7.6. Arguments involving restricted universals

7.6.0. Overview

Since a restricted universal is equivalent to an unrestricted universal applied to a conditional formula, its logical properties are analogous in some respects to those of universals and in other respects to those of conditionals.

7.6.1. Principles for restricted universals
A restricted universal behaves like an indefinitely long conjunction of conditionals and the principles governing it derive from this fact.

7.6.2. Derivations for restricted universals
The principles for restricted universals can be implemented either by a group of four rules analogous to those for conditionals (but also reflecting rules for unrestricted universals) or by rules for restating restricted universals in unrestricted form or vice versa.

Glen Helman 25 Aug 2005