Dichotomy Table (Tencer-Minaev)

Classes of IM Dichotomies

	Positions Democratic Information	Does Not Position Democratic Information
Positions Aristocratic Information	$V$ Vector Dichotomy 1. Valid / Null 2. Static / Dynamic 3. Democratic / Aristocratic 4. Asking / Declaring	$A$ Aristocratic Dichotomy 1. 1stInternal / 1stExternal 2. 1stDelta / 1stBeta 3. 2ndExternal / 2ndInternal 4. 2ndBeta / 2ndDelta
Does Not Position Aristocratic Information	$D$ Democratic Dichotomy 1. 1stAbstract / 1stInvolved 2. 1stAlpha / 1stGamma 3. 2ndAbstract / 2ndInvolved 4. 2ndAlpha / 2ndGamma	$C$ Converse Dichotomy 1. Irrational / Rational 2. Extroverted / Introverted 3. Process / Result 4. Positivist / Negativist

Sets

Vector Set

$V=\{V_1,V_2,V_3,V_4\}$

Aristocratic Set

$A=\{A_1,A_2,A_3,A_4\}$

Democratic Set

$D=\{D_1,D_2,D_3,D_4\}$

Converse Set

$C=\{C_1,C_2,C_3,C_4\}$

General Set

$G=\{V_1,V_2,C_1,C_2\}$

Supralocal Set

$U=\{V_3,V_4,C_3,C_4\}$

Accepting Set

$AC=\{A_1,A_2,D_1,D_2\}$

Producing Set

$PR=\{A_3,A_4,D_3,D_4\}$

Faculty Set

$F=\{A_1,A_3,D_1,D_3\}$

Axis Set ($Q$ = Quadra)

$Q=\{A_2,A_4,D_2,D_4\}$

Central Set

$Z=\{V_1,V_3,C_1,C_3\}$

Square / Dihedral Set

$S=\{V_2,V_4,C_2,C_4\}$

Displacement Set

$\Delta =\{V_1,V_4,C_1,C_4\}$

Extrapolative Set

$E=\{V_2,V_3,C_2,C_3\}$

Orientation Set

$O=\{V_1,V_3,C_2,C_4\}$

Pivotal Set

$P=\{V_2,V_4,C_1,C_3\}$

Orbital / Ordinal Set - $(V\cup C)\in \mathcal{O}$

$\mathcal{O}=\{V_1,V_2,V_3,V_4,C_1,C_2,C_3,C_4\}$

Non-Orbital / Cardinal / Wall Set - $(A\cup D)\in W_{14}$

$W_{14}=\{A_1,A_2,A_3,A_4,D_1,D_2,D_3,D_4\}$

Level One Set

$X_1=\{V_1,A_1,D_1,C_1\}$

Level Two Set

$X_2=\{V_2,A_2,D_2,C_2\}$

Level Three Set

$X_3=\{V_3,A_3,D_3,C_3\}$

Level Four Set

$X_4=\{V_4,A_4,D_4,C_4\}$

Universal Set

$\mathbb{U}=\{V_i,A_i,D_i,C_i\mid i=1,2,3,4\}$

Mathematical Correspondences

Alphabetic Correspondences

Let:

$\begin{array}{c}\mathcal{A}:=\mathbb{U}\\ \mathcal{A}=V\bigsqcup A\bigsqcup D\bigsqcup C\end{array}$

We introduce a binary operation:

$\star :\mathcal{A}\times \mathcal{A}⟶\mathcal{A}.$

Complement map:

$\kappa :\mathcal{A}⟶\mathcal{A},{\kappa }^2=\text{identity},$

such that:

$\kappa (V_i)=C_i,\kappa (C_i)=V_i,\kappa (A_i)=D_i,\kappa (D_i)=A_i.$

This is an involution:

$\kappa (\kappa (x))=x$

and it respects indices.

Axioms Written as an Operation

$x\star y=\{\begin{array}{l}{V}_i\text{if }x=y,\\ x\text{if }y=V_i,\\ C_i\text{if }x=\kappa (y),\\ \kappa (x)\text{if }y=C_i.\end{array}$

Numeric Correspondences

Let:

$\begin{array}{c}\mathcal{N}:=\mathbb{U}\\ \mathcal{N}=X_1\bigsqcup X_2\bigsqcup X_3\bigsqcup X_4\end{array}$

The binary operation:

$\star :\mathcal{N}\times \mathcal{N}⟶\mathcal{N}.$

Axioms Written as an Operation

$x\star y=\{\begin{array}{l}{X}_1\text{if }x=y,\\ X_2\text{if }x=X_1\text{ and }y=X_4,\\ X_3\text{if }x=X_2\text{ and }y=X_4,\\ X_4\text{if }x=X_2\text{ and }y=X_3.\end{array}$

