but in nothing like a Kuhnian paradigm or a Lakatosian thing.  

"1950 N.Z. Jrnl. Agric. June 514 (caption) The Rukuhia Soil Research  Station 
(Hamilton)..carries out a *research programme in soil physics. 1958  Bull. 
Amer. Assoc. Petroleum Geologists XLII. 701 Some years ago the Field  Research 
Laboratory of the Magnolia Petroleum Company began a Recent sediments  research 
program in the Gulf of Mexico. 1977 Sci. Amer. Dec. 15/1 He  now..carries on 
a research program in the behavioral ecology of ants."
 
 
For the record, there are only 5 hits for Lakatos in the OED -- so far  -- 
cfr. OED3 and _mailto:oed3 at oup.co.uk_ (mailto:oed3 at oup.co.uk) .
 
Under

"maturation" --not really Lakatos but his Argentine philosopher, Mario  
Bunge, in  I.  Lakatos & A. Musgrave Probl. Philos 
"mediate",  again (c) M. Bunge in I.  Lakatos & A. Musgrave Probl. Philos  
"Popperian" -- a reference _to_ Lakatos, not by him: "Lakatos's studies,  
although nominal ..."
"self-", again a reference _to_ "Lakatos's  sophisticated methodological..." 

and finally, Lakatos -- the man!, under 
 
"stellated"     
 
         "Take for instance the  ‘great stellated dodecahedron’ (fig. 15). 
         It consists, like the  ‘small stellated dodecahedron’ of 
pentagrams, 
          but differently  arranged. It has 12 faces, 30 edges and 20 
          vertices, so that V  - E + F = 2.


I.  Lakatos Proofs & Refutations, 1976, p. 62  

under definition of 'stellated' as "[said] of a polygon, polyhedron, or  
polytope: capable of being generated from a convex polygon, etc., by extending  
the edges, etc., until they once more meet at a new set of vertices, etc. [The  
sense is due to L. Poinsot, who used F. étoilé in Jrnl. de l'École Polytechn.  
(1810) IV. 41).]"
 
of course from 'stella', Latin for 'star'
 
Cheers,

JL




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