World and World State

Definition

With respect to a specific system $S$ we want to model, a world state for $S$ is a maximal observable state of affairs, i.e., a unique assignment of values to all the observable variables that characterize the system.

A world is a totally ordered set of world states, corresponding to the system’s evolution in time. If we abstract from time for the sake of simplicity, a world state coincides with a world.

Key Characteristics

• Maximal observability: A world state captures all observable variables at a specific granularity level
• Epistemic humility: We don’t claim to capture all possible states, but rather all states observable at our chosen level of analysis
• Temporal ordering: A world represents the evolution of world states over time
• Methodological choice: The granularity of observation is a deliberate analytical decision

Relationship to Other Concepts

World states form the foundation for defining intensional relations and conceptualizations. Together with a domain $D$, they form a domain space $⟨D,W⟩$ that captures the space of variability of the universe of discourse.

In the context of intensional relational structures, world states enable the distinction between:

• Extensional relations: Relations that hold in a particular world state
• Intensional relations: Functions that map each world state to its corresponding extensional relations

Examples

Biological System

For a metabolic system characterized by substrate concentration $S$, enzyme concentration $E$, and product concentration $P$:

• World states: Each world state $w\in W$ assigns specific values to $(S(w),E(w),P(w))$
• World: The temporal sequence of these concentration assignments
• Observable variables: $\{S,E,P\}$

Organizational System

For an enterprise with employees and departments:

• World states: Each configuration of employee assignments, reporting structures, and project allocations
• World: The evolution of organizational structure over time
• Observable variables: Employee positions, department memberships, project assignments

Physical System

For von Bertalanffy’s general system characterized by variables $Q_1,Q_2,\dots ,Q_n$:

• World states: Assignments of specific values to all system variables
• World: The trajectory through state space as governed by differential equations $\frac{d{Q}_i}{dt}=f_i(Q_1,Q_2,\dots ,Q_n)$

Philosophical Context

This definition embeds a critical methodological choice: we fix a granularity of observation and declare certain variable configurations “maximal.” The epistemic humility here is noteworthy—we do not claim to capture all possible states of $S$, but rather all states observable at our chosen level of analysis.

Key References

Meaning and Necessity

Rudolf Carnap (1956) DOI: N/A

The classical Carnapian approach to intension treats intensional relations as functions from possible worlds to extensions, providing the philosophical foundation for the world/world-state distinction.

Related Concepts

• intensional-relation - Functions defined over world states
• conceptualization - Structures defined using domain spaces $⟨D,W⟩$
• intensional-relational-structure - Uses world states to capture invariant conceptual relations
• extensional-relational-structure - Captures only a single world state

Bibliography Keys

• Carnap1956
• Backlund2000a
• Bertalanffy1968