Using the 'set_exception_handler' function within a class, the defined 'exception_handler' method must be declared as 'public' (preferrable 'public static' if you use the "array('example', 'exception_handler')" syntax). 

<?php
class example {
    public function __construct() {
        @set_exception_handler(array('example', 'exception_handler'));
        throw new Exception('DOH!!');
    }

    public static function exception_handler($exception) {
        print "Exception Caught: ". $exception->getMessage() ."\n";
    }
}

$example = new example;

echo "Not Executed\n";
?> 

Declaring the 'exception_handler' function as 'private' causes a FATAL ERROR.

[derick: red. updated statement about static a bit]