Re: [PEIRCE-L] Meta-languages. Re: Four branches of existential graphs: Alpha, Beta, Gamma, Delta
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 sulfate ion (SO4) with a positive charge. The resulting combination NaSO4 is a compound with a neutral charge that corresponds to a sentence that states a proposition. The negative NP ion corresponds to a rheme, which combines with a positive VP ion to form a neutral 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 molecule to a positive ion? That could correspond to the word 'that'. John__ On Sun, Mar 24, 2024 at 8:20 PM Jerry LR Chandler 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 _ _ _ _ _ _ _ _ _ _ ARISBE: THE PEIRCE GATEWAY is now at https://cspeirce.com and, just as well, at https://www.cspeirce.com . It'll take a while to repair / update all the links! ► 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 UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Meta-languages. Re: Four branches of existential graphs: Alpha, Beta, Gamma, Delta
Jerry, List: Roberts is not discussing metalanguage at all in that excerpt from p. 22 of his 1973 book, he is talking about rhemata/rhemes (Peirce uses both terms). These are incomplete propositions, with blanks where subjects need to be added in order to turn them into complete propositions. Metalanguage only comes into play if the blank in a rhema/rheme is filled with a proposition, resulting in a proposition *about *a proposition. In Beta EGs, general concepts are attributed to indefinite individuals by attaching names to heavy lines of identity. In Gamma EGs, a line of identity attached to a name can be replaced by a dotted (or lightly drawn) line attached to a dotted (or lightly drawn) oval that contains the EG for a complete proposition. Roberts discusses Peirce's 1903 version of this notation on pp. 76-77, but as John Sowa has observed all along, a much simpler example is on RLT 151 (1898)--"That you are a good girl is much to be wished." [image: image.png] Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt 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 > > The collection of Peirce papers at Harvard University contains a number of > undated manuscripts on logical graphs to which Peirce could here be > referring. Consider in the second place Peirce's use of dashes in place of > demonstrative terms and nouns to produce blank forms of propositions called > 'rhemata'. If only one noun is erased~ a non-relative rhema is produced, as > '__ is mortal'. If two or more nouns are erased, the result is a relative > rhema, such as '__ is bought by __ from __ for __ ' (3.420). Consider in > the third place the expressed analogy between logical compounds and > chemical compounds: > A rhema is somewhat closely analogous to a chemical atom or radicle with > unsaturated bonds. A non-relative rhema is like a univalent radicle; it has > but one unsaturated bond. A relative rhema is like a multivalent radicle. > The blanks of a rhema can only be filled by terms, or, what is the same > thing, by "something which" (or the like) followed by a rhema; or, two can > be filled together by means of "itself" or the like. So, in chemistry, > unsaturated bonds can only be saturated by joining two of them, which will > usually, though not necessarily, belong to different radicles. If two > univalent radicles are united, the result is a saturated compound. So, two > non-relative rhemas being joined give a complete proposition. Thus, to join > "__ is mortal" and "__is a man", we have "X is mortal and X is a man", or > some man is mortal. So likewise, a saturated compound may result from > joining two bonds of a bivalent radicle; and, in the same way, the two > blanks of a dual rhema may be joined to make a complete proposition. Thus, > "__ loves __", "X loves X", or something loves itself [3.421]. > This article is important for several reasons. It shows clearly that the > parallel existing between these diagrams and chemical diagrams was strong > in Peirce's mind; > _ _ _ _ _ _ _ _ _ _ ARISBE: THE PEIRCE GATEWAY is now at https://cspeirce.com and, just as well, at https://www.cspeirce.com . It'll take a while to repair / update all the links! ► 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 UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Meta-languages. Re: Four branches of existential graphs: Alpha, Beta, Gamma, Delta
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 The collection of Peirce papers at Harvard University contains a number of undated manuscripts on logical graphs to which Peirce could here be re- ferring. Consider in the second place Peirce's use of dashes in place of demonstrative terms and nouns to produce blank forms of propositions called 'rhemata'. If only one noun is erased~ a non-relative rhema is produc- ed, as '_ _ is mortal'. If two or more nouns are erased, the result is a relative rhema, such as '__ is bought by __ from __ for __ ' (3.420). Consider in the third place the expressed analogy between logical compounds and chemical compounds: A rhema is somewhat closely analogous to a chemical atom or radicle with unsaturated bonds. A non-relative rhema is like a univalent radicle; it has but one unsaturated bond. A relative rhema is like a multivalent radicle. The blanks of a rhema can only be filled by terms, or, what is the same thing, by "something which" (or the like) followed by a rhema; or, two can be filled together by means of "itself" or the like. So, in chemistry, unsaturat- ed bonds