recasting to timestamp from varchar

I am trying to re-cast a column as a timestamp>

ALTER TABLE sixty_min ALTER COLUMN time2 TYPE timestamp;
ERROR: column "time2" cannot be cast to type timestamp without time zone

The column time2 is currently a varchar. I actually do not want to mess with time zones, but it seems that postgres will not let me do this. The actual values in the column time2 look like this:

7/15/08 12:00

Is this possible?

Thanks in advance.