Showing posts with label barber paradox. Show all posts
Showing posts with label barber paradox. Show all posts

Tuesday, February 27, 2024

The Shortcoming Of Absolutes

Each thought must carry with it only one of many perspectives. As such, a single perspective by its very nature implies limitation. Which means any given perspective and its associated thoughts can not be absolutely true. 

For example, one might suggest the absolute truth of the sun "rising and setting" every day. But this statement is not absolutely true. Surely an observer on a planet three million star systems away would not agree, let alone an observer merely three star systems away. It is relatively true based on the perspective of one who happens to reside on an arbitrarily named planet known as “Earth” in an arbitrarily named galaxy known as “The Milky Way”. Certainly our truth of the sun "rising and setting" every day is not false, but then neither is it absolutely true. Any other interplanetary observers might experience a daily "rising and setting" of a nearby star but certainly not our star.

I thoughtfully quoted "rising and setting" to make a most important distinction. This expression is merely metaphoric as the sun neither rises nor sets in a literal and hence absolute manner. It is but an illusion created by the Earth's rotation.

Yet another distinction to point out is that technically even this metaphoric "rising and setting" every day is problematic. What about observers on the Earth’s poles during the height of their summer and winter months? Their sun either "stays" risen or "stays" set, this of course being the same sun all of us more tropical types observe. At this point, even the absolute truth of the metaphor is lost.

Another critical distinction to make is that there is nothing absolutely true or real about a day. It is just a relative construct. Presumably, no other planet rotates around itself in the same amount of time. Additionally, the earth's rotational speed is slowing down which means the amount of time it takes to rotate around itself is NOT absolute! It's actually increasing every day! Imperceptibly, to us at least.

In summary, our perception of the sun "rising and setting" every day (this itself a metaphor which cannot hold absolutely true even for Earth's inhabitants) is certainly not false but then neither is it absolutely true. Such is the case with most claims of “absolute” truth.

I will admit, it seems absurd to see things as absolute. Then again, it seems equally absurd to see things as relative. There seems to be an irreconcilable paradox with the absolute/relative dichotomy*.

Many will be annoyed by my "nitpicking" of details. Most overlook or discount them out of the mistaken belief that they are frivolous. However, they are absolutely (a self-professed contradiction, but only for effect) pertinent to any reasonable argument. Any conclusion based on the false notion that variables are necessarily absolute misleads people into believing they can account for all truth with their individual perspectives.

I will end with one of my favorite Kurtisms: do not overlook the profound wisdom of scrutinizing trivial things as this becomes a stepping stone to critically evaluating far bigger things.


*see link that follows for clarification

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

Tuesday, April 13, 2010

What's Your Favorite Color?

There is a story based on ancient Greek thought concerning a professor who teaches a young boy law without charging tuition. It is only stipulated that fees be collected upon the boy's first successful case. However, after countless hours of being taught law, the boy decides to become a musician instead, much to the chagrin of his professor.

Wanting to collect fees from the boy, the professor figures he can sue the boy and win whether the court rules in his favor or not. His reasoning is thus: if he wins, the court rules the boy must pay tuition fees but even if he loses, the boy wins his first case, which, as per the agreement, would entitle the boy to pay up. The boy, who represents himself in the matter, sees things in a slightly different light. If he loses, obviously nothing is owed the professor because he fails to win his first case. But even if he wins his first case, the court rules in his favor meaning he owes nothing to the professor. So who is right?

Both are right. Each argument is logically sound. This paradox has puzzled many a philosopher for centuries without resolution. It is impossible to resolve this with any sort of “absolute” solution. Ultimately, whichever “right” answer is chosen is as subjective as one's favorite color. Neither answer is the moral imperative. This is how I see much of reality. I think this paradox illustrates why accepting alternative viewpoints is so beneficial for society. We need to stop claiming there is necessarily a good/bad or right/wrong dichotomy to everything just as a means to feel more right(eous). I used to discredit the idea that what is right for one is not necessarily right for another as liberal nonsense but in light of the aforementioned argument I now deem this mantra valid.

An example of this argument might concern God and fairness. What is fairness concerning financial matters? Many “conservative” people believe God's fairness concerning financial prosperity is based on the idea that one should reap what he sows. People that are smart and productive will thrive whereas those that are not will struggle. Where then is the grace (as in a man should not reap what he sows)?

On the other hand, the more “liberal” types tend to believe God's fairness concerning prosperity is based on the idea that one should not reap what he sows. Prosperity should in this case be distributed more evenly than will naturally occur thus necessitating higher income redistribution. Take wealth from productive people and give it to those, God bless 'em, that just don't want to produce or are very poor at it. There is of course grace here but where is the personal responsibility (as in a man should reap what he sows)?

Before progressing further, I want to say it is my belief that both of these viewpoints are valid or invalid if you like. In other words, neither is a moral imperative in itself. They are different ways of dealing with the fact that reality as we experience it is a trade-off.

