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May 5, 2023, 2:00:52 PMMay 5

to Cybernetic Communications, Laws of Form, Structural Modeling, SysSciWG

Cf: Systems of Interpretation • 1

https://inquiryintoinquiry.com/2023/05/05/systems-of-interpretation-1-2/

All,

Questions have arisen about the different styles of diagrams

and figures used to represent triadic sign relations in Peircean

semiotics. What do they mean? Which style is best? Among the

most popular pictures some use geometric triangles while others

use the three‑pronged graphs Peirce used in his logical graphs

to represent triadic relations.

Diagrams and figures, like any signs, can serve to communicate

the intended interpretants and thus to coordinate the conduct of

interpreters toward the intended objects — but only in communities of

interpretation where the conventions of interpretation are understood.

Conventions of interpretation are by comparison far more difficult to

communicate.

That brings us to the first question we have to ask about the possibility

of communication in this area, namely, what conventions of interpretation

are needed to make sense of these diagrams, figures, and graphs?

Regards,

Jon

https://inquiryintoinquiry.com/2023/05/05/systems-of-interpretation-1-2/

All,

Questions have arisen about the different styles of diagrams

and figures used to represent triadic sign relations in Peircean

semiotics. What do they mean? Which style is best? Among the

most popular pictures some use geometric triangles while others

use the three‑pronged graphs Peirce used in his logical graphs

to represent triadic relations.

Diagrams and figures, like any signs, can serve to communicate

the intended interpretants and thus to coordinate the conduct of

interpreters toward the intended objects — but only in communities of

interpretation where the conventions of interpretation are understood.

Conventions of interpretation are by comparison far more difficult to

communicate.

That brings us to the first question we have to ask about the possibility

of communication in this area, namely, what conventions of interpretation

are needed to make sense of these diagrams, figures, and graphs?

Regards,

Jon

May 7, 2023, 4:44:48 PMMay 7

to Cybernetic Communications, Laws of Form, Structural Modeling, SysSciWG

Cf: Systems of Interpretation • 2

https://inquiryintoinquiry.com/2023/05/07/systems-of-interpretation-2-2/

All,

Let's start as simply as possible. The following Figure

is typical of many I have used to illustrate sign relations

from the time I first began studying Peirce's theory of signs.

Figure 2. An Elementary Sign Relation

• https://inquiryintoinquiry.files.wordpress.com/2023/05/elementary-sign-relation.png

The above variant comes from a paper Susan Awbrey and I presented at

a conference in 1999, a revised version of which was published in 2001.

As the drafter of that drawing I can speak with authority about the

artist's intentions in drawing it and also about the conventions of

interpretation forming the matrix of its conception and delivery.

Just by way of refreshing my own memory, here is how we set it up —

Figure 2 represents an “elementary sign relation”. It is a single

transaction taking place among 3 entities, the object o, the sign s,

and the interpretant sign i, the association of which is typically

represented by means of the ordered triple (o, s, i).

One of the interpretive conventions implied in that setup is hallowed

by long tradition, going back to the earliest styles of presentation in

mathematics. In it one draws a figure intended as “representative” of

many figures. Regarded as a concrete drawing the figure is naturally

imperfect, individual, peculiar, and special but it's meant to be taken

purely as a representative of its class — generic, ideal, and typical.

That is the main convention of interpretation which goes into giving

diagrams and figures their significant power.

References —

Conceptual Barriers to Creating Integrative Universities

• https://www.academia.edu/1266492/Conceptual_Barriers_to_Creating_Integrative_Universities

Organizations of Learning or Learning Organizations:

The Challenge of Creating Integrative Universities

• https://arisbe.sitehost.iu.edu/menu/library/aboutcsp/awbrey/integrat.htm

Regards,

Jon

https://inquiryintoinquiry.com/2023/05/07/systems-of-interpretation-2-2/

All,

Let's start as simply as possible. The following Figure

is typical of many I have used to illustrate sign relations

from the time I first began studying Peirce's theory of signs.

Figure 2. An Elementary Sign Relation

• https://inquiryintoinquiry.files.wordpress.com/2023/05/elementary-sign-relation.png

The above variant comes from a paper Susan Awbrey and I presented at

a conference in 1999, a revised version of which was published in 2001.