Cayley Table for ${\mathcal{D}}_{14}$

$\times$	$V_1$	$V_2$	$V_3$	$V_4$	$A_1$	$A_2$	$A_3$	$A_4$	$D_1$	$D_2$	$D_3$	$D_4$	$C_1$	$C_2$	$C_3$	$C_4$
$V_1$	$V_1$	$V_2$	$V_3$	$V_4$	$A_1$	$A_2$	$A_3$	$A_4$	$D_1$	$D_2$	$D_3$	$D_4$	$C_1$	$C_2$	$C_3$	$C_4$
$V_2$	$V_2$	$V_1$	$V_4$	$V_3$	$A_2$	$A_1$	$A_4$	$A_3$	$D_2$	$D_1$	$D_4$	$D_3$	$C_2$	$C_1$	$C_4$	$C_3$
$V_3$	$V_3$	$V_4$	$V_1$	$V_2$	$A_3$	$A_4$	$A_1$	$A_2$	$D_3$	$D_4$	$D_1$	$D_2$	$C_3$	$C_4$	$C_1$	$C_2$
$V_4$	$V_4$	$V_3$	$V_2$	$V_1$	$A_4$	$A_3$	$A_2$	$A_1$	$D_4$	$D_3$	$D_2$	$D_1$	$C_4$	$C_3$	$C_2$	$C_1$
$A_1$	$A_1$	$A_2$	$A_3$	$A_4$	$V_1$	$V_2$	$V_3$	$V_4$	$C_1$	$C_2$	$C_3$	$C_4$	$D_1$	$D_2$	$D_3$	$D_4$
$A_2$	$A_2$	$A_1$	$A_4$	$A_3$	$V_2$	$V_1$	$V_4$	$V_3$	$C_2$	$C_1$	$C_4$	$C_3$	$D_2$	$D_1$	$D_4$	$D_3$
$A_3$	$A_3$	$A_4$	$A_1$	$A_2$	$V_3$	$V_4$	$V_1$	$V_2$	$C_3$	$C_4$	$C_1$	$C_2$	$D_3$	$D_4$	$D_1$	$D_2$
$A_4$	$A_4$	$A_3$	$A_2$	$A_1$	$V_4$	$V_3$	$V_2$	$V_1$	$C_4$	$C_3$	$C_2$	$C_1$	$D_4$	$D_3$	$D_2$	$D_1$
$D_1$	$D_1$	$D_2$	$D_3$	$D_4$	$C_1$	$C_2$	$C_3$	$C_4$	$V_1$	$V_2$	$V_3$	$V_4$	$A_1$	$A_2$	$A_3$	$A_4$
$D_2$	$D_2$	$D_1$	$D_4$	$D_3$	$C_2$	$C_1$	$C_4$	$C_3$	$V_2$	$V_1$	$V_4$	$V_3$	$A_2$	$A_1$	$A_4$	$A_3$
$D_3$	$D_3$	$D_4$	$D_1$	$D_2$	$C_3$	$C_4$	$C_1$	$C_2$	$V_3$	$V_4$	$V_1$	$V_2$	$A_3$	$A_4$	$A_1$	$A_2$
$D_4$	$D_4$	$D_3$	$D_2$	$D_1$	$C_4$	$C_3$	$C_2$	$C_1$	$V_4$	$V_3$	$V_2$	$V_1$	$A_4$	$A_3$	$A_2$	$A_1$
$C_1$	$C_1$	$C_2$	$C_3$	$C_4$	$D_1$	$D_2$	$D_3$	$D_4$	$A_1$	$A_2$	$A_3$	$A_4$	$V_1$	$V_2$	$V_3$	$V_4$
$C_2$	$C_2$	$C_1$	$C_4$	$C_3$	$D_2$	$D_1$	$D_4$	$D_3$	$A_2$	$A_1$	$A_4$	$A_3$	$V_2$	$V_1$	$V_4$	$V_3$
$C_3$	$C_3$	$C_4$	$C_1$	$C_2$	$D_3$	$D_4$	$D_1$	$D_2$	$A_3$	$A_4$	$A_1$	$A_2$	$V_3$	$V_4$	$V_1$	$V_2$
$C_4$	$C_4$	$C_3$	$C_2$	$C_1$	$D_4$	$D_3$	$D_2$	$D_1$	$A_4$	$A_3$	$A_2$	$A_1$	$V_4$	$V_3$	$V_2$	$V_1$

IM Octads Index

Disclaimer

Since $V_1$ is not a dichotomy (proper), the sets that are derived from it are not octadic, therefore containing no real octads of types. While a dichotomy (proper) entails equal partitioning, this set is tautologically defined by the criteria for TIM validity and thus does not constitute an even distribution of octadic sets.