can only be saturated by joining two of them, which will usually, though not necessarily, belong to different radicles. If two univalent radicles are united, the result is a saturated compound. So, two non-relative rhemas being joined give a complete proposition. Thus, to join "_ _ is mortal" and "__isaman",wehave"XismortalandXisaman",orsomemanis mortal. So likewise, a saturated compound may result from joining two bonds of a bivalent radicle; and, in the same way, the two blanks of a dual rhema may be joined to make a complete proposition. Thus, " _ _ loves _ _", "X loves X", or something loves itself [3.421]. This article is important for several reasons. It shows clearly that the parallel existing between theSe diagrams and chemical diagrams was strong in Peirce's mind; > On Mar 23, 2024, at 4:46 PM, John F Sowa wrote: > > Jerry, Jon, List, > > JLRC: If the critical concept that is under scrutiny here the issue of > “graphs of graphs” , how is this related to the arithmetical notion of > division? > > I agree with Jon's explanation below that Peirce did not use the word > "division" to mean the numerical operation of dividing two numbers. He was > talking about dividing different parts of a text. > > As for the phrase "graph of graphs", that excerpt occurred in the > introductory paragraphs of Lecture V of Peirce's Lowell lectures of 1903. > Immediately before that, he used the synonym "graphs about graphs''. Since > the word 'metalanguage' had not yet been introduced in English, the phrase > "graphs about graphs" is his best and clearest term. It he had used his > Greek, he might have coined the word 'metagraph'. > > I am happy to say that I completely agree with Jon's note below. However, > the following passage from another note is misleading about Peirce, Euclid, > and mathematical practice from ancient times to the present. > > JAS: The "red pencil" notation (1909) is entirely different from this--a red > line is drawn just inside the physical edge of the sheet, and postulates are > written in the resulting margin. These are not propositions about the > propositions written inside the red line (metalanguage), they are premisses > (antecedent) from which the propositions written inside the red line follow > necessarily as deductive conclusions (consequent). For example, if the EGs > for Euclid's five postulates are scribed in the margin, then they can be > iterated to the interior, where the EGs for all the theorems of Euclidean > geometry can be derived from them in accordance with the usual permissions. > > It's true that postulates are iterated (or copied) during the process of > proving a theorem. But it's also possible to iterate a statement from a > that-clause of metalanguage to a collection of statements that are being > discussed in other ways. > > In mathematical texts, it's common to say "Given A1, A2, A3..., it follows > THAT T1, T2, T3... where the A's are axioms, and the T's are theorems that > follow from the axioms. > > Note the word 'that'. It is a sign of METALANGUAGE, bet
Re: [PEIRCE-L] Meta-languages. Re: Four branches of existential graphs: Alpha, Beta, Gamma, Delta
Jon, List, All the commentary, quotations, and citations below by both of us are irrelevant to mathematical practice from ancient times to the present. Following is a definitive statement of mathematical practice from Euclid to the present: In mathematics, the distinction between axioms, postulates, and theorems is stated by metalanguage. That is a convenience for classifying, citing, and finding them. But during any proof or reasoning of any kind, all relevant statements are placed in a single common area (paper, blackboard, whiteboard, computer storage, or phemic sheet). The metalanguage that distinguishes axioms, postulates, and theorems is useful information for finding and citing the sources in a published proof. But during a proof, the axioms, postulates, and previously proved theorems are copied into the current workspace (or phemic sheet). They are used in exactly the same way, independent of their source or what they may be called. This is not a debatable opinion. It is a fact that can be verified by looking at any proof in any well-edited textbook of any branch of mathematics from the ancient past to the latest and greatest. John PS: I majored in mathematics and related topics (logic and physics) at MIT and Harvard. I later taught, lectured, and published books and articles on mathematics, logic, computer science, and computational linguistics. The above facts are indisputable. Peirce knew them very well. He would not make a careless mistake about them. From: "Jon Alan Schmidt" Sent: 3/23/24 10:51 PM John, List: JFS: I am happy to say that I completely agree with Jon's note below. However, the following passage from another note is misleading about Peirce, Euclid, and mathematical practice from ancient times to the present. The quoted passage is from my same note below. JFS: In mathematical texts, it's common to say "Given A1, A2, A3..., it follows THAT T1, T2, T3... where the A's are axioms, and the T's are theorems that follow from the axioms. Note the word 'that'. It is a sign of METALANGUAGE, between two clauses of a sentence. It is not a sign of implication. The word 'follows' or more precisely 'my be proved from' indicate the steps of a proof. "Given A, it follows that T" is logically equivalent to "if A, then T," which is logically equivalent to "A implies T." A is the premiss or antecedent (e.g., postulates), and T