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 Computability and Decidability"
Split Justification: Understanding Computability and Decidability fundamentally involves two distinct inquiries: first, establishing the foundational theoretical models and formal definitions that characterize what an algorithm is and what problems are effectively computable or decidable; and second, rigorously demonstrating and proving the existence of problems that inherently lie beyond the capabilities of any algorithm, thus exploring the ultimate boundaries of computation. These two domains are mutually exclusive in their primary focus (definition vs. limitation) and comprehensively exhaustive, covering the entire scope of understanding both the potential and the ultimate limits of algorithmic problem-solving.
11
From: "Theoretical Models and Characterizations of Computability"
Split Justification: ** Understanding Theoretical Models and Characterizations of Computability fundamentally involves two distinct aspects: first, the detailed study and development of the various concrete formal mechanisms (such as Turing machines or lambda calculus) that serve to define computation; and second, the overarching theoretical concept of 'universal computability' that arises from the proven equivalence of these models, along with the foundational assertion that these models capture the intuitive notion of an effectively computable function, as embodied by the Church-Turing Thesis. These two domains are mutually exclusive in their primary focus (concrete mechanisms versus abstract unifying concept) and comprehensively exhaustive, covering the full scope of defining what computation and computability entail.
12
From: "Specific Formal Models of Computation (e.g., Turing Machines, Lambda Calculus)"
Split Justification: ** This dichotomy divides specific formal models of computation based on their fundamental approach to defining computation: either through a sequence of discrete state changes and explicit operations on a memory-like structure, or through the abstract transformation and reduction of expressions via function application and rewriting rules. These two paradigms represent distinct, yet exhaustively comprehensive, conceptual frameworks for formally characterizing computation.
✓
Topic: "Models Based on Expression Transformation and Function Application" (W6386)