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Suppose we take a picture containing a full image of a duck and slice it right through, leaving some of the duck image (including its head) on one slice and some of it on the other. How many duck images will we be left with? Received theories of pictorial representation presuppose that a surface cannot come to contain new images just by changing its physical relations with other surfaces, such as physical continuity. But as it turns out, this is in tension with received theories’ approach to incomplete images. I address three views with respect to the circumstances in which incomplete images of X represent X. 1. A liberal, non-restrictive view: ‘Iff they meet relevant requirements posed by received theory of pictorial representation.’ 2. Moderate restrictions of this view (‘iff they meet requirements posed by theory of pictorial representation and...’) and 3. A fully restrictive view (‘never’). After investigating challenges for the liberal view, I end up supporting it. The main challenges rest on the fact that only the fully restrictive view can plausibly accommodate some principles that seem inherent to our theory of representation. For instance: only this view accommodates received theories’ presupposition that the representational properties of a surface depend on its configurational properties such that new images may appear on a surface only if its configurational properties have changed. Since the liberal view is overall more plausible than the restrictive view, I reject this presupposition and bear the consequences.

DOI: 10.1007/s11229-015-0981-0

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