As the drafter of that drawing I can speak with authority about the

artist's intentions in drawing it and also about the conventions of

interpretation forming the matrix of its conception and delivery.

Just by way of refreshing my own memory, here is how we set it up —

Figure 2 represents an “elementary sign relation”. It is a single

transaction taking place among 3 entities, the object o, the sign s,

and the interpretant sign i, the association of which is typically

represented by means of the ordered triple (o, s, i).

One of the interpretive conventions implied in that setup is hallowed

by long tradition, going back to the earliest styles of presentation in

mathematics. In it one draws a figure intended as “representative” of

many figures. Regarded as a concrete drawing the figure is naturally

imperfect, individual, peculiar, and special but it's meant to be taken

purely as a representative of its class — generic, ideal, and typical.

That is the main convention of interpretation which goes into giving

diagrams and figures their significant power.

References —

Conceptual Barriers to Creating Integrative Universities

• https://www.academia.edu/1266492/Conceptual_Barriers_to_Creating_Integrative_Universities

Organizations of Learning or Learning Organizations:

The Challenge of Creating Integrative Universities

• https://arisbe.sitehost.iu.edu/menu/library/aboutcsp/awbrey/integrat.htm

Regards,

Jon

May 10, 2023, 5:28:23 PMMay 10

to Cybernetic Communications, Laws of Form, Structural Modeling, SysSciWG

Cf: Systems of Interpretation • 3

https://inquiryintoinquiry.com/2023/05/10/systems-of-interpretation-3-2/

Figure 2. An Elementary Sign Relation

• https://inquiryintoinquiry.files.wordpress.com/2023/05/elementary-sign-relation-1.0.png

That “triskelion” stick-figure for an elementary sign relation

or individual triple (o, s, i) is about the simplest possible.

Susan Awbrey and I used a less skeletal figure in an earlier paper,

where our aim was to articulate the commonalities Peirce's concept

of a sign relation shares with its archetype in Aristotle.

Figure 1. The Sign Relation in Aristotle

• https://inquiryintoinquiry.files.wordpress.com/2022/04/awbrey-awbrey-1995-e280a2-figure-1.png

Here is the corresponding passage from “On Interpretation”.

❝Words spoken are symbols or signs (symbola) of affections or

impressions (pathemata) of the soul (psyche); written words

are the signs of words spoken. As writing, so also is speech

not the same for all races of men. But the mental affections

themselves, of which these words are primarily signs (semeia),

are the same for the whole of mankind, as are also the objects

(pragmata) of which those affections are representations or

likenesses, images, copies (homoiomata).❞ (De Interp. i. 16a4).

Reference —

Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”,

Inquiry : Critical Thinking Across the Disciplines 15(1), 40–52.

Journal ( https://www.pdcnet.org/inquiryct/content/inquiryct_1995_0015_0001_0040_0052 )

Online (doc) ( https://www.academia.edu/1266493/Interpretation_as_Action_The_Risk_of_Inquiry )

Online (pdf) ( https://www.academia.edu/57812482/Interpretation_as_Action_The_Risk_of_Inquiry )

Regards,

Jon

https://inquiryintoinquiry.com/2023/05/10/systems-of-interpretation-3-2/

Figure 2. An Elementary Sign Relation

That “triskelion” stick-figure for an elementary sign relation

or individual triple (o, s, i) is about the simplest possible.

Susan Awbrey and I used a less skeletal figure in an earlier paper,

where our aim was to articulate the commonalities Peirce's concept

of a sign relation shares with its archetype in Aristotle.

Figure 1. The Sign Relation in Aristotle

• https://inquiryintoinquiry.files.wordpress.com/2022/04/awbrey-awbrey-1995-e280a2-figure-1.png

Here is the corresponding passage from “On Interpretation”.

❝Words spoken are symbols or signs (symbola) of affections or

impressions (pathemata) of the soul (psyche); written words

are the signs of words spoken. As writing, so also is speech

not the same for all races of men. But the mental affections

themselves, of which these words are primarily signs (semeia),

are the same for the whole of mankind, as are also the objects

(pragmata) of which those affections are representations or

likenesses, images, copies (homoiomata).❞ (De Interp. i. 16a4).

Reference —

Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”,

Inquiry : Critical Thinking Across the Disciplines 15(1), 40–52.

