[PEIRCE-L] metalanguage, possibility, WAS: Logical Content of Graphical Signs (was Higher-Order Logics)
List, I put a new name to this, because I am not inside the discussion, just want to mention a problem I have with the topic. First, there are different types of possibility: Is it not definite but possible about the past or about the future, is it due to limited knowledge or to different options of decision, and so on. All in all it is the same problem as with metalanguage, like "A says B": Who heard him/her saying so?, and "A thinks, that B": Who knows how, what A thinks? Like with possibility: Who or what group of people regards it merely for possible instead of true, and might there not exist somebody, e.g. God or "the universe", who knows, whether it is true or false? For example, if you have an EG with the term "A thinks, that B", it is written on the so called blank sheet, which shows the universe of discourse. If this discourse is that of a certain group of people, none of these people except A has access to what A thinks. So to write "A thinks" , if in words or as a symbol, on this sheet, is not justified. Because maybe A is a liar, and thinks the opposite of what he/she claims to think. It may seem possible to circumvene this problem, by e.g. saying: This certain group of discoursers consists of both theists and atheists, so we now incude God or the universe (according to belief) into the universe of discourse. Both God and the universe should know, what A thinks. But then there still is a problem, when it is about possibility in the future. I vaguely remember a quantum physicist, was it Newman, who spoke of hidden variables, and also somebody with "B", who claimed, that everything, even the farthest future, can be precalculated. I dont think so, but it shows, that a possibility about the future cannot be proved to be a mere possibility. Therefore it is not justified to write it on a blank sheet, I guess. That is, because I think, that not only atheists, but also theists don´t have a clear concept about what the universe or God knows about the future, and what not. Maybe some theists say, that God knows everything about the future too, but then His job would be quite boring and futile, and there would be no need e.g. for angels. You dont need a post office, if no message would be able to change the future. So, if this deterministic view is right, then possibility does not exist, and if it is false (of course it is), possibility cannot be proved to be one. Best regards, helmut Dienstag, 12. März 2024 um 22:59 Uhr Von: "Jon Alan Schmidt" An: "Peirce-L" Betreff: [PEIRCE-L] Logical Content of Graphical Signs (was Higher-Order Logics) Jerry, List: Your questions as posed are extremely general, and their answers depend heavily on the particular context of interest. Peirce assigns specific logical content to certain signs in his Existential Graphs (EGs) and develops the transformation rules for them accordingly. In all parts, the blank sheet represents the universe of discourse, graphs scribed on it represent propositions that are asserted as true in that universe, juxtaposition represents coexistence in that universe (conjunction), and a scroll (double cut or ring-shaped shaded area) represents a consequence (material implication) from which a single cut or shaded area is derived as representing negation (implication of falsity/absurdity). In the Beta part, heavy lines of identity denote indefinite individuals and attached names denote general concepts being attributed to those individuals. In the Gamma part, there are various additional signs for various purposes, such as the broken cut for possible falsity (modal logic), the heavy line with dotted lines along both sides for quantifying predicates (second-order logic), and the dotted oval for treating a proposition as a subject that fills the blank in a rheme attached to the oval by a dotted line (metalanguage). As I keep emphasizing, we cannot know for sure what Peirce had in mind for the Delta part, other than that it would "deal with modals," unless and until new manuscript evidence turns up, such as the missing pages of R L376. My hypothesis is that he was considering a new notation for representing and reasoning about modal propositions involving possibility or necessity, such as the one that he introduces in his Logic Notebook (R 339:[340r], 1909 Jan 7). In that case, heavy lines represent "circumstances" or "times"--more formally, possible states of things (PSTs)--and attached letters represent propositions that would be true under those circumstances, at those times, or in those PSTs. The transformation rules for these "lines of compossibility" (my term) are different from the ones for the "lines of identity" (Peirce's term) in the Beta part because of the obvious and fundamental semiotic difference between describing things with names (rhemes/semes) and describing states of things with propositions (dicisigns/phemes). Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synec
Re: [PEIRCE-L] metalanguage, possibility, WAS: Logical Content of Graphical Signs (was Higher-Order Logics)
