1065 I am compelled to diagram these dyadic actualities, with their contiguities in tow.

Here is a picture that looks like an interscope that I have seen before.

1066 This figure differs from previous interscopes of the specifying, exemplar and interventional sign-relations.

The contiguities no longer correspond to the three potentials₁ underlying a spoken word₂ in the normal context of defintion₃.

The contiguities are labeled with a superscript that indicates the category of that level of the dyadic actuality.  The superscripts are “a” for content level, “b” for situation level and “c” for perspective level.

1067 Each dyadic actuality₂ is a hylomorphe, similar to Aristotle’s matter [substance] form.

For each actuality₂, the sign-object is like matter, the contiguity is similar to [substance] and the sign-vehicle mimics form.

The sign-object confers presence (or esse_ce as matter [substantiating]).  

The sign-vehicle for the next sign-relation is like a shape that contains the presence (or essence as [substantiated] form).

1068 The diagram may be confusing. 

For each sign-relation, the sign-vehicle and the sign-object are on adjacent levels.  In other words, each sign-relation crosses levels.

But, within each level, the dyadic actuality₂ consists of a contiguity between a sign-object (for one sign-relation) and a sign-vehicle (for the next sign-relation in the sequence: specifying, exemplar, interventional, specifying, and so on).

1069 Why do I construct this somewhat ambiguous interscope?

The answer will soon be obvious.

1070 In the introduction (section 6.1), the author opens with three situations where the word, “meaning” is typically used (which corresponds to the three sign-objects in the above interscope).  Then, the author says that he will analyze all three types of situations, starting with the third and using Gottlob Frege’s semantic triangle: referent, symbol and concept (or meaning).

To me, this announcement runs counter to a prior announcement, made a few paragraphs prior, that the author intends to focus on the first two situations.

Dear reader, when a sequential contradiction appears in a text, when the author makes one point and then later presents the same point in a completely different manner, take note.  Either there is something wrong with the author or the author offers a clue that there is a frame shift in the text.  Here, the shift is from common uses of the term, “meaning” to Frege’s referent, symbol and concept.

1071 Just as the three common uses correspond with the three sign-objects within the semiotic interscope, Frege’s three terms associate to the three contiguities.

Here is a picture.

1072 What a coincidence!

1073 Here, the superscripts and the subscripts provide cues.

The superscripts for the contiguities denote Peirce’s categories of firstness, secondness and thirdness with respect to levels.

The subscripts on the sign-elements denote the type of sign-relation.

The subscripts for the actualities denote level (a, b, c) and location in a category-based nested form (1,2,3).

1074 What about the sign-relation?

The sign-relation does not appear in the figure above.

A sign-relation crosses levels, so it would have two superscripts, one for the SV and one for the SO and SI.

1075 Can I say that again?

The specifying sign-relation^a,b is an index^a,b, because its sign-object, {SO_s}_2b or information_2b, is based on the qualities of pointing, contact, contiguity, cause and effect, and so on.

The exemplar sign-relation^b,c may be labeled as a symbol^b,c, because its sign-object, {SO_e}_2c or goal_2c, is based on the qualities of habit, convention, law, tradition and so forth.

1076 The interventional sign-relation^c,a can be labeled as an icon^c,a, because its sign-object, {SO_i}_2a or real initiating (semiotic) event_2a, is based on the qualities of images, pictures, similarity, and so on.

Indeed, all five senses offer iconic qualities.  Images are not only visual.

I am sure that Daisy and her duck have told me that, through various real initiating (semiotic) events_2a.

1077 The term, “Frege’s three corners”, is not merely a stylish title.

Each of the three actualities listed in the above figure stand at the corner of a triangle.

1078 Why Frege?

The biosemiotic noumenal overlay, diagrammed in the course of these examinations, reflects the work of modern philosophers writing in the late 1800s and the early 1900s.  For the topic at hand, these include Charles Peirce (1839-1914 AD), Ferdinand de Saussure (1859-1914), Gottlob Frege (1848-1925) and Edmund Husserl (1859-1938).

The first (Peirce) rediscovers the definition of sign as a triadic relation after consulting the writings of Baroque scholastics.  The second (Saussure) technically defines “language” as “two arbitrarily related systems of differences”.  The third (Frege) explores semantics, symbolic logic, the philosophy of language and mind, and distinguishes between “sense” and “reference”.  The fourth (Husserl) formalizes a practice performed out-of-sight by the social sciences of the late-nineteenth century.  Phenomenology offers techniques for identifying what a noumenon must be.

1079 Once again, why Frege?

Oh, because the author calls upon Frege’s triangle, consisting of three corners, corresponding to symbol^a, referent^b and concept^c.

