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.

Jdog1998

"" "" In the context of mainstream math, it would appear so. Take the real line for example. This consists of points with no extent and the real line has extent. "" "" I've seen this before. But is there any way to highlight that intuition? It may make sense to some people, but I honestly get confused when I hear that a line is made up of an infinite number of points, or a plane is made up of an infinite number of lines, or a 3D space is made up of an infinite number of planes. How do you make this conceptually meaningful - expansion by infinitely adding non-expansion?

Mozibur Ullah

@ Jdog1998: I think your confusion is understandable; I'm not exactly sure how to go about it when I'm doing math - real line construction is one of the first things learned in a good analysis course. You first construct the Rationals and then show that there are gaps because you cannot go beyond all the limits. Then they construct ideal numbers to fill in those gaps, using boundaries as names to denote those numbers.

Mozibur Ullah

Another view is to look at the points on the line to determine positions on the line, not an actual point. and then ask the question whether there is a unique name or number for each position. It turns out that it can, and this is the real line. How do you feel about positions on of a line as opposed to a point of a line? Are they more respectable?

Jdog1998

//... Positions on a line as opposed to a point on a line ... // Yes! I tend to interpret points in this way - they are actually place names, and only places and places are necessarily abstract objects. They are not and cannot represent a specific part of something expanded ... so I guess. But is the actual interpretation of the "point of a line" ever coherent? Or are points ALWAYS just "positions on a line" and cannot be interpreted as something else coherent in any other framework?

Jdog1998

And as for math, I took math classes down to differential equations and ended up studying Laplace transforms. So leave it at that, or easier if you use math!