Many staunch conservatives will claim liberals use income redistribution as a means to buy votes. And this certainly is true. But can not the liberal perspective claim the same thing concerning conservative dogma? “If you vote for me, I will create income tax sanctuaries for your hard earned dollars!” It is the same method of “buying” votes that liberals use so effectively.

It is so hard for one side to see the other as being in any way valid because each so badly wants to be “absolutely” right. The challenge in dealing with this conservative/liberal dichotomy is that we ultimately must reach a compromise because there is little chance either extreme would or could ever happen.

And herein lies the dilemma. What is the “proper” level of moderation concerning, for instance, taxes and income redistribution? It's just like picking a favorite color! We will be arguing about this for the rest of time to no avail! How about trading democracy for a dictatorship?

Though many will likely cringe at the thought of a dictatorship, who do people think rules Heaven? The Supreme (perhaps benevolent) Dictator a.k.a. GOD. So what could possibly be wrong with a dictatorship? Maybe democracy isn't the optimal form of government after all? So what's your favorite color?

Monday, March 29, 2010

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.....

Monday, August 10, 2009

The Duality Of Relativism/Absolutism

There is a blinding paradox inherent in the relative/absolute dichotomy. I do not believe everything is absolute. Nor do I believe everything is relative. I think most people would agree with me thus far.

However, the implication of both statements being true is problematic. If things are neither entirely absolute nor entirely relative, then it must be the case that some things are absolute and some things are relative.

But this just begs the question of what things must necessarily be absolute and what things must necessarily be relative? Well, it can only depend on whom you ask which ultimately renders everything relative. But one of my initial assumptions contradicts this conclusion!

Furthermore, upon closer inspection of this circular nonsense, an obfuscatory corollary crops up. If everything is relative, then it would seem everything can simultaneously be absolute. Why must this be so? Well, if something is relative, could it not be represented by any value, even an absolute one? This paradox puzzles me.

Is the set of all sets that are not members of itself a member of itself, or is it not, and if it is not, is it? It seems absolutism and relativity must be either both true or both false. Or perhaps they are both true and both false? But those statements are nonsensical at best or at least appear so. HUH?

Thursday, July 9, 2009

More Uncertainty!

Difficult lines must be drawn but many will not like them! I will attempt to explain why this is so.

For instance, concerning tax breaks, it seems obvious to most that those of limited means with many hungry children to feed should be entitled to tax breaks more so than others. But what if you were just beyond any given line of entitlement? What if your income and number of children just missed this “line”? Would you not feel cheated? Perhaps you think the line should be drawn to include you? Trouble is, there is always another unlucky bloke who happens to be just beyond this new line of entitlement leaving him feeling cheated just the same as you were before!

There is a seemingly never-ending succession of "yous", at least until everybody is entitled to said benefit. But of course this will never happen because we as a society can ill afford to offer entitlements to everybody. (also problematic with this approach is that it would simply be a case of "robbing Peter to pay Paul" in turn being ineffectual in redistributing wealth) Things will seldom if ever be “fair” drawing lines because they are by their very nature predicated on discontinuities. But most of life's matters can not be treated as such. Rather, most of life's matters tend to be based on continuities.

For instance, where does an embryo become a living, breathing human being? Clearly, it is not a living, breathing human being at its insemination (this being the left end of the spectrum) but clearly it is a living, breathing human being when it comes out of the birth canal (this being the right end of the spectrum).

Does it ever become a living, breathing human being? If not, is it always a human being or is it never a human being? This is silly, as a small clump of cells certainly can not be a living, breathing human being but I'm pretty positive I am a living, breathing human being! Perhaps it is both human and less than human all the while being neither? This exemplifies what is known as the “barber paradox”: if it can not be human, it must be human. Conversely, if it must be human, it can not be human. Is the set of all sets that are not members of itself a member of itself, or is it not, and if it is not, is it?

On the other hand, if it becomes a living, breathing human being, at what discrete point does it become so? It does not seem to at all but it must. If there is a discrete point whereby an embryo becomes a living, breathing human being, all we can be certain of is its uncertainty. I am using this example as a way to demonstrate the difficulty of drawing 1 absolutely right line in any given situation!

In any case, it appears people instinctively like to draw absolute lines, in all likelihood because they are slaves to their egos' pursuits. The problem with this is the lines themselves are arbitrary because lines are ultimately predicated on discontinuities whereas issues in life, especially the most difficult ones, are predicated on continuities. Therein lies the root of all (intelligent) controversy!

It is tempting to believe there is a discrete point whereby a fertilized egg becomes a baby worthy of protection. Just the same, it is tempting to believe there is a discrete point whereby a person is becoming of a given entitlement. But this is all opinion no doubt shaped by each person's perspective. Project this argument on all issues in life, especially the most difficult ones.

Can we all just learn to get along with all of our differences by realizing nobody is “absolutely” right?