Notation

A dichotomy is a partition:

$\mathfrak{d}=\{{\mathfrak{d}}_0,{\mathfrak{d}}_1\},{\mathfrak{d}}_0\bigsqcup {\mathfrak{d}}_1=T$

with the dichotomy function:

$\mathfrak{d}:T\to {\mathbb{Z}}_2$

by

$\mathfrak{d}(t):=\{\begin{array}{l}0,\text{if }t\in {\mathfrak{d}}_0,\\ 1,\text{if }t\in {\mathfrak{d}}_1.\end{array}$

We fix the sociotype ILE as the reference element and identify it with the zero vector. Accordingly, for every dichotomy $\mathfrak{d}$, the assignment of values for $0$ and $1$ is chosen so that $\mathfrak{d}(\mathrm{ILE})=0$. All trait values and vector representations are therefore understood relative to this basepoint. Under this convention, every type $t\in T$ is represented by a binary vector encoding its deviation from the ILE across the fixed dichotomy system.

Orbital / Ordinal Octads ($\mathcal{O}$)

Octad v

Vector Octads ($V$)

Valid / Null ($V_1$)

$T=\{\mathrm{ILE},\mathrm{SEI},\mathrm{ESE},\mathrm{LII},\mathrm{EIE},\mathrm{LSI},\mathrm{SLE},\mathrm{IEI},\mathrm{SEE},\mathrm{ILI},\mathrm{LIE},\mathrm{ESI},\mathrm{LSE},\mathrm{EII},\mathrm{IEE},\mathrm{SLI}\}$
$\mathcal{E}=\{?\mathrm{N}{\mathrm{e}}^{+},!\mathrm{S}{\mathrm{i}}^{-},!\mathrm{F}{\mathrm{e}}^{+},?\mathrm{T}{\mathrm{i}}^{-},?\mathrm{F}{\mathrm{e}}^{-},!\mathrm{T}{\mathrm{i}}^{+},!\mathrm{S}{\mathrm{e}}^{-},?\mathrm{N}{\mathrm{i}}^{+},?\mathrm{S}{\mathrm{e}}^{+},!\mathrm{N}{\mathrm{i}}^{-},!\mathrm{T}{\mathrm{e}}^{+},?\mathrm{F}{\mathrm{i}}^{-},?\mathrm{T}{\mathrm{e}}^{-},!\mathrm{F}{\mathrm{i}}^{+},!\mathrm{N}{\mathrm{e}}^{-},?\mathrm{S}{\mathrm{i}}^{+}\}$

Static / Dynamic ($V_2$)

$V_{2,0}^T=\{\mathrm{ILE},\mathrm{LII},\mathrm{LSI},\mathrm{SLE},\mathrm{SEE},\mathrm{ESI},\mathrm{EII},\mathrm{IEE}\}$
$V_{2,0}^{\mathcal{E}}=\{?\mathrm{N}{\mathrm{e}}^{+},?\mathrm{T}{\mathrm{i}}^{-},!\mathrm{T}{\mathrm{i}}^{+},!\mathrm{S}{\mathrm{e}}^{-},?\mathrm{S}{\mathrm{e}}^{+},?\mathrm{F}{\mathrm{i}}^{-},!\mathrm{F}{\mathrm{i}}^{+},!\mathrm{N}{\mathrm{e}}^{-}\}$

$V_{2,1}^T=\{\mathrm{SEI},\mathrm{ESE},\mathrm{EIE},\mathrm{IEI},\mathrm{ILI},\mathrm{LIE},\mathrm{LSE},\mathrm{SLI}\}$
$V_{2,1}^{\mathcal{E}}=\{!\mathrm{S}{\mathrm{i}}^{-},!\mathrm{F}{\mathrm{e}}^{+},?\mathrm{F}{\mathrm{e}}^{-},?\mathrm{N}{\mathrm{i}}^{+},!\mathrm{N}{\mathrm{i}}^{-},!\mathrm{T}{\mathrm{e}}^{-},?\mathrm{T}{\mathrm{e}}^{+},?\mathrm{S}{\mathrm{i}}^{+}\}$

Democratic / Aristocratic ($V_3$)

$V_{3,0}^T=\{\mathrm{ILE},\mathrm{SEI},\mathrm{ESE},\mathrm{LII},\mathrm{SEE},\mathrm{ILI},\mathrm{LIE},\mathrm{ESI}\}$
$V_{3,0}^{\mathcal{E}}=\{?\mathrm{N}{\mathrm{e}}^{+},!\mathrm{S}{\mathrm{i}}^{-},!\mathrm{F}{\mathrm{e}}^{+},?\mathrm{T}{\mathrm{i}}^{-},?\mathrm{S}{\mathrm{e}}^{+},!\mathrm{N}{\mathrm{i}}^{-},!\mathrm{T}{\mathrm{e}}^{+},?\mathrm{F}{\mathrm{i}}^{-}\}$

