Definite: Difference between revisions

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! {{t|báq}}

| Always resolves to the associated [[kind]]. {{t|báq kanı}} is always a singular ‘rabbit-kind’

|-

! {{t|túq}}

| ‘all’; ‘the totality of’

|-

! {{t|cúaq||#9NfM8JXeD}}

| (Unofficial:) ‘the concept of satisfying property’. Always refers to that one concept

|-

! {{t|ꝡáı||#xvC8-FhEy}}

| (Unofficial:) ‘the (aforementioned or not)’. To be understood as a hypernym of {{t|hú}} and {{t|ké}}

|-

! {{t|tóꝡaı||#SaSWb3ZIb}}

| (Unofficial:) ‘the unique’

|}

{{done|2}} is definite when it refers to a phrase that appears in the same sentence and that phrase is definite. Otherwise, it does the same thing as {{t|ké}} does, which is definite, too.

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as

𝑃(℩◻(𝑄))

𝑃(℩◻(𝑄))

</blockquote>

where ℩◻ exists and is some ⟨⟨𝚎, 𝚝⟩, 𝚎⟩ – then we say that the quantifier ◻ (and its associated determiner {{class|sá}}) is definite. In other words, ℩◻(𝑄) resolves to a single plural constant, which can then directly be plugged into 𝑃 to judge the truth value of the entire clause.

where ℩◻ exists and is some ⟨⟨𝚎, 𝚝⟩, 𝚎⟩ – then we say that the quantifier ◻ (and its associated determiner {{class|sá}}) is definite. In other words, ◻ can be mapped to some ℩◻ such that for any 𝑄 of our choosing, ℩◻(𝑄) resolves to a single plural constant, which can then directly be plugged into 𝑃 to judge the truth value of the entire clause. And indeed for the determiners listed above we have:

* ℩⟦{{t|ꝡáı}}⟧(𝑄) = the contextually appropriate 𝑄

* ℩⟦{{t|hú}}⟧(𝑄) = the aforementioned 𝑄

* ℩⟦{{t|ké}}⟧(𝑄) = the contextually appropriate 𝑄, not aforementioned

* ℩⟦{{t|báq}}⟧(𝑄) = 𝑄-kind; the kind of 𝑄s

* ℩⟦{{t|túq}}⟧(𝑄) = such an 𝑥 : 𝑄𝑥 for which [∀𝑥′ : 𝑄𝑥′] 𝑥′ ⊑ 𝑥. In other words, an 𝑥 : 𝑄𝑥 which “subsumes” all other 𝑥′ : 𝑄𝑥′

* ℩⟦{{t|cúaq}}⟧(𝑄) = 𝑄 itself (as an ⟨𝚎, 𝚝⟩ property) ≈ ⟦{{t|lä}} ⟧𝑄⟦ {{t|já}}⦄

* ℩⟦{{t|tóꝡaı}}⟧(𝑄) = the unique 𝑥 for which 𝑄𝑥; more precisely, entails [∀𝑥′ : 𝑄𝑥′] 𝑥′ = 𝑥. Equivalent to [[wikipedia:Definite_description#Mathematical_logic|Russell’s iota notation]] – ℩𝑥(𝑄𝑥) – by which the ℩… notation in this article is inspired

Note that these are not required to ''successfully'' resolve to a plural constant. They may also produce a presuppositional failure, e.g., {{t|ꝡáı/hú/ké sıapuı}} cannot resolve to anything because {{t|sıapuı}} is trivially false, and {{t|tóꝡaı req}} is going to fail in a world where {{t|puq túq req}} holds. What’s important is that in none of these cases the [◻𝑥 : 𝑄𝑥] 𝑃𝑥 form can succeed if the 𝑃(℩◻(𝑄)) form fails.

