Visualizing Spatiotemporal Concepts
In addition to notebooks of text, I also keep notebooks of images. I have always tried to find graphical representations of ideas, exapting geometrical intuition for the purpose of better understanding — not only in terms of clarification of ideas, but also in terms of extending ideas. When an idea can be depicted graphically, the representation itself often suggests ways of extending an idea, as well as relations with other ideas. I was flipping through an old notebook of of sketches (from 2012) and I found the first three diagrams here, all formulated to distinguish concepts of space.
At the time I was working on a distinction between weak distinctions and strong distinctions (cf. Of Distinctions, Weak and Strong), and I realized that some concepts of space are strongly distinct while some concepts of space are only weakly distinct. As a result of increasing formal rigor on the one hand, and, on the other hand, increasing precision in empirical science, it became necessary to make a distinction between pure geometry and empirical geometry, i.e., between an abstract theory of space and the actual properties of physical space. Abstract theories of space run the gamut from simple to incomprehensible, but actual physical space has a unique structure, which means that some one abstract theory of space may describe actual space, but all of the other abstract theories of space are no less legitimate as theoretical constructions. In any case, and whatever terms we use to make the distinction, pure geometry and empirical geometry, once we understand them, are strongly distinct, but they lie at opposite ends of a continuum, and between the two are concepts of space from which each is only weakly distinct.
My idea sketches are often left incomplete, as in the above case, but the reader can easily fill in the presumptive content for the squares on the left, which would mirror the content of the squares on the right, but emphasizing the methodological sequence of Platonism (essentially deductive), beginning with principles and working toward facts, in contradistinction to the methodological sequence of naturalism or empiricism (essentially inductive), beginning with facts and working toward principles. This illustration should make plain the methodological implications of concepts sequenced along a continuum, with the end points anchored by strongly distinct polar opposites and the mid points representing greater or lesser proximity to one pole or the other, and being only weakly distinct from each other, and therefore offering a methodological bridge between concepts. Also note how working through a continuum of concepts according to one methodological implies the possibility of working through the same concepts coming from the opposite methodological direction.
When I looked at these illustrations of concepts from space from 2012 I was surprised that I didn’t take the time to sketch out the parallel temporal concepts following the same principles, so I did so several years after the fact. Once I had translated the spatial into the temporal in the above diagram, I realized that the concepts that populate the region of mind overlap with the concepts that populate the region of the world, and that this gives us a simple Venn diagram in which perceptual space or time is the point of overlap between concepts of space and time primarily inherent in mind and facts of space and time ascribed the to world (definable and quantifiable without reference to mind, but unambiguously entering into perceptions, and, through perceptions, entering into the mind of any perceiving subject). And while I could easily write a commentary on these diagrams that would run to volumes, it might actually be more interesting for the reader to study the diagrams and see if they take away anything interesting from these attempts to diagram ideas of space and time.