Notation

I got a question concerning notation for evaluating multiple variables with respect to an assignment. In case others were unsure about what to do, I thought I would post the standard notation. g(x/d1) is the function just like g except it assigns d1 to 'x'. g(x/d1)(y/d2) is the function just like g except that it assigns d1 to 'x' and d2 to 'y'. So, for example, when working on problem 4, you will need to consider g(x/d) for all d in D. In order to do that, you'll need to consider g(x/d)(y/d) for some d in D. In M, there are four options here: g(x/d1)(y/d1), g(x/d1)(y/d2), g(x/d2)(y/d1), and g(x/d2)(y/d2). Hopefully this will make sense when you get to problem 4. If not, comment on this post.

I also received a question about how to think about the terms in FOPL. It is helpful to think that individual constants behave like proper names in English and variables behave like indexicals or demonstratives. So here are two ways of saying the same thing:

Albert is fat.
That is fat. (or 'He is fat'.)

The first may be symbolized in a language like FOPL as 'Fa'; the second as 'Fx'. You can think of the assignment function as something like a context; with respect to different contexts, the second displayed sentence above will say different things. But (ignoring the fact that many people have the same name) the first displayed sentence says the same thing with respect to any context. So a "model" of English would determine the meaning of the first displayed sentence all by itself. But it would not determine the second; for that, we need a context (assignment).

If this last bit is more confusing than helpful, then just ignore it.