Mix flour, salt, ginger, baking soda, nutmeg and allspice in a medium bowl. In a large mixmaster bowl, beat together the molasses, shortening and brown sugar.Combine hot water and rum.
To the sugar-molasses mixture, add alternately the dry ingredients and the diluted rum. (If the dough is dry, add an additional tablespoon or two of water, one at a time.)
Roll out the dough between two sheets of waxed paper until 1/4 inch thick. Refrigerate for at least two hours. If desired, refrigerated dough may then be put into freezer bags and frozen for later use).
Preheat oven to 375 degrees F. Grease 2 baking sheets.
Cut the dough into 3-inch cookies with a cookie cutter (or coffee can for the traditional larger size). Place them on greased baking sheets. Bake at 375 for 10 -12 minutes. Cookies should be dark around the edges and firm in centers. Set baking sheet on a rack to cool for 3 minutes. Then remove the cookies to a rack to cool completely.