On 11/22/2017 10:50 AM, Jerry LR Chandler wrote:
This is common in the formal logic of the chemical sciences.
Peirce studied logic long before he studied chemistry. He picked up his brother's copy of Whatley's logic when he was 12. Boole's two books (1847, 1854) were published when he was 8 and 15. He must have read them very early. His degree in chemistry came after he finished his 4 years as an undergraduate at Harvard. The metaphor of logic graphs as a kind of chemical graph may have been in the back of his mind for many years. He used the word 'valence' in his 1870 article on relational algebra. That word showed an influence. From 1880 to 1885, he was strongly influenced by his father's book on linear algebra, which he had edited and extended for the second edition. The repeated summation and product determined his representation and definition of the quantifiers in his algebraic notation. When he developed EGs, he was careful to ensure that every feature of his algebraic notation had an exact mapping to to and from the Alpha and Beta versions of EGs.
I believe that CSP is referring to the fact that the same symbol (logical term) can be used with many different meanings, depending on the context within the ecoment of the sheet of assertion (diagram, text, graph).
There is a significant difference between negative and positive contexts. Those differences result in different mappings to and from the algebraic notation. He used many metaphors to explain the graphs to himself and others. But there is no feature of the graphs that cannot not be mapped to and from the algebraic notation. When interpreting the metaphors, it's always important to be clear about which aspects are significant (have a mapping to the algebra) and which are unintended (no mapping to the algebra).
The term “trust” is remote from the logic of symbolic substitutions.
Yes. Peirce used the word 'trustee' in an example, and he explicitly cited its use as a legal term in Massachusetts. Those remote meanings are part of the example. They have no mapping to or from the algebraic notation. If Peirce had intended any further meaning, he would have mentioned it explicitly. The absence of any further comment confirms the point the word 'trustee' is just part of the example -- it shows how C is related to A and B. There is no notion of 'trust' in the EGs themselves. John
----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