Journal ( https://www.pdcnet.org/inquiryct/content/inquiryct_1995_0015_0001_0040_0052 )

Online (doc) ( https://www.academia.edu/1266493/Interpretation_as_Action_The_Risk_of_Inquiry )

Online (pdf) ( https://www.academia.edu/57812482/Interpretation_as_Action_The_Risk_of_Inquiry )

Regards,

Jon

Jun 10, 2023, 9:24:45 AMJun 10

to Cybernetic Communications, Laws of Form, Structural Modeling, SysSciWG

Cf: Systems of Interpretation • 4

http://inquiryintoinquiry.com/2023/06/10/systems-of-interpretation-4-2/

Re: Mike Bergman

• https://web.archive.org/web/20160410151041/http://permalink.gmane.org/gmane.science.philosophy.peirce/18534

Re: Valentine Daniel

• https://web.archive.org/web/20160328163000/http://permalink.gmane.org/gmane.science.philosophy.peirce/18540

All,

For its pertinence to the present discussion, here again

is what Peirce wrote about the mathematical way of using

individual or particular cases to make general hypotheses

or suppositions:

Mathematical Demonstration and the Doctrine of Individuals • 1

• https://inquiryintoinquiry.com/2023/05/16/mathematical-demonstration-and-the-doctrine-of-individuals-1-2/

And just so we don't forget Peirce's theory of individuals is not the

run-of-the-mill absolute kind but makes the quality of individuality

relative to the context of discussion — or the frame of reference

as they say in physics — here is what he wrote about that:

Mathematical Demonstration and the Doctrine of Individuals • 2

• https://inquiryintoinquiry.com/2023/05/16/mathematical-demonstration-and-the-doctrine-of-individuals-2-2/

Regards,

Jon (https://mathstodon.xyz/@Inquiry)

http://inquiryintoinquiry.com/2023/06/10/systems-of-interpretation-4-2/

Re: Mike Bergman

• https://web.archive.org/web/20160410151041/http://permalink.gmane.org/gmane.science.philosophy.peirce/18534

Re: Valentine Daniel

• https://web.archive.org/web/20160328163000/http://permalink.gmane.org/gmane.science.philosophy.peirce/18540

All,

For its pertinence to the present discussion, here again

is what Peirce wrote about the mathematical way of using

individual or particular cases to make general hypotheses

or suppositions:

Mathematical Demonstration and the Doctrine of Individuals • 1

• https://inquiryintoinquiry.com/2023/05/16/mathematical-demonstration-and-the-doctrine-of-individuals-1-2/

And just so we don't forget Peirce's theory of individuals is not the

run-of-the-mill absolute kind but makes the quality of individuality

relative to the context of discussion — or the frame of reference

as they say in physics — here is what he wrote about that:

Mathematical Demonstration and the Doctrine of Individuals • 2

• https://inquiryintoinquiry.com/2023/05/16/mathematical-demonstration-and-the-doctrine-of-individuals-2-2/

Regards,

Jon (https://mathstodon.xyz/@Inquiry)

Jun 11, 2023, 2:00:44 PMJun 11

to Cybernetic Communications, Laws of Form, Structural Modeling, SysSciWG

Cf: Systems of Interpretation • 5

• https://inquiryintoinquiry.com/2023/06/11/systems-of-interpretation-5-2/

Figure 2. An Elementary Sign Relation

• https://inquiryintoinquiry.files.wordpress.com/2023/05/elementary-sign-relation-1.0.png

An elementary sign relation is an ordered triple (o, s, i). It is called

“elementary” because it is one element of a sign relation L ⊆ O × S × I,

where O is a set of “objects”, S is a set of “signs”, and I is a set of

“interpretant signs” collectively called the “domains” of the relation.

But what is the significance of that ordering?

In any presentation of subject matter we have to distinguish

the natural order of things from the order of consideration or

presentation in which things are taken up on a given occasion.

The natural order of things comes to light through the discovery

of invariants over a variety of presentations and representations.

That type of order tends to take a considerable effort to reveal.

The order of consideration or presentation is often more arbitrary,

making some aspects of the subject matter more salient than others

depending on the paradigm or perspective one has chosen.

