recursion, definitions of

[Prof. Dr. Wolfgang Schulze]

Dear David,
as far as I can see your assumption according to which

>  the "standard" definition [involves] a "rewrite rule" with an 
> identical symbol on either side of the arrow

is crucial for defining recursive processes. As for syntactic issues, we 
most often have to deal with some sort of Pythagoras Trees (see my 
http://www.ats.lmu.de/downloads/Blueprints.pdf, page 7 for an example). 
That is, fractal structures become relevant (with exact, quasi or 
statistical self-similarity, as fractals are conventionally classified). 
The point is that such recursive structures are not mere iterations or 
serializations (such as she ran ran ran... etc,), but that the recursive 
structure is by itself more complex that its mirrored 'parts'. 
Personally, I see the danger that the term recursive (well-defined e.g. 
in mathematics) bcomes semantically over-strechted within the world of 
linguistic terminology. In this sense, the term does not seem to me to be

> sufficiently broad as to encompass all of the [above] examples. 

If recursion is a linguistic (!) topic at all, we should find a general 
function/semantics of this hypothetic strategy. Personally, I do not 
think that all the examples you have given have in common a 'basic' 
function that constitutes by recursion the semantics of the 'whole'. 
Things are different with respect to cognition: here, we can safely 
assume that much of what cognition does happens in terms of recursion 
(see e.g. my http://www.ats.lmu.de/downloads/Bolzano_I.pdf; 
http://www.ats.lmu.de/downloads/ICLC.pdf [pp.8-13]).  
Very best wishes,
Wolfgang


-- 
Prof. Dr. Wolfgang Schulze
Institut fuer Allgemeine und Typologische Sprachwissenschaft
Ludwig-Maximilians-Universitaet Muenchen
Geschwister-Scholl-Platz 1
D-80539 Muenchen
Tel.: ++49-(0)89-2180-2486 (Sekr.)
Tel.: ++49-(0)89-2180-5343 (Office)
Fax : ++49-(0)89-2180-5345
E-mail: 
W.Schulze at lrz.uni-muenchen.de
schulze at fhv.umb.sk
Web: http://www.ats.lmu.de/profil/mitarbeiter/index.php

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