Helmut, List: Different kinds of possibility can be addressed with different formal systems of modal logic--alethic, deontic, doxastic, dynamic, epistemic, temporal, etc. For example, deontic logic defines possibility as *permissibility *and necessity as *obligation*, which is why its alternativeness/accessibility relation is merely serial and not reflexive--every obligation is permissible, but not every obligation is actually fulfilled, i.e., people can (and do) behave in ways that are *not * permissible. It is a fundamental principle of Peirce's Existential Graphs (EGs) that the blank sheet represents the universe of discourse *as already agreed upon* by the utterer (or graphist) who scribes discrete EGs on them and the interpreter who reads them. In other words, the underlying assumption is that both are genuine inquirers who are sincerely seeking the truth together. If the utterer scribes the EG for "A thinks that B," then this is true within that universe of discourse--it has nothing to do with what A *claims *to think, only what A *really does *think, unless the utterer instead scribes "A claims that A thinks that B." By the way, since B designates a proposition instead of a name for a general concept, the Gamma EG for "A thinks that B" has A attached by a heavy line of identity to "thinking," which is then attached by a dotted line to a dotted oval around B, preferably spelled out as a Beta EG ( https://list.iupui.edu/sympa/arc/peirce-l/2024-02/msg00141.html). Likewise, the Gamma EG for "A claims that A thinks that B" has A attached by a heavy line of identity to "claiming," which is then attached by a dotted line to a dotted oval around the Gamma EG for "A thinks that B" as just described, except that A is not repeated; instead, the one heavy line is branched and extended to "thinking." Here are those Gamma EGs, substituting "C is a good girl" for B. [image: image.png] As far as I know, the only place in Peirce's writings where he discusses a specific role for God in EGs is R 280 (c. 1905). In three different drafts, he states the following. CSP: The Graphist is really Plastic Nature, or the Artifex of Nature; and the special permissions are the experiences given to the interpreter of Nature, to the man, to which he is at liberty to attend, or not to attend at all, or to attend and immediately put out of sight, as he will. CSP: The sheet of assertion is the mirror of the interpreter’s mind, and through that it is the sign of what the Graphist authorizes. Now the graphist, as the author of truth (for we have seen that falsity is what he forbids and truth what he permits) and source of all the interpreter’s knowledge must be recognized as being either Plastic Nature or the Artifex of Nature. The universe is simply the collective whole of all things to the assertion of whose existence the Graphist interposes no veto, or extends a positive permission. CSP: We further conceive that this feigned sensible state of things is the icon or emblem of a mental state of things. Namely, the immense surface with the graphs scribed upon it is the image of the interpreter’s experience, while the sheet of assertion, his field of view is the image of his field of attention. His experience is forced upon him, while he attends to what he pleases, if he puts forth sufficient effort. The Graphist must be regarded as corresponding to the "Plastic Nature" of Cudworth, or else to the Artifex of Nature. Again, everything that is asserted on the sheet is true, in this case because the one scribing all the EGs is "the author of truth"--either God the Creator himself or what Peirce describes elsewhere (referencing Cudworth) as "a blind agent intermediate between God and the world" (R 870, 1901). Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Wed, Mar 13, 2024 at 12:15 PM Helmut Raulien wrote: > List, > > I put a new name to this, because I am not inside the discussion, just > want to mention a problem I have with the topic. First, there are different > types of possibility: Is it not definite but possible about the past or > about the future, is it due to limited knowledge or to different options of > decision, and so on. All in all it is the same problem as with > metalanguage, like "A says B": Who heard him/her saying so?, and "A thinks, > that B": Who knows how, what A thinks? Like with possibility: Who or what > group of people regards it merely for possible instead of true, and might > there not exist somebody, e.g. God or "the universe", who knows, whether it > is true or false? > > For example, if you have an EG with the term "A thinks, that B", it is > written on the so called blank sheet, which shows the universe of > discourse. If this discourse is that of a certain group of people, none of > these people except A has access to what A thinks. So to write "A thinks" , > if in
Re: [PEIRCE-L] metalanguage, possibility, WAS: Logical Content of Graphical Signs (was Higher-Order Logics)
Jon, In both graphs in your note below, the thin line may be read as "that"' A thinks THAT C is a good girl. A is claiming THAT A is thinking THAT C is a good girl. Both of those sentences and both of those EGs can be translated to and from the IKL logic of 2006, which uses the symbol "that" to represent metalanguage. They can also be translated to and from Peirce's Delta graphs, which can be translated to and from the IKL logic. But neither of those two sentences can be translated to any version of modal logic based on the modal logics by C. I. Lewis or later variations of it. John From: "Jon Alan Schmidt" Sent: 3/13/24 5:39 PM To: Peirce-L Subject: Re: [PEIRCE-L] metalanguage, possibility, WAS: Logical Content of Graphical Signs (was Higher-Order Logics) Helmut, List: Different kinds of possibility can be addressed with different formal systems of modal