In the case of sign relations, the order in which we take up the

domains O, S, I or the components of a triple (o, s, i) is wholly

arbitrary so long as we maintain the same order throughout the

course of discussion.

Regards,

Jon

• https://inquiryintoinquiry.com/2023/06/11/systems-of-interpretation-5-2/

Figure 2. An Elementary Sign Relation

• https://inquiryintoinquiry.files.wordpress.com/2023/05/elementary-sign-relation-1.0.png

“elementary” because it is one element of a sign relation L ⊆ O × S × I,

where O is a set of “objects”, S is a set of “signs”, and I is a set of

“interpretant signs” collectively called the “domains” of the relation.

But what is the significance of that ordering?

In any presentation of subject matter we have to distinguish

the natural order of things from the order of consideration or

presentation in which things are taken up on a given occasion.

The natural order of things comes to light through the discovery

of invariants over a variety of presentations and representations.

That type of order tends to take a considerable effort to reveal.

The order of consideration or presentation is often more arbitrary,

making some aspects of the subject matter more salient than others

depending on the paradigm or perspective one has chosen.

In the case of sign relations, the order in which we take up the

domains O, S, I or the components of a triple (o, s, i) is wholly

arbitrary so long as we maintain the same order throughout the

course of discussion.

Regards,

Jon

Jun 14, 2023, 12:04:27 PMJun 14

to Cybernetic Communications, Laws of Form, Structural Modeling, SysSciWG

Cf: Systems of Interpretation • 6

• https://inquiryintoinquiry.com/2023/06/14/systems-of-interpretation-6-2/

Figure 2. An Elementary Sign Relation

• https://inquiryintoinquiry.files.wordpress.com/2023/05/elementary-sign-relation-1.0.png

Re: Peirce List

• https://web.archive.org/web/20160410151020/http://comments.gmane.org/gmane.science.philosophy.peirce/18558

Re: John Collier

• https://web.archive.org/web/20160405154804/http://permalink.gmane.org/gmane.science.philosophy.peirce/18570

<QUOTE JC:>

I strongly agree, Jon. Reading meaning into artefacts of the

representation is not typically transparent. I would say that

the whole symbol represents the sign with its threefold character

and that the node is not some separate signifier. To put it on

this level is, as you suggest, a category error.

</QUOTE>

Precisely. And “artefact” is a very choice word here, with all

the right connotations. It would be unfortunate if this trivial

“triskelion” figure became a caltrop to our thought, blocking the

way of inquiry.

Aside from the ellipses we added to call attention to a couple of

derivative dyadic relations, somewhat loosely called denotative and

connotative in our paper, it is merely typical of the 3-spoke figures

in common use when I was first learning Peirce's theory of signs, often

arising to point out the differences between Saussure's dyadic semiology

and Peirce's triadic semiotics.

But the intervening decades have taught me mostly all the ways diagrams

and figures of that sort can be misinterpreted when the conventions of

interpretation needed to understand them are not up and running. It can

be instructive to carry out post mortems on the various maps of misreading,

though. If one is not up for the morbidity of that then it is probably wiser

to move on to more viable representations.

Regards,

Jon

• https://inquiryintoinquiry.com/2023/06/14/systems-of-interpretation-6-2/

Figure 2. An Elementary Sign Relation

• https://inquiryintoinquiry.files.wordpress.com/2023/05/elementary-sign-relation-1.0.png

• https://web.archive.org/web/20160410151020/http://comments.gmane.org/gmane.science.philosophy.peirce/18558

Re: John Collier

• https://web.archive.org/web/20160405154804/http://permalink.gmane.org/gmane.science.philosophy.peirce/18570

<QUOTE JC:>

I strongly agree, Jon. Reading meaning into artefacts of the

representation is not typically transparent. I would say that

the whole symbol represents the sign with its threefold character

and that the node is not some separate signifier. To put it on

this level is, as you suggest, a category error.

</QUOTE>

Precisely. And “artefact” is a very choice word here, with all

the right connotations. It would be unfortunate if this trivial

“triskelion” figure became a caltrop to our thought, blocking the

way of inquiry.

Aside from the ellipses we added to call attention to a couple of

derivative dyadic relations, somewhat loosely called denotative and

connotative in our paper, it is merely typical of the 3-spoke figures

in common use when I was first learning Peirce's theory of signs, often

arising to point out the differences between Saussure's dyadic semiology

and Peirce's triadic semiotics.

