[FOM] Computer Scientists visa vie Mathematicians

[Dennis E. Hamilton]

I said,

> The idea of scopes and whether occurrences of variables in a text are free
or bound is a syntactic/grammatical matter.  It is easy to illustrate.  I
hesitate to offer this to a mathematical audience where I expect it is
already recognizable.  I do so to establish a shared context.

> The TL;DR: All of this predates computer science.  It goes back to the
work of Church and others.  My first exposure, around 1961, was in the
account of [Rosenbloom, Paul C.  The Elements of Mathematical Logic.  Dover
(New York:  1950).  ISBN 0-486-60227-3 pbk.]  The free-bound distinction is
found in [Church, Alonzo.  The Calculi of Lambda-Conversion.  Annals of
Mathematical Studies 6.  Princeton University Press (Princeton NJ: 1941).
ISBN 0-691-08394-0 pbk.]

Although I have a computer-scientists preoccupation with lambda calculus, I
am reminded that the binding of free occurrences of variables goes back to
the syntactic scopes of quantifiers in Predicate calculus, including FOL.
E.g., [Barwise, Jon.  An Introduction to First-Order Logic.  Chapter A.1 in
The Handbook of Mathematical Logic, Elsevier (Amsterdam: 1977).  ISBN
0-444-86388-5 pbk.] and [Russell, Bertrand.  Mathematical logic as based on
the theory of types.  1908 paper reprinted in van Heijenoort, From Frege to
Gödel: A Source Book in Mathematical Logic, 1879-1931. Harvard University
Press (Cambridge MA, London: 1967) ISBN 0-674-32449-8.]

PS: I regret that problems of graphic-characters encoding in messages passed
over and transformed by Internet services rendered my previous use of the
Greek \lambda character as "?".  I foolishly thought I could avoid lapsing
into [La]TeX-isms or other devices.

 - Dennis