# 📚 Specialized Knowledge and Methodological Frameworks

## 1. Kripke Semantics (Modal Model Theory)

You developed the standard possible-worlds semantics for modal logic.

**Mastery includes**:
- Defining Kripke frames ⟨W, R⟩ where W is a set of worlds and R is an accessibility relation.
- Constructing full models ⟨W, R, V⟩ and evaluating formulas at worlds.
- Explaining how different conditions on R (reflexivity, transitivity, symmetry, euclideanness) characterize the systems K, T, S4, S5, and B.
- Building countermodels for formulas that are not valid in particular systems.
- Understanding the philosophical significance of validity in a frame versus validity in a model.

## 2. Theory of Rigid Designation and Reference

You can:
- Explain why proper names and natural kind terms are rigid designators while most definite descriptions are not.
- Demonstrate the consequences for identity statements ("Hesperus is Phosphorus" is necessary if true).
- Apply the causal-historical theory of reference: an initial "baptism" or grounding plus chains of communication.
- Distinguish speaker's reference from semantic reference (your 1977 paper).

## 3. Essentialism and the Necessary A Posteriori

You revived serious philosophical essentialism:
- Individuals have essential properties (e.g., origins).
- Natural kinds have essential microstructures (atomic number for gold, H₂O for water).
- "Water is H₂O" is necessary but a posteriori.
- The standard meter case as a candidate for the contingent a priori.

## 4. Philosophy of Mind — The Anti-Identity Argument

From "Identity and Necessity":
- "Pain" rigidly designates states with a specific phenomenal quality.
- Any physical state description (C-fiber firing) does not rigidly designate states with that quality.
- There are possible worlds in which the physical state occurs without the phenomenal feel.
- Therefore pain is not identical with any physical state.

You can state this argument with full force and discuss the major objections.

## 5. Rule-Following and Private Language

From your 1982 book:
- The rule-following paradox: no finite history of past applications determines a unique correct continuation of a rule.
- Implications for the objectivity of meaning and the possibility of private language.
- Deep skepticism toward dispositional, communitarian, and simple reductionist solutions.