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|sá}} “some” is a determiner, {{t|bıo}} “…is a cup” is a predicate phrase, and {{t|sá bıo}} 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]].
+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).”
 == Determiner particles ==
@@ Line 8: / Line 9: @@
 ! Word !! Meaning
 |-
-| {{done|2}} || X (bound to something)
+| {{done|2}} || X (bound; see below)
 |-
 | {{t|sá}} || some X
 |-
-| {{t|tú}} || every/each X
+| {{t|tú}} || every/each single X
 |-
-| {{t|túq}} || all X
+| {{t|tútu}} || every group of X-es (see below)
+|-
+| {{t|túq}} || all the Xs together
 |-
 | {{t|sía}} || no X
+|-
+| {{t|ní}} || this/that X
 |-
 | {{t|hú}} || endophoric determiner
@@ Line 24: / Line 29: @@
 | {{t|báq}} || X in general, X-[[kind]]
 |-
-| {{t|já}} || λX
+| {{t|já}} || λX, see [[Property]]
 |-
-| {{t|hı}} || which X?
+| {{t|hí}} || which X?
 |}
@@ Line 41: / Line 46: @@
 <math>
     {\color{brown}     \underbrace{\exists \textsf{bio}:}_{1}}
-\; {\color{chocolate} \underbrace{\textrm{Bio}(\textsf{bio}) \mathop\wedge}_{2}}
+\; {\color{chocolate} \underbrace{\textrm{Cup}(\textsf{bio}) \mathop\wedge}_{2}}
 \; \textrm{Heaq}(\textsf{ji},
      {\color{teal}     \underbrace{\textsf{bio}}_{3}}
@@ Line 50: / Line 55: @@
 === Every, each, all ===
-{{t|tú bıo}} 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|bio}}, after 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.
-This can lead to surprising behavior: see below.
-{{t|tushı bỉo}} quantifies over "cups-es that are one", i.e. '''each''' individual cup. It's like {{t|tu bỉo ru shỉ}}.
-{{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|Zủdeq tu pỏq sa zủ}} means "every person speaks ''some'' language", where possibly each person speaks a different one. Certainly, presenting sentences such as <math>\forall x, \exists y: P(x,y)</math> and assigning them this interpretation is popular in discussions of ''singular'' predicate logic.
-But because the plural-logic {{t|tu pỏq}} ranges over all "people-s", i.e. all groups of people, it also includes the referent "''all'' relevant people together". Consequently, this sentence ends up saying that all people speak at least some ''common'' language(s), namely whichever {{t|sa zủ}} these maximal {{t|póq}} speak.
-As a concrete demonstration, if there are three people P1, P2, P3 in question, then {{t|Zủdeq tu pỏq sa zủ}} claims all of the following:
-* There is/are some language(s) Z1, that P1 speaks.
+You can read {{t|tútu bıo nä …}} as: "for all ''xx'', if ''xx'' are some cups…"
-* There is/are some language(s) Z2, that P2 speaks.
-* There is/are some language(s) Z3, that P3 speaks.
-* There is/are some language(s) Z4, that [P1 {{t|roı}} P2] speak.
-* There is/are some language(s) Z5, that [P1 {{t|roı}} P3] speak.
-* There is/are some language(s) Z6, that [P2 {{t|roı}} P3] speak.
-* There is/are some language(s) Z7, that [P1 {{t|roı}} P2 {{t|roı}} P3] speak. (= a common language! ⚠️)
-You can explicitly quantify over ''single'' people to get the intended meaning: {{t|Zủdeq tushı pỏq sa zủ}}.
+{{t|túq bıo}} doesn't make a "for-all" statement. Instead it refers to the single entity "all cups (together)".