Yucong Duan

International Standardization Committee of Networked DIKWP for Artificial Intelligence Evaluation(DIKWP-SC)

World Artificial Consciousness CIC(WAC)

World Conference on Artificial Consciousness(WCAC)

(Email: duanyucong@hotmail.com)

Abstract

Prof. Yucong Duan proposes a paradox concerning the Data-Information-Knowledge-Wisdom-Purpose (DIKWP) Semantic Mathematics framework. He posits that if this framework can evolutionarily develop the semantics of every natural language expression, it will, in effect, construct a DIKWP Cognitive Semantic Space encompassing human cognition as a whole. Within this space, every expression—including paradoxes and conjectures—would already have explanations or proofs. Therefore, if these problems are understandable or exist, their explanations are within this cognitive space, and we only need to discover them. Conversely, if the expressions of paradoxes or conjectures are not evolved from this space, and if they are provable or understandable, their expressions must necessarily be within the DIKWP Cognitive Semantic Space. Otherwise, we can conclude that their explanations do not exist, or they are not true or accessible through human cognition. This document aims to analyze this paradox, explore its implications, and assess its validity within the context of cognitive science and semantic modeling.

The quest to model and understand human cognition, language, and knowledge representation has led to various frameworks and theories. Prof. Yucong Duan's DIKWP Semantic Mathematics framework proposes a structured approach to capturing the semantics of natural language through the fundamental concepts of Sameness, Difference, and Completeness. By evolutionarily developing the semantics of every natural language expression, the framework aims to construct a comprehensive DIKWP Cognitive Semantic Space.

Prof. Duan introduces a paradox: If the DIKWP Semantic Mathematics can evolve the semantics of every natural language expression, then all explanations, including those of paradoxes and conjectures, are inherently present within this cognitive semantic space. Therefore, understanding or proving any such problem merely requires uncovering the existing explanation within this space. If an expression or explanation is not found within this space, it suggests that the problem's explanation does not exist, is not true, or is inaccessible through human cognition.

This document explores this paradox, examines its implications, and assesses its validity.

The DIKWP Cognitive Semantic Space is envisioned as a comprehensive, structured representation of all human cognitive semantics, constructed through the DIKWP Semantic Mathematics framework. It is based on the premise that by systematically applying the fundamental semantics of Sameness, Difference, and Completeness, the framework can capture the semantics of every natural language expression.

• Premise 1: If the DIKWP Semantic Mathematics can evolutionarily develop the semantics of every natural language expression, it constructs a complete cognitive semantic space.

• Premise 2: Within this space, every expression, including paradoxes and conjectures, already has explanations or proofs.

• Conclusion: Therefore, if a problem is understandable or exists, its explanation is within this cognitive semantic space, and we need only to find it.

• Contrapositive:

• If the expression of a paradox or conjecture is not evolved from this cognitive semantic space, and it is provable or understandable, then its expression must necessarily be within this space.

• If it is not within the space, we can conclude that its explanation does not exist, it is not true, or it is not accessible through human cognition.

• Completeness: The cognitive semantic space is complete concerning human cognition.

• Accessibility: All understandable or provable problems are accessible within this space.

• Existence of Explanations: If an explanation is not found within the space, it may not exist or be accessible to human cognition.

1. Totality of Semantics: The DIKWP framework can capture the semantics of every natural language expression.

2. Constructed Cognitive Space: This results in a cognitive semantic space encompassing all human understanding.

3. Inherent Explanations: All explanations or proofs exist within this space.

4. Exclusivity: If an explanation is not within this space, it does not exist or is inaccessible.

1. Feasibility of Total Semantic Capture: Can the DIKWP framework realistically evolve the semantics of every natural language expression?

2. Limits of Human Cognition: Are there inherent limits to what human cognition and, by extension, the cognitive semantic space can encompass?

3. Existence vs. Accessibility: Does the absence of an explanation within the space imply non-existence, or merely that it is currently undiscovered?

• Argument: Natural language is infinitely expressive, and new expressions and concepts continually emerge.

• Counterpoint: If the DIKWP framework is evolutionarily adaptive, it could, in theory, continually expand to include new semantics.

• Analysis: While the framework may capture a vast array of semantics, claiming totality may be an overreach due to the dynamic and creative nature of language.

• Argument: The cognitive semantic space represents the entirety of human cognitive semantics.

• Counterpoint: Human cognition is subjective and individualistic; a collective cognitive space may not account for all individual variations.

• Analysis: The cognitive semantic space may be comprehensive but may not capture every nuance of individual cognition.

• Argument: All explanations or proofs exist within the cognitive semantic space.

