5.1 Predicate Logic

1. 5.1 Predicate Logic Gregory Chapter 5

2. 5.1.1 Introducing P The language of Predicate Logic

3. 5.1.1 Quantificational Logic • What Propositional Logic can’t do • All humans are mortal • Socrates is human • Socrates is mortal • Quantificational Logic is the logic of sentences involving quantifiers, predicates, and names. It investigates the properties that arguments, sentences, and sets of sentences have in virtue of their quantificational structure.

4. 5.1.2 Predicates and Singular Terms • Subject-Predicate sentences • Socrates is human • Seven is less than twenty • A singular term is a word or phrase that designates or is supposed to designate some individual object. Natural language singular terms are either proper nouns or definite descriptions (a phrase that is supposed to designate an object via a unique description of it) • A predicate is a series of words with one or more blanks that yields a sentence when all its blanks are filled with singular terms. Conversely, we could think of a predicate as what remains after removing one or more singular terms from a sentence.

5. 5.1.3 Predicate Letters & Individual Constants • Predicate Letters: uppercase letters ‘A’ through ‘Z’ • Individual Constants: lowercase letters ‘a’ through ‘u’ • Variables: lowercase letters ‘v’ through ‘z’ • An interpretation of P consists of 3 components: • (1)  a non-empty universe of discourse, UD, specifying the things about which we’ll be talking • (2)  an assignment of truth values or natural language statements to statement letters and of natural language predicates to predicate letters via a translation key • (3)  an assignment of objects from the UD to constants via a translation key such that • (a) every individual constant is assigned to an object, and • (b) no individual constant is assigned to more than one object

6. 5.1.4 Pronouns & Quantifiers

7. 5.1.5 Variables & Quantifiers

8. 5.2 The Syntax of P