logic--alethic, deontic, doxastic, dynamic, epistemic, temporal, etc. For example, deontic logic defines possibility as permissibility and necessity as obligation, which is why its alternativeness/accessibility relation is merely serial and not reflexive--every obligation is permissible, but not every obligation is actually fulfilled, i.e., people can (and do) behave in ways that are not permissible. It is a fundamental principle of Peirce's Existential Graphs (EGs) that the blank sheet represents the universe of discourse as already agreed upon by the utterer (or graphist) who scribes discrete EGs on them and the interpreter who reads them. In other words, the underlying assumption is that both are genuine inquirers who are sincerely seeking the truth together. If the utterer scribes the EG for "A thinks that B," then this is true within that universe of discourse--it has nothing to do with what A claims to think, only what A really does think, unless the utterer instead scribes "A claims that A thinks that B." By the way, since B designates a proposition instead of a name for a general concept, the Gamma EG for "A thinks that B" has A attached by a heavy line of identity to "thinking," which is then attached by a dotted line to a dotted oval around B, preferably spelled out as a Beta EG (https://list.iupui.edu/sympa/arc/peirce-l/2024-02/msg00141.html). Likewise, the Gamma EG for "A claims that A thinks that B" has A attached by a heavy line of identity to "claiming," which is then attached by a dotted line to a dotted oval around the Gamma EG for "A thinks that B" as just described, except that A is not repeated; instead, the one heavy line is branched and extended to "thinking." Here are those Gamma EGs, substituting "C is a good girl" for B. [image.png] As far as I know, the only place in Peirce's writings where he discusses a specific role for God in EGs is R 280 (c. 1905). In three different drafts, he states the following. CSP: The Graphist is really Plastic Nature, or the Artifex of Nature; and the special permissions are the experiences given to the interpreter of Nature, to the man, to which he is at liberty to attend, or not to attend at all, or to attend and immediately put out of sight, as he will. CSP: The sheet of assertion is the mirror of the interpreter’s mind, and through that it is the sign of what the Graphist authorizes. Now the graphist, as the author of truth (for we have seen that falsity is what he forbids and truth what he permits) and source of all the interpreter’s knowledge must be recognized as being either Plastic Nature or the Artifex of Nature. The universe is simply the collective whole of all things to the assertion of whose existence the Graphist interposes no veto, or extends a positive permission. CSP: We further conceive that this feigned sensible state of things is the icon or emblem of a mental state of things. Namely, the immense surface with the graphs scribed upon it is the image of the interpreter’s experience, while the sheet of assertion, his field of view is the image of his field of attention. His experience is forced upon him, while he attends to what he pleases, if he puts forth sufficient effort. The Graphist must be regarded as corresponding to the "Plastic Nature" of Cudworth, or else to the Artifex of Nature. Again, everything that is asserted on the sheet is true, in this case because the one scribing all the EGs is "the author of truth"--either God the Creator himself or what Peirce describes elsewhere (referencing Cudworth) as "a blind agent intermediate between God and the world" (R 870, 1901). Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Wed, Mar 13, 2024 at 12:15 PM Helmut Raulien
Re: [PEIRCE-L] metalanguage, possibility, WAS: Logical Content of Graphical Signs (was Higher-Order Logics)
John, List: JFS: In both graphs in your note below, the thin line may be read as "that"' Yes, of course; that is obvious from the syntax of the English sentences that I translated into those two graphs--although, as I said in that post, it is a *dotted *line, not a *thin *line. JFS: But neither of those two sentences can be translated to any version of modal logic based on the modal logics by C. I. Lewis or later variations of it. No, of course not; that is obvious from the fact that neither of those two sentences expresses a *modal *proposition, i.e., one that involves possibility or necessity. JFS: They can also be translated to and from Peirce's Delta graphs No, this is incorrect; that is obvious from the fact that such propositions about propositions can already be represented by *Gamma *EGs using the dotted oval/line notation that Peirce introduced in 1903 (LF 2/1:166), which is isomorphic with the thinly drawn oval/line notation that he used in 1898 (RLT 151). In 1911, he did not need a new Delta part of EGs in order to deal with *metalanguage*; according to his own explicit statement in R L376, he needed a new Delta part of EGs in order to deal with *modals*, due to his dissatisfaction with the cuts (including broken cuts) of 1903 and the tinctures of 1906. With that in mind, in your candidate for Delta EGs, how would you scribe the graph for "A thinks that B is *possibly *true"? Or will you continue refusing to provide *any *examples of how you would represent (and reason about) even *very simple* modal propositions, despite my multiple requests? By contrast, I am happy to show you how I would scribe that graph in my candidate for Delta EGs