ABSTRACT
Quantificational logic studies arguments whose validity depends on “all,” “no,” “some,” and similar notions.1 This chapter covers the basics, and the next adds relations and identity.
To help us evaluate quantificational arguments, we’ll construct a little quantificational language. Our language builds on propositional logic and includes all the vocabulary, wffs, inference rules, and proofs of the latter. We add two new vocabulary items: small letters and “ .” Here are sample formulas:
“Romeo is Italian” is “Ir”; we write the capital letter first. Here “I” is for the general category “Italian” and “r” is for the specific individual “Romeo”:
Capital and small letters have various uses in our quantificational language. Capitals can represent statements, general terms, or relations (but we won’t study relations until the next chapter):
Similarly, small letters can be constants or variables:
A variable stands for an unspecified person or thing. “Ix” (“x is Italian”) is incomplete, and thus not true or false, since we haven’t said whom we are talking about; but we can add a quantifier to complete the claim.
