### Sense and reference

If we change the sense of a turn, we may change its reference as well. (Not always: if we change the sense of X from "the evening star" to "the morning star," X still refers to the same thing!)

But we have not changed any of the facts about what X used to refer to. So if we were to change the sense of the term "cat" to "a large, leaping Australian marsupial," it would henceforth refer to what we now call kangaroos. But that does not mean that the non-human mammal currently living in my house will suddenly have a pouch! Similarly, if we define a new mathematical symbolism, call it Mnew , that is the same as ours (which we can call Mold) for the first use of number, but every subsequent time it is mentioned, its value goes up by one, so that in Mnew, 2 + 2 = 5, since the second '2' means what '3' means in Mold. That 2 + 2 = 4 is always true in ordinary arithmetic, whatever symbols we choose to employ for the concepts involved, so, we are saying the same thing when we say "II + II = IV", or "dos más dos es igual a cuatro." But in Mnew we are talking about different concepts when we write 2 + 2 = 5. The fact that in this different language the symbols don't mean the same thing as in Mold, and different propositions turn out to be true, should not be very surprising if properly understood.

Nor does the fact that the definition of a term is merely conventional mean that there is no correct or incorrect applications of the term! Given our current definition of "cat," it is correct call the creature who haunts all our waking hours with its meows a cat, and incorrect to say it is a kangaroo. Thinking again about other languages should make this obvious: it is correct to call our hosted mammal 'cat' if we are speaking English, but not if we are speaking Spanish or Russian! If I say "ore" in Yoruba, I am talking about my friend, but if I then switch to English, and say "Ore is metallic," it does not make it true that my friend is metallic.