On 9/22/2010 11:19 AM, John F. Sowa wrote:
> ...
> PS: Whenever you read a math paper that starts off by saying
> "A whatchamacallit is an ntuple (A, B, C, D, E)..." you have
> found somebody whose mind was warped by people like Dieudonné. (01)
This is just not true, John. In many branches of mathematics  set
theory and computability theory especially spring to mind  it is often
important to represent a complex mathematical notion as a class of
welldefined mathematical *objects* for which one can define properties
and on which one can define operations. Representing the separate
components of a complex notion by means of ntuples is a very clear and
convenient way of doing so  indeed, I can't think of any other way of
doing it that wouldn't amount to the same thing. A particularly clear
example: In model theory, interpretations for firstorder languages have
to be welldefined objects that can stand in, e.g., the "truein"
relation. An intepretation, however, is a complex entity, requiring at
the least a domain D and an interpretation function V mapping lexical
elements into appropriate semantic values constructed over the domain.
(Interpretations of Common Logic dialects are more complex still.) The
obvious way to present such an entity as a welldefined object is to
define it as an ordered pair <D,V>. The matter becomes especially
critical when one is doing formal model theory in the context of set
theory where one has to be careful that a given notion can be
represented as a legitimate set. (02)
chris (03)
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