We are in a philosophy forum, thus any general dictionary is of secondary importance in contrast to the direct meaning from Kant.Atla wrote: ↑Sat Oct 12, 2019 8:54 amA perfect circle is most likely an abstraction and does not actually exist in itself. But that's not what 'noumenal' means today, get a dictionary already.Veritas Aequitas wrote: ↑Sun Sep 29, 2019 4:52 am Here is an explanation why 'Perfect Circle' cannot and is impossible to exist as real.

1. What is empirically real is confined to sensibility + understanding.

2. A perfect circle is noumenon [from Reason] that is beyond empirical "sensibility + understanding".

3. Therefore a perfect-circle is impossible to be real.

The realm of Sensibility + Understanding = real empirical things.

This how empirical things are derived from experiences.

Humans perceived things of all shapes, e.g. roundish ones.

From such observations and using understanding, the empirical concept of circle is abstracted with its various defined qualities.

In this case we can verify and know empirical circles existing as real.

However we have a faculty of Reason which can think of PERFECT CIRCLES and attributed it with a definition and qualities.

But the point while a Perfect circle as extrapolated from empirical circles, they are impossible to exists as real. There can NEVER be any absolute PERFECT Circles in the empirical world of sensibility + understanding.

Show me where can one find a real perfect_circle-in-itself?

The argument is related to Plato's ideas, forms and universals as real things that are independent of humans.

Thus a PERFECT circle can be thought of but cannot be really real in the empirical world.

The Perfect Circle is the noumenal-circle which a limit to what is a circle.

This is the principle of the Noumenon that is applicable a limit to all sensible and empirical things.

Here is the impossibility of a perfect circle in reality;

Mathematical Perfection

Mathematically speaking, a circle is the set of points in a plane that are equidistant from a given point. For a circle to be perfect, you'd need all those points in the circle's circumference to match up exactly.

And for all those points to match up exactly you'd need this precision to remain constant no matter how closely you looked: the particles, the cells, the atoms... And are these "points" stationary or are they in motion?

The maddening search for perfection simply breaks down.

Only in the abstract world of pure mathematics can we find our perfect circle -- a world of points and infinitely-thin lines with no room for particle inconsistencies or spherical oblateness.

https://www.stufftoblowyourmind.com/blo ... iverse.htmMy Point;Forms From Beyond

The situation brings to mind Plato's Theory of Forms. We live in the material realm, it states, but beyond our plane exists an immaterial realm of ideal forms. You can think of these ideal forms as the absolute perfection of a given thing, a truth that cannot be manifested in our universe. All we can do is echo it.

In our world there is no true beauty, but we have an innate understanding and longing for the true form of beauty as it exists beyond the limits of our reality. There's no true justice here, but we have a sense of it because the unreachable ideal exists in the realm of forms.

The Theory of Forms applies to chairs, apples, fears, sex, art -- everything we can comprehend and long for, really. For each there is a godlike ideal beyond our worldly grasp, residing in a pantheon of other awesome and terrible forms.

The circle is but one of them, its perfection impossible in our imperfect world.

https://www.stufftoblowyourmind.com/blo ... iverse.htm

A Perfect Circle is impossible to exists as real, i.e. within the field of sensibility + understandng + rationality.

Any counter to the above?

I believe most dictionary will refer the term 'noumenal' from noumenon back to Kant.