What is the concept of a point object
What is the ontology of the points?
In terms of points and mereology
An interesting idea of points is made in category theory, here the point is any end object * (all these points are isomorphic so you can take each one), then given any object A, then gives us a map * -> A a point in this object. This is interesting because it leads to the idea of points of different shapes and types.
Is it coherent to make points - entities without extension - compose extended objects?
In the context of mainstream math, it would appear that way. Take the real line for example. This consists of points with no extent and the real line has extent.
Some might say, as I have seen, that material point objects are incoherent
However, if we look at it through the topology, we also find that this real line is not connected. It is not possible to move from one point to another as none of the points are connected to another (here we consider the real line dynamically).
To satisfy this, we make sure that the real line has a topology, its standard topology; these consist of open sets; Each open set has an extension.
In the so called pointless topology we can remove the points and this still gives us a line unless there are no points here - why? because they are without extension and have no ontological weight.
The extension is irrevocable. The connection makes physicality (objects that are expanded) an irreducible concept.
The nature of the continuum is important in physics. One philosophical reason for studying string theory is that point particles shouldn't exist at first glance. Point particles in physics are, as Landau explained, particles whose size can be neglected; but what happens when they can no longer be neglected - for example when we approach the Planck scale? One answer is strings and branes. These have extension.
String theory may turn out not to be a theory of everything, but it has at least taught us how to view point particles (among other things) as extension; and for that it will have been invaluable.
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