Cook potatoes until tender in 2 c. water. While cooking, add salt, pepper, onion and celery salts.
Drain. Add milk and remaining 2 c. water to the drained, seasoned potato water. Heat to boiling; simmer.
While liquid simmers, cut butter into flour until mixture looks like crumbs. Brown these in small heavy skillet, stirring constantly. Stir browned crumbs into hot liquid; cook about 5 minutes, stirring.
Add potatoes, and heat about 5 minutes more. Serve hot.