Let's Talk Paradoxes!

originally posted by: Involutionist


The paradox introduced in the OP is a modern adaptation of the ancient Chinese paradox of 'the spear and the shield'.

There once was a man who was attempting to sell both a spear and a shield.

A) He claimed that the spear can pierce any shield.

B) He also claimed the shield cannot be penetrated by any sword.

C) He was then questioned: What would happen if his sword was used on his own shield?

Here lies the paradox.

Thoughts?

Thank you for trying to bring a better example of a paradox. Unfortunately, I do not consider this to be a paradox either.

Again , I will refer to the above as a paradoxical speculation (a phrase I have coined whlst reading this thread).

How can there be a paradox when you are merely stating the claims of a" salesman" - the owner of the sword. As someone has aready pointed out in this thread, one of the two sides is usually a lie or exageration.

I think this thread can become interesting inasmuch as it may focus on what a paradox really is. My understanding of a paradox is more in the nature of "something that is and is not as the same time.

I love paradoxes because they are truly the language of mysteries.

a reply to: Involutionist

There once was a man who was attempting to sell both a spear and a shield.
A) He claimed that the spear can pierce any shield.
B) He also claimed the shield cannot be penetrated by any sword.
C) He was then questioned: What would happen if his sword was used on his own shield?

That's easy to answer. The shield would stop the sword according to B. A is just a red herring, it has no impact on proposition B.

a reply to: crowdedskies

Do you make any distinction between paradox and reductio ad absurdum?

a reply to: Involutionist

There once was a man who was attempting to sell both a spear and a shield. A) He claimed that the spear can pierce any shield. B) He also claimed the shield cannot be penetrated by any sword. C) He was then questioned: What would happen if his sword was used on his own shield?

The spear would fail to penetrate the shield. I know this might be considered cheating but there's a weak link in this paradox, that being the strength of the person wielding the spear. So in my opinion, investigation of the claim would remain inconclusive; blamed on the wielder's limited ability to apply sufficient force to drive the spear through the alleged impenetrable shield. Unless the wielder possessed infinite strength, the claim would forever remain unsubstantiated.

originally posted by: VP740
a reply to: crowdedskies

Do you make any distinction between paradox and reductio ad absurdum?

Yes, I do . They are very different propositions.

A paradox is a situation where something is and is not at the same time or ,to put it simply, something is true and false at the same time. I find such propositions very interesting and revealing.

reductio ad absurdum is more of an argumentative tactic. Nothing to do with paradoxes.

Unfortunately, scientific types are trying to break down paradoxes into different types, etc and giving them names. In fact, for me, there is only one type of paradox: Something that is and yet is not.

a reply to: facedye

I would say God can create a boulder even too big for himself to move. It would be his choice to circumvent his own omnipotence, like a G

a reply to: crowdedskies

I probably should have asked the OP that LOL.

originally posted by: Plotus

Exactly, it is a contradiction and can not exist, nor can a round square ......

An average American is an example of a round square

originally posted by: VP740
a reply to: crowdedskies

I probably should have asked the OP that LOL.

You did; even if indirectly.

a reply to: crowdedskies

I think this thread can become interesting inasmuch as it may focus on what a paradox really is. My understanding of a paradox is more in the nature of "something that is and is not as the same time.

The ancient thought exercise about the sword and the shield demonstrates quite clearly the nature of a paradox. It demonstrates what something is and not is at the same time. How ideas can contradict each other.

At the most basic level, a paradox is a statement that is self contradictory because it often contains two statements that are both true, but in general, cannot both be true at the same time.

All paradox are meant to be an exercise in logic. It is not meant to be postulated as a possible reality. No conclusive answer can be arrived at by contemplating paradoxes.

I love paradoxes because they are truly the language of mysteries.

Cool. Perhaps this classic paradox that dates back thousands of years might be more in alignment with how you personally define what a paradox is:

"Ship of Theseus"

The ship wherein Theseus and the youth of Athens returned from Crete had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their places, in so much that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same. — Plutarch, Theseus

en.wikipedia.org...

In other words: If a ship has been dramatically overhauled (repaired) over the years, to the point every part has been replaced, is it still the same ship?

