UC Berkeley

In this dissertation, I develop a novel account of spatial experience that—unlike most contemporary theories of perception—situates our experience of space within a broader context of non-sensory cognitive activities. On my account, to perceive an object as square is, in part, to deploy an a priori Euclidean concept of squareness – a concept that features in, but is not derived from, experience. I use this rationalist analysis of spatial experience to shed light on three issues: the connection between Euclidean proof and our perception of physical objects; the distinction between primary and secondary qualities; and the challenge posed to the veridicality of our spatial experience by the findings of relativistic physics.

In light of the discovery of consistent non-Euclidean geometries and the empirical evidence that our own universe is not perfectly Euclidean, many have rejected the Kantian idea that Euclidean proof gives us a priori knowledge of physical space. But there does seem to be a cognitive connection between the theorems we prove in Euclidean geometry and the spatial features we perceive physical objects to have: having proven the Pythagorean theorem, a carpenter will expect a particular relation to hold among the lengths of the sides of a right triangle she is constructing from wooden beams. This suggests that we represent the empirical objects we perceive as subject to the results we obtain in the domain of Euclidean geometry, even if we no longer think that such representations are guaranteed to be correct.

In order to account for this phenomenon, I develop a view on which the concepts we employ in Euclidean proof are a priori, but also feature in perception. After setting out the motivations for this view and offering a brief sketch of its contours, in Chapter 1, I go on to defend its central claims in Chapters 2 and 3. I argue that our use of spatial concepts in Euclidean geometry shows that they cannot be derived from experience: certain aspects of these concepts, such as the idea of continuity built into our concept of a circle, outstrip anything we can glean from our sensory cognition. At the same time, I suggest, an experience of an object as square is one that deploys our a priori concept of squareness, and does so simply in virtue of its phenomenal character. That is, such an experience, independent of any causal relations it might bear to objects in the external world, represents its object as instantiating the very geometrical property about which we reason in Euclidean proof. It is this fact that explains why the carpenter takes the results of her a priori reasoning to apply to the empirical objects she perceives – her experience of shape has specific geometrical content built into it, in virtue of the a priori Euclidean concepts that feature in its content.

This account of spatial experience helps shed light on a topic with a long philosophical history: the distinction between primary and secondary qualities. In Chapter 4, I argue that, lacking any a priori grasp of a secondary quality like redness, we can represent that property only by way of its role in experience – as whatever property plays the relevant role in generating experiences of red. Since perception does not inform us which specific property is playing that role, we are left in the dark about the nature of the secondary qualities. By contrast, in the case of a primary quality like squareness, we are not constrained to represent the property by way of its role in experience. When we experience an object as square, we grasp the nature of the property represented, in virtue of our a priori concept of squareness – the property of having four equal sides joined at four right angles. Color and shape, then, feature in our cognitive lives in very different ways; these conceptual and experiential differences are, I contend, the real basis of the distinction between primary and secondary qualities.

In the final chapter of the dissertation, I consider how, on my account, we should evaluate the veridicality of our experience of shape in light of Einstein’s special theory of relativity (STR). According to the standard interpretation, STR reveals that no purely spatial properties are instantiated in our universe; instead, all that objectively exists is a four-dimensional spatiotemporal manifold. Since, on my account of spatial perception, our experience represents the presence of purely spatial properties—the Euclidean properties about which we reason in performing abstract proof—STR might seem to imply that our spatial experience is never veridical. Against this, I argue that STR gives us no reason to abandon the idea that the Euclidean spatial properties represented in our experience are in fact physically instantiated. Instead, what Einstein’s discoveries show is that those properties are instantiated in a particular manner: namely, relative to various inertial frames of reference. This analysis allows us to hold onto the intuitive idea that there is a tight connection between our a priori geometrical reasoning and our experience of space, without being forced to accept that our spatial experience is universally illusory.