[FOM] 820: Sugared ZFC Formalization/2

Tennant, Neil tennant.9 at osu.edu
Tue Jun 19 21:48:05 EDT 2018

I am sure members of this list will wish to join me in welcoming Harvey's interest in scholarly matters of provenance.

Nolt's SEP article on free logics classifies them into positive, negative and neutral versions. The kind of free logic that Harvey (and I) prefer is a negative free logic. It originated in the work of Rolf Schock. Nolt cites Schock's 1968 book, but Schock's paper in NDJFL 1964 is the earliest source (but also a devilishly difficult, overly technical treatment of the topic).

Harvey wrote "Perhaps people will want to comment on [Nolt's] article." I have two comments.

Nolt is apparently unacquainted with my 1975 LMPS piece. I mentioned it in my earlier posting mainly because of its suggestion that term-insertion is a 'scopy' operation, which can be used to good effect in making the sorts of distinctions that a free logician wishes to draw.

Nolt appears also not to have noted the explicit development of a system of natural deduction for universally free logic in my 1978 book Natural Logic, pp. 163-173, including a proof of its completeness. The book is available for download at https://u.osu.edu/tennant.9/publications/ . (Don't worry, I own the copyright, and copies of it are free.)

If Harvey's own historical researches have uncovered a source even earlier than Schock for the negative free logic that we both advocate, I would be most interested to learn about it.


From: fom-bounces at cs.nyu.edu [fom-bounces at cs.nyu.edu] on behalf of Harvey Friedman [hmflogic at gmail.com]
Sent: Tuesday, June 19, 2018 12:26 PM
To: Foundations of Mathematics
Subject: Re: [FOM] 820: Sugared ZFC Formalization/2

There is a lengthy article on Free Logic and history thereof at
https://plato.stanford.edu/entries/logic-free/ with perhaps relevant
references going back to 1951.

Perhaps people will want to comment on that article.

Harvey Friedman

On Tue, Jun 19, 2018 at 8:22 AM, Tennant, Neil <tennant.9 at osu.edu> wrote:
> Harvey in effect relies on the scope distinctions that can be made fully explicit by the following use of bound variables to indicate term-insertions:
> t_x (x=x)         false if the term t does not denote; true if the term t does denote
> ~ t_x (x=x)      true if the term t does not denote; false if the term t does denote
> t_x ~(x=x)       false if the term t does not denote; false if the term t does denote
> The free logic that captures these intuitions about term-denotations and truth-conditions is set out in my paper
> Natural deduction for first order logic with identity, descriptions and restricted quantification’, in Contributed Papers of the 5th International Congress of Logic, Methodology and Philosophy of Science, London, Ontario, 1975, pp. I 51-2.
> See iterm 123 at https://u.osu.edu/tennant.9/publications/
> Neil
FOM mailing list
FOM at cs.nyu.edu

More information about the FOM mailing list