# [FOM] informal poll terms in logic I: pure and applied logic

John Baldwin jbaldwin at uic.edu
Thu May 11 19:32:46 EDT 2017

There were 15 responses to the rather ill-constructed survey asking
whether certain distinction between pairs of terms were archaic,
specialized or unknown to the respondent.

I deliberately gave no explanation of context and this sometimes
resulted in quite different rationales for the answers.

Given the loose phrasing of the question there were many different
responses to some the pairs.  I primarily report numbers that give
insight about the community's understanding.

Since I think fom posts should be short, I will report the responses
to each question in a different post over the next week.

Survey question 1: pure and applied logic.

I had in mind the specific difference between pure and applied
functional calculus -- a term that appears at least as late as Church
1956 - but not in modern mathematical logic texts (Shoenfield,
Ershov-Palyutin, Enderton, Marker, etc.)

The `official difference' is that pure logic contains only variable
symbols and logical connectives; applied logics contain constant
symbols

Six people said unknown; 5 said distinct; 1 said archaic

Two respondents were well-acquainted with higher order logic and made
the clear distinction. The distinction is highly important for higher
order logic as seen by  work on "internal categoricity" by Parsons,
McGee, Vanaanen, Wang and Button-Walsh. The disappearance of the
terminology appears to me correlated with the dominance of first
order logic. Godel noticed in his thesis that there is an easy
translation between completeness of pure and applied first order
logic.

But the use of `applied' ties in with the emphasis since the 50's on
vocabularies (aka similarity, type, signature, language ...) chosen
that are relevant to the specific subject being studied (groups,
orders..) rather than a universal language for studying reasoning

This is one of the first signals of the paradigm shift in model
theory that I explore in my book which should go to press soon.

John T. Baldwin
Professor Emeritus
Department of Mathematics, Statistics,
and Computer Science M/C 249
jbaldwin at uic.edu
851 S. Morgan
Chicago IL
60607
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