$V_{3,1}^T=\{\mathrm{EIE},\mathrm{LSI},\mathrm{SLE},\mathrm{IEI},\mathrm{LSE},\mathrm{EII},\mathrm{IEE},\mathrm{SLI}\}$
$V_{3,1}^{\mathcal{E}}=\{?\mathrm{F}{\mathrm{e}}^{-},!\mathrm{T}{\mathrm{i}}^{+},!\mathrm{S}{\mathrm{e}}^{-},?\mathrm{N}{\mathrm{i}}^{+},?\mathrm{T}{\mathrm{e}}^{-},!\mathrm{F}{\mathrm{i}}^{+},!\mathrm{N}{\mathrm{e}}^{-},?\mathrm{S}{\mathrm{i}}^{+}\}$

Asking / Declaring ($V_4$)

$V_{4,0}^T=\{\mathrm{ILE},\mathrm{LII},\mathrm{EIE},\mathrm{IEI},\mathrm{SEE},\mathrm{ESI},\mathrm{LSE},\mathrm{SLI}\}$
$V_{4,0}^{\mathcal{E}}=\{?\mathrm{N}{\mathrm{e}}^{+},?\mathrm{T}{\mathrm{i}}^{-},?\mathrm{F}{\mathrm{e}}^{-},?\mathrm{N}{\mathrm{i}}^{+},?\mathrm{S}{\mathrm{e}}^{+},?\mathrm{F}{\mathrm{i}}^{-},?\mathrm{T}{\mathrm{e}}^{-},?\mathrm{S}{\mathrm{i}}^{+}\}$

$V_{4,1}^T=\{\mathrm{SEI},\mathrm{ESE},\mathrm{LSI},\mathrm{SLE},\mathrm{ILI},\mathrm{LIE},\mathrm{EII},\mathrm{IEE}\}$
$V_{4,1}^{\mathcal{E}}=\{!\mathrm{S}{\mathrm{i}}^{-},!\mathrm{F}{\mathrm{e}}^{+},!\mathrm{T}{\mathrm{i}}^{+},!\mathrm{S}{\mathrm{e}}^{-},!\mathrm{N}{\mathrm{i}}^{-},!\mathrm{T}{\mathrm{e}}^{+},!\mathrm{F}{\mathrm{i}}^{+},!\mathrm{N}{\mathrm{e}}^{-}\}$

Octad c

Converse Octads ($C$)

Irrational / Rational ($C_1$)

$C_{1,0}^T=\{\mathrm{ILE},\mathrm{SEI},\mathrm{SLE},\mathrm{IEI},\mathrm{SEE},\mathrm{ILI},\mathrm{IEE},\mathrm{SLI}\}$
$C_{1,0}^{\mathcal{E}}=\{?\mathrm{N}{\mathrm{e}}^{+},!\mathrm{S}{\mathrm{i}}^{-},!\mathrm{S}{\mathrm{e}}^{-},?\mathrm{N}{\mathrm{i}}^{+},?\mathrm{S}{\mathrm{e}}^{+},!\mathrm{N}{\mathrm{i}}^{-},!\mathrm{N}{\mathrm{e}}^{-},?\mathrm{S}{\mathrm{i}}^{+}\}$

$C_{1,1}^T=\{\mathrm{ESE},\mathrm{LII},\mathrm{EIE},\mathrm{LSI},\mathrm{LIE},\mathrm{ESI},\mathrm{LSE},\mathrm{EII}\}$
$C_{1,1}^{\mathcal{E}}=\{!\mathrm{F}{\mathrm{e}}^{+},?\mathrm{T}{\mathrm{i}}^{-},?\mathrm{F}{\mathrm{e}}^{-},!\mathrm{T}{\mathrm{i}}^{+},!\mathrm{T}{\mathrm{e}}^{+},?\mathrm{F}{\mathrm{i}}^{-},?\mathrm{T}{\mathrm{e}}^{-},!\mathrm{F}{\mathrm{i}}^{+}\}$

Extroversion / Introversion ($C_2$)

$C_{2,0}^T=\{\mathrm{ILE},\mathrm{ESE},\mathrm{EIE},\mathrm{SLE},\mathrm{SEE},\mathrm{LIE},\mathrm{LSE},\mathrm{IEE}\}$
$C_{2,0}^{\mathcal{E}}=\{?\mathrm{N}{\mathrm{e}}^{+},!\mathrm{F}{\mathrm{e}}^{+},?\mathrm{F}{\mathrm{e}}^{-},!\mathrm{S}{\mathrm{e}}^{-},?\mathrm{S}{\mathrm{e}}^{+},!\mathrm{T}{\mathrm{e}}^{+},?\mathrm{T}{\mathrm{e}}^{-},!\mathrm{N}{\mathrm{e}}^{-}\}$

$C_{2,1}^T=\{\mathrm{SEI},\mathrm{LII},\mathrm{LSI},\mathrm{IEI},\mathrm{ILI},\mathrm{ESI},\mathrm{EII},\mathrm{SLI}\}$
$C_{2,1}^{\mathcal{E}}=\{!\mathrm{S}{\mathrm{i}}^{-},?\mathrm{T}{\mathrm{i}}^{-},!\mathrm{T}{\mathrm{i}}^{+},?\mathrm{N}{\mathrm{i}}^{+},!\mathrm{N}{\mathrm{i}}^{-},?\mathrm{F}{\mathrm{i}}^{-},!\mathrm{F}{\mathrm{i}}^{+},?\mathrm{S}{\mathrm{i}}^{+}\}$