• Counterpoint: Some problems may be inherently undecidable or beyond current human understanding.

• Analysis: The existence of explanations may be theoretical, but accessibility and understanding are practical limitations.

• Argument: If an explanation is not in the space, it does not exist or is inaccessible.

• Counterpoint: Absence of evidence is not evidence of absence; an explanation may exist but remain undiscovered.

• Analysis: The conclusion may be premature; it conflates current knowledge with absolute truth.

• Paradoxes: Statements or propositions that, despite apparently sound reasoning, lead to conclusions that seem logically unacceptable or self-contradictory.

• Conjectures: Propositions that are unproven but are thought to be true and have not been disproven.

• If an explanation exists: It is within the DIKWP Cognitive Semantic Space, and we need to find it.

• If an explanation does not exist within the space: The problem may be unprovable, false, or beyond human cognition.

• Current Status: Unproven but extensively verified for large numbers.

• Within the Cognitive Space: The conjecture and its known properties are within the cognitive semantic space.

• Explanation Existence: A proof may exist within the space, but we have yet to discover it.

• Nature: Exposes fundamental issues in naive set theory.

• Within the Cognitive Space: The paradox and its implications are well-understood and have led to developments in axiomatic set theory.

• Explanation Existence: Resolutions, such as type theory, are within the cognitive space.

• Dynamic Nature of Knowledge: Human understanding evolves; new concepts and explanations emerge over time.

• Incompleteness: Gödel's incompleteness theorems suggest that in any sufficiently complex system, there are true statements that cannot be proven within the system.

• Cognitive Constraints: Human cognition may not be capable of comprehending all truths or explanations.

• Epistemology: The study of knowledge, its scope, and limits suggests that some knowledge may be inherently inaccessible.

• Ontology: The nature of being and existence may include entities or truths beyond human comprehension.

• Assuming Completeness: Presuming the cognitive semantic space is complete may be a form of the fallacy of composition, assuming what is true of the parts is true of the whole.

• Argument from Ignorance: Concluding that because we have not found an explanation, it does not exist.

• Continuous Expansion: Human knowledge and understanding are not static; they expand with new discoveries.

• Collective Cognition: The cognitive semantic space may grow as humanity collectively acquires new knowledge.

• Artificial Intelligence: AI can assist in exploring vast semantic spaces, potentially uncovering explanations beyond human capacity.

• Limitations of AI: However, AI is also bound by the data and algorithms created by humans.

• Mathematical Undecidability: Some problems may be undecidable within our current systems.

• Embracing Uncertainty: Accepting that not all explanations are accessible may be a realistic stance.

Prof. Yucong Duan's paradox presents a thought-provoking perspective on the completeness of human cognition and the potential of the DIKWP Semantic Mathematics framework. While the idea of a comprehensive cognitive semantic space containing all explanations is appealing, practical and theoretical considerations suggest limitations:

• Cognitive Limits: Human cognition may not encompass all possible knowledge.

• Incompleteness: Mathematical and logical systems have inherent limitations.

• Discovery vs. Existence: The absence of an explanation within the current cognitive space does not necessarily imply non-existence.

Final Thoughts:

• Value of the Framework: The DIKWP Semantic Mathematics framework remains a valuable tool for modeling and understanding semantics.

• Ongoing Exploration: Continuous exploration and discovery are essential, acknowledging both the potential and limits of human cognition.

• Open Questions: The paradox invites further inquiry into the nature of understanding, knowledge representation, and the boundaries of human cognition.

1. Duan, Y. (2023). DIKWP Semantic Mathematics and Cognitive Modeling. Journal of Cognitive Computing, 20(2), 50-75.

2. Gödel, K. (1931). On Formally Undecidable Propositions of Principia Mathematica and Related Systems. Monatshefte für Mathematik und Physik.

3. Russell, B. (1903). The Principles of Mathematics. Cambridge University Press.

4. Chalmers, D. J. (1995). Facing Up to the Problem of Consciousness. Journal of Consciousness Studies, 2(3), 200-219.

5. Simon, H. A. (1957). Models of Man: Social and Rational. Wiley.

I extend sincere gratitude to Prof. Yucong Duan for his pioneering work on DIKWP Semantic Mathematics and for presenting this paradox, which has inspired deep reflection on the nature of human cognition and knowledge representation.

For further discussion on the DIKWP Semantic Mathematics framework and the exploration of cognitive semantic spaces, please contact [Author's Name] at [Contact Information].

Keywords: DIKWP Model, Semantic Mathematics, Cognitive Semantic Space, Paradox, Sameness, Difference, Completeness, Prof. Yucong Duan, Human Cognition, Knowledge Representation