Jerry, John, List,
 
There are copulas that donot need another agent besides A, B, C, D, like "to give", or "to take", which is transfer of property. But "to buy" needs other agents: Who defines the currency? Some state or bank or other institute E. The currency may have been picked by the market place, or (international trade, or crypto currency)  by A, or C, or due to an agreement of both. Who has defined the cost of B? Maybe A is only the vendor, and some boss of A´s, F, has fixed the price. Maybe A has defined it, maybe A and C have negotiated it. Maybe there is a boss F, who is a person, or an institution, like an agricultural cooperative. "A gives B to C and C gives D dollars to A" does not say that this is a buying process, or the same buying process. It may also be, that both the good B, and the money, are gifts. Or that the dollars are not for B, but for a former trade good G, and the exchange simultaneity is due to the fact, that A and C are just now meeting, and C now has a month time to pay for B.
 
Best, Helmut
 
30. November 2021 um 18:45 Uhr
 "Jerry LR Chandler" <jerry_lr_chand...@mac.com>
wrote:
 
List, John:
 
Thank you for recognizing the nature of my concerns with respect to the meaning and importance of the word "grand” in the classification of notations for logics.
 
That being said, it is not clear how your response, precise thou it is, can be associated with the conceptual grounding of the different notations for logics that convey truth functions.  
 
After all, the title of this paper includes the word “notation” which is a very very “deep” term in the conceptualizations of human communications.
 
Further more, one can puzzle about HOW MANY forms of relations are necessary for scientific communications that bear constitutive  semantic and syntactical, geometrical nd non-geometric, terms?  
 
In other words, the example of the verb “buy” must be replaced by a meaningful binary “copula” that associates polynomial predicates.
 
Cheers
 
Jerry 
 
On Nov 29, 2021, at 11:27 PM, John F Sowa <s...@bestweb.net> wrote:
 
Jon A and Jerry LRC,
 
There are multiple issues here:  (1) The syntax of the logical notation, (2) The number of  participants related by a particular relation, and (3) the question whether a relation that relates N participants can be replaced by two or more relations, each with a fewer number of participants..
 
For example, the verbs buy and sell normally relate four things each:  "A buys B from C for D dollars" and "C sells B to A for D dollars".
 
:But each of those verbs that relate four things can be replaced by two verbs, each of which only relates three things:  :"A gives B to C and C gives D dollars to A:".  That is an example of  a tetradic relation that is replaced by two triadic relations  Those two acts of giving may be separated by an arbitrarily long period of time.
 
But the verb give has three obligatory participants, which must always be present in any act of giving.
 
However, some people claim that  a triple store which uses only dyadic relations is sufficient to represent anything.  But that is true only under one condition:  Some triads such as give can only be replaced by three dyadic relations if and only if each of the three dyads are never separated..  They must occur in a single indivisible event..
 
For example, "A gives B to C" my be replaced by three dyads and a monad:  "Giving(X) and Agent(X,A) and Patient(X,B) and Recipient(X,C)".  In this translation of an obligatory triad to a monad and three dyads, the act of giving X has three parts that must occur at the same time.. You can't perform the different dyads in separable actions.
 
John
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