Leibniz's Works

Tree Summary (Hierarchy)

Leibniz's Works

├── Characteristica Universalis (Universal Language)

│ └── Symbolic representation of all knowledge

├── Calculus Ratiocinator (Logical Calculus)

│ └── Symbolic manipulation of reasoning

├── Binary Logic (0 and 1)

│ ├── Arithmetic foundation

│ └── Logic encoding (true/false)

├── Philosophical Logic

│ ├── Principle of Sufficient Reason

│ ├── Identity of Indiscernibles

│ └── Pre-established Harmony

└── Influence Tree

├── Boolean Algebra

├── Set Theory

├── Predicate Logic

├── Computing & Algorithms

└── Knowledge Representation (AI, Ontologies)

If by → Then Leibniz’s Core Vision Partially Realized:

1. George Boole (Boolean Algebra)

• If by symbolic logic using binary values,
• Then Calculus Ratiocinator (algebra of reasoning) was partially fulfilled.

2. Gottlob Frege (Predicate Logic)

• If by formal symbolic language for logic and mathematics,
• Then Characteristica Universalis moved closer to realization.

3. Bertrand Russell & Alfred N. Whitehead (Principia Mathematica)

• If by an attempt to reduce mathematics to logic,
• Then both Characteristica and Calculus foundations were advanced.

4. Alan Turing (Turing Machine)

• If by mechanical procedures to simulate reasoning,
• Then Calculus Ratiocinator was implemented in computational terms.

5. Claude Shannon (Digital Circuit Logic)

• If by using Boolean algebra to build real-world machines,
• Then Binary Logic and Symbolic Reasoning were operationalized.

6. John McCarthy et al. (Artificial Intelligence)

• If by building machines to represent and reason with knowledge,
• Then Characteristica Universalis was functionally approached.

7. Semantic Web (Tim Berners-Lee, OWL, RDF)

• If by formal languages to represent knowledge on the web,
• Then Characteristica Universalis moved toward practical application.

8. Modern Programming Languages (Haskell, Prolog, etc.)

• If by using logic and symbolic manipulation as core principles,
• Then Calculus Ratiocinator is embedded in software systems.