On pp. 273-274, the book says that I[d/c] is "just like the interpretation I except it also assigns the name c to the object d". In the more official statement on the top of p. 274, it is not said c should be a new/newly interpreted name. But I was more surprised about the idea of interpretations assigning names to objects. I had expected to read it the other way round, namely, that I[d/c] also assigns to the name c the object d. At first I thought perhaps my English is deficient here, but then the book repeatedly says that truth-values are assigned to sentence letters. By analogy then, interpretations should assign objects to names, right? This is only a minor point. But it may create a little confusion in the students. For instance, an object may have several names, but in logic a name refers only to a single object – assignments are functional. (I am wondering whether it would be good to phrase the definition of an interpretation on p. 266 a little bit more formally. The "we care to consider" phrase means that interpretations are partial functions, right? Perhaps clause 2 should substitute "an assignment of a truth value" for "a truth value" in order to align it better with the other clauses.
rzach
commented
5 months ago
On pp. 273-274, the book says that I[d/c] is "just like the interpretation I except it also assigns the name c to the object d". In the more official statement on the top of p. 274, it is not said c should be a new/newly interpreted name. But I was more surprised about the idea of interpretations assigning names to objects. I had expected to read it the other way round, namely, that I[d/c] also assigns to the name c the object d. At first I thought perhaps my English is deficient here, but then the book repeatedly says that truth-values are assigned to sentence letters. By analogy then, interpretations should assign objects to names, right? This is only a minor point. But it may create a little confusion in the students. For instance, an object may have several names, but in logic a name refers only to a single object – assignments are functional. (I am wondering whether it would be good to phrase the definition of an interpretation on p. 266 a little bit more formally. The "we care to consider" phrase means that interpretations are partial functions, right? Perhaps clause 2 should substitute "an assignment of a truth value" for "a truth value" in order to align it better with the other clauses.