Definite - Revision history

Uakci: use template:unofficial

2024-05-30T16:23:40Z

← Older revision		Revision as of 16:23, 30 May 2024
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	\| ‘all’; ‘the totality of’		\| ‘all’; ‘the totality of’
	\|-		\|-
	! {{t\|cúaq\|\|#9NfM8JXeD}}		! {{unofficial\|{{t\|cúaq\|\|#9NfM8JXeD}}}}
	\| ~~(Unofficial:)~~ ‘the concept of satisfying property’. Always refers to that one concept		\| ‘the concept of satisfying property’. Always refers to that one concept
	\|-		\|-
	! {{t\|ꝡáı\|\|#xvC8-FhEy}}		! {{unofficial\|{{t\|ꝡáı\|\|#xvC8-FhEy}}}}
	\| ~~(Unofficial:)~~ ‘the (aforementioned or not)’. To be understood as a hypernym of {{t\|hú}} and {{t\|ké}}		\| ‘the (aforementioned or not)’. To be understood as a hypernym of {{t\|hú}} and {{t\|ké}}
	\|-		\|-
	! {{t\|tóꝡaı\|\|#SaSWb3ZIb}}		! style=white-space:nowrap \| {{unofficial\|{{t\|tóꝡaı\|\|#SaSWb3ZIb}}}}
	\| ~~(Unofficial:)~~ ‘the unique’		\| ‘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.		{{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.

Uakci: add túq, (tó)ꝡaı; flesh out denotations for the ℩… functionals

2024-02-07T09:58:54Z

add túq, (tó)ꝡaı; flesh out denotations for the ℩… functionals

← Older revision		Revision as of 09:58, 7 February 2024
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	! {{t\|báq}}		! {{t\|báq}}
	\| Always resolves to the associated [[kind]]. {{t\|báq kanı}} is always a singular ‘rabbit-kind’		\| Always resolves to the associated [[kind]]. {{t\|báq kanı}} is always a singular ‘rabbit-kind’
			\|-
			! {{t\|túq}}
			\| ‘all’; ‘the totality of’
	\|-		\|-
	! {{t\|cúaq\|\|#9NfM8JXeD}}		! {{t\|cúaq\|\|#9NfM8JXeD}}
	\| (Unofficial:) ‘the concept of satisfying property’. Always refers to that one concept		\| (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.		{{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		as
	<blockquote>		<blockquote>
	𝑃(℩◻(𝑄))		𝑃(℩<sub>◻</sub>(𝑄))
	</blockquote>		</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		Then, any free determiner phrase is definite if all indices inside it are

Uakci: hóbo → hobo

2023-12-03T18:03:45Z

hóbo → hobo

← Older revision		Revision as of 18:03, 3 December 2023
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	So for example, the following examples are all definite:		So for example, the following examples are all definite:
	* {{t\|pó sá}} ({{t\|sá}} is contained within {{t\|po}}’s internal CPᵣₑₗ, hence does not escape)		* {{t\|pó sá}} ({{t\|sá}} is contained within {{t\|po}}’s internal CPᵣₑₗ, hence does not escape)
	* {{t\|ké kune bï, cho jí <u>réo ~~hóbo~~</u>}} ({{t\|hóbo}} points to {{t\|ké kune}}, which is itself definite)		* {{t\|ké kune bï, cho jí <u>réo hobo</u>}} ({{t\|hóbo}} points to {{t\|ké kune}}, which is itself definite)

Uakci: speaker → hearer

2023-12-02T19:14:00Z

speaker → hearer

← Older revision		Revision as of 19:14, 2 December 2023
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	{\| class=wikitable		{\| class=wikitable
	! {{t\|hú}}		! {{t\|hú}}
	\| ‘the aforementioned’. Always resolves to one concrete thing, even if that thing might not be clear to the ~~speaker~~		\| ‘the aforementioned’. Always resolves to one concrete thing, even if that thing might not be clear to the hearer
	\|-		\|-
	! {{t\|ké}}		! {{t\|ké}}

Uakci: Created page with "== Determiners == The following determiners are '''definite''', which means that they refer to one concrete things and not multiple possible thingses, like with {{t|sá}}. In other words, they act like constants. {| class=wikitable ! {{t|hú}} | ‘the aforementioned’. Always resolves to one concrete thing, even if that thing might not be clear to the speaker |- ! {{t|ké}} | ‘the not aforementioned’. Same as above |- ! {{t|báq}} | Always reso..."

2023-12-02T18:59:56Z

Created page with "== Determiners == The following determiners are '''definite''', which means that they refer to one concrete things and not multiple possible thingses, like with {{t|sá}}. In other words, they act like constants. {| class=wikitable ! {{t|hú}} | ‘the aforementioned’. Always resolves to one concrete thing, even if that thing might not be clear to the speaker |- ! {{t|ké}} | ‘the not aforementioned’. Same as above |- ! {{t|báq}} | Always reso..."

New page

== [[Determiner]]s ==
The following determiners are '''definite''', which means that they refer to one concrete [[Plural_logic|things]] and not multiple possible thingses, like with {{t|sá}}. In other words, they act like constants.
{| class=wikitable
! {{t|hú}}
| ‘the aforementioned’. Always resolves to one concrete thing, even if that thing might not be clear to the speaker
|-
! {{t|ké}}
| ‘the not aforementioned’. Same as above
|-
! {{t|báq}}
| Always resolves to the associated [[kind]]. {{t|báq kanı}} is always a singular ‘rabbit-kind’
|-
! {{t|cúaq||#9NfM8JXeD}}
| (Unofficial:) ‘the concept of satisfying property’. Always refers to that one concept
|}
{{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.

== Semantics jank ==
We say a noun phrase is '''definite''' if it’s a function of just one plural constant.

For a clause like {{t|{{small caps|P}} {{class|sá}} {{small caps|Q}}}}, where the quantifier is represented as ◻, if we’re able to rephrase the usual denotation
<blockquote>
[◻𝑥 : 𝑄𝑥] 𝑃𝑥
</blockquote>
as
<blockquote>
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.

Then, any free determiner phrase is definite if all indices inside it are
* bound inside the 𝑛P
* bound outside the 𝑛P, to a phrase that is itself transitively definite
So for example, the following examples are all definite:
* {{t|pó sá}} ({{t|sá}} is contained within {{t|po}}’s internal CPᵣₑₗ, hence does not escape)
* {{t|ké kune bï, cho jí <u>réo hóbo</u>}} ({{t|hóbo}} points to {{t|ké kune}}, which is itself definite)