This is, in part, a response to the recent John Wilkins blog post “More on phenomena.” It is based on my ideas on human cognition and human perception. Unavoidably, this will be a tad mathematical. However, I will avoid getting into technical terminology to the extent that I can, though I’ll give enough as hints to the mathematical literature for those who want to pursue the underlying mathematics.

Think of the world as a topological space, call it *W*. (For the mathematicians, I am taking *W* to be a normal Hausdorff space). Because *W* is a topological space, we can think about continuous functions over that space. So for a point *x* in *W*, and a continuous function *f*, there is a value *f(x)* for that function at that point. For technical reasons, mathematicians usually take their continuous functions to have values that are complex numbers. However, I suggest thinking about them as functions with values that are real numbers.

If we look at this in terms of science, then we can think of the function *f* as a method of measuring, and we can think of the value *f(x)* as an actual measurement (or as a datum).