Analyzing The Completeness, Consistency, and Overlap Relationships of The 12 Philosophical Problems with DIKWP*DIKWP 

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)

Introduction

This analysis aims to apply the DIKWP Semantic Mathematics framework to a set of philosophical problems to reveal their mathematical meanings and relationships. By using the mathematical formulations of Data (D), Information (I), Knowledge (K), Wisdom (W), and Purpose (P), we will examine each problem individually and collectively in terms of completeness, consistency, and overlap relationships. Tables will be provided to summarize the components and highlight the mathematical interconnections.

Before delving into the analysis, let's recall the key mathematical concepts:

1. Data (D): Represented by equivalence classes based on shared semantic attributes (Sameness). Mathematically defined using equivalence relations.

2. Information (I): Quantified differences between data elements (Difference). Modeled using distance metrics in metric spaces.

3. Knowledge (K): Structured understanding formed through abstraction (Completeness). Represented as a complete and consistent formal system.

4. Wisdom (W): Application of knowledge in decision-making, incorporating ethics (Decision Function).

5. Purpose (P): Goal-directed behavior and alignment (Transformation Function).

Overview:

Explores the relationship between mental states (mind) and physical brain states (body).

DIKWP Components and Mathematical Representations:

a. Data (D):

• Semantic Attribute Set (S):

  $S=\{\text{Neural activity patterns},\text{Brain regions},\text{Subjective reports}\}$

• Data Concept Set (D):

  $D=\{d\mid d\text{ shares }S\}$

• Equivalence Relation (~): Defines sameness in neural data sharing identical attributes.

b. Information (I):

• Information Semantics Processing Function (FI):

  $FI:D\to I$

• Distance Metric (δ): Measures differences between data classes (e.g., Euclidean distance between neural patterns).

• Information Set (I):

  I={δ([di],[dj])∣[di],[dj]∈D/ ,[di]≠[dj]}I = \{ \delta([d_i], [d_j]) \mid [d_i], [d_j] \in D/~, [d_i] \neq [d_j] \}I={δ([di​],[dj​])∣[di​],[dj​]∈D/ ,[di​]=[dj​]}

c. Knowledge (K):

• Knowledge Formation Function (FK):

  $FK:I\to K$

• Knowledge System (K):

  $K=\{\varphi \mid \varphi \text{ is a logical consequence of }I\}$

• Ensuring Completeness and Consistency:

• Completeness Criterion:

  $\forall \varphi \in L,\varphi \in K\vee \neg \varphi \in K$

• Consistency Criterion:

  $\nexists \varphi \text{ such that }\varphi \in K\text{ and }\neg \varphi \in K$

d. Wisdom (W):

• Decision Function:

  W:{D,I,K,W,P}→D∗W: \{ D, I, K, W, P \} \rightarrow D^*W:{D,I,K,W,P}→D∗

• **Applies ethical considerations to knowledge for decision-making.

e. Purpose (P):

• Purpose Tuple:

  $P=(\text{Input},\text{Output})$

• Transformation Function:

  $T:\text{Input}\to \text{Output}$

Analysis:

• Completeness: Knowledge $K$ must account for all logical propositions regarding the mind-body relationship, ensuring no gaps.

• Consistency: Theories within $K$ must not contradict each other.

• Overlap with Other Problems: Shares concepts with the Hard Problem of Consciousness (e.g., subjective experience).

Summary Table:

Overview:

Questions how physical processes give rise to subjective experiences (qualia).

DIKWP Components and Mathematical Representations:

a. Data (D):

• $S=\{\text{Neural correlates},\text{Qualia reports}\}$

• $D=\{d\mid d\text{ shares }S\}$

b. Information (I):

• $FI:D\to I$

• $I$ captures the differences highlighting the explanatory gap.

c. Knowledge (K):

• $K=\{\varphi \mid \varphi \text{ is a logical consequence of }I\}$

• May exhibit incompleteness due to the hard problem's nature.

d. Wisdom (W):

• Recognizes limitations in current knowledge.

e. Purpose (P):

• Aims to develop new theories bridging the gap.

Analysis:

• Completeness: Challenged due to the inability to fully derive subjective experience from physical data.

• Consistency: Must avoid contradictions in theoretical frameworks.

Summary Table:

Overview:

Explores whether human actions are freely chosen or predetermined.

