Final answer:
Benjamin Franklin's story of the smith symbolizes the importance of perseverance in character improvement, as the man in the story ceases his effort to perfect the ax and settles for a 'speckled' one, reflecting a compromise of ideals.
Step-by-step explanation:
The main idea Franklin is trying to convey through the story of the smith is a lesson about perseverance and commitment to self-improvement. Franklin uses the anecdote to illustrate that working diligently towards polishing one's character, much like the painstaking process of grinding an ax, is arduous but necessary for achieving one's desired level of accomplishment. The speckled ax represents a compromise of these ideals, as the man settles for an imperfect ax rather than continuing the challenging work needed to make it fully bright. The anecdote suggests that Franklin believes in the importance of continuous effort, despite difficulties and temptations to settle for mediocrity.