Svalaksana literally means “the real”. The ancient Indian debate concerning svalaksana essentially asks, what is real? When we identify an object, is it that we identify that object by first identifying all of its constituent atoms, and then assembling them together? Or do we (also) identify an object in virtue of its larger context? Are points svalaksana? Is the whole a svalaksana? What about regions in between? Is the requirement that objects are simple applicable to their unanalyzed appearance to the mind or their ultimate (psychophysical) unanalyzability?
In the Western philosophical tradition, this debate has focused on the reality of particulars (or concrete things) vs universals (or abstract things). In early theories of both Buddhism and Mathematics, spatial regions are identified by the points (or “partless particles”) they contain, where those points are taken as primitive (either as axiomatic within geometry, or as the atoms of physical reality). In other words, particulars (as opposed to abstract things) are real, and the smaller the better.
Later Buddhist theories arrive at the conclusion that atoms are no more real than larger objects, in that both are imputed (or nominal) entities. Several recent Mathematical theories similarly abandon points in favor of point-free topologies. So both ontologically and mathematically, there has been movement away from their respective reductionist positions (which define objects in terms of their parts, and therefore ontologically depend of partless entities). Since Cognitive Set Theory similarly adopts a more holistic (instead of reductionistic) view, we present a few more details about the evolution of Buddhist psychology, and how that might map onto mathematics.
A simplified version of the evolution of the theory of svalaksana proceeds as follows:
- According to Pramana theorists, the real is simple, or singular (“eka”): we might say more precisely that what is real is spatiotemporally contiguous: a thing which is whole is not distributed. Mathematically, we will call it a well-connected region in N-space.
- According to the Sautrantika view (or the “external realism” of Dunne), there are “real” external things: momentary, partless particles. This view has been expounded in depth by Tscherbatsky [Buddhist Logic Vols 1&2], and it is compatible with the mathematical theory of points (which cannot be divided).
- According to Chittamatra and Madhyamaka views, the objects of awareness are of the nature of mind, and only imputed. In other words, there is no a priori reason to divide reality into a certain set of objects as opposed to another. In other words, space is no more composed of points than it is composed of bricks: tiny and large particles are equally real (or equally unreal).
To establish the spatial analogue to the later Buddhist schools, we summarize the divergence from point-space as follows:
- Regions are well-connected
- Space is not composed of points
- Regions are imputed
The first and second tenets are easily established in mereotopology, where space is divided into regions that are not (inherently) composed of points.
We alter the third tenet by saying that an object only exists in virtue of an imputed boundary. Since that boundary does not exist as an object within the original space, we say that it is an imputed boundary. The details of how an object (the boundary) may demarcate events within a space without being an actual object within that space is taken up in more detail in another blog post.