But the intervening decades have taught me mostly all the ways diagrams

and figures of that sort can be misinterpreted when the conventions of

interpretation needed to understand them are not up and running. It can

be instructive to carry out post mortems on the various maps of misreading,

though. If one is not up for the morbidity of that then it is probably wiser

to move on to more viable representations.

Regards,

Jon

Jun 15, 2023, 11:36:36 AMJun 15

to Cybernetic Communications, Laws of Form, Structural Modeling, SysSciWG

Cf: Systems of Interpretation • 7

• https://inquiryintoinquiry.com/2023/06/15/systems-of-interpretation-7-2/

Figure 2. An Elementary Sign Relation

• https://inquiryintoinquiry.files.wordpress.com/2023/05/elementary-sign-relation-1.0.png

Re: Peirce List

• https://web.archive.org/web/20160410151020/http://comments.gmane.org/gmane.science.philosophy.peirce/18558

Re: Gary Fuhrman

• https://web.archive.org/web/20160405155834/http://permalink.gmane.org/gmane.science.philosophy.peirce/18574

All,

Peirce's existential graphs are a general calculus for expressing the

same subject matter as his logic of relative terms and thus they serve

to represent the structures of many‑place relations. Cast at that level

of generality, there is nothing to prevent existential graphs from being

used to express the special cases of relative terms needed for a theory of

triadic sign relations, for example, terms like “s stands to i for o” or

“__ stands to __ for __” or any number of other forms, depending on the

style one prefers. It may give us pause that we have to use sign relations

in order to mention sign relations but the fact is we do that all the time

whether we are using Peirce's semiotics or not. Peirce's pragmatic analysis

of the process simply provides a clearer account than most other approaches do.

Regards,

Jon

• https://inquiryintoinquiry.com/2023/06/15/systems-of-interpretation-7-2/

Figure 2. An Elementary Sign Relation

• https://inquiryintoinquiry.files.wordpress.com/2023/05/elementary-sign-relation-1.0.png

Re: Peirce List

• https://web.archive.org/web/20160410151020/http://comments.gmane.org/gmane.science.philosophy.peirce/18558

• https://web.archive.org/web/20160405155834/http://permalink.gmane.org/gmane.science.philosophy.peirce/18574

All,

Peirce's existential graphs are a general calculus for expressing the

same subject matter as his logic of relative terms and thus they serve

to represent the structures of many‑place relations. Cast at that level

of generality, there is nothing to prevent existential graphs from being

used to express the special cases of relative terms needed for a theory of

triadic sign relations, for example, terms like “s stands to i for o” or

“__ stands to __ for __” or any number of other forms, depending on the

style one prefers. It may give us pause that we have to use sign relations

in order to mention sign relations but the fact is we do that all the time

whether we are using Peirce's semiotics or not. Peirce's pragmatic analysis

of the process simply provides a clearer account than most other approaches do.

Regards,

Jon

Jun 16, 2023, 1:45:32 PMJun 16

to Cybernetic Communications, Laws of Form, Structural Modeling, SysSciWG

Systems of Interpretation • 8

• http://inquiryintoinquiry.com/2023/06/16/systems-of-interpretation-8-2/

Figure 3. Aspects of a Sign Relation

• https://inquiryintoinquiry.files.wordpress.com/2023/06/aspects-of-a-sign-relation-2.0.png

Re: Peirce List

• https://web.archive.org/web/20160410151020/http://comments.gmane.org/gmane.science.philosophy.peirce/18558

Re: Kirsti Määttänen

• https://web.archive.org/web/20160405155000/http://permalink.gmane.org/gmane.science.philosophy.peirce/18573

All,

One of the chief advantages of Peirce's logical graphs, entitative

and existential, is the way they escape the bounds of 1‑dimensional

syntax and thus make it clear that many constraints of order imposed

by the ordinary lines of linguistic text are not of the essence for

logic but purely rhetorical accidents. That does, of course, leave

open the question of what constraints imposed by the 2‑dimensional

medium of Peirce's logical graphs might also be inessential to logic.