Here is a picture for how those corners fall out.

1080 This figure can be compared to author’s “semantic prism” (Figure 6.1).  The purpose of depicting this triangle as a prism is to show how one referent may have more that one concept and how one symbol can link to more than one concept and referent.

To me, this triangular constellation suggests that multiplicity must be distinguished from spirality.  The triangle spirals through time as index^a,b (specifying^a,b) goes to symbol^b,c (exemplar^b,c) and symbol^b,c (exemplar^b,c) goes to icon^c,a(interventional^c,a) and so on.

1081 That is to say, multiplicity does not necessarily raise the question of how one sign leads to another.  Spirality does.

But, spirality is not obvious, as the author shows.

1082 It stands right below the surface of his discussion.

If Frege labels the corners of the semantic triangle, then what do the lines between the corners represent?

If each of the corners of Frege’s triangle belongs to a different level, then the lines must transit from one level of an interscope to another.

That is precisely what the sign-relation does.

1083 Here is a picture.

1084 I first consider the corners.

In this figure, the actuality₂ for each level is depicted as a dyad.  [Contiguity] occupies the corner.  The two real elements occupy either side of the vertex.  Colors code for level. 

Aristotle’s hylomorphe is exemplar here.  SO equates to matter.  The contiguity is [substance].  SV is like form.  A thing₂ is matter [substance] form.  A thing₂ belongs to the realm of actuality₂.

Rounding each corner corresponds to a thing_2, composed like matter [substance] form, with SO [contiguity] SV.  Frege’s terms are substantial, because they label the contiguities.

1085 What about the lines?

An index^a,b is as sign based on indication and pointing.  On the first side, a symbol^a as substance points to a referent^bas substance.  A real initiating (semiotic) event_2a indicates information_2b.

A symbol^b,c is a sign based on habit and convention.  On the second side, a referent^b as substance makes a habit of a concept^c as substance.  Information_2b symbolizes a goal_2c.

An icon^c,a is a sign based on imagery or similarity.  On the third side, a concept^c as substance images a symbol^a as substance.  A goal_2c images a real initiating (semiotic) event_2a.

1086 Do the lines connect in a true triangle?

No, the lines spiral, in time, in space, and in human cognition.  The triangle never closes.

Instead, the triangle spirals.

1087 Spiral?

As an analogy, imagine our solar system traveling in orbit of the galactic center, along with millions of other stellar entities.  Our planet rotates around the Sun.  The Sun has gone around the galactic center only 18 times.  That is not many orbits.  The Earth is rotating in a local pocket of gravity generated by our Sun.  Yet, our Sun is moving too.  So, the Earth is spiraling through space.

1088 To me, this concept is rather disconcerting.  Or, is it just an image?

I would prefer a moving Earth orbiting a stationary Sun.

Okay, I would really prefer the situation where the Earth is not moving and the Sun is going around it.

After, that is what my world looks like to me.

Similarly, I would rather have a hierarchy rather than a spirality.

With a spirality, one never knows what will happen next.

1089 The previous examination of the constructivist approach (by Alexander Kravchenko) arrives at a claim that pertains to this chapter.  Meanings are the products of the operations of distinction made by a mindful observer in the domain of language.

The author of this chapter of Pathways strives to perform operations of distinction in order to elucidate the evolution of a hierarchy of semiotic beings in our universe.

Yes, hierarchies of semiotic beings manifest as multiple spiralities of the biosemiotic noumenal overlay.

1090 Section 6.2 is titled, “Hierarchogenesis and Its Stages During the General Evolution of the Universe”.  In this section, the author isolates fifteen beginnings (hierarchogenetic events) in the history of the universe.  The first six are “cosmic”, since they concern the universe to which we belong.  The next six are “substantive”, since they have to do with the stuff of life.  The last three are “questionable”, since they have to do with humans in our current Lebenswelt.

I wonder whether I can coin the word, “spiralogenesis”?

1091 Or maybe, “stageogenesis”?

Each beginning serves as a platform for further spiralogenesis… er… hierarchogenesis.

Plus, the selection of hierarchogenetic events is um… selective.

For example, are the earliest galaxies, which I label “cosmic #6” or C6, “galaxies” in the same fashion as later galaxies?

Or are they the purest form of galaxy, since they are initially composed of unspoiled H and He?

1092 The same goes for early and later stars.

Here is the list of my selection of the author’s cosmic entries.

1093 Now, I want to travel the spiral for C1.

To start, I must wonder, “What is the goal of the universe?”

