Looking at George Mikhailovsky’s Chapter (2024) “Meanings, Their Hierarchy, and Evolution” (Part 3 of 9)
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 symbola, referentb and conceptc.
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 indexa,b (specifyinga,b) goes to symbolb,c (exemplarb,c) and symbolb,c (exemplarb,c) goes to iconc,a(interventionalc,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 thing2, 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 indexa,b is as sign based on indication and pointing. On the first side, a symbola as substance points to a referentbas substance. A real initiating (semiotic) event2a indicates information2b.
A symbolb,c is a sign based on habit and convention. On the second side, a referentb as substance makes a habit of a conceptc as substance. Information2b symbolizes a goal2c.
An iconc,a is a sign based on imagery or similarity. On the third side, a conceptc as substance images a symbola as substance. A goal2c images a real initiating (semiotic) event2a.
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.