Euclid's point?

Question

In "The Elements" Euclid defines a point as "that which has no parts."

How can any "that" exist with no parts?

(No, I'm not doing my homework.)

Answer 1

Existence is irrelevant. Geometry is a theoretical construct only, completely without real world correlates. A point is that which cannot be divided into parts, unlike a line, for instance, which is composed of multiple points. Rather than looking for some form of existence, remember that the point is defined, not observed.

Answer 2

If everything had "smaller" parts then so would the parts.Then everything would have infinitely many parts. Then another Greek
(Aristotle) would come along and say you can't have an infinite multitude of actually existing things. Therefore everything has only a finite number of parts, and some of these parts have no parts. I wonder if Ari and Euclid hung out.

Answer 3

Euclid was trying to define every term. Now we know that a geometry needs to have a few undefined terms. But his definition was descriptive in the sense that a point has no dimension. No lenght, no width , no depth.

Answer 4

A point has no parts because it as no appendages. A line is two points with at least one appendage each.

Answer 5

"That" is soul.