After all, goal_2c corresponds to the exemplar sign-object (SO_e) along with the interventional sign-vehicle (SV_i).  So, if SV_i is the postulated Big Bang (the initiating event where the laws of physics for our particular universe pop out of a pinprick concentrated enough to contain the energy equivalent of the mass of the universe), then SO_e has some explaining to do.

Er… I should rather say… someone may need to speculate on the nature of {SO_e[concept^c]SV_i}_2c for the instance when SV_i is the current postulation of the Big Bang in astrophysics.

1094 That said, let me consider the interventional sign-relation in Frege’s triangle for this beginning.

1095 I follow the formula for the bottom line.

A perspective-level Big Bang_2c (SV_i) stands for a content-level sign-object {(SO_i)}_2a on the basis of (something akin to) what is happening_3a operating on the potential of ‘something’ happening’_1a (SI_i).  Plus, this SO_i operates on the basis of imagery and similarity.  The entire sign-relation is an icon.  A message images a meaning.  A symbol^a pictures a concept^c.

1096 How do I get around the Frege’s corner 2a?

This corner corresponds to a real initiating (semiotic) event_2a.  The roles of SO_i and SV_s differ within that actuality_2a.

Hmmm, maybe I need to go back to the interventional sign-relation.

In C1, SV_i acts as a universe-manifesting pinprick in an emptiness before the universe.  If this is so, and if SO_i is the intention of the expression_2a, then SO_i is the manifestation of time, space, energy and law_2a.

Here is a picture of the interventional sign-relation for C1.

1097 I am still trying to get around the lower-left corner, corresponding to the content-level actuality as a dyad.

As far as the category-based three-level interscope goes, the corner is the content-level actuality_2a of a real initiating (semiotic) event_2a.

As far as the embedded sign-relations go, the corner is the dyad, {SO_i[symbol^a]SV_s.}_2a

Frege’s symbol^a corresponds to the message₁ that makes a spoken word₂ possible in the normal context of definition₃.

1098 Here are my associations.

The real initiating (semiotic) event_2a consists of {the manifestation of time, space, energy and law (SO_i) [symbol^a] the first 10^-19 seconds of the expansion of the universe (SV_s)}_2a.

Whew!

1099 Wait a microsecond!

One-thousand nanoseconds?

Or ten-trillion 10^-19 seconds?

1100 Let me look at section 6.3, titled “Potential Meanings During the Abiotic Period of the Evolution of the Universe”.  The C1 spiralogenetic event is discussed a couple of pages into this section.

For the interventional sign-relation, the Big Bang_2c (SV_i) stands for the manifestation of space, time, energy, natural laws, the fundamental constants, and more_2a (SO_i) in regards to (a normal context similar to) what is happening_3aoperating on the potential of ‘something’ happening_1a (SI_i).

1101 This is 13 billion years ago.

But, that is not the distinctive feature.  The feature that differs from all other features, in the sense that it captures the attention of the reader (and author) is the time frame: 3.17 x 10^-20 seconds.  That is an outstanding feature.  So, to me, it seems that this feature would be a good choice for SV_s side of the real initiation (semiotic) event_2a.

1102 Let me say that in a different manner.

The content-level thing_2a is a real initiating (semiotic) event_2a.

The actuality_2a is a hylomorphe, somehow re-enacting Aristotle’s hylomorphe of matter [substance] form.

1103 The matter-like element is SO_i, the manifestation of space, time, energy, natural laws, fundamental constants and so on.

The form-like element is SV_s, the first 10^-19 seconds of the expansion of the universe.

The substance-like [contiguity] is [symbol^a] for Frege and [message] for the category-based nested form for the definition of a spoken word.

1104 Here is a snapshot of different ways to depict the same corner.

1105 This raises a question about the word, “symbol”.

For Frege, a symbol^a is a corner of a semantic triangle.  The other corners are referent^b and concept^c.  All three terms apply to the character of spoken words.  Every speech act is a symbol^a, pointing to a referent^b, and representing a concept^c. 

Frege’s term, symbol^a, is not the same as Peirce’s use of the same term, symbol^b,c, describing a sign-relation whose sign-object is based on habit, routine, convention, law as so on.

1106 The superscripts tell a story.

Frege’s symbol^a is a contiguity that belongs to the content-level of a three-level interscope.

Peirce’s symbol^b,c is a sign-relation that entangles the situation and perspective levels.

1107 Here is a picture, in terms of Frege’s triangle.

1108 So I ask, “What is it about the spoken word that is captured by symbol^a that is not grasped by symbol^b,c?”

Ferdinand de Saussure’s definition of spoken language provides a clue.  Spoken language consists of two arbitrarily related systems of differences, parole and langue.  I prefer to use the French, because an English translation of these words is misleading.  Maybe, “speech” and “cogitation” will suffice.  But, not for me.

