3. Tarskian Semantics and Set-Theoretic Models
Historical Materialist Hook
[RESEARCH REQUIRED: Analyze the shift to set-theoretic models and the strict separation of object language and metalanguage through the lens of state-building. Utilize Alfred Tarski’s The Concept of Truth in Formalized Languages to mirror the rational-legal bureaucratic optimization required by the interwar Polish state to integrate disparate legal and economic systems.]
Core Technical Synthesis
[RESEARCH REQUIRED: Define objective mapping processes using Tarskian Semantics. Detail how to establish formal set-theoretic interpretations by defining domains of discourse and mapping relations and properties to those specific domains.]
Guided Example: Defining a Model
To evaluate ∀x Fx -> Gx:
Domain: {1, 2, 3} Extension of F: {1, 2} Extension of G: {1, 2, 3}
In this model, the formula evaluates to True.
Problem Set
Exercise 3.1
Explicitly define a domain with at least 4 elements. Define two predicate extensions such that the formula ∃x (Fx /\ ~Gx) evaluates to true.
Dictionary Reference Map
- For set-theoretic truth definitions: forall x Calgary (Magnus et al. 2025, 225-245)