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re: reference required
[------ The Types Forum ------- http://www.dcs.gla.ac.uk/~types ------]
I'd like to thank everybody who replied to my query about the origins
of "typical ambiguity". A number of people pointed out that I was
looking in the wrong part of Principia. Melvin Fitting gave a precise
list:
Page 161, starting with the bottom paragraph.
Page 165, first complete paragraph.
Page 189, first complete paragraph.
Page 347, second paragraph. [page 345 in the paperback edition]
Twan Laan furthermore noted,
In *24 (p. 216), the "class of all objects" is defined via the
propositional function x=x Immediately after this definition it is
stated that "this definition is ambiguous as to type", i.e. that
implicitly, x is of the lowest order that is concerned in the context
of the text. This notion of "being ambiguous as to type" is exactly
the same notion as "relative type" of *12.
Also Joshua Guttman suggested looking elsewhere:
"Mathematical Logic as based on a theory of types" (by Russell alone,
1908). It's in van Heijenoort, pp 150-82.
Nobody located the literal phrase "typical ambiguity". However
Russell is quite fond of talking about "ambiguity" in various forms.
One dictionary definition of "typical" is "pertaining to type".
Thanks again to all (even if your reply was not specifically
mentioned).
--
Larry Paulson