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{{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. | {{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. | ||
This can lead to surprising behavior | 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|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)". | {{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> is popular in discussions of 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: | |||
* 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}}. | |||