Hesperus/Phosphorus: The Informativeness Puzzle #
Frege's puzzle: "Hesperus = Phosphorus" is informative (empirical discovery by the Babylonians), yet "Hesperus = Hesperus" is trivial.
If names are rigid designators (Kripke), both sentences are necessarily true. The puzzle: how can two necessary truths differ in cognitive significance?
Kaplan's answer: different characters (modes of presentation). Kripke's answer: a posteriori necessity (epistemically contingent, metaphysically necessary).
- identity_true : Bool
"Hesperus is Phosphorus" is true (both are Venus)
- informative : Bool
The identity is informative (empirical discovery)
- self_identity_trivial : Bool
"Hesperus is Hesperus" is trivial
- both_rigid : Bool
Both names are rigid designators
Instances For
The Modal Argument #
Kripke's modal argument: names and descriptions behave differently in modal contexts, showing names are rigid.
"Nixon might not have been president" is true — there are worlds where Nixon exists but isn't president. The name "Nixon" picks out the same individual (Nixon) at every world.
"The president might not have been president" is trivially false on the rigid reading, or means "whoever is actually president might not have been" on the non-rigid reading.
This asymmetry shows that names ≠ descriptions.
- name : String
The name
- description : String
The description that happens to co-refer
- name_modal_true : Bool
"N might not have been D" is true (natural reading)
- name_is_rigid : Bool
The name is rigid across possible worlds
- description_is_rigid : Bool
The description is NOT rigid (varies across worlds)
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Equations
- Phenomena.Reference.DirectReference.nixonPresident = { name := "Nixon", description := "the president", name_modal_true := true }
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Donnellan's Martini Case #
@cite{donnellan-1966}: "The man drinking a martini is happy" said at a party.
The speaker points at Jones, who is actually drinking water. Smith, unbeknownst to the speaker, is the one drinking a martini.
- Referential use: the speaker refers to Jones → evaluates Jones's happiness
- Attributive use: whoever is drinking a martini → evaluates Smith's happiness
The two uses come apart because the description misfits.
- intended : String
The speaker's intended referent
- actualSatisfier : String
Who actually satisfies the description
- description : String
The description
- intendedFails : Bool
The intended referent doesn't satisfy the description
- referentialSucceeds : Bool
Referential use: speaker successfully communicates about Jones
- attributivePicksOther : Bool
Attributive use: picks out Smith instead
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Substitutivity Failure in Belief Contexts #
Substitutivity failure: co-referential names are not interchangeable in belief contexts.
"Lois believes Superman can fly" is true. "Lois believes Clark Kent can fly" is false. Yet Superman = Clark Kent.
This shows that attitude contexts are opaque — they are sensitive to the mode of presentation, not just the referent. Singular propositions (structured content) explain this: ⟨Superman, can-fly⟩ ≠ ⟨Clark, can-fly⟩ even though Superman = Clark.
- name₁ : String
The two co-referential names
- name₂ : String
- predicate : String
The predicate
- believer : String
The believer
- belief₁ : Bool
"B believes name₁ is P"
- belief₂ : Bool
"B believes name₂ is P"
- coreferential : Bool
name₁ = name₂ (co-referential)
- substitutionFails : Bool
belief₁ ≠ belief₂ (substitution failure)
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Equations
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Kaplan's "I am here now" #
@cite{kaplan-1989}: "I am here now" is a logical truth — true at every context of utterance — yet its content is contingent.
At a context where Alice is in Paris on Monday, the content is the proposition "Alice is in Paris on Monday", which is contingent (Alice might have been in London).
This separates two notions of truth:
- Logical truth (truth at every context)
- Necessity (truth at every world)
- logicallyTrue : Bool
True at every context of utterance
- contentContingent : Bool
Content is contingent (not true at every world)
- logicalTruthNotNecessity : Bool
Separates logical truth from necessity
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Kripke's Necessity of Identity #
@cite{kripke-1980}: if an identity "a = b" is true and both terms are rigid designators, then the identity is necessarily true.
"Hesperus = Phosphorus" is true. Both "Hesperus" and "Phosphorus" are rigid designators. Therefore "Hesperus = Phosphorus" is necessarily true — true at every possible world.
Yet the identity is a posteriori — it was an empirical discovery. This yields the category of a posteriori necessities.
- name₁ : String
The two names
- name₂ : String
- identityTrue : Bool
The identity is true
- bothRigid : Bool
Both names are rigid
- identityNecessary : Bool
The identity is necessary (true at every world)
- identityAPosteriori : Bool
The identity is a posteriori (empirical discovery)
Instances For
Equations
- Phenomena.Reference.DirectReference.hesperusPhosphorusNecessity = { name₁ := "Hesperus", name₂ := "Phosphorus" }
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Equations
- Phenomena.Reference.DirectReference.waterH2O = { name₁ := "water", name₂ := "H₂O" }
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Kaplan's Anti-Monster Thesis #
@cite{kaplan-1989}'s thesis that natural language has no context-shifting operators ("monsters").
Status: holds for English; challenged cross-linguistically by indexical shift under attitude verbs in Amharic, Zazaki, Slave, Navajo, and Uyghur.
Theoretical account: Theories/Semantics.Intensional/Reference/Monsters.lean.
- thesis : String
The thesis: no NL operator shifts the context of utterance
- holdsForEnglish : Bool
Holds for English
- challengedCrossLinguistically : Bool
Challenged by at least some languages
Languages with documented indexical shift
- quotationExcluded : Bool
Quotation is excluded from the thesis