Lexicon of Arguments

 

I 159
Names/Pronouns/Bigelow/Pargetter: we have allowed a name to be replaced by a pronoun.
>Names, >Pronouns, >Ontology.
Example:

The stock market in Japan has collapsed.
The stock market in it has collapsed.

>Anaphora, >Index words, >Indexicality.
Quantification/Name/Pronoun/Bigelow/Pargetter: after we have replaced the name with a pronoun, we can quantify via it. Example:
For each country: the stock market in it has collapsed.
Quantification of 2nd level/logic of 2nd level/Bigelow/Pargetter: then one might ask, why should this not also work for predicates, if it is possible for names?
The idea goes like this: we start with a sentence, for example:
The Wombat is sleeping tonight.
I 160
Then we replace the predicate with a pronoun:
The Wombat it today.
Instead of a pronoun, we will take something better:
The Wombat is doing whatnot today.
Then we quantify:
For a whatnot, the Wombat is doing whatnot today.
Formally: we introduce a new variable (Greek letters)ψ, ψ 1, ψ 2,... then we replace each predicate of an atomic formula to provide another atomic formula: so
Fa equi Fb
becomes
ψa ⇔ ψb.
Then we will put a quantifier of the 2nd level in front of it:
(ψ)(ψa ⇔ ψb).
Translation into everyday language: "for something, a is doing whatnot iff b is doing whatnot".