314 15 On Being Surprised Wittgenstein on Aspect-Perception, Logic, and Mathematics Juliet Floyd Wittgenstein’s remarks invoking aspect-perception mirror his overall development as a philosopher. While I do not want overly to geneti- cize the philosophical terrain connected with aspect-perception, I do think it worth emphasizing that the duck-rabbit of the Philosophical Investigations is only one kind of example of aspect-perception, and that some of the most vivid, natural, and compelling uses of the idea of see- ing aspects, interpreting one system in another, or being struck by a new aspect of a diagram, word, or sentence – as well as the earliest, most frequent, and systematic appearances of these themes in his philoso- phy – occur in Wittgenstein’s discussions of mathematics and logic. After a few remarks about the constructive nature of Wittgenstein’s preoccupation with pictures (Section 1 ), I consider the earliest pas- sage in his writing invoking puzzle-pictures (Section 2 ), then consider PI §§523–25 in relation to his earliest thoughts (Section 3), and inally look at how his uses of aspect-perception bridge the evolution in his thought from earlier to later (Section 4). 1. In his writings on logic and mathematics, Wittgenstein points recur- rently toward cases of seeing aspects anew, not to maintain that math- ematical objectivity is based upon intuition in anything like Kant’s sense, but instead to transform Kantian ideas about how mathemat- ics and logic structure our forms of perception and understanding. 9780521838436c15.indd 314 9780521838436c15.indd 314 10/21/2009 8:41:06 PM 10/21/2009 8:41:06 PM In William Day and Victor Krebs, Seeing Wittgenstein Anew: New Essa Seeing Aspects (Cambridge Univ. Press, 2010). Penultimate version; please cite final published version