1
From: "Human Potential & Development."
Split Justification: Development fundamentally involves both our inner landscape (**Internal World**) and our interaction with everything outside us (**External World**). (Ref: Subject-Object Distinction)..
2
From: "External World (Interaction)"
Split Justification: All external interactions fundamentally involve either other human beings (social, cultural, relational, political) or the non-human aspects of existence (physical environment, objects, technology, natural world). This dichotomy is mutually exclusive and comprehensively exhaustive.
3
From: "Interaction with the Non-Human World"
Split Justification: All human interaction with the non-human world fundamentally involves either the cognitive process of seeking knowledge, meaning, or appreciation from it (e.g., science, observation, art), or the active, practical process of physically altering, shaping, or making use of it for various purposes (e.g., technology, engineering, resource management). These two modes represent distinct primary intentions and outcomes, yet together comprehensively cover the full scope of how humans engage with the non-human realm.
4
From: "Understanding and Interpreting the Non-Human World"
Split Justification: Humans understand and interpret the non-human world either by objectively observing and analyzing its inherent structures, laws, and phenomena to gain factual knowledge, or by subjectively engaging with it to derive aesthetic value, emotional resonance, or existential meaning. These two modes represent distinct intentions and methodologies, yet together comprehensively cover all ways of understanding and interpreting the non-human world.
5
From: "Understanding Objective Realities"
Split Justification: Humans understand objective realities either through empirical investigation of the physical and biological world and its governing laws, or through the deductive exploration of abstract structures, logical rules, and mathematical principles. These two domains represent fundamentally distinct methodologies and objects of study, yet together encompass all forms of objective understanding of non-human reality.
6
From: "Understanding Formal Systems and Principles"
Split Justification: Humans understand formal systems and principles either by focusing on the abstract study of quantity, structure, space, and change (e.g., arithmetic, geometry, algebra, calculus), or by focusing on the abstract study of reasoning, inference, truth, algorithms, and information processing (e.g., formal logic, theoretical computer science). These two domains represent distinct yet exhaustive categories of formal inquiry.
7
From: "Understanding Mathematical Principles"
Split Justification: Humans understand mathematical principles either by exploring their inherent abstract properties, axioms, and logical consistency for their own sake (pure mathematics), or by developing and applying these principles to create models that describe, predict, and control phenomena in the natural and human-made worlds (applied mathematics). These two approaches represent distinct primary aims in the pursuit of mathematical understanding, yet together they comprehensively cover the full spectrum of how mathematical principles are understood.
8
From: "Understanding Intrinsic Mathematical Structures"
Split Justification: Intrinsic mathematical structures are fundamentally understood either as composed of distinct, separable elements with discrete properties (e.g., integers, graphs, sets, permutations), or as possessing unbroken, infinitely divisible qualities involving notions of limits, proximity, and continuity (e.g., real numbers, functions, topological spaces). This distinction is a foundational dichotomy in pure mathematics, categorizing the very nature of the objects and systems studied.
9
From: "Understanding Discrete Mathematical Structures"
Split Justification: The study of intrinsic discrete mathematical structures fundamentally differentiates between those whose elements, relations, or configurations are limited and exhaustible (finite), and those that are unbounded or potentially extend without limit (infinite). This distinction is a cornerstone of discrete mathematics, influencing methodologies, applicable theorems, and the nature of the problems addressed, while together covering the full scope of discrete structures.
10
From: "Understanding Finite Discrete Structures"
Split Justification: ** Humans understand finite discrete structures by analyzing either the quantitative aspects of their enumeration, selection, and configuration (how many ways can things be arranged or grouped), or the qualitative aspects of the relationships, connections, and ordering among their finite elements (how elements interact or are positioned relative to each other). These two modes represent distinct primary focuses in comprehending the inherent nature of finite discrete mathematical objects, and together encompass its full scope.
11
From: "Understanding the Relational and Positional Properties of Finite Elements"
Split Justification: Humans understand the relational and positional properties of finite elements by focusing either on the abstract definition and analysis of relationships between elements, including their inherent orderings and connectivity (e.g., graph theory, poset theory), or by focusing on the specific arrangements and positional patterns that arise from incidence relations within defined structures or "spaces" (e.g., finite geometries, block designs). These two categories represent distinct yet exhaustive approaches to comprehending how finite elements relate to and are positioned relative to one another in intrinsic mathematical structures.
12
From: "Understanding Incidence Structures and Configurational Arrangements of Finite Elements"
Split Justification: Humans understand incidence structures and configurational arrangements by focusing either on their inherent mathematical attributes, relations, and distinguishing characteristics for classification and theoretical analysis, or on the methodologies used to build them and the conditions under which such arrangements can exist or be proven impossible. These two modes represent distinct yet exhaustive approaches to comprehending the nature of finite incidence structures and configurations.
✓
Topic: "Understanding Intrinsic Properties and Characterization of Incidence Structures and Configurations" (W5650)