Process / Result ($C_3$)

$C_{3,0}^T=\{\mathrm{ILE},\mathrm{SEI},\mathrm{EIE},\mathrm{LSI},\mathrm{SEE},\mathrm{ILI},\mathrm{LSE},\mathrm{EII}\}$
$C_{3,0}^{\mathcal{E}}=\{?\mathrm{N}{\mathrm{e}}^{+},!\mathrm{S}{\mathrm{i}}^{-},?\mathrm{F}{\mathrm{e}}^{-},!\mathrm{T}{\mathrm{i}}^{+},?\mathrm{S}{\mathrm{e}}^{+},!\mathrm{N}{\mathrm{i}}^{-},?\mathrm{T}{\mathrm{e}}^{-},!\mathrm{F}{\mathrm{i}}^{+}\}$

$C_{3,1}^T=\{\mathrm{ESE},\mathrm{LII},\mathrm{SLE},\mathrm{IEI},\mathrm{LIE},\mathrm{ESI},\mathrm{IEE},\mathrm{SLI}\}$
$C_{3,1}^{\mathcal{E}}=\{!\mathrm{F}{\mathrm{e}}^{+},?\mathrm{T}{\mathrm{i}}^{-},!\mathrm{S}{\mathrm{e}}^{-},?\mathrm{N}{\mathrm{i}}^{+},!\mathrm{T}{\mathrm{e}}^{+},?\mathrm{F}{\mathrm{i}}^{-},!\mathrm{N}{\mathrm{e}}^{-},?\mathrm{S}{\mathrm{i}}^{+}\}$

Positivist / Negativist ($C_4$)

$C_{4,0}^T=\{\mathrm{ILE},\mathrm{ESE},\mathrm{LSI},\mathrm{IEI},\mathrm{SEE},\mathrm{LIE},\mathrm{EII},\mathrm{SLI}\}$
$C_{4,0}^{\mathcal{E}}=\{?\mathrm{N}{\mathrm{e}}^{+},!\mathrm{F}{\mathrm{e}}^{+},!\mathrm{T}{\mathrm{i}}^{+},?\mathrm{N}{\mathrm{i}}^{+},?\mathrm{S}{\mathrm{e}}^{+},!\mathrm{T}{\mathrm{e}}^{+},!\mathrm{F}{\mathrm{i}}^{+},?\mathrm{S}{\mathrm{i}}^{+}\}$

$V_{4,1}^T=\{\mathrm{SEI},\mathrm{LII},\mathrm{EIE},\mathrm{SLE},\mathrm{ILI},\mathrm{ESI},\mathrm{LSE},\mathrm{IEE}\}$
$V_{4,1}^{\mathcal{E}}=\{!\mathrm{S}{\mathrm{i}}^{-},?\mathrm{T}{\mathrm{i}}^{-},?\mathrm{F}{\mathrm{e}}^{-},!\mathrm{S}{\mathrm{e}}^{-},!\mathrm{N}{\mathrm{i}}^{-},?\mathrm{F}{\mathrm{i}}^{-},?\mathrm{T}{\mathrm{e}}^{-},!\mathrm{N}{\mathrm{e}}^{-}\}$

Wall / Cardinal / Non-Orbital Octads ($W_{14}$)

Octad a

Aristocratic Octads ($A$)

1stInternal / 1stExternal ($A_1$)

$A_{1,0}^T=\{\mathrm{ILE},\mathrm{ESE},\mathrm{EIE},\mathrm{IEI},\mathrm{ILI},\mathrm{ESI},\mathrm{EII},\mathrm{IEE}\}$
$A_{1,0}^{\mathcal{E}}=\{?\mathrm{N}{\mathrm{e}}^{+},!\mathrm{F}{\mathrm{e}}^{+},?\mathrm{F}{\mathrm{e}}^{+},?\mathrm{N}{\mathrm{i}}^{+},!\mathrm{N}{\mathrm{i}}^{-},?\mathrm{F}{\mathrm{i}}^{-},!\mathrm{F}{\mathrm{i}}^{+},!\mathrm{N}{\mathrm{e}}^{-}\}$

$A_{1,1}^T=\{\mathrm{SEI},\mathrm{ESE},\mathrm{EIE},\mathrm{SLE},\mathrm{SEE},\mathrm{ESI},\mathrm{EII},\mathrm{SLI}\}$
$A_{1,1}^{\mathcal{E}}=\{!\mathrm{S}{\mathrm{i}}^{-},?\mathrm{T}{\mathrm{i}}^{-},!\mathrm{T}{\mathrm{i}}^{+},!\mathrm{S}{\mathrm{e}}^{-},?\mathrm{S}{\mathrm{e}}^{+},!\mathrm{T}{\mathrm{e}}^{+},?\mathrm{T}{\mathrm{e}}^{-},?\mathrm{S}{\mathrm{i}}^{+}\}$