As far as visualizations of sign relations go, without worrying about

their use as a calculus, there is the above 3‑dimensional example from

a paper Susan Awbrey and I presented at conference in 1999 and revised

for publication in 2001.

Resources —

Logical Graphs • Introduction

• https://inquiryintoinquiry.com/2008/07/29/logical-graphs-introduction/

Logical Graphs • Formal Development

• https://inquiryintoinquiry.com/2008/09/19/logical-graphs-formal-development/

Logical Graphs • With Animated Proofs

• https://oeis.org/wiki/Logical_Graphs

Regards,

Jon

• http://inquiryintoinquiry.com/2023/06/16/systems-of-interpretation-8-2/

Figure 3. Aspects of a Sign Relation

• https://inquiryintoinquiry.files.wordpress.com/2023/06/aspects-of-a-sign-relation-2.0.png

Re: Peirce List

• https://web.archive.org/web/20160410151020/http://comments.gmane.org/gmane.science.philosophy.peirce/18558

• https://web.archive.org/web/20160405155000/http://permalink.gmane.org/gmane.science.philosophy.peirce/18573

All,

One of the chief advantages of Peirce's logical graphs, entitative

and existential, is the way they escape the bounds of 1‑dimensional

syntax and thus make it clear that many constraints of order imposed

by the ordinary lines of linguistic text are not of the essence for

logic but purely rhetorical accidents. That does, of course, leave

open the question of what constraints imposed by the 2‑dimensional

medium of Peirce's logical graphs might also be inessential to logic.

As far as visualizations of sign relations go, without worrying about

their use as a calculus, there is the above 3‑dimensional example from

a paper Susan Awbrey and I presented at conference in 1999 and revised

for publication in 2001.

Resources —

Logical Graphs • Introduction

• https://inquiryintoinquiry.com/2008/07/29/logical-graphs-introduction/

Logical Graphs • Formal Development

• https://inquiryintoinquiry.com/2008/09/19/logical-graphs-formal-development/

Logical Graphs • With Animated Proofs

• https://oeis.org/wiki/Logical_Graphs

Regards,

Jon

Jun 17, 2023, 2:04:56 PMJun 17

to Cybernetic Communications, Laws of Form, Structural Modeling, SysSciWG

Cf: Systems of Interpretation • 9

• https://inquiryintoinquiry.com/2023/06/17/systems-of-interpretation-9-2/

Figure 2. An Elementary Sign Relation

• https://inquiryintoinquiry.files.wordpress.com/2023/05/elementary-sign-relation-1.0.png

Re: Peirce List

• https://web.archive.org/web/20160401033602/http://comments.gmane.org/gmane.science.philosophy.peirce/18534

Jerry Chandler

• https://web.archive.org/web/20160324201000/http://permalink.gmane.org/gmane.science.philosophy.peirce/18552

All,

It is above all important to understand that Peirce's concept

of a sign relation is defined at a higher order of abstraction

than any notion of causal or temporal order.

A sign relation L ⊆ O × S × I is a structure which can “generate” the

temporal sequences of signs making up a semiotic process but there is

no necessary temporal order associated with the relational domains

O, S, I nor with the roles of objects, signs, and interpretant signs

in any triple of the form (o, s, i).

As it happens, generative relationships between a generating structure and

a generated class of structures are very common throughout mathematics and

not unique to semiotics.

Regards,

Jon

• https://inquiryintoinquiry.com/2023/06/17/systems-of-interpretation-9-2/

Figure 2. An Elementary Sign Relation

• https://inquiryintoinquiry.files.wordpress.com/2023/05/elementary-sign-relation-1.0.png

Re: Peirce List

Jerry Chandler

• https://web.archive.org/web/20160324201000/http://permalink.gmane.org/gmane.science.philosophy.peirce/18552

All,

It is above all important to understand that Peirce's concept

of a sign relation is defined at a higher order of abstraction

than any notion of causal or temporal order.

A sign relation L ⊆ O × S × I is a structure which can “generate” the

temporal sequences of signs making up a semiotic process but there is

no necessary temporal order associated with the relational domains

O, S, I nor with the roles of objects, signs, and interpretant signs

in any triple of the form (o, s, i).

As it happens, generative relationships between a generating structure and

a generated class of structures are very common throughout mathematics and

not unique to semiotics.

Regards,

Jon

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