Frances to William with thanks... 
It seems reasonable that the historical identity of architecture
would be an initial starting point in defining architecture in
theory, even if much of its history might now be a speculative
interpretation. It may be that the first mobile case of quasi
architecture outside of a cave was the holding up of a cape as a
tent to protect the wearer. If a cape as a tent is in fact and in
deed made to be like a cave, then the historic criteria would be
based mainly on iconicity and its similarity, rather than on
indexicity and its contiguity or on symbolicity and its
arbitrarity. My instinctive tendency in considering theory is
clearly exposed to lean in the direction of biotics and semiotics
and linguistics and logics, rather than historics and anthropics
and praxics and epistemics, because it seems to me that the one
thing that all architecture may be found as would be as a sign,
whether mainly iconic or indexic or symbolic, or mainly in
combination of this tern. To support this leaning or bent of
mine, the most technically and scientifically advanced
architecture after all seems to have occurred in those societies
that were highly literate, but further whose linguistic literal
language system lent itself easily to typesetting and printing,
so that scientific information about the tech and techne and
technics of building edifices could be communicated to other
persons in other places at other times. This is not to imply that
out of literacy will necessarily flow intelligence, but it does
suggest that records of fact and law can be kept. 

You wrote... 
Our ideas of architecture, what it is, stem from Vitruvius' 10
books of architecture. I suggest the Loeb Classical Library
editions.  Another source to look at would be Louis Mumford's The
City in History. He says architecture began with the notion of a
citadel and buildings expressing power, and evoking "respectful
terror". However architecture is defined in theory, its
historical definition is a starting point. 

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