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Modal And Intensional Logic·Advanced·5 lessons·~320 min
Reasoning about what must, might, and could have been
What you'll learn
Lessons
Introduces modality as a step beyond truth-functional logic, explains the difference between actual and necessary truth, and gives an informal first look at the box and diamond operators.
Introduces the box and diamond operators formally, establishes the duality between them, and presents the core modal axioms K and T together with simple rules of necessity elimination and possibility introduction.
Trains students to translate natural-language modal arguments into box and diamond notation and to recognize de dicto and de re scope distinctions in quantified modal claims.
Introduces the Lewis-Stalnaker nearness semantics for counterfactual conditionals, distinguishes 'would' from 'might' conditionals, and explains why counterfactuals resist strengthening the antecedent.
Students apply the unit's modal concepts to arguments in metaphysics, ethics, and science, analyzing cases that each require multiple unit concepts working together.
How to study
Each lesson opens with a guided walkthrough — read it before the activity.
Look at why each step follows, not just what the answer is.
Know which rule applies and what would make the response weak before you start.
Optional context for the unit. Each lesson surfaces the concepts and rules it uses — these are here when you want the bigger picture.
A proposition is necessary when it is true in every possible world; written as the box operator in front of the proposition.
A proposition is possible when it is true in at least one possible world; written as the diamond operator in front of the proposition.
A complete way things could consistently be, usually represented as a point in a model at which every proposition has a definite truth value.
A relation between possible worlds that says which worlds count as 'available' from a given world when evaluating modal operators.
A term that picks out the same object in every possible world in which that object exists, as opposed to terms whose reference can shift across worlds.
A conditional of the form 'if it had been the case that P, it would have been the case that Q', evaluated by looking at the nearest possible worlds where P is true.
De dicto modal claims are about the modality of a whole proposition; de re modal claims are about a modal property attributed to a particular thing.
The equivalence between box and diamond via negation: the box of P is equivalent to not the diamond of not P, and vice versa.