1stDelta / 1stBeta ($A_2$)

$A_{2,0}^T=\{\mathrm{ILE},\mathrm{SEI},\mathrm{LIE},\mathrm{ESI},\mathrm{LSE},\mathrm{EII},\mathrm{IEE},\mathrm{SLI}\}$
$A_{2,0}^{\mathcal{E}}=\{?\mathrm{N}{\mathrm{e}}^{+},!\mathrm{S}{\mathrm{i}}^{-},!\mathrm{T}{\mathrm{e}}^{+},?\mathrm{F}{\mathrm{i}}^{-},?\mathrm{T}{\mathrm{e}}^{-},!\mathrm{F}{\mathrm{i}}^{+},-\mathrm{N}{\mathrm{e}}^{-},?\mathrm{S}{\mathrm{i}}^{+}\}$

$A_{2,1}^T=\{\mathrm{ESE},\mathrm{LII},\mathrm{EIE},\mathrm{LSI},\mathrm{SLE},\mathrm{IEI},\mathrm{SEE},\mathrm{ILI}\}$
$A_{2,1}^{\mathcal{E}}=\{!\mathrm{F}{\mathrm{e}}^{+},?\mathrm{T}{\mathrm{i}}^{-},?\mathrm{F}{\mathrm{e}}^{-},!\mathrm{T}{\mathrm{i}}^{+},!\mathrm{S}{\mathrm{e}}^{-},?\mathrm{N}{\mathrm{i}}^{+},?\mathrm{S}{\mathrm{e}}^{+},!\mathrm{N}{\mathrm{i}}^{-}\}$

2ndExternal / 2ndInternal ($A_3$)

$A_{3,0}^T=\{\mathrm{ILE},\mathrm{ESE},\mathrm{LSI},\mathrm{SLE},\mathrm{ILI},\mathrm{ESI},\mathrm{LSE},\mathrm{SLI}\}$
$A_{3,0}^{\mathcal{E}}=\{?\mathrm{N}{\mathrm{e}}^{+},!\mathrm{F}{\mathrm{e}}^{+},!\mathrm{T}{\mathrm{i}}^{+},!\mathrm{S}{\mathrm{e}}^{-},!\mathrm{N}{\mathrm{i}}^{-},?\mathrm{F}{\mathrm{i}}^{-},?\mathrm{T}{\mathrm{e}}^{-},?\mathrm{S}{\mathrm{i}}^{+}\}$

$A_{3,1}^T=\{\mathrm{SEI},\mathrm{LII},\mathrm{EIE},\mathrm{IEI},\mathrm{SEE},\mathrm{LIE},\mathrm{EII},\mathrm{IEE}\}$
$A_{3,1}^{\mathcal{E}}=\{?\mathrm{S}{\mathrm{i}}^{-},?\mathrm{T}{\mathrm{i}}^{-},?\mathrm{F}{\mathrm{e}}^{-},?\mathrm{N}{\mathrm{i}}^{+},?\mathrm{S}{\mathrm{e}}^{+},!\mathrm{T}{\mathrm{e}}^{+},!\mathrm{F}{\mathrm{i}}^{+},!\mathrm{N}{\mathrm{e}}^{-}\}$

2ndBeta / 2ndDelta ($A_4$)

$A_{4,0}^T=\{\mathrm{ILE},\mathrm{SEI},\mathrm{EIE},\mathrm{LSI},\mathrm{SLE},\mathrm{IEI},\mathrm{LIE},\mathrm{ESI}\}$
$A_{4,0}^{\mathcal{E}}=\{?\mathrm{N}{\mathrm{e}}^{+},!\mathrm{S}{\mathrm{i}}^{-},?\mathrm{F}{\mathrm{e}}^{-},!\mathrm{T}{\mathrm{i}}^{+},!\mathrm{S}{\mathrm{e}}^{-},?\mathrm{N}{\mathrm{i}}^{+},!\mathrm{T}{\mathrm{e}}^{+},?\mathrm{F}{\mathrm{i}}^{-}\}$

$A_{4,1}^T=\{\mathrm{ESE},\mathrm{LII},\mathrm{SEE},\mathrm{ILI},\mathrm{LSE},\mathrm{EII},\mathrm{IEE},\mathrm{SLI}\}$
$A_{4,1}^{\mathcal{E}}=\{!\mathrm{F}{\mathrm{e}}^{+},?\mathrm{T}{\mathrm{i}}^{-},?\mathrm{S}{\mathrm{e}}^{+},!\mathrm{N}{\mathrm{i}}^{-},?\mathrm{T}{\mathrm{e}}^{-},!\mathrm{F}{\mathrm{i}}^{+},!\mathrm{N}{\mathrm{e}}^{-},?\mathrm{S}{\mathrm{i}}^{+}\}$