based on R 339:[340r] (1909). [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 Wed, Mar 13, 2024 at 4:51 PM John F Sowa wrote: > Jon, > > In both graphs in your note below, the thin line may be read as "that"' > > A thinks THAT C is a good girl. > > A is claiming THAT A is thinking THAT C is a good girl. > > Both of those sentences and both of those EGs can be translated to and > from the IKL logic of 2006, which uses the symbol "that" to represent > metalanguage. They can also be translated to and from Peirce's Delta > graphs, which can be translated to and from the IKL logic. > > But neither of those two sentences can be translated to any version of > modal logic based on the modal logics by C. I. Lewis or later variations of > it. > > John > _ _ _ _ _ _ _ _ _ _ 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] metalanguage, possibility, WAS: Logical Content of Graphical Signs (was Higher-Order Logics)
Jon, Every statement about a thought expresses a possibility. Every statement about a claim, a wish, a fear, etc, expresses a possibility. That is why metalanguage is a more explicit method for expressing and reasoning about possibility. Quine said that in the 1960s, and other logicians have been developing methods for doing that since the 1970s. Today, nobody uses the Lewis-style of modal logic for any practical purpose. JAS: how would you scribe the graph for "A thinks that B is possibly true"? I'm sorry that I forgot to answer that question. I was commenting on other points, and I forgot to state the translation for the EG you drew. For my recommended version of metalevel EGs, I would first replace the dotted line of your EG with a solid line. That would express the sentence "A is thinking the proposition that there exists a B." Then I would connect that solid line by a ligature to the word 'possible'. Literally, that new EG could be read "A is thinking the possible proposition that there exists a B." But it could be read more simply "A thinks it's possible that there is a B." Exactly the same procedure can be used to attach any other adjective or phrase, such as 'necessary', 'impossible', 'probable', 'useful', 'desirable', 'feared', 'doubted', 'lawful', 'illegal' or 'written in Holy Scriptures". That is the reason why the version of modality that C. I. Lewis specified in 1932 is a dead end. Anything you can express with it can be expressed more clearly and generally with metalanguage. I believe that Peirce recognized the need for more expressive power. And metalanguage adds that power without losing anything that might be expressed with the 1903 EGs. Some people dabbled with methods for computing with a Lewis-style of reasoning, but they have never been used for any practical applications. Metalanguage is simpler and more general. John From: "Jon Alan Schmidt" John, List: JFS: In both graphs in your note below, the thin line may be read as "that"' Yes, of course; that is obvious from the syntax of the English sentences that I translated into those two graphs--although, as I said in that post, it is a dotted line, not a thin line. JFS: But neither of those two sentences can be translated to any version of modal logic based on the modal logics by C. I. Lewis or later variations of it. No, of course not; that is obvious from the fact that neither of those two sentences expresses a modal proposition, i.e., one that involves possibility or necessity. JFS: They can also be translated to and from Peirce's Delta graphs No, this is incorrect; that is obvious from the fact that such propositions about propositions can already be represented by Gamma EGs using the dotted oval/line notation that Peirce introduced in 1903 (LF 2/1:166), which is isomorphic with the thinly drawn oval/line notation that he used in 1898 (RLT 151). In 1911, he did not need a new Delta part of EGs in order to deal with metalanguage; according to his own explicit statement in R L376, he needed a new Delta part of EGs in order to deal with modals, due to his dissatisfaction with the cuts (including broken cuts) of 1903 and the tinctures of 1906. With that in mind, in your candidate for Delta EGs, how would you scribe the graph for "A thinks that B is possibly true"? Or will you continue refusing to provide any examples of how you would represent (and reason about) even very simple modal propositions, despite my multiple requests? By contrast, I am happy to show you how I would scribe that graph in my candidate for Delta EGs based on R 339:[340r] (1909). [image.png] Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Wed, Mar 13, 2024 at 4:51 PM John F Sowa wrote: Jon, In both graphs in your note below, the thin line may be read as "that"' A thinks THAT C is a good girl. A is claiming THAT A is thinking THAT C is a good girl. Both of those sentences and both of those EGs can be translated to and from the IKL logic of 2006, which uses the symbol "that" to represent metalanguage. They can also be translated to and from Peirce's Delta graphs, which can be translated to and from the IKL logic. But neither of those two sentences can be translated to any version of modal logic based on the modal logics by C. I. Lewis or later variations of it. John _ _ _ _ _ _ _ _ _ _ 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 LIN
Re: [PEIRCE-L] metalanguage, possibility, WAS: Logical Content of Graphical Signs (was Higher-Order Logics)
John, List:
JAS: how would you scribe the graph for "A thinks that B is *possibly *
true"?