And, If one concludes it is NOT the same ship; at what point did it stop being the same ship?

My understanding of a paradox is more in the nature of "something that is and is not as the same time.

I present to you the Ship of Theseus, then.

a reply to: Visitor2012

The spear would fail to penetrate the shield. I know this might be considered cheating but there's a weak link in this paradox, that being the strength of the person wielding the spear

That's actually an interesting creative angle. However, the *variable* of strength does not make a difference in scenario (A).

A) He claimed that the spear can pierce any shield: this means the spear can pierce any shield regardless of the strength OR skill set of the person wielding it.

a reply to: Involutionist

Why do I feel that this thread has still not addressed a real paradox yet ?

Your explanations are simply a scientific and logical look at viewpoints - not paradoxes.

A Paradox for me is an experience rather than a viewpoint.

Can anybody not remember those moments when something came across as both "true" and "false". Even better, can nobody remember a time when a paradox sunked in and the truthfulness and falseness both manifested harmoniously inside our mind and psyche. I am not talking about argumentative viewpoints like the case of the ship. That was not my idea of a paradox.

This is not my thread and I have to be caution not to derail it. However, I find it difficult to understand how everyone so far seems to relate paradoxes to arguments on whether something is one thing or another; one party having one view and another party having another and both being right. That is not a paradox. Neither is the sword and shield story, which is purely an artificially created argumentative exercise. No such situation arises in real life.

WHoever brings to this thread a real example of a paradox should be commended.

a reply to: Involutionist


Nothing would happen to either the shield or the spear they would cancel each other out.

No different than throwing a spear made of steel against a shield made of steel and assuming respectively the correct thickness.

a reply to: crowdedskies

Responding because I love armchair philosophy.

Why do I feel that this thread has still not addressed a real paradox yet ?

That is a great question. I've been asking myself that very question concerning you...

Your explanations are simply a scientific and logical look at viewpoints - not paradoxes.

I'm going need a moment to wrap my mind around what you stated. You are entitled to your views, but I disagree.

For thousands of years philosophers and intellectuals have mislabelled "The Ship of Theseus" as a paradox. Cool.

WHoever brings to this thread a real example of a paradox should be commended.

I suggest you do so.

Can anybody not remember those moments when something came across as both "true" and "false".

Can you?

Life involves many moments such as that."The Ship of Theseus" paradox reflects that. When understood in its proper context, you will come to understand "The Ship of Theseus" paradox has nothing to do with science and logic and more to do with:

the truthfulness and falseness both manifested harmoniously inside our mind and psyche.

Perhaps to contemplate the following might spark something: You right now in this present moment and your 10 year old self are two different people. You are not that person and are that person at the same time. This is both true and false at the same time, is it not?

“Which you is ‘who’? The person you are today? Five years ago? Who you’ll be in fifty years? And when is ‘am’? This week? Today? This hour? This second? And which aspect of you is ‘I’? Are you your physical body? Your thoughts and feelings? Your actions?”

a reply to: Involutionist

Darn! You've closed the loop hole

Fun to pontificate on nonetheless.

a reply to: Involutionist

a reply to: crowdedskies

Wait a second - there are MANY legitimate paradoxes in this thread, many of them pointed to by Involutionist.

A paradox can simply be described as acceptable premises leading to an unacceptable conclusion.

All of these different instances we've brought forth are of the same logical structure!

Let's have a go at Zeno's Paradox, which is truly my favorite:

In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead. – as recounted by Aristotle, Physics VI:9, 239b15

Zeno's Paradox

At first, this made no reasonable sense to me, and then i remembered that reason and logic are two separate compartments of our consciousness.

logic is the math that organizes and structures our thoughts. reason is logic applied to the observable world.

the problem here is truly a metaphysical one, and not simply mathematical.

understanding the concepts of time and space is crucial to function in the world we live in. Concepts like infinite divisibility touch on our supposition that numbers can go on forever, since they are mental constructs.

however, when we attempt to apply these logical consistencies to the real world, something gets lost in translation.

simply put, in reading that paradox, we have to come to terms with two things:

1. in the real world, the hare will always beat the tortoise.

