The Paradox Of Circles

What is a circle? Essentially an infinitely-sided polygon. But if it has an infinite number of sides, how is it ALL circles are not infinitely long around? These are the kinds of issues Zeno of antiquity brought up. As long as each side of a circle has a length greater than ZERO, should not ALL circles be infinitely long around?

On the other hand, if each side of a circle has a length less than or equal to ZERO, a singularity results thus rendering it something less than a circle. Of course the resolution of this dilemma lies within the realm of recognizing a duality between infinities and limits thereupon! Hence, an infinite entity can be intertwined within something merely finite in scope. Apart from this though, these kind of mind exercises are rather interesting.

This is a perfect example of the "barber paradox". It is not the least bit tempting to believe that a circle, or at least all of them*, are infinite in circumference. But if they are all essentially infinitely-sided polygons with sides > zero length, how could they not all be infinite in circumference? With this then, perhaps it IS tempting to believe all circles are infinitely long around.

But this can't be because I have seen many circles and know them to be finite in circumference! Therefore: if a circle MUST be of infinite circumference, then it CAN'T be! Conversely, if a circle CAN'T be of infinite circumference, then it MUST be!

*A most bizarre implication rears its head. Can there exist a circle infinitely long around outside of an abstract mental construct? What is needed to describe a circle? A definition.....for example, its radius. But does not defining an object or concept systematically render said object or concept to something less than infinite? Perhaps I should now feel compelled to "disbelieve" in circles. They are nothing short of absurd!

My overarching point with this seemingly silly and useless exercise is to demonstrate how much of what we believe or assume about reality is really absurd! Maybe we don't know what we THINK we know? Humility overwhelms me with this realization.....

Firmly Planted In Mid-Air

Many will say my open-mindedness leaves me with no absolute moral foundation in which to approach life. Noted theologian and writer Ravi Zacharias cleverly expresses this by saying that those who lack an absolute moral foundation have their feet firmly planted in mid-air. This brilliant cliché is more or less true but is this necessarily a bad place to be?

Without this absolute moral foundation, it is thought, one is forever precluded from knowing the fine line between what is right and what is wrong. This will then systematically lead to what is commonly perceived as perverse and wicked behavior. It can lead to this type of behavior but it can also lead to a very open and understanding person who feels no need to judge and criticize others who do or believe seemingly peculiar things.

Additionally, many require an absolute foundation only because they need to “know” they are right in order to feel fulfilled. This is a form of control motivated by nothing more than ego. I don't need to be in control of “truth”. I can just be who I am without such control.

Perhaps some are suspicious of their own intentions and as such need a firm foundation in “truth” lest their real self might come out and wreak havoc on themselves and worse, others. Furthermore, I presume many have been indoctrinated with the belief that one must have a worldview based on absolutes to have any semblance of peace and fulfillment. This then commonly becomes self-fulfilled prophesy.

Alas, there is a crippling flaw with any sort of "absolute" moral foundation: contradictions inevitably ensue. This is not the fault of the person per se, rather it is the fault of this system of thinking. It doesn't work. Different absolutes are clearly in opposition to one another but are believed wholeheartedly nonetheless. Doublethink as George Orwell so wisely termed this.

In addition, many absolutes are arbitrarily embraced on a preferential basis. At this point, absolutes are merely relatively absolute. Which means they are not absolute. Are they relative? Certainly not, for if they are relative, they could simultaneously be absolute.

I have reflected extensively on the absolute/relative dichotomy and have comfortably concluded it to be an irreconcilable paradox*. On the other hand, not establishing an absolute foundation does not create these contradictions but is of course replete with its own set of problems. Everything pertaining to the morality and well being of societies is a trade-off and therefore nothing can ever be absolute.


*Please see a couple of my writings on a more thorough examination of this paradox:

The Duality Of Relativism/Absolutism

http://kurtsthoughtemporium.blogspot.com/2009/08/duality-of-relativismabsolutism.html

The Shortcoming Of Absolutes
http://kurtsthoughtemporium.blogspot.com/2009/07/shortcoming-of-absolutes.html