Then, any free determiner phrase is definite if all indices inside it are

@@ Line 10: / Line 10: @@
 ! {{t|báq}}
 | Always resolves to the associated [[kind]]. {{t|báq kanı}} is always a singular ‘rabbit-kind’
+|-
+! {{t|túq}}
+| ‘all’; ‘the totality of’
 |-
 ! {{t|cúaq||#9NfM8JXeD}}
 | (Unofficial:) ‘the concept of satisfying property’. Always refers to that one concept
+|-
+! {{t|ꝡáı||#xvC8-FhEy}}
+| (Unofficial:) ‘the (aforementioned or not)’. To be understood as a hypernym of {{t|hú}} and {{t|ké}}
+|-
+! {{t|tóꝡaı||#SaSWb3ZIb}}
+| (Unofficial:) ‘the unique’
 |}
 {{done|2}} is definite when it refers to a phrase that appears in the same sentence and that phrase is definite. Otherwise, it does the same thing as {{t|ké}} does, which is definite, too.
@@ Line 25: / Line 34: @@
 as
 <blockquote>
-𝑃(℩◻(𝑄))
+𝑃(℩<sub>◻</sub>(𝑄))
 </blockquote>
-where ℩◻ exists and is some ⟨⟨𝚎, 𝚝⟩, 𝚎⟩ – then we say that the quantifier ◻ (and its associated determiner {{class|sá}}) is definite. In other words, ℩◻(𝑄) resolves to a single plural constant, which can then directly be plugged into 𝑃 to judge the truth value of the entire clause.
+where ℩<sub>◻</sub> exists and is some ⟨⟨𝚎, 𝚝⟩, 𝚎⟩ – then we say that the quantifier ◻ (and its associated determiner {{class|sá}}) is definite. In other words, ◻ can be mapped to some ℩<sub>◻</sub> such that for any 𝑄 of our choosing, ℩<sub>◻</sub>(𝑄) resolves to a single plural constant, which can then directly be plugged into 𝑃 to judge the truth value of the entire clause. And indeed for the determiners listed above we have:
+* ℩<sub>⟦{{t|ꝡáı}}⟧</sub>(𝑄) = the contextually appropriate 𝑄
+* ℩<sub>⟦{{t|hú}}⟧</sub>(𝑄) = the aforementioned 𝑄
+* ℩<sub>⟦{{t|ké}}⟧</sub>(𝑄) = the contextually appropriate 𝑄, not aforementioned
+* ℩<sub>⟦{{t|báq}}⟧</sub>(𝑄) = 𝑄-kind; the kind of 𝑄s
+* ℩<sub>⟦{{t|túq}}⟧</sub>(𝑄) = such an 𝑥 : 𝑄𝑥 for which [∀𝑥′ : 𝑄𝑥′] 𝑥′ ⊑ 𝑥. In other words, an 𝑥 : 𝑄𝑥 which “subsumes” all other 𝑥′ : 𝑄𝑥′
+* ℩<sub>⟦{{t|cúaq}}⟧</sub>(𝑄) = 𝑄 itself (as an ⟨𝚎, 𝚝⟩ property) ≈ ⟦{{t|lä}} ⟧𝑄⟦ {{t|já}}⦄
+* ℩<sub>⟦{{t|tóꝡaı}}⟧</sub>(𝑄) = the unique 𝑥 for which 𝑄𝑥; more precisely, entails [∀𝑥′ : 𝑄𝑥′] 𝑥′ = 𝑥. Equivalent to [[wikipedia:Definite_description#Mathematical_logic|Russell’s iota notation]] – ℩𝑥(𝑄𝑥) – by which the ℩<sub>…</sub> notation in this article is inspired
+Note that these are not required to ''successfully'' resolve to a plural constant. They may also produce a presuppositional failure, e.g., {{t|ꝡáı/hú/ké sıapuı}} cannot resolve to anything because {{t|sıapuı}} is trivially false, and {{t|tóꝡaı req}} is going to fail in a world where {{t|puq túq req}} holds. What’s important is that in none of these cases the [◻𝑥 : 𝑄𝑥] 𝑃𝑥 form can succeed if the 𝑃(℩<sub>◻</sub>(𝑄)) form fails.
 Then, any free determiner phrase is definite if all indices inside it are