DIKWP Components and Mathematical Representations:

a. Data (D):

• $S=\{\text{Neural data},\text{Behavioral observations}\}$

• $D=\{d\mid d\text{ shares }S\}$

b. Information (I):

• $FI:D\to I$

• Identifies patterns suggesting determinism or randomness.

c. Knowledge (K):

• Theories about free will and determinism.

• $K=\{\varphi \mid \varphi \text{ is a logical consequence of }I\}$

d. Wisdom (W):

• Considers ethical implications for moral responsibility.

e. Purpose (P):

• Understand human agency, inform legal and ethical systems.

Analysis:

• Completeness: Requires exhaustive exploration of theories.

• Consistency: Must reconcile conflicting theories logically.

Summary Table:

Overview:

Debates whether moral principles are universal or culturally dependent.

DIKWP Components and Mathematical Representations:

a. Data (D):

• $S=\{\text{Cultural practices},\text{Moral codes}\}$

• $D=\{d\mid d\text{ shares }S\}$

b. Information (I):

• $FI:D\to I$

• Identifies differences and similarities between moral systems.

c. Knowledge (K):

• Ethical theories derived from information.

• $K=\{\varphi \mid \varphi \text{ is a logical consequence of }I\}$

d. Wisdom (W):

• Applies knowledge to promote understanding and tolerance.

e. Purpose (P):

• Foster ethical understanding and respect for diversity.

Analysis:

• Completeness: Must account for all cultural moral systems.

• Consistency: Address potential contradictions between moral codes.

Summary Table:

Overview:

Questions the possibility of certain knowledge.

DIKWP Components and Mathematical Representations:

a. Data (D):

• $S=\{\text{Perceptual experiences},\text{Beliefs}\}$

• $D=\{d\mid d\text{ shares }S\}$

b. Information (I):

• $FI:D\to I$

• Highlights inconsistencies and doubts.

c. Knowledge (K):

• Explores limits of knowledge.

• $K=\{\varphi \mid \varphi \text{ is a logical consequence of }I\}$

d. Wisdom (W):

• Accepts uncertainty, guides practical decision-making.

e. Purpose (P):

• Navigate doubt to function effectively.

Analysis:

• Completeness: Challenged due to inherent uncertainty.

• Consistency: Must avoid paradoxes and contradictions.

Summary Table:

Overview:

Questions the justification of inductive reasoning.

DIKWP Components and Mathematical Representations:

a. Data (D):

• Observations from past experiences.

b. Information (I):

• Patterns and regularities identified.

c. Knowledge (K):

• Generalizations and scientific laws.

d. Wisdom (W):

• Application of inductive reasoning cautiously.

e. Purpose (P):

• Predict future events, advance knowledge.

Analysis:

• Completeness: Inductive reasoning may not guarantee completeness.

• Consistency: Must recognize potential for exceptions.

Summary Table:

Overview:

Examines theories of truth and their implications.

DIKWP Components and Mathematical Representations:

a. Data (D):

• Statements and propositions.

b. Information (I):

• Differences between statements and reality.

c. Knowledge (K):

• Theories such as correspondence, coherence, pragmatism.

d. Wisdom (W):

• Application in communication and understanding.

e. Purpose (P):

• Achieve accurate understanding and convey truth.

Analysis:

• Completeness: Must cover all aspects of truth theories.

• Consistency: Avoid contradictions between theories.

Summary Table:

Overview:

Debates whether entities exist independently of our perceptions.

DIKWP Components and Mathematical Representations:

a. Data (D):

• Perceptual experiences, scientific observations.

b. Information (I):

• Differences in interpretations of data.

c. Knowledge (K):

• Philosophical positions on reality.

d. Wisdom (W):

• Balancing perspectives for practical purposes.

e. Purpose (P):

• Understand the nature of reality.

Analysis:

• Completeness: Needs to encompass all arguments.

• Consistency: Must reconcile conflicting viewpoints.

Summary Table:

Overview:

Explores purpose and significance of human existence.

DIKWP Components and Mathematical Representations:

a. Data (D):

• Human experiences, cultural narratives.

b. Information (I):

• Differences in life interpretations.

c. Knowledge (K):

• Philosophical and religious theories.

d. Wisdom (W):

• Personal and collective application.

e. Purpose (P):

• Seek fulfillment and understanding.

Analysis:

• Completeness: Incorporate diverse perspectives.

• Consistency: Harmonize conflicting views.

Summary Table:

Overview:

Examines ethical implications of technological advancements.

