I am indebted here to conversations with N.J.J. Smith, and some correspondence years ago with Susan Haack. My main contention here should not be attributed to either of them though - at least, not on the basis of this post.
I believe that the Tarskian device of using sequences of numbers in the definition of satisfaction in first order logic, and in turn of truth, is stupid. (For information about this device, see here or just Google it.) Either it is the product of philosophical confusion, or it panders to philosophical confusion.
Some believe otherwise. For instance, Peter Milne in his 'Tarski, Truth and Model Theory' calls it a 'stroke of genius':