is the conclusion or consequent (e.g., theorems). There is no need for metalanguage to express this in EGs since it is represented by a scroll or nested cuts or a ring-shaped shaded area--including a sheet with a red line drawn just inside its edges (or a shaded margin). JFS: As for the notations in R514 and L376, Peirce made another distinction: postulates are propositions on which the utterer and the interpreter agree. The choice of postulates is the result of an AGREEMENT between the utterer and the interpreter. The results inside the red line are the result of an INVESTIGATION that may be far more complex than an mathematical proof. In R 514, Peirce only states that "in the margin outside the red line, whatever is scribed is merely asserted to be possible. Thus, if the subject were geometry, I could write in that margin the postulates, and any pertinent problems stated in the form of postulates." He does not say anything about "an agreement between the utterer and the interpreter," nor about the "results inside the red line" before the text breaks off in mid-sentence. In R L376, Peirce does not say anything about "the red line" nor "an investigation," complex or otherwise. The "agreement between the utterer and the interpreter" is on the subject of the graphs scribed on each piece of paper, which represents a portion of the overall universe of discourse that "is before the common attention" of both parties at one time or another. He only discusses postulates in the paragraph right before the section on "The Phemic Sheet," and only for the purpose of explaining why "any valid deductive conclusion" is not "instantaneously evident upon an examination of the premisses." Here is what he says. CSP: My second reason is found in the peculiar character of mathematical postulates. These pronounce that certain things are possible. But these possibles are not, of course, single things, for a single thing must be more or less than possible: they embrace whole infinite series of infinite series of objects in each postulate; and it is upon the statement of the possibility of one single one of those objects or single one for each set of certain others, that some essential part of the conclusion is founded. How many demonstrations, for example, and very simple ones too, as mathematics goes, depend, each of them, upon the possibility of a single straight line; while this possibility is only asserted in the postulate that there is, or may be, a straight line through a
Re: [PEIRCE-L] Meta-languages. Re: Four branches of existential graphs: Alpha, Beta, Gamma, Delta
John, List: JFS: I am happy to say that I completely agree with Jon's note below. However, the following passage from another note is misleading about Peirce, Euclid, and mathematical practice from ancient times to the present. The quoted passage is from my same note below. JFS: In mathematical texts, it's common to say "Given A1, A2, A3..., it follows THAT T1, T2, T3... where the A's are axioms, and the T's are theorems that follow from the axioms. Note the word 'that'. It is a sign of METALANGUAGE, between two clauses of a sentence. It is not a sign of implication. The word 'follows' or more precisely 'my be proved from' indicate the steps of a proof. "Given A, it follows that T" is logically equivalent to "if A, then T," which is logically equivalent to "A implies T." A is the premiss or antecedent (e.g., postulates), and T is the conclusion or consequent (e.g., theorems). There is no need for metalanguage to express this in EGs since it is represented by a scroll or nested cuts or a ring-shaped shaded area--including a sheet with a red line drawn just inside its edges (or a shaded margin). JFS: As for the notations in R514 and L376, Peirce made another distinction: postulates are propositions on which the utterer and the interpreter agree. The choice of postulates is the result of an AGREEMENT between the utterer and the interpreter. The results inside the red line are the result of an INVESTIGATION that may be far more complex than an mathematical proof. In R 514, Peirce only states that "in the margin outside the red line, whatever is scribed is merely asserted to be possible. Thus, if the subject were geometry, I could write in that margin the postulates, and any pertinent problems stated in the form of postulates." He does not say anything about "an agreement between the utterer and the interpreter," nor about the "results inside the red line" before the text breaks off in mid-sentence. In R L376, Peirce does not say anything about "the red line" nor "an investigation," complex or otherwise. The "agreement between the utterer and the interpreter" is on the *subject *of the graphs scribed on each piece of paper, which represents a *portion *of the overall universe of discourse that "is before the common attention" of both parties at one time or another. He only discusses postulates in the paragraph right *before *the section on "The Phemic Sheet," and only for the purpose of explaining why "any valid deductive conclusion" is *not *"instantaneously evident upon an examination of the premisses." Here is what he says. CSP: My second reason is found in the peculiar character of mathematical postulates. These pronounce that certain things are possible. But these possibles are not, of course, single things, for a single thing must be more or less than possible: they embrace whole infinite series of infinite series of objects in each postulate; and it is upon the statement of the