Calling a javascript function recursively

I can create a recursive function in a variable like so:

/* Count down to 0 recursively.
 */
var functionHolder = function (counter) {
    output(counter);
    if (counter > 0) {
        functionHolder(counter-1);
    }
}

With this, functionHolder(3); would output 3 2 1 0. Let's say I did the following:

var copyFunction = functionHolder;

copyFunction(3); would output 3 2 1 0 as above. If I then changed functionHolder as follows:

functionHolder = function(whatever) {
    output("Stop counting!");

Then functionHolder(3); would give Stop counting!, as expected.

copyFunction(3); now gives 3 Stop counting! as it refers to functionHolder, not the function (which it itself points to). This could be desirable in some circumstances, but is there a way to write the function so that it calls itself rather than the variable that holds it?

That is, is it possible to change only the line functionHolder(counter-1); so that going through all these steps still gives 3 2 1 0 when we call copyFunction(3);? I tried this(counter-1); but that gives me the error this is not a function.