Edwin Mares wrote:
Who was the first logician to present rigorous formation rules for a formal language? And where (and when) did they do it?
The very first, I am not absolutely sure. But Frege does so in Grundgesetze,
published in 1893: See, in particular, sections 28 and 30. Frege is
there characterizing "correctly formed names", and the characterization
has to be rigorous enough to underwrite the induction on the complexity
of expressions used in the the argument, given in sections 30-31, that
all correctly formed names denote. Frege's specification is, to be
sure, not as rigorous as what one finds in Goedel 1930, but one
shouldn't expect it to be. What makes it particularly messy is that the
specification is spread out over two sections, and perhaps the most
interesting part of it---Frege's explanation of how "complex
predicates" may be formed---is separated from the main exposition.
There's also a slight inaccuracy there, since Frege explicitly mentions
this method of formation only in connection with first-level predicates
when it is clearly needed at all levels. But what he says generalizes
smoothly up through the hierarchy, so we can let that pass.
It's possible that one could find something earlier in the work of the
Booleans, but I don't know of anything---Boole seems simply to assume,
not unreasonably, that one understands how to form simple algebraic
expressions, and he's not really interested in the language
itself---and then there's the Indian tradition, of which I know
essentially nothing. And of course the languages in which these groups
were interested lacked the expressive power of Frege's, and so some of
the problems that arise for Frege---in particular, nesting of bound
variables---simply don't arise in that context.
So if one were to rephrase the question as "Who was the first logician
to give rigorous formation rules for a language of reasonable
expressive power?" then the answer is definitely: Frege.
Richard Heck
--
Richard G Heck Jr
rgheck-u5Aw1N0zcJ6HXe+LvDLADg@xxxxxxxxxxxxxxxx
http://bobjweil.com/heck/
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