Determiner: Difference between revisions

Latest revision as of 22:41, 5 February 2024

A determiner is a particle that consumes a verb form and produces a noun form — specifically, a determiner phrase.

For example: sá “some” is a determiner, bıo “…is a cup” is a predicate phrase, and sá bıo is a noun form meaning “some cup(s).”

Determiner particles

Word	Meaning
	X (bound; see below)
sá	some X
tú	every/each single X
tútu	every group of X-es (see below)
túq	all the Xs together
sía	no X
ní	this/that X
hú	endophoric determiner
ké	exophoric determiner
báq	X in general, X-kind
já	λX, see Property
hí	which X?

Semantics

Formally, grammatical determiners tend to correspond to logical quantifiers over a now-bound variable, plus an occurrence of that variable. For example, the sa determiner corresponds to the $\exists$ quantifier. The tagged predicate phrase doubles both as a domain and a name for the variable.

In short, sá bıo does three things:

introduces an existentially bound variable bío to the clause;
specifies that it refers to a cup (or some cups: see plural logic);
acts in its place in the sentence as an instance of this variable.

Heaq jí sá bıo.
${\color {brown}\underbrace {\exists {\textsf {bio}}:} _{1}}\;{\color {chocolate}\underbrace {{\textrm {Cup}}({\textsf {bio}})\mathop {\wedge } } _{2}}\;{\textrm {Heaq}}({\textsf {ji}},{\color {teal}\underbrace {\textsf {bio}} _{3}})$
I'm holding some cup(s).

Every, each, all

tú bıo quantifies over single cups, i.e. each individual cup. This is often what we want to say, despite not being the "purest" form of for-all quantification in plural logic; after all, groups of several cups are also bıo. The expression tútu bıo quantifies over the range of "cups-es": the possible values of bío then include not only individual cups, but also groups of cups.

You can read tútu bıo nä … as: "for all xx, if xx are some cups…"

túq bıo doesn't make a "for-all" statement. Instead it refers to the single entity "all cups (together)".

