Validity implies necessity for every sentence exactly when there is at most one world.
Docs / Studies / Studies.Kaplan1989
Demonstratives
Kaplan, D. (1989). In Themes from Kaplan (pp. 481–563). Oxford University Press
A sentence is valid in Kaplan's logic of demonstratives when it is true at every context, and
necessary when what it says at every context is true at every world. Necessity implies validity
(Kaplan.Character.IsNecessary.isAPriori), but necessitation fails
as soon as there are two worlds, and for
sentences whose content does not vary with the context it holds only if every world is the world
of a context. α = dthat[α]
is valid, and necessary exactly when α is directly
referential; I exist and I am here now are
valid but contingent.
Implementation notes
- Validity of I exist and I am here now quantifies over the proper contexts alone
(
ProperContext): over every tuple, I exist would be true at every context only if every agent existed at every world, and so would be necessary. - An index is a world; Kaplan's circumstances also fix a time, which the necessity of these sentences does not need.
References
- Kaplan 1989, Demonstratives
The failure of necessitation
The identity of a term with its rigidification is necessary exactly when the term is directly referential.
For sentences whose content is the same at every context, Kaplan's stable characters, validity implies necessity exactly when every world is the world of some context.
Proper contexts
A context is proper when its agent exists at its world and is at its position at its time there.
Used by ProperContext
Used in Schlenker2004a
The proper contexts.
- ProperContext exists_ located = { c : Kaplan.Context W E P T // Proper exists_ located c }
Built from
Used by existsAgent, locatedAgent, isAPriori_existsAgent, isAPriori_locatedAgent, actualContext, model_isAPriori_not_isNecessary
The character of I exist: the agent of the context exists at the world of evaluation.
- existsAgent exists_ located c w = exists_ (↑c).agent w
Built from
Used by isAPriori_existsAgent, model_isAPriori_not_isNecessary
The character of I am here now: the agent of the context is at its position at its time in the world of evaluation.
- locatedAgent exists_ located c w = located (↑c).agent (↑c).position (↑c).time w
Built from
Used by isAPriori_locatedAgent, model_isAPriori_not_isNecessary
Built from ,
I am here now is valid.
Built from ,
A one-agent, two-world model
The actual world and one alternative.
Derives DecidableEq, Repr.
Used by existsAt, locatedAt, worldOfEvaluation
The only agent exists at the actual world alone.
Built from
The agent is wherever it exists.
Built from
The only proper context of the model.
- actualContext = ⟨{ agent := (), addressee := (), world := World.w0, time := (), position := () }, actualContext._proof_1⟩
Built from , ,
I exist and I am here now are valid but not necessary: the actual world is the world of the only proper context, and what both say there is false at the alternative, where no one exists.
Built from , , , ,
The description the world of evaluation, which is not directly referential.
- worldOfEvaluation x✝ w = w
Built from