Newbie question: what does the term "For all x ..." mean here?

The argument could be written in ordinary English as follows:

  • Charlie believes anything Thomas said.

  • Thomas said A.

  • So, Charlie believes A.

The "for all x" language is useful for more complicated sentences which are difficult to write in ordinary English. For example, I don't know an easy way to say the following sentence in ordinary English:

  • For any numbers x, y, and z: (x+y)+z = (y+z)+x

Why did the author use the "for all x" language in this particular example when he could have just as easily used ordinary English? It's hard to say without knowing the context. Some philosophers have a tendency to use logical notation where it isn't really needed.

/r/askphilosophy Thread