Stanley Lobel of Lobel's butcher shop in New York explains that a sharp knife means you have to make fewer cuts. A dull knife makes you work harder; several cuts are required where one or two would do.
It's really a simple law of averages: fewer cuts means fewer chances of cutting yourself over the long run. More cuts, and the risk goes up. A sharp knife will also cut more cleanly and precisely than a dull knife, and with much less chance of slippage.
A few other knife safety tips from the article: make sure you cut away from your body at all times, keep the handle of your knife (and your palm) dry, and don't leave knives in the sink where they can become hidden under soapy water.
Any other tips to add?
(Image: Emma Christensen)