N. Goodman and W. V. Quine, "Steps Toward a Constructive Nominalism",Journal of Symbolic Logic, 12 (1947).## 7. Variables and Quantification

A variable of our object language is a vee, or a vee together with a string of one or more accents following it. We first define a string of accentsas any inscription of which every part that is a character is an accent.

- D13.
- AcString
x=. Inscx& (z)(Segzx& Charz.--> Acz).The definition of a variableis then readily formulated.

- D14.
- Vbl
x=. VeexV (]y)(]z)(Veey& AcStringz& Cxyz) .A variable is a vee or the result of concatenating a vee with a string of accents.

A quantifier will be simply a variable in parentheses. But it is more useful to define a string of(one or more)quantifiersdirectly. A method for doing this becomes evident when we reflect that any inscription will be a string of quantifiers if it begins and ends with facing parentheses and is such that every pair of facing parentheses within it frames an inscription that is either a variable or contains parentheses back to back.

- D15.
- QfrString
x= (]y)(]z){LPary& RParz& (]w)Cxywz& (s)(t)(u)(k)[LPart& RPark& Segsx.-->: ~Cstk: Cstuk.-->. VbluV (]p)(]q)(]r)(RParq& LParr& Cpqr& Segpu)]}.Then let us call xaquantification of yifxconsists of a string of quantifiers followed byy.

- D16.
- Qfn
xy= (]z)(QfrStringz& Cxzy) .Contents -- Go to §8