Documentation

Linglib.Phenomena.Modality.Studies.Mandelkern2019

@cite{mandelkern-2019}: Wittgenstein Sentences and Distributivity Failure #

@cite{mandelkern-2019}

Mandelkern (2019) "Bounded Modality" (Philosophical Review 128(1):1-61) sharpens Yalcin's (2007) program in two ways:

  1. Terminology: Mandelkern coined the term Wittgenstein sentences for the symmetric form ◇¬p ∧ p ("It might not be raining and it is raining"). Yalcin's original term was "epistemic contradiction" and focused on the p ∧ ◇¬p ordering. Mandelkern argues both orderings are equally infelicitous and have the same source — a claim contested by dynamic-semantic accounts (Veltman 1996; Groenendijk-Stokhof-Veltman 1996) that make the two inequivalent. See also @cite{holliday-mandelkern-2024} p. 4 for discussion.

  2. Distributivity-failure argument: Mandelkern argues that classical distributivity of conjunction over disjunction fails for sentences mixing modal and non-modal content. The canonical example: a sentence schema of the form (p ∨ ¬p) ∧ (◇p ∧ ◇¬p) is felicitous (the LHS is a tautology, the RHS is "full uncertainty"), but its classical-distributive re-expression (p ∧ ◇p ∧ ◇¬p) ∨ (¬p ∧ ◇p ∧ ◇¬p) is infelicitous (each disjunct is a Wittgenstein sentence). HM 2024 (10a-b) restate the example with a winner-of-race scenario.

This file records the Mandelkern-attributed empirical observation — the distributivity-failure intuition. Holliday-Mandelkern 2024 then provide a formal semantic account (the orthologic) that derives this failure from non-distributivity of the underlying ortholattice.

source
structure Phenomena.Modality.Studies.Mandelkern2019.DistribIntuition :
Type

Distributivity-failure intuition: a felicitous sentence becomes infelicitous when classically distributed. The natural-language LHS and RHS are recorded as String for documentation; cross-theory verification requires a formula-tree representation that's currently unavailable (deferred substrate work).

  • lhs : String

    The original (felicitous) sentence.

  • rhs : String

    The classically-equivalent re-expression (infelicitous).

  • lhsFelicitous : Bool

    Whether the LHS is felicitous as asserted.

  • rhsFelicitous : Bool

    Whether the RHS is felicitous as asserted.

Instances For
    source
    @[implicit_reducible]
    instance Phenomena.Modality.Studies.Mandelkern2019.instReprDistribIntuition :
    Repr DistribIntuition
    Equations
    source
    def Phenomena.Modality.Studies.Mandelkern2019.instReprDistribIntuition.repr :
    DistribIntuition → Nat → Std.Format
    Equations
    • One or more equations did not get rendered due to their size.
    Instances For
      source
      def Phenomena.Modality.Studies.Mandelkern2019.distribFailure :
      DistribIntuition

      The Mandelkern (2019) distributivity-failure example, in the form @cite{holliday-mandelkern-2024} (10a-b) restate it: a sentence about Sue being the winner that is felicitous as a "might/might-not + tautology" but not under classical distribution.

      LHS: "Sue might be the winner and she might not be, and either she is the winner or she isn't" — felicitous (the conjunction is consistent; the second conjunct is a tautology).

      RHS: distributing the second conjunct yields a disjunction of two Wittgenstein sentences — infelicitous.

      Equations
      • One or more equations did not get rendered due to their size.
      Instances For