For years I have heard individuals dismiss the validity of logic by making the following proposition: This proposition is incorrect. The recent Radiolab show Loops discussed this. The idea is that because this statement can be neither true nor false, there is something empty about all logic, and something vapid about every statement. Or, at least, the claim is that logic has its limitations.
Someone probably offered this response decades ago, but I haven't heard it yet, so here it goes.
A tool cannot be used upon itself, and logic is a tool. By simply stating that a proposition is automatically false, you are trying to use logic against logic, and that is not how tools work. Suppose I have a hammer and tell you that you can hit anything within your reach with that hammer. You then ask me, "Can I hit the hammer with the hammer?" I answer impatiently, "No." But I am not responding to a clever argument. It is implicit when using tools that the tool cannot be used upon itself, because it is so obvious that it can't.
You can't hit a hammer with the same hammer, and you cannot make an proposition that the proposition is false. Both the hammer and proposition are tools used for other endeavors, and should only be judged in their ability to do so.