JFS: For my recommended version of metalevel EGs, I would first replace the
dotted line of your EG with a solid line. That would express the sentence
"A is thinking the proposition that there exists a B."
Thanks for the attempt, but this incorrectly treats B as denoting the *subject
*of a proposition ("there exists a B") instead of a *complete *proposition
(e.g., B = "C is a good girl"). Moreover, as Roberts explains (1973, pp.
76-77), the dotted line and oval are necessary to signify that what A is
thinking is an *abstraction*--in this case, a proposition--not a concrete
individual as denoted by a heavy (solid) line of identity. Accordingly,
here is the Gamma EG for "A is thinking the proposition that there exists a
B" or simply "A thinks that there exists a B."
[image: image.png]
It is almost identical to the Delta EG that I posted last night--the only
difference is that within the dotted oval, the heavy line is attached to
the left side of the B instead of its top side, but this is a *crucial
*notational
distinction. The horizontal heavy line is a Beta line of *identity*,
denoting an indefinite individual to which the general concept denoted by
the name B is being attributed; in English, "there exists a B" or simply
"something is B." The vertical heavy line is a Delta line of
*compossibility*, denoting a possible state of things in which the
proposition denoted by the letter B would be true; in English, "there
exists a possible state of things in which the proposition B would be true"
or simply "proposition B is possibly true."
JFS: Then I would connect that solid line by a ligature to the word
'possible'. Literally, that new EG could be read "A is thinking the
possible proposition that there exists a B." But it could be read more
simply "A thinks it's possible that there is a B."
Not exactly--the English translation of what you describe would be "A
thinks something that is possible and is the proposition that there exists
a B." What you need to represent is not "A thinks that the *proposition '*there
exists a B' is possible," but "A thinks that the *existence *of something
that is B is possible," i.e., "A thinks that the proposition 'there exists
a B' is *possibly true*." Can you see the difference? With that in mind, I
suggest this Gamma EG instead.
[image: image.png]
Its English translation is "A thinks *that *it is possible *that *there
exists a B"--the two instances of "that" correspond to the two dotted
line/oval combinations. Returning now to Helmut's original example in which
B denotes a complete proposition (e.g., "C is a good girl"), not a name for
a general concept, the Gamma EG for "A thinks that proposition B is
possibly true" is exactly the same, except with no line of identity
attached to B. Alternatively, substitute the Beta EG for proposition B
inside the innermost dotted oval--"A thinks *that *it is possible *that *C
is a good girl."
[image: image.png]
Or another option--"C is a girl, and A thinks *that *it is possible *that *she
is good."
[image: image.png]
These examples demonstrate conclusively that Gamma EGs could *already
*represent
modal propositions using metalanguage with the dotted line/oval notation
that Peirce anticipated in 1898 and introduced in 1903. He did not need a
new Delta part for *that *purpose in 1911.
JFS: Exactly the same procedure can be used to attach any other adjective
or phrase, such as 'necessary', 'impossible', 'probable', 'useful',
'desirable', 'feared', 'doubted', 'lawful', 'illegal' or 'written in Holy
Scriptures". That is the reason why the version of modality that C. I.
Lewis specified in 1932 is a dead end. Anything you can express with it can
be expressed more clearly and generally with metalanguage.
The goal here is not only to *express *modal propositions, but also to *reason
*about them. Another question that I keep asking but you (so far) have not
answered is, How would your approach facilitate this? What transformation
rules would there be for dotted lines/ovals? How would iterated modalities
be represented--perhaps with nested dotted lines/ovals attached to "is
possible" and/or "is necessary"? What permissions would correspond to the
standard modal axioms--perhaps explicit stipulations like a dotted
line/oval attached to "is necessary" can always be erased and a dotted
line/oval attached to "is possible" can always be added (axiom T)? What
could we validly deduce from the assertion that something is "probable,"
"useful," "desirable," "feared," or "written in Holy Scriptures"? How
exactly would that *inference *be carried out by a series of erasures,
insertions, iterations, and/or deiterations?
JFS: I believe that Peirce recognized the need for more expressive power.
And metalanguage adds that power without losing anything that might be
expressed with the 1903 EGs.
Again, the 1903 Gamma EGs *already *included the dotted oval/line no
