4.1 Transitive and intransitive verbs

• A simple intransitive verb example
  1. John walks.
  2. $\mathrm{\:\bf Walk\:}(\mathrm{\:j\:})$
  1. $\lbrack\!\lbrack \mathrm{\:John walks\:} \rbrack\!\rbrack = \mathrm{\:true\:} ... ...n\:} \rbrack\!\rbrack \in \lbrack\!\lbrack \mathrm{\:walks\:} \rbrack\!\rbrack$
  2. $\lbrack\!\lbrack \mathrm{\:\bf Walk\:}(\mathrm{\:j\:}) \rbrack\!\rbrack = \mat... ...j\:} \rbrack\!\rbrack \in \lbrack\!\lbrack \mathrm{\:walks\:} \rbrack\!\rbrack$

• Points of interest
  • $\lbrack\!\lbrack \mathrm{\:\bf Walk\:} \rbrack\!\rbrack$ is a set, just the way $\lbrack\!\lbrack \mathrm{\:walks\:} \rbrack\!\rbrack$ was in our little extensional mini-semantics in Chapter 1.
  • Later we will want to replace such extensional denotations with intensional denotations just the way we did in Chapter 1.
  • The important thing is (4.1a). The fact that we redo this semantics in logical notation in (4.1b) is just a convenience.
  • The is not to translate English into logic. The goal is to give English sentences a semantics. (4.1b) doesn't do this any better than (4.1a).
  • The logical notation is just a convenience for helping us get our heads clear.
  • Historically the program of giving a language a clear and complete semantics comes from logic. THis is why logic has some useful ideas for us.
• Transitive verb
  1. John loves Mary
  2. $\mathrm{\:\bf Love\:}(\mathrm{\:j\:},\:\mathrm{\:m\:})$