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 Logical and Computational Systems"
Split Justification: Humans understand logical and computational systems either by focusing on the abstract rules and structures that govern valid inference, truth, and formal argumentation, or by focusing on the abstract principles and methods that govern information processing, problem-solving procedures, and the limits of computation. These two domains represent distinct yet exhaustive categories within the study of logical and computational systems.
8
From: "Understanding Algorithms and Computability"
Split Justification: Understanding Algorithms and Computability fundamentally encompasses two core areas: the principles involved in designing, implementing, and evaluating the efficiency and correctness of specific computational procedures to solve problems; and the theoretical study of what problems can be solved computationally at all, the fundamental limits of computation, and the inherent difficulty (complexity) of problems. These two domains are distinct in their focus—one on constructive methods and their evaluation, the other on theoretical boundaries and problem classification—yet together they comprehensively cover the entire scope of understanding algorithms and computability.
9
From: "Understanding Computability and Complexity Theory"
Split Justification: Understanding Computability and Complexity Theory fundamentally divides into two core inquiries: first, the theoretical exploration of what problems can be solved by algorithms at all and the inherent limitations of computation (decidability and undecidability); and second, for problems that are computable, the study of the minimal computational resources (time, space) required to solve them and the classification of problems based on their inherent difficulty. These two inquiries are mutually exclusive in their primary focus (existence vs. efficiency) and comprehensively exhaustive, covering the full scope of theoretical limits and resource requirements for algorithmic problem-solving.
10
From: "Understanding Computational Resource Complexity"
Split Justification: Understanding computational resource complexity fundamentally involves two distinct yet complementary areas: first, the detailed analysis and determination of the minimal and maximal resource requirements (e.g., time, space) for solving specific computational problems; and second, the theoretical study of classifying problems into broader categories based on their inherent computational difficulty (complexity classes) and exploring the relationships between these classes. These two endeavors are mutually exclusive in their primary focus (individual analysis vs. categorical framework) and comprehensively exhaustive, covering the full scope of how we understand the resource demands of computation.
11
From: "Understanding Complexity Class Theory"
Split Justification: Understanding Complexity Class Theory fundamentally involves two distinct yet complementary areas: first, the precise definition of individual complexity classes, their internal structures, properties, and specific problems that characterize them (e.g., completeness); and second, the study of how these classes relate to each other, including their hierarchical organization, provable inclusions or separations, and the major open theoretical questions (e.g., P vs. NP). These two perspectives are mutually exclusive in their primary focus (individual class essence vs. inter-class structure) and comprehensively exhaustive, covering the entire scope of how complexity classes are understood.
12
From: "Definition and Intrinsic Properties of Complexity Classes"
Split Justification: ** Understanding the intrinsic properties of complexity classes fundamentally involves two distinct lines of inquiry: first, establishing the precise formal criteria that define a class and exploring its general mathematical characteristics, such as closure properties and internal hierarchies; and second, identifying specific problems that are maximally difficult within that class, thereby serving as benchmarks for its computational power and providing a means to relate other problems to the class. These two aspects are mutually exclusive in their primary focus (abstract class definition vs. concrete problem characterization) and comprehensively exhaustive in describing the inherent nature of individual complexity classes.
✓
Topic: "Completeness and Hardness for Complexity Classes" (W7154)