John, Kirsti, List (This is a technical post wrt to the role of possibility and actuality in the exact abductive logic of organic mathematics.)
I would just add an extremely important fact about the relationship between possibility and actuality in the chemical sciences. In the modern era, the logic of the chemical sciences is constrained to numeric operations on atomic numbers. (The physical concept of atomic numbers was constructed shortly before CSP past.) A root notion of organic mathematics is that atoms are composed into molecules. The wholeness of the molecule emerges from the necessity that every atom must be adjacent to at least one other atom such that all atoms become relatives in the emergent molecule. Logically, the relation is a "many to one” mapping, many atoms form one molecule. In other words, a part-whole relation is composed into a specific spatial form. The consequence of this many:1 mapping is an adjacency matrix that specifies the organization of the whole. Given a fixed number (N) of atomic parts, the minimal number of possible molecular graphs can often be calculated. Note that this calculation of the number of possible different molecules from the same set of atoms is an exact form of abductive reasoning. Chemical logic is then used to specify the actualities of the relationships in the formal logical structure of the molecule. This mathematical logic for organizing atoms into molecules does NOT use traditional mathematical variables because of the constraints of the identities of the ipseities. CSP conceptualized abductive qualitatively. The science of chemistry was not sufficiently advanced to provide the data for quantitative abductive logic necessary to describe handedness of biological molecules. Cheers Jerry > On Aug 27, 2018, at 9:58 AM, John F Sowa <s...@bestweb.net> wrote: > Kirsti >> I wonder why science(s) seems to be left out of the context >> in the discussions in this thread. To my mind they are direly >> needed in order to make sense , esp. of the latter part of >> the title, to start with. > > Yes. Every variable must refer to something that can be specified, > formally or informally, by one of the sciences. See the attached > diagram, cspsci.gif, for Peirce's classification of 1903. > ' > Janos >> Predicate logic allows you to write ∃x.P(x) for variable x >> and predicate P; x is typed by P... Interpretation of a free >> variable, such as x in ∃x.P(y), can be more complex, but may >> not be fundamentally different. > > Yes. Pure mathematics on the left of cspsci.gif specifies all > possible patterns that may be defined by any formal or informal > theory. Only a countable set of predicates can be specified with > any finite set of symbols and finite-length sentences. But as > Cantor showed, the set of instances may be uncountably infinite. > > KM >> I was left wondering whether the ontology context proves to be >> a Procrustean bed for a Peircean frame of thought? > > The reason why I introduced the issues raised in Ontolog Forum is > that the proposed ISO standard is an extremely narrow, nominalist > bed that makes it impossible to represent or even talk about the > full range of issues in Peirce's classification. > > Many people who subscribe to Ontolog forum agree with me. But > I'm trying to make a case that is strong enough for them to make > the necessary changes in the proposed ISO standard. To make it > convincing, I have to state the case as clearly as possible. > > KM >> When *applied* math enters, it never does so but within and into >> a stage and scene and plot already *there*. > > Yes. Pure mathematics can specify any predicate P about any x > that may be possible in any domain of discourse. An applied > ontology (the theme of Ontolog Forum) specifies the predicates > for some specific subject matter. To do so, it may use any > predicates specified by any science on which the subject depends. > > Since Peirce's classification shows that every science depends on > mathematics, any predicates from any branch of mathematics (which > includes any version of logic) may be used in applied ontology. > > John > <cspsci.GIF> > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu > . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu > with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at > http://www.cspeirce.com/peirce-l/peirce-l.htm . > > > >
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