Octad d

Democratic Octads ($D$)

1stAbstract / 1stInvolved ($D_1$)

$D_{1,0}^T=\{\mathrm{ILE},\mathrm{LII},\mathrm{LSI},\mathrm{IEI},\mathrm{ILI},\mathrm{LIE},\mathrm{LSE},\mathrm{IEE}\}$
$D_{1,0}^{\mathcal{E}}=\{?\mathrm{N}{\mathrm{e}}^{+},?\mathrm{T}{\mathrm{i}}^{-},!\mathrm{T}{\mathrm{i}}^{+},?\mathrm{N}{\mathrm{i}}^{+},!\mathrm{N}{\mathrm{i}}^{-},!\mathrm{T}{\mathrm{e}}^{+},?\mathrm{T}{\mathrm{e}}^{-},!\mathrm{N}{\mathrm{e}}^{-}\}$

$D_{1,1}^T=\{\mathrm{SEI},\mathrm{ESE},\mathrm{EIE},\mathrm{SLE},\mathrm{SEE},\mathrm{ESI},\mathrm{EII},\mathrm{SLI}\}$
$D_{1,1}^{\mathcal{E}}=\{!\mathrm{S}{\mathrm{i}}^{-},!\mathrm{F}{\mathrm{e}}^{+},?\mathrm{F}{\mathrm{e}}^{-},!\mathrm{S}{\mathrm{e}}^{-},?\mathrm{S}{\mathrm{e}}^{+},?\mathrm{F}{\mathrm{i}}^{-},!\mathrm{F}{\mathrm{i}}^{+},?\mathrm{S}{\mathrm{i}}^{+}\}$

1stAlpha / 1stGamma ($D_2$)

$D_{2,0}^T=\{\mathrm{ILE},\mathrm{SEI},\mathrm{ESE},\mathrm{LII},\mathrm{EIE},\mathrm{LSI},\mathrm{IEE},\mathrm{SLI}\}$
$D_{2,0}^{\mathcal{E}}=\{?\mathrm{N}{\mathrm{e}}^{+},!\mathrm{S}{\mathrm{i}}^{-},!\mathrm{F}{\mathrm{e}}^{+},?\mathrm{T}{\mathrm{i}}^{-},?\mathrm{F}{\mathrm{e}}^{-},!\mathrm{T}{\mathrm{i}}^{+},-\mathrm{N}{\mathrm{e}}^{-},?\mathrm{S}{\mathrm{i}}^{+}\}$

$D_{2,1}^T=\{\mathrm{SLE},\mathrm{IEI},\mathrm{SEE},\mathrm{ILI},\mathrm{LIE},\mathrm{ESI},\mathrm{LSE},\mathrm{EII}\}$
$D_{2,1}^{\mathcal{E}}=\{!\mathrm{S}{\mathrm{e}}^{-},?\mathrm{N}{\mathrm{i}}^{+},?\mathrm{S}{\mathrm{e}}^{+},!\mathrm{N}{\mathrm{i}}^{-},!\mathrm{T}{\mathrm{e}}^{+},?\mathrm{F}{\mathrm{i}}^{-},?\mathrm{T}{\mathrm{e}}^{-},!\mathrm{F}{\mathrm{i}}^{+}\}$

2ndAbstract / 2ndInvolved ($D_3$)

$D_{3,0}^T=\{\mathrm{ILE},\mathrm{LII},\mathrm{EIE},\mathrm{SLE},\mathrm{ILI},\mathrm{LIE},\mathrm{EII},\mathrm{SLI}\}$
$D_{3,0}^{\mathcal{E}}=\{?\mathrm{N}{\mathrm{e}}^{+},?\mathrm{T}{\mathrm{i}}^{-},?\mathrm{F}{\mathrm{e}}^{-},!\mathrm{S}{\mathrm{e}}^{-},!\mathrm{N}{\mathrm{i}}^{-},!\mathrm{T}{\mathrm{e}}^{+},!\mathrm{F}{\mathrm{i}}^{+},?\mathrm{S}{\mathrm{i}}^{+}\}$

$D_{3,1}^T=\{\mathrm{SEI},\mathrm{ESE},\mathrm{EIE},\mathrm{IEI},\mathrm{SEE},\mathrm{LIE},\mathrm{EII},\mathrm{IEE}\}$
$D_{3,1}^{\mathcal{E}}=\{?\mathrm{S}{\mathrm{i}}^{-},!\mathrm{F}{\mathrm{e}}^{+},!\mathrm{T}{\mathrm{i}}^{+},?\mathrm{N}{\mathrm{i}}^{+},?\mathrm{S}{\mathrm{e}}^{+},?\mathrm{F}{\mathrm{i}}^{-},?\mathrm{T}{\mathrm{e}}^{-},!\mathrm{N}{\mathrm{e}}^{-}\}$

