Re: Minimal Negation Operators • (1) • (2) • (3) • (4)
Re: Peirce List (1) (2) (3) • Jerry Chandler

JC:

As a chemist, CSP often inscended hyle terminology into his logical corpse as he sought to extend the 15–17th century historical usages of the meaning of the concept of a “term”.

One particularity of chemical synthesis is the absence of the “negative” operators on the chemical elements.  Each element is a logical constant in the language of chemistry and hence can not be negated.  Yet, in the notation for chemistry it is necessary to assert and signify the absence of a chemical unit in a logical product.  This could be referred to as a minimal negation in a logically consistent semantics of a chemical syntax.

I have no information, either positive or negative, of the meaning Jon intends to infer logically with his usage of this non-standard semantics.  However, this semantics is obviously useful in attempting to give a logical semantics for the well‑established semiosis of hyle.

Dear Jerry,

I’ve been spending a lot of time lately thinking about how I first got into all the things I’ve gotten into over the years.  The thing that surprised me the most was how much of my life I’ve been immersed in raw data despite my best efforts to rise above it in flights of theory and just plain fancy.  The honors chemistry course I took my first year in college was pretty advanced — we “hit the ground running” as my Dad used to say from his paratroop days — moving from covalent bonding theory the first term to molecular orbital theory the second.

It was there I first encountered the triple interaction of theory, experiment, and electronic computation.  Aside from the routine programs we ran to analyze our data, drawing least squares lines through experimental scatterplots and all that, I began my first attempts to compute with symbolic forms, trying to get Fortran to place the electron dots around and between chemical symbols in various molecular combinations.  Mostly I learned to dislike Fortran — wrong tool for the job, I guess — and it would be years before I woke to Lisp.

At any rate, let me beg off on chemical logic or logical chemistry.  My experiences in that borderland are more a tale of fits and starts than anything conclusive and reconstructing the details would take a search through the darker corners of my basement archives.

The matter of “non-standard semantics”, however, is a timely and topical subject to address, one it would dispel a mass of obscurities about the link between logic and semiotics to clarify as much as we can.

To begin, we may pose the question as follows.

• In what way does a propositional calculus based on minimal negation operators deviate from standard semantics?

I will take that up next time, perhaps under a different heading.

Regards,

Jon

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