possibility of one single one of those objects or single one for each set of certain others, that some essential part of the conclusion is founded. How many demonstrations, for example, and very simple ones too, as mathematics goes, depend, each of them, upon the possibility of a single straight line; while this possibility is only asserted in the postulate that there is, or may be, a straight line through any two points of space. In that statement the possibility of every single straight line in space is asserted, including the single one whose existence is pertinent and concerning which a similar postulate directly or mediately asserts something which is an essential ingredient of the conclusion. Consistent with R 514, postulates "pronounce that certain things are possible." Moreover, the *only *kind of investigation that Peirce discusses here is a mathematical demonstration. JFS: The complexity of the investigation is the reason why Delta graphs are a completely new branch of EGs. Again, Peirce's *only *stated reason for needing "to add a *Delta *part" to EGs is "in order to deal with modals"--not for metalanguage, and not for complex investigations. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Sat, Mar 23, 2024 at 4:46 PM John F Sowa wrote: > Jerry, Jon, List, > > JLRC: If the critical concept that is under scrutiny here the issue of > “graphs of graphs” , how is this related to the arithmetical notion of > division? > > I agree with Jon's explanation below that Peirce did not use the word > "division" to mean the numerical operation of dividing two numbers. He was > talking about dividing different parts of a text. > > As for the phrase "graph of graphs", that excerpt occurred in the > introductory paragraphs of Lecture V of Peirce's Lowell lectures of 1903. > Immediately before that, he used the synonym "graphs about graphs''. Since > the word 'metalanguage' had not yet
Re: [PEIRCE-L] Meta-languages. Re: Four branches of existential graphs: Alpha, Beta, Gamma, Delta
Jerry, Jon, List, JLRC: If the critical concept that is under scrutiny here the issue of “graphs of graphs” , how is this related to the arithmetical notion of division? I agree with Jon's explanation below that Peirce did not use the word "division" to mean the numerical operation of dividing two numbers. He was talking about dividing different parts of a text. As for the phrase "graph of graphs", that excerpt occurred in the introductory paragraphs of Lecture V of Peirce's Lowell lectures of 1903. Immediately before that, he used the synonym "graphs about graphs''. Since the word 'metalanguage' had not yet been introduced in English, the phrase "graphs about graphs" is his best and clearest term. It he had used his Greek, he might have coined the word 'metagraph'. I am happy to say that I completely agree with Jon's note below. However, the following passage from another note is misleading about Peirce, Euclid, and mathematical practice from ancient times to the present. JAS: The "red pencil" notation (1909) is entirely different from this--a red line is drawn just inside the physical edge of the sheet, and postulates are written in the resulting margin. These are not propositions about the propositions written inside the red line (metalanguage), they are premisses (antecedent) from which the propositions written inside the red line follow necessarily as deductive conclusions (consequent). For example, if the EGs for Euclid's five postulates are scribed in the margin, then they can be iterated to the interior, where the EGs for all the theorems of Euclidean geometry can be derived from them in accordance with the usual permissions. It's true that postulates are iterated (or copied) during the process of proving a theorem. But it's also possible to iterate a statement from a that-clause of metalanguage to a collection of statements that are being discussed in other ways. In mathematical texts, it's common to say "Given A1, A2, A3..., it follows THAT T1, T2, T3... where the A's are axioms, and the T's are theorems that follow from the axioms. Note the word 'that'. It is a sign of METALANGUAGE, between two clauses of a sentence. It is not a sign of implication. The word 'follows' or more precisely 'my be proved from' indicate the steps of a proof. As for the notations in R514 and L376, Peirce made another distinction: postulates are propositions on which the utterer and the interpreter agree. The choice of postulates is the result of an AGREEMENT between the utterer and the interpreter. The results inside the red line are the result of an INVESTIGATION that may be far more complex than an mathematical proof. The complexity of the investigation is the reason why Delta graphs are a completely new branch of EGs. In summary, metalanguage is the "secrete sauce" that makes Gamma graphs a third branch. But investigation makes Delta graphs the fourth branch. That difference is very important. John From: "Jon Alan Schmidt" Jerry, List: No one is claiming that Peirce ever used the term "metalanguage," only the concept. Specifically, he provided a Gamma EG notation for asserting a proposition about a proposition--the lightly drawn (1898) or dotted (1903) oval for treating a complete proposition as a subject that fills the blank in a rheme attached to the oval by a lightly drawn (1898) or dotted (1903) line to compose another complete proposition (CP 4.560, 1906). For example, here is the Gamma EG for "A thinks that it is possible that B," where A is a person, B