2ndAlpha / 2ndGamma ($D_4$)

$D_{4,0}^T=\{\mathrm{ILE},\mathrm{SEI},\mathrm{ESE},\mathrm{LII},\mathrm{SLE},\mathrm{IEI},\mathrm{LSE},\mathrm{EII}\}$
$D_{4,0}^{\mathcal{E}}=\{?\mathrm{N}{\mathrm{e}}^{+},!\mathrm{S}{\mathrm{i}}^{-},!\mathrm{F}{\mathrm{e}}^{+},?\mathrm{T}{\mathrm{i}}^{-},!\mathrm{S}{\mathrm{e}}^{-},?\mathrm{N}{\mathrm{i}}^{+},?\mathrm{T}{\mathrm{e}}^{-},!\mathrm{F}{\mathrm{i}}^{+}\}$

$D_{4,1}^T=\{\mathrm{EIE},\mathrm{LSI},\mathrm{SEE},\mathrm{ILI},\mathrm{LIE},\mathrm{ESI},\mathrm{IEE},\mathrm{SLI}\}$
$D_{4,1}^{\mathcal{E}}=\{?\mathrm{F}{\mathrm{e}}^{-},!\mathrm{T}{\mathrm{i}}^{+},?\mathrm{S}{\mathrm{e}}^{+},!\mathrm{N}{\mathrm{i}}^{-},!\mathrm{T}{\mathrm{e}}^{+},?\mathrm{F}{\mathrm{i}}^{-},!\mathrm{N}{\mathrm{e}}^{-},?\mathrm{S}{\mathrm{i}}^{+}\}$

Classes of Tetrachotomies

Orbital Class $\mathcal{O}$

#3: $V_2\cap V_3\cap V_4=V=$ “Vector” Tetrachotomy
#4: $V_4\cap C_1\cap C_4=\Delta =$ “Displacement” Tetrachotomy
#7: $V_4\cap C_2\cap C_3$
#21: $V_3\cap C_1\cap C_3=Z=$ “Central” Tetrachotomy
#22: $V_3\cap C_2\cap C_4=O=$ “Orientation” Tetrachotomy
#30: $V_2\cap C_1\cap C_2=G=$ “General” Tetrachotomy
#31: $V_2\cap C_3\cap C_4$

Non-Orbital Classes $\overline{\mathcal{O}}$

Static/Dynamic Class $V_2$

#11: $V_2\cap D_1\cap D_2$
#16: $V_2\cap A_1\cap A_2$
#24: $V_2\cap D_3\cap D_4$
#27: $V_2\cap A_3\cap A_4$

Democratic/Aristocratic Class $V_3$

#9: $V_3\cap D_1\cap D_3$
#14: $V_3\cap A_1\cap A_3$
#19: $V_3\cap D_2\cap D_4$
#20: $V_3\cap A_2\cap A_4$

Asking/Declaring Class $V_4$

#1: $V_4\cap D_1\cap D_4$
#2: $V_4\cap A_1\cap A_4$
#5: $V_4\cap D_2\cap D_3$
#6: $V_4\cap A_2\cap A_3$

Irrational/Rational Class $C_1$

#8: $A_1\cap D_1\cap C_1$
#23: $A_4\cap D_4\cap C_1$
#32: $A_3\cap D_3\cap C_1$
#33: $A_2\cap D_2\cap C_1$

Extroverted/Introverted Class $C_2$

#13: $A_2\cap D_1\cap C_2$
#18: $A_1\cap D_2\cap C_2$
#25: $A_3\cap D_4\cap C_2$
#28: $A_4\cap D_3\cap C_2$

Process/Result Class $C_3$

#12: $A_3\cap D_1\cap C_3$
#17: $A_1\cap D_3\cap C_3$
#26: $A_2\cap D_4\cap C_3$
#29: $A_4\cap D_2\cap C_3$

Positivist/Negativist Class $C_4$

#10: $A_4\cap D_1\cap C_4$
#15: $A_1\cap D_4\cap C_4$
#34: $A_2\cap D_3\cap C_4$
#35: $A_3\cap D_2\cap C_4$

Additional Note

• Also check out the modern dichotomy classifications table for the Reinin space Kimani White and Andrew Joynton have mapped out: https://docs.google.com/document/d/1xcek3L5mTOrljxb24NXyxyqnhG8tFx7TInfAQ0H_pdc/edit?tab=t.0#heading=h.1vmsoe7mj6yf.
• For an alternate arrangement of the Tencer-Minaev (TM) Table, check out Kimani White’s iteration of the table, accessible here: https://docs.google.com/document/d/1YTDf0oXVmxGEDrOLUyqZZz2lOIDw76yuWAA3ppjHMH0/edit?tab=t.0#heading=h.100owmjgo0e.
• For the list of tetrachotomies for the Tencer-Minaev Space of dichotomies: Tetrachotomy Table (Tencer-Minaev).