We show how an epistemology informed by cognitive science promises to shed light on an ancient problem in the philosophy of mathematics: the problem of exactness. The problem of exactness arises because geometrical knowledge is thought to concern perfect geometrical forms, whereas the embodiment of such forms in the natural world may be imperfect. There thus arises an apparent mismatch between mathematical concepts and physical reality. We propose that the problem can be solved by emphasizing the ways in which the (...) brain can transform and organize its perceptual intake. It is not necessary for a geometrical form to be perfectly instantiated in order for perception of such a form to be the basis of a geometrical concept. (shrink)

The coding mechanism of sensory memory on the neuron scale is one of the most important questions in neuroscience. We have put forward a quantitative neural network model, which is self-organized, self-similar, and self-adaptive, just like an ecosystem following Darwin's theory. According to this model, neural coding is a “mult-to-one”mapping from objects to neurons. And the whole cerebrum is a real-time statistical Turing Machine, with powerful representing and learning ability. This model can reconcile some important disputations, such as: temporal coding (...) versus rate-based coding, grandmother cell versus population coding, and decay theory versus interference theory. And it has also provided explanations for some key questions such as memory consolidation, episodic memory, consciousness, and sentiment. Philosophical significance is indicated at last. (shrink)