@@ Line 1: / Line 1: @@
-A '''determiner''' is a particle that consumes a predicate phrase and produces a noun phrase.
-For example: {{t|sa}} “some” is a determiner, {{t|bỉo}} “…is a cup” is a predicate phrase, and {{t|sa bỉo}} is a noun phrase meaning “some cup(s)”.
+A '''determiner''' is a particle that consumes a [[verb form]] and produces a [[noun form]] — specifically, a [[determiner phrase]].
-Semantically, these particles tend to correspond to logical '''quantifiers''' over a now-bound variable, plus an occurence of that variable. For example, the {{t|sa}} determiner corresponds to the <math>\exists</math> quantifier. The tagged predicate phrase doubles both as a ''domain'' and a ''name'' for the variable.
+For example: {{t|sá}} “some” is a determiner, {{t|bıo}} “…is a cup” is a predicate phrase, and {{t|sá bıo}} is a noun form meaning “some cup(s).”
-In short, {{t|sa bỉo}} does three things:
-# <span style="color:brown">introduces</span> an existentially bound variable {{t|bío}} to the clause;
-# <span style="color:chocolate">specifies</span> that it refers to a cup (or some cups: see [[plural logic]]);
-# acts in its place in the sentence as an <span style="color:teal">instance</span> of this variable.
-<blockquote>
-{{t|Hẻaq jí <u>sa bỉo</u>.}}<br>
-<math>
-   {\color{brown}     \underbrace{\exists \textsf{bio}:}_{1}}
-\; {\color{chocolate} \underbrace{\textrm{Bio}(\textsf{bio}) \mathop\wedge}_{2}}
-\; \textrm{Heaq}(\textsf{ji},
-    {\color{teal}     \underbrace{\textsf{bio}}_{3}}
-   )
-</math><br>
-I'm holding some cup(s).
-</blockquote>
 == Determiner particles ==
@@ Line 27: / Line 9: @@
 ! Word !! Meaning
 |-
-| {{t|sa}} || some X
+| {{done|2}} || X (bound; see below)
+|-
+| {{t|sá}} || some X
+|-
+| {{t|tú}} || every/each single X
 |-
-| {{t|tu}} || every X
+| {{t|tútu}} || every group of X-es (see below)
 |-
-| {{t|tushı}} || each X
+| {{t|túq}} || all the Xs together
 |-
-| {{t|tuq}} || all X
+| {{t|sía}} || no X
 |-
-| {{t|sıa}} || no X
+| {{t|ní}} || this/that X
 |-
-| {{t|ke}} || the X
+| {{t|hú}} || endophoric determiner
 |-
-| {{t|hoı}} || the aforementioned X
+| {{t|ké}} || exophoric determiner
 |-
-| {{t|baq}} || X in general, X-[[kind]]
+| {{t|báq}} || X in general, X-[[kind]]
 |-
-| {{t|hı}} || which X?
+| {{t|já}} || λX, see [[Property]]
 |-
-| {{t|ja}} || λX
+| {{t|hí}} || which X?
 |}
-Additionally, {{tone|2}} can be analyzed as a tonal pseudo-determiner that refers to bound variables, or falls back to "implicitly-bound" {{t|ke X}} if there is no earlier binding.
+== Semantics ==
+Formally, grammatical determiners tend to correspond to logical '''quantifiers''' over a now-bound variable, plus an occurrence of that variable. For example, the {{t|sa}} determiner corresponds to the <math>\exists</math> quantifier. The tagged predicate phrase doubles both as a ''domain'' and a ''name'' for the variable.
-=== Every, each, all ===
+In short, {{t|sá bıo}} does three things:
-{{t|tu bỉo}} quantifies over the range of "cups-es". The possible values of {{t|bío}} include not only individual cups, but also groups of cups. A group of cups is also a {{t|bỉo}}, after all.
+# <span style="color:brown">introduces</span> an existentially bound variable {{t|bío}} to the clause;
+# <span style="color:chocolate">specifies</span> that it refers to a cup (or some cups: see [[plural logic]]);
+# acts in its place in the sentence as an <span style="color:teal">instance</span> of this variable.
-This can lead to surprising behavior: see below.
+<blockquote>
+{{t|Heaq jí <u>sá bıo</u>.}}<br>
+<math>
+   {\color{brown}     \underbrace{\exists \textsf{bio}:}_{1}}
+\; {\color{chocolate} \underbrace{\textrm{Cup}(\textsf{bio}) \mathop\wedge}_{2}}
+\; \textrm{Heaq}(\textsf{ji},
+    {\color{teal}     \underbrace{\textsf{bio}}_{3}}
+   )
+</math><br>
+I'm holding some cup(s).
+</blockquote>
-{{t|tushı bỉo}} quantifies over "cups-es that are one", i.e. '''each''' individual cup. It's like {{t|tu bỉo ru shỉ}}.
+=== Every, each, all ===
+{{t|tú bıo}} quantifies over single cups, i.e. each individual cup. This is often what we want to say, despite not being the "purest" form of for-all quantification in [[plural logic]]; after all, ''groups'' of several cups are also {{t|bio}}. The expression {{t|tútu bıo}} quantifies over the range of "cups-es": the possible values of {{t|bío}} then include not only individual cups, but also groups of cups.
-{{t|tuq bỉo}} doesn't make a "for-all" statement. Instead it refers to the single entity "all cups (together)".
-=== Inappropriate {{t|tu}} ===
-You might think that {{t|Nẻo tu bỉo sa tỏqfua}} means "every cup is on ''some'' table", where possibly each cup is on its own table. Certainly, presenting sentences such as <math>\forall b, \exists t: N(b,t)</math> and assigning them this interpretation is popular in discussions of ''singular'' predicate logic.
-But because the plural-logic {{t|tu bỉo}} ranges over all "cups-es", i.e. all groups of cups, it also includes the referent "{{t|bío}} = ''all'' relevant cups together". Consequently, this sentence ends up saying that all cups are on the ''same'' table, namely whichever {{t|sa tỏqfua}} this maximal {{t|bío}} is on.
-As a concrete demonstration, if there are three cups B1, B2, B3, then {{t|Nẻo tu bỉo sa tỏqfua}} claims all of the following:
+You can read {{t|tútu bıo nä …}} as: "for all ''xx'', if ''xx'' are some cups…"
-* There is some table that B1 is on.
-* There is some table that B2 is on.
-* There is some table that B3 is on.
-* There is some table that [B1 {{t|roı}} B2] are on.
-* There is some table that [B1 {{t|roı}} B3] are on.
-* There is some table that [B2 {{t|roı}} B3] are on.
-* There is some table that [B1 {{t|roı}} B2 {{t|roı}} B3] are on. (So they are all on the same table!)
-You can explicitly quantify over single cups to get the intended meaning: {{t|Nẻo tushı bỉo sa tỏqfua}}.
+{{t|túq bıo}} doesn't make a "for-all" statement. Instead it refers to the single entity "all cups (together)".