1109 What does this imply?

Each parole (spoken word) differs from any other parole, constituting a system of differences. This system of differences must exist by convention, since there is no way for a symbolic order to exist on the qualities of similarity and pointing.  So, the system of differences of symbol^as touches base with symbol^b,cs (sign-relations), because each symbol^a (spoken word) is different from any other symbol^a (spoken word).  This allows the spoken word (symbol^a) to signify on the basis of habit, convention, law and so on (that is, what defines symbol^b,c ).

1110 So, my selection of {SO_i [symbol^a] SV_s}_2a is similar to a speaking person choosing just the right word (SV_s) to label what is being manifested in the interventional sign-relation (SO_i).

Yes, [symbol^a] is like choosing the right word (SV_s) to image the message of the interventional sign-object (SO_i).

Symbol^b,c labels when information_2b (SV_e) stands for a goal_2c (SO_e) in regards to a normal context_3c and potential_1cthat are similar to what makes sense_3c operating on the potential of ‘contextualizing the situation_1c (SI_e).

For other views on the word, “symbol”, see Comments on Robert Berwick and Noam Chomsky’s Book (2016) Why Only Us? (by Razie Mah, available at smashwords and other e-book venues).

1111 Of course, I must admit that my SV_s may not be the right feature to label (symbol^a) what is being manifested by the emergence of time, space, energy, mass, and the fundaments of physics (SO_i).

Let me put it the other way.  If I simulate the expansion of the universe with time going backwards, then I am simulating a contraction that, after 13 billion years of shrinking, ends up with the entire universe contracting (backwards) into one point, which is called, by the calculating physicists, “the first singularity”.  But, who knows what it is, because “the first singularity is just a label for this theoretical time-limit, which is so incredible, that within 10^-19seconds, all the gluons and quarks_2b and what they do_2b constellates.

1112 The corresponding specifying sign-relation goes like this.  The first 10^-19 seconds in the expansion of the universe_2a (SV_s) stands for gluons and quarks_2b (as matter) (SO_s) in regards to the universe’s self-governance_3boperating on potential courses of action_1b (SI_s).

Here is a picture.

1113 While it may seem that I have strayed far from the biosemiotic noumenal overlay, I have not.  I am simply going through it using a geometric motif.  The author suggests doing this.  So, I I continue my path around the triangle.

1114 I have already rounded into Frege’s corner 2b, the situation-level actuality_2b, called “information_2b“.

Here is a list of configurations.

1115 The dyads are notable.  The upper element is like Aristotle’s matter. The contiguity is like [substance].  The lower element is like Aristotle’s form. 

The author says that before life, “potential meaning” is the thing itself.  From prior examinations, I know that [message] is “potential sign” and [presence] is “potential meaning”.  The first cosmic hierarchogenetic cycle, C1, exemplifies the lesson.

[Message] is the continuity between the manifestation of time, space, energy, laws and physical constants (SO_i) and the first 10^-19 seconds of the contraction point from a backwards simulation of the expansion of the universe (SV_s).

[Presence] marks the contiguity between the appearance the most elementary forms within the expanding pinprick(now moving forwards in time in the simulation, SO_s) and what they do (SV_e).

1116 Next, information_2b (SV_e) stands for a goal_2c (SO_e) with respect to salience_3c((1c)) (SI_e).

In the exemplar sign-relation of C1, what gluons and quarks do_2b (SV_e) stands for elementary particle physics_2c (SO_e) in regards to the universal natural laws_3c operating on the potential of these elementary forms_1c (SI_e).

1117 Here is a picture.

1118 Now, this exemplar sign-relation sounds perfectly circular.  What the thing itself does (SV_e) stands for what our model says it does (SO_e) in regards to the laws that we program into our simulations_3c operating on the data that we have observed and measured_1c (SI_e).

1119 I mean, like… how does a physicist even observe and measure an elementary particle like a gluon (the glue that holds quarks together)?

It cannot be easy.  It must be so difficult as to require billions of (put in your favorite fiat currency) in order to fund even a small number of experiments.  The apparatus may take years to build.  No, it may take decades.  So, few physicists will be able to replicate the conditions that go into each experiment.  Unless, they spend billions of {put in your favorite fiat currency}.

Well, let me not dwell on that.

1120 After all, I now face Frege’s corner 2c.

1121 Elementary particle physics (SO_e) is like matter.  Hadrons (SV_i) appear like form.  The contiguity between them is [meaning], which is like [substance].

