Place raspberries in work bowl of a food processor, and process until smooth. If an extra smooth sorbet is desired, press pureed raspberries through a fine sieve to remove seeds. Whisk together pureed raspberries and honey in a large bowl.
Combine 3 cups of water, sugar, and corn syrup in a large saucepan; stir to combine. Bring to a boil over high heat. Boil until sugar is dissolved, about 2 minutes; do not stir. Stir the sugar water and the remaining 1 cup of water into the raspberry puree.
Make an ice bath by filling a very large bowl with water and ice. Set the bowl of raspberry puree in the ice bath, and whisk until cool. Pour cooled puree into a 9x13 baking dish, and cover; freeze until solid, 6 to 8 hours.
To make a coarsely textured granita, use a fork to scrape frozen puree into small crumbs. For a deliciously silky sorbet, transfer frozen puree to a food processor and process until smooth.