DIKWP Components and Mathematical Representations:

a. Data (D):

• Technological developments, AI capabilities.

b. Information (I):

• Differences in impact assessments.

c. Knowledge (K):

• Ethical frameworks, regulations.

d. Wisdom (W):

• Responsible application of technology.

e. Purpose (P):

• Enhance human well-being.

Analysis:

• Completeness: Must consider all potential impacts.

• Consistency: Align technological use with ethical standards.

Summary Table:

Overview:

Addresses fair distribution of resources and opportunities.

DIKWP Components and Mathematical Representations:

a. Data (D):

• Socioeconomic data, legal statutes.

b. Information (I):

• Differences highlighting inequalities.

c. Knowledge (K):

• Theories of justice and rights.

d. Wisdom (W):

• Policy-making considering ethics.

e. Purpose (P):

• Achieve social equity.

Analysis:

• Completeness: Encompass all aspects of justice.

• Consistency: Policies must be logically coherent.

Summary Table:

Overview:

Examines the nature of language and its influence on thought.

DIKWP Components and Mathematical Representations:

a. Data (D):

• Linguistic expressions, communication data.

b. Information (I):

• Differences in meanings, language structures.

c. Knowledge (K):

• Theories of semantics, pragmatics.

d. Wisdom (W):

• Effective communication strategies.

e. Purpose (P):

• Enhance understanding and expression.

Analysis:

• Completeness: Cover all aspects of language theories.

• Consistency: Ensure coherence in linguistic models.

Summary Table:

To analyze overlaps, we identify shared components or concepts across the problems.

Table of Overlapping Concepts:

• Completeness: Collectively, the problems cover a wide range of philosophical inquiries, contributing to a more complete understanding of human thought.

• Consistency: Ensuring that knowledge across problems does not contradict requires careful reconciliation of differing theories.

Mathematical Integration:

• Unified Knowledge Graph (K_total):

  Ktotal=⋃iKiK_{\text{total}} = \bigcup_{i} K_iKtotal​=⋃i​Ki​

• Consistency Criterion for K_total:

  ∄ϕ such that ϕ∈Ktotal and ¬ϕ∈Ktotal\nexists \phi \text{ such that } \phi \in K_{\text{total}} \text{ and } \neg \phi \in K_{\text{total}}∄ϕ such that ϕ∈Ktotal​ and ¬ϕ∈Ktotal​

• Completeness Criterion for K_total:

  ∀ϕ∈Ltotal,ϕ∈Ktotal∨¬ϕ∈Ktotal\forall \phi \in L_{\text{total}}, \phi \in K_{\text{total}} \lor \neg \phi \in K_{\text{total}}∀ϕ∈Ltotal​,ϕ∈Ktotal​∨¬ϕ∈Ktotal​

By applying the DIKWP Semantic Mathematics framework, we have:

• Mathematically represented each philosophical problem in terms of Data (D), Information (I), Knowledge (K), Wisdom (W), and Purpose (P).

• Analyzed each problem for completeness and consistency, using formal logical criteria.

• Identified overlaps and mathematical relationships among the problems, enhancing our understanding of their interconnections.

• Provided tables to summarize components and highlight relationships.

This mathematical approach allows for a structured and precise analysis of complex philosophical issues, revealing underlying patterns and connections.

Note to Readers

This analysis aims to provide a comprehensive mathematical examination of philosophical problems using the DIKWP Semantic Mathematics framework. If further mathematical details or specific expansions are desired, please feel free to request additional information.

1. International Standardization Committee of Networked DIKWP for Artificial Intelligence Evaluation (DIKWP-SC),World Association of Artificial Consciousness(WAC),World Conference on Artificial Consciousness(WCAC). Standardization of DIKWP Semantic Mathematics of International Test and Evaluation Standards for Artificial Intelligence based on Networked Data-Information-Knowledge-Wisdom-Purpose (DIKWP ) Model. October 2024 DOI: 10.13140/RG.2.2.26233.89445 .  https://www.researchgate.net/publication/384637381_Standardization_of_DIKWP_Semantic_Mathematics_of_International_Test_and_Evaluation_Standards_for_Artificial_Intelligence_based_on_Networked_Data-Information-Knowledge-Wisdom-Purpose_DIKWP_Model

2. Duan, Y. (2023). The Paradox of Mathematics in AI Semantics. Proposed by Prof. Yucong Duan:" As Prof. Yucong Duan proposed the Paradox of Mathematics as that current mathematics will not reach the goal of supporting real AI development since it goes with the routine of based on abstraction of real semantics but want to reach the reality of semantics. ".