With that said, the title of the book, Pathways to the Origin and Evolution of Meanings in the Universe (2024, edited by Alexei Sharov and George Mikhailovsky, the latter being the author of this article) can be reconfigured into the much less extravagant and more academic-sounding title, The Nature of the Exemplar Sign-Object and Its Contiguity with the Interventional Sign-Vehicle.

But, that would result in a completely different book altogether.

Just look at the expanse that this chapter covers.

1122 Rounding the corner 2c, I consider the interventional sign-relation for C2.

The appearance of hadrons_2c (SV_i) stands for the strong force interactions_2a (SO_i) in regards to what is happening_3aoperating on the potential that a hadron-binding  strong force may happen_1a (SI_i).

1123 This raises the difficulty posed earlier.  The strong force manifesting_2a is a sign-object based on images and similarities.  The interventional sign-relation is an icon.  Whether strong-force interaction is the proper image, the “correct” image, so to speak, depends on the content normal context_3a and potential_1a, which do not even appear in the purely relational structure of semiotic agency.  They belong to the interventional sign-relation.

In the first part of the chapter (section 6.1), the author emphasizes that one concept^c can connect to a variety of symbol^as and a symbol^a can correspond to a number of referent^bs and more than one referent^b may go into a concept^c.  I feel that I am running into that multiplicity here, on the second spiral, C2, after the spiral for the Big Bang, C1.

At Frege’s corner 2a, I get the impression that I face a system of differences, where symbol^a is a substance for one SO_iand more than one SV_s.

1124 Here is my guess.

1125 After symbol^a, the specifying sign-relation follows.

Energy conversion to mass_2a (SV_s) stands for (in a specifying manner) protons and neutrons (the most notable hadrons, SO_s) in regards to the self-governance of energy at very high temperatures_3b operating on potential courses of natural action_1b (SI_s).

1126 Does that work for Frege’s triangle?

1127 Hadrons appear as the SV_i and they manifest the strong force as SO_i.  But, what is the message?

The message has to do with a semiotics of energy converting into mass in the early universe (yes, the time now is much later, at around 10^-13 seconds).  This conversion (SV_s) stands for the types of hadrons that we commonly encounter: protons and neutrons, plus more (SO_s).  The typology is complex, because electrons, which have so little mass that they are charged waves, must be in the mix.

I wonder whether models of self-governance (SI_s) within hadrons is fully appreciated.  

I imagine that the potential courses of action (SI_s) are modeled from particle collision experiments.

But, this story-line is outside my expertise.

1128 Here is my take for Frege’s corner 2b.

Yes, I am starting to appreciate that the potential meanings of inanimate things are the things themselves.

The specification of protons and neutrons (and electrons and other hadron-related manifestations) is like matter.  The exemplification of what they do is like form.  The contiguity between them is [referent^b] for Frege and [presence] for Peirce.

1129 At this moment, I notice that Frege’s [referent^b] reminds me of a scientific model overlaying its noumenon and Peirce’s [presence] give me the impression of the thing itself, as what it is [presence] what it does.

1130 Here is my guess for the exemplar sign-relation that follows in C2. 

What these scientifically familiar subatomic particles do_2b (SV_e) stands for nuclear physics_2c (SO_e) in regards to natural laws_3c contextualizing second spiral (C2) forms_1c (SI_e).

1131 Now, approaching Frege’s corner 2c, I wonder, “What is the goal_2c of nuclear physics_2c (SO_e)?”

In addressing this question both hierarchogenesis and spiralogenesis face the same problem.

1132 How does one cross the bridge of [meaning]?

In one way, a perspective-level decision_2c comes from within the semiotic agency of the universe itself (in the sign-element of SO_e).

In another way, the intervention starts with an actual action_2c (SV_i) triggering the content-level of a new interscope_3a((1a)) (SI_i)…

1133 …and it ends with an expression of intention_2a (SO_i) that stands on the threshold of [message].

1134 This harkens back to the author’s picture of a semantic prism (Figure 6.1) where one concept^c may connect to several symbol^as.

1135 My choices render the following interventional sign-relation.

The appearance of hydrogen and helium nuclei (SV_i) stands for the ability to manifest gravity (due to the nuclear mass) and electromagnetism (due to particles with charge) (SO_i) in the normal context of what is happening_3a operating on the potential that ‘energy transferring to particles with mass’ happens_1a (SI_i).

1136 Now, I need to step out of the loop, because I am proceeding into C5 in the author’s Table 6.2.

Yes, the next triangle takes me to the formation of the earliest stars.