HOWEVER

2. if we believe that time and space are infinitely divisible, the hare should logically never be able to catch up with the tortoise - as it will take the hare an infinite amount of steps to get to the tortoise's location.

it's not about the details, ladies and gentleman. it's about recognizing how narrow and limited our understanding of our environment really is.

it's quite literally hitting the wall of our mentality.

...which leads to my next assertion:

paradoxes MUST exist in exactly the way they do, as they can easily be seen as universally necessary. crudely put, the yin and yang must exist separately and with relation to one another at the same time. this constant duality strangely reminds us that there is no hot without cold, nor sweetness without bitterness. both must exist in embrace and opposition to allow themselves their own space and function.

You know whats most funny to me? How seriously people take their feelings!

If you understand that the feelings you feel are records of your past experiences of enlivenment with reference to whatever your encountering now, then it should be obvious that it is impossible to think of our consciousness outside of the lived contexts which build our minds.

I always think of this whenever I encounter insane philosophies or mysticisms that claim incoherent things about reality. Poor friggin people are caught up in a delusion built by Action-Perception experiences run through a dynamical affective core that chooses what it wants - with the ignorant consciousness building sand-castles of self-explanation - sub-optimal coherencies - to keep its picture of reality untarnished by unwanted information.

If you think about it (I know I've gone off topic, I apologize) it unfortunate that brain science came after mysticism and occultism, as the former completely obliterates the plausibility of claims made by the latter about the nature of reality.

As to your question, I don't think its a coherent question. Just because something can be thought doesn't mean it makes sense to ask it.

For me, being a single body is whats remarkable. How can there be infinity besides finitude? This is said to be the mystery behind the number 10 - the 1 besides the 0. A duality, an individual, holding within itself the mystery of infinity.

a reply to: facedye

I think the problem with your example is the assumptions that are being made which are in fact not logical at all.

Assumptions like the possibility of a God which is All Powerful for example.

Also the definitions of the terms you're using being undefined.
What is a God??
What kind of Power are you talking about and can any one thing possess all of it???

Things like that.

Paradoxes are fun to think about, but that doesn't mean they are logical at all. Often times they are just a problem within language which is symbolic and not really representative of our reality in it's true form. So we're able to create linguistic paradoxes that seem real but are only symbolic or conceptual and not possible in reality at all.

originally posted by: chr0naut

originally posted by: facedye

originally posted by: DISRAELI
a reply to: facedye
The "omnipotent God" paradox is created by the chosen definition of "omnipotent", which makes it artificial. If the word is re-defined to exclude whatever is not logically possible. the paradox disappears.

This can be illustrated by other examples. The famous paradox "What happens when an irresistable force meets an immovable object?" is created by offering up two definitions which are incompatible with each other. The only possible answer is "One of them is exposed as a fraud".

Or again, the "Cretan liar" paradox. The man who said "All Cretans are liars" was a Cretan himself, as Paul observed.
But this only becomes a paradox by using an artificial and abnormal definiton of "liar", viz "someone who NEVER makes a true statement".
In more normal usage, a "liar" is merely somebody who makes untrue statements slightly more frequently than other people.

If you find a statement paradoxical, look first to the definitions.

Starred, great response!

however, i have trouble agreeing with it since it seems like you're choosing a semantic route to resolve the contradiction.

i agree that paradoxes can be made not so by different applications in the real world - Zeno's time paradox comes to mind. Theoretically the hare will never catch up to the tortoise if we believe in infinite divisibility, but any reasonable person would know a rabbit would beat a turtle in a race. however, this doesn't take away from the phenomenon of logical legitimacy constantly ending up in paradoxical states.

in my mind, this phenomenon is an essential element to what makes our universe the way it is. it's a building block of sorts.

Surely his answer can be applied at a more than semantic level. The paradox is phrased to suggest one limitation over another but applied to the limitless.

The 'possibility' of the scenario is at the heart of its solution. The paradoxical nature of the scenario evaporates when the impossibilities are removed, as stated. God could not be limited if God is unlimited.

Indeed it is easier for God to fit into gaps if his properties are left as open-ended as possible.