is a proposition, "A thinks ___" and "___ is possible" are rhemes, and each instance of "that" in English corresponds to a dotted oval/line in the graph. [image.png] The "red pencil" notation (1909) is entirely different from this--a red line is drawn just inside the physical edge of the sheet, and postulates are written in the resulting margin. These are not propositions about the propositions written inside the red line (metalanguage), they are premisses (antecedent) from which the propositions written inside the red line follow necessarily as deductive conclusions (consequent). For example, if the EGs for Euclid's five postulates are scribed in the margin, then they can be iterated to the interior, where the EGs for all the theorems of Euclidean geometry can be derived from them in accordance with the usual permissions. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Fri, Mar 22, 2024 at 11:43 PM Jerry LR Chandler wrote: Jon, List On Mar 20, 2024, at 12:46 PM, Jon Alan Schmidt wrote: - Peirce's 1898 and 1903 notations for metalanguage are identical, except that the oval and line are lightly drawn in the former and dotted in the latter. - Peirce's "red pencil" notation in R 514 has nothing to do
Re: [PEIRCE-L] Meta-languages. Re: Four branches of existential graphs: Alpha, Beta, Gamma, Delta
Jerry, List: No one is claiming that Peirce ever used the *term *"metalanguage," only the *concept*. Specifically, he provided a Gamma EG notation for asserting a proposition about a proposition--the lightly drawn (1898) or dotted (1903) oval for treating a complete proposition as a *subject *that fills the blank in a rheme attached to the oval by a lightly drawn (1898) or dotted (1903) line to compose another complete proposition (CP 4.560, 1906). For example, here is the Gamma EG for "A thinks that it is possible that B," where A is a person, B is a proposition, "A thinks ___" and "___ is possible" are rhemes, and each instance of "that" in English corresponds to a dotted oval/line in the graph. [image: image.png] The "red pencil" notation (1909) is entirely different from this--a red line is drawn just inside the physical edge of the sheet, and postulates are written in the resulting margin. These are not propositions *about *the propositions written inside the red line (metalanguage), they are premisses (antecedent) from which the propositions written inside the red line follow necessarily as deductive conclusions (consequent). For example, if the EGs for Euclid's five postulates are scribed in the margin, then they can be iterated to the interior, where the EGs for all the theorems of Euclidean geometry can be derived from them in accordance with the usual permissions. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Fri, Mar 22, 2024 at 11:43 PM Jerry LR Chandler < jerry_lr_chand...@icloud.com> wrote: > Jon, List > > On Mar 20, 2024, at 12:46 PM, Jon Alan Schmidt > wrote: > >- Peirce's 1898 and 1903 notations for metalanguage are *identical*, >except that the oval and line are lightly drawn in the former and dotted in >the latter. >- Peirce's "red pencil" notation in R 514 has nothing to do with >metalanguage--it turns an entire sheet into nested cuts for implication, >with the antecedent (postulates) in the margin and the consequent >(theorems) inside the red line. > > In these two paragraphs, the term “metalanguage” is used. > Was I misled by the assertion (by another logician) that Tarski was the > first to use this term? > > Although this may seem as a trivial point, it becomes rather critical from > the perspectives of emergence and evolution with the putative levels of > development and the corresponding grammatical distinctions between the > social and natural sciences and current notions of “metalogics”. > > At issue is the languages in which propositions are posited. > > Cheers > Jerry > _ _ _ _ _ _ _ _ _ _ ARISBE: THE PEIRCE GATEWAY is now at https://cspeirce.com and, just as well, at https://www.cspeirce.com . It'll take a while to repair / update all the links! ► 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 UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
[PEIRCE-L] Meta-languages. Re: Four branches of existential graphs: Alpha, Beta, Gamma, Delta
Jon, List > On Mar 20, 2024, at 12:46 PM, Jon Alan Schmidt > wrote: > > Peirce's 1898 and 1903 notations for metalanguage are identical, except that > the oval and line are lightly drawn in the former and dotted in the latter. > > Peirce's "red pencil" notation in R 514 has nothing to do with > metalanguage--it turns an entire sheet into nested cuts for implication, with > the antecedent (postulates) in the margin and the consequent (theorems) > inside the red line. > In these two paragraphs, the term “metalanguage” is used. Was I misled by the assertion (by another logician) that Tarski was the first to use this term? Although this may seem as a trivial point, it becomes rather critical from the perspectives of emergence and evolution with the putative levels of development and the corresponding grammatical distinctions between the social and natural sciences and current notions of “metalogics”. At issue is the languages in which propositions are posited. Cheers Jerry _ _ _ _ _ _ _ _ _ _ ARISBE: THE PEIRCE GATEWAY is now at https://cspeirce.com and, just as well, at https://www.cspeirce.com . It'll take a while to repair / update all the links! ► 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 UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
