Bring potatoes, 3 1/2 cups water, and 1 1/2 teaspoons salt to a boil in a large saucepan. Cover, reduce heat, and simmer 30 minutes or until tender; drain and cool 5 minutes. Peel potatoes, if desired; place in a bowl.
Melt 2 tablespoons butter in saucepan; add celery and onion, and saute until tender.
Add celery mixture to potatoes; beat at low speed with an electric mixer until blended. Add remaining butter, milk, remaining 1/4 teaspoon salt, and pepper; beat at high speed until fluffy (do not overbeat). Serve immediately.