Leibniz's Characteristica Universalis

Gottfried Wilhelm Leibniz (born in Leipzig), attempted to create a universal language, the "characteristica universalis," that would be able to express mathematical, scientific, and philosophical concepts in a simple, logical form. His vision was to simplify complex thoughts into basic symbols. Here are some smart symbols or concepts he might have considered or developed for his universal language:

1. Logical Operators:

• Conjunction (∧): Symbolizing "and" for combining concepts or propositions.
• Disjunction (∨): Symbolizing "or" for alternatives or choices in reasoning.
• Negation (¬): To express the opposite or denial of a concept.

2. Quantifiers:

• Universal Quantifier (∀): To express statements about all members of a set, e.g., "for all."
• Existential Quantifier (∃): To denote that there exists at least one member of a set with certain properties.

3. Relation Symbols:

• Equality (=) or Identity (≡): To denote that two expressions are the same or equivalent in meaning.
• Inequality (≠): To signify that two things are not equal.

4. Hierarchy and Structure:

• Brackets or Parentheses ((), [], {}): To denote grouping, order, or hierarchy within complex expressions, helping to structure logical arguments.

5. Concepts and Categories:

• Generic Symbols for Concepts: Leibniz might have used symbols to represent basic concepts like substance, quantity, quality, relation, place, time, position, action, passion, etc., each with a unique symbol or set of symbols to avoid ambiguity.

6. Variables and Constants:

• Alphabetic Symbols (A, B, C, ...): To represent variables or specific instances of concepts where the exact nature isn't crucial to the argument but their roles are.

7. Operations on Concepts:

• Composition (○) or Combination: To symbolize how concepts can be combined to form new, complex ideas or judgments.

8. Modal Operators:

• Necessity (□): To denote that something must be true in all possible worlds.
• Possibility (◇): To express that something can be true in at least one possible world.

9. Symbols for Change and Process:

• Differentiation (d/dx): Although this would be more in line with later mathematical developments, the concept of change could be symbolized to represent processes or transformations in reasoning about natural phenomena or abstract concepts.

10. Axioms and Rules:

• Logical Axioms: Unique symbols or notations to denote fundamental truths or assumptions upon which further reasoning could be built.

Leibniz's idea was to create a language where every symbol had a precise, unambiguous meaning, allowing for a kind of calculus of thought. This would not only facilitate communication but also enable the mechanical solving of disputes by reducing complex arguments to symbolic calculations. While Leibniz's full vision was never realized, many of his concepts have influenced modern logic, mathematics, and computer science, particularly in the development of formal languages and programming.