Jerry, In the note below, I made a careless mistake of writing NaSO4 for sodium sulfate instead of Na2SO4. (I know chemistry quite well. I skipped the freshman year at MIT, and took organic chemistry instead -- and got an A.)
Before correcting and clarifying the mistake I made in my previous note, I'll answer your question: JLRC: What is a reasonable interpretation about the “blanks” in sentences relative to concatenations of logical operations between the posits and the consequences? The example by Roberts (page 22) is a copy of CP 3.421. A formal technical answer is: For Peirce, a sentence with one or more blanks is equivalent to the lambda calculus by Church with a variable, such as x1, x2, ..., xN inserted in each blank space and with the prefix (lambda x1, x2, ..., xN) in from of the result. In other words, it corresponds to a function from a list of N English words or phrases (which Peirce called rhemata) to a complete sentence in English that represents a proposition. Simpler answer: If you replace each blank with an English word or phrase, you will get a complete sentence that represents a proposition. Each word or phrase that you insert is called a rhema. The complete sentence could be mapped to an EG, in which each rhema is mapped to a node in the EG, possibly with some additional subgraphs attached to it. As in the more technical explanation above, it represents a function from English phrases to English sentences that represent propositions. Back to the note below: I had started to write an example of sodium chloride, NaCl, as the example for subject + verb phrase. But I changed the example to sodium sulfate without adding 2 after Na. Reason for the change: an SO4 ion with five atoms is a better illustration of a complex verb phrase. It illustrates Peirce's point of saying that a relation has two subjects instead of subject + object (or even three subjects instead of subject + object + indirect object}. I corrected the text below, and added more explanation. The point of this chemistry is to illustrate a question that Peirce never asked or answered: Is there any kind of chemical combination that could represent the word 'that' as a marker of metalanguage. Since the word 'metalanguage' was coined about 20 years after Peirce, his term was "graph of graphs" or "graphs about graphs". I know enough chemistry to understand an answer, but not enough to know what chemical structure could represent metalanguage. I would guess that it might be some organic pattern, perhaps with nitrogen, or maybe a metal. John ---------------------------------------- From: "John F Sowa" <s...@bestweb.net> Jerry, As you know very well, there is a huge difference in the various kinds of chemical bonds. In a combination of a noun phrase (NP) and a verb phrase (VP). The NP is analogous to a sodium ion Na with a negative charge, and the VP is analogous to a Chloride ion CL with a positive charge. The neutral NaCL, which is analogous to a proposition, illustrates a rheme (NP) linked to an EG with an unattached line of identity that represents the VP. Sodium sulfate (Na2SO4) is even more interesting, since a sulfate ion (SO4) has two positive charges. The resulting compound with a neutral charge states a proposition. The two negative Na ions (NPs) correspond to rhemes. One of them corresponds to a subject of the SO4 verb phrase, and the other corresponds to the object. But Peirce preferred to call both of them subjects. They combine with a verb phrase to represent a proposition. But in organic chemistry, bonds between carbon atoms share electrons. Those chemical bonds don't have the same kinds of analogies with linguistic bonds or with the links in EGs. JLRC: Which of the logical particles would associated with a metalanguage in the example cited by Roberts? Peirce's first recorded example of metalanguage in RLT had a complete sentence "you are a good girl" (which would correspond to a neutral chemical compound) as the subject of a verb phrase, which would have a positive charge. In effect, the word 'that' when attached to a neutral sentence gives it a negative charge so that it could be used as the subject of a positively charged verb phrase "--is much to be wished." As far as I know, Peirce did not use a chemical analogy to explain that combination. Can you suggest some example in chemistry that would correspond to the word 'that'? It would have to take a neutral compound that would correspond to a sentence such as "You are a good girl" and attach some atoms that could form a link to a positive radical, such as "--is much to be wished." For example, the organic acid pattern -COOH would link a neutral organic radical to negative -OH radical or to a negative Na ion. Is there some organic pattern that could link a neutral compound to a positive ion? That could be a chemical representation for the word 'that'. John__________ On Sun, Mar 24, 2024 at 8:20 PM Jerry LR Chandler <jerry_lr_chand...@icloud.com> wrote: John, Jon: In my opinion your responses to the issues surrounding Tarski’s “metalanguage" are so weak from a scientific point of view that it is simpler to just pose an example of the meanings of metalanguages in the relevant logic used by CSP. The following is an excerpt from Robert’s book, page 22: What is a reasonable interpretation about the “blanks” in sentences relative to concatenations of logical operations between the posits and the consequences? How would the blanks be relative to the copula? Copula’s of “metalanguages? What would be the number of metalanguages necessary for a conclusion from a posited pragmatic sentence with n blanks? Which of the logical particles would associated with a metalanguage in the example cited by Roberts? Have fun! Cheers Jerry
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