Der må være en kant. En diskussion af forskellige opfattelser af rum og virkelighed i lyset af Kants teori om rummet

This article discusses to what extent is makes sense to talk about different conceptions of space, and different experiences of space. According to Kant our sense perceptions are organized by a unique set of categories and by the form of our inner and outer sense, time and space respectively. To Kant, this spatial intuition is culturally invariant because it is a condition for the possibility of any experience whatsoever. Without accepting Kant’s terminology the author agrees that certain rudimentary abilities of spatial orientation have to be presupposed as universally shared. However, we do seem to have different ways of conceiving and thinking about space. Within our own culture we can distinguish between subjective/personal, public/official and scientific conceptions of space. It is argued that in other cultures, where these conceptions are different, we should be weary of a quasi-Kantian position which attributes such differences to differences in ‘categorial schemes’, and which further claims that these are conditions for the possibility of experience in this specific culture. Such a culturally speciftc a priori category confuses conditions for any possible experience with possible experiences. Furthermore, it ignores epistemological distinctions we readily employ within our own cultures.

Embodied Cognition in Berkeley and Kant: The Body’s Own Space

Berkeley and Kant are known for having developed philosophical critiques of materialism, critiques which lead them to propose instead an epistemology based on the coherence of our mental representations. For all that the two had in common, however, Kant was adamant in distinguishing his own ‘transcendental idealism’ from the immaterialist consequences entailed by Berkeley’s account. In this essay I return to their respective theories of spatial intuition, since it is by paying attention to Berkeley’s account of space that we discover a surprising account of embodied cognition, of spatial distance and size that can only be known by way of the body’s motion and touch. More striking than this, is the manner in which Kant’s approach to the problem of incongruent counterparts also relies on a proprioceptive cognition. Thus while cognition theorists today have recognized that certain challenges faced by perception and cognition can only be resolved by way of an appeal to the facts of embodiment, my aim in this essay is to show that such recourse is not new.

After Non-Euclidean Geometry: Intuition, Truth and the Autonomy of Mathematics

The mathematical developments of the 19th century seemed to undermine Kant’s philosophy. Non-Euclidean geometries challenged Kant’s view that there is a spatial intuition rich enough to yield the truth of Euclidean geometry. Similarly, advancements in algebra challenged the view that temporal intuition provides a foundation for both it and arithmetic. Mathematics seemed increasingly detached from experience as well as its form; moreover, with advances in symbolic logic, mathematical inference also seemed independent of intuition. This paper considers various philosophical responses to these changes, focusing on the idea of modifying Kant’s conception of intuition in order to accommodate the increasing abstractness of mathematics. It is argued that far from clinging to an outdated paradigm, programs based on new conceptions of intuition should be seen as motivated by important philosophical desiderata, such as the truth, apriority, distinctiveness and autonomy of mathematics.

Geometric Generalisation of Surrogate Model-Based Optimisation to Combinatorial and Program Spaces

Surrogate models (SMs) can profitably be employed, often in conjunction with evolutionary algorithms, in optimisation in which it is expensive to test candidate solutions. The spatial intuition behind SMs makes them naturally suited to continuous problems, and the only combinatorial problems that have been previously addressed are those with solutions that can be encoded as integer vectors. We show how radial basis functions can provide a generalised SM for combinatorial problems which have a geometric solution representation, through the conversion of that representation to a different metric space. This approach allows an SM to be cast in a natural way for the problem at hand, without ad hoc adaptation to a specific representation. We test this adaptation process on problems involving binary strings, permutations, and tree-based genetic programs.