Documentation

Linglib.Studies.CarianiGoldstein2020

Cariani & Goldstein 2020 — "Conditional Heresies" #

[CG20]

Philosophy and Phenomenological Research 101(2): 251–282.

Sibling homogeneity account #

[CG20] and [San18b] are sibling homogeneity accounts of the conditional. [ZCS26] (p. 8) writes the C&G truth conditions for if A, C as:

⟦if A, C⟧ʷ = 1   if ∀p ∈ Alt(A) : min_w(p) ⊆ C
            = 0   if ∀p ∈ Alt(A) : min_w(p) ⊆ ¬C
            = undef otherwise

This is literally Santorio 2018's homogeneityEval truth-table: TRUE iff every alternative simplification holds, FALSE iff every alternative simplification fails, GAP otherwise. The two accounts coincide on truth-conditional content and diverge primarily on motivation (C&G derive homogeneity from their projection theory of conditionals; Santorio derives it from the truthmaker-stability algorithm).

Sole content #

This file establishes the truth-conditional coincidence as a near-rfl bridge: the C&G conditional verdict on a DAC equals Santorio's homogeneityEval. Worked examples that differentiate the two accounts (e.g., scope-of-undef for embedded conditionals, or the projection-vs-stability mechanism distinction) require infrastructure not yet present in linglib and are left as future work.

source
def CarianiGoldstein2020.cgConditional {W : Type u_1} [DecidableEq W] [Fintype W] (sim : Core.Order.SimilarityOrdering W) (alts : List (Santorio2018.DecAlt W)) (C : W → Prop) [DecidablePred C] (w : W) :
Core.Duality.Truth3

[CG20]'s trivalent conditional verdict for a DAC if A, C over an alternative set. Per [ZCS26] p. 8: TRUE iff all alternative simplifications hold, FALSE iff all fail, undefined otherwise.

Equations
Instances For
    source
    theorem CarianiGoldstein2020.cgConditional_eq_santorioHomogeneityEval {W : Type u_1} [DecidableEq W] [Fintype W] (sim : Core.Order.SimilarityOrdering W) (alts : List (Santorio2018.DecAlt W)) (C : W → Prop) [DecidablePred C] (w : W) :
    cgConditional sim alts C w = Santorio2018.homogeneityEval sim alts C w

    C&G ↔ Santorio coincidence. [CG20]'s trivalent conditional and [San18b]'s homogeneityEval deliver the same verdict on every alternative set. The two accounts diverge on mechanism (projection vs. truthmaker stability) but agree on truth-conditional content — a load-bearing fact for the [ZCS26] acquisition study, which treats both as members of the homogeneity-of-DACs family.