Partly Paradoxes, Part 4

Ahh, here we are at last!  We have arrived at the final five memes in our Partly Paradoxes miniseries.  Perhaps you’d like to check out Part 1, Part 2, and Part 3 before proceeding.

As before, we’re still working our way through the article called 20 Paradoxes Most Human Minds Can’t Wrap Themselves Around.  It’s not that the meme-based article is particularly bad; it’s just that the person who compiled the memes doesn’t seem to fully understand what a paradox is.  I’ll admit, it can be difficult to determine whether a proposition is truly paradoxical or not, but that’s why I’m doing this.  I thought it would be an educational and challenging mental exercise to examine each of the article’s memes and determine whether they depict paradoxes or something else.  And you know what?  It has been!  I feel that I’ve learned a lot over the past week, and if you’ve been following along, I hope you did too.  So without further ado, let’s finish this!


Is this a paradox?  Yes.  Maybe.  Yesterday I waffled on a similar question concerning the infinity of the Universe.  I ultimately decided that Archytas’s question is not a paradox because Archytas was attempting to prove that the Universe must be infinite by showing that the opposite assumption led to a contradiction.  In a similar vein, Heinrich Wilhelm Olbers was probably attempting to prove that an infinitely large, infinitely old, static Universe is inconsistent with the fact that the sky is dark at night.  However, Olbers’s argument is slightly different from Archytas’s question in that Olbers is not starting from a premise that is obviously, absurdly false.  The compactness and age of the Universe are long-standing cosmological questions, with numerous vocal proponents on all sides of the argument.  Olbers’s paradox raises a legitimate contradiction that must be addressed before cosmology can move forward.

We will attempt to resolve this paradox, but first we should note that the meme is incomplete.  Olbers’s paradox starts with several controversial assumptions not mentioned here: not only is the Universe infinitely large, but it contains infinitely many stars which are spread out more or less evenly throughout the cosmos.  Furthermore, the Universe is eternal, having had no beginning, and unchanging.  It is in this hypothetical Universe that Olbers argues the night sky should not be dark.  In such a Universe, every line of sight would end on the surface of a star.  Instead of a vast black void peppered with bright stars, the night sky should glow as brightly as the Sun itself.  Clearly it does not glow; ergo, there is a contradiction.

Is there a resolution?  Yes.  Olbers’s paradox is two centuries old, and humanity has made vast leaps in our understanding of the Universe since then.  For example, modern cosmology teaches us that this Universe is not infinitely old.  It had a starting point 13.8 billion years ago, give or take a hundred million years.  (By starting point, I’m referring to the Big Bang.  We don’t know what happened before the Big Bang, or whether there even was a before.  We might never know.)  We have also learned that light has a finite speed, which means that there are stars whose light simply has not had time to reach us.

We’ve learned that stars are not evenly distributed in space.  They tend to clump together into galaxies, with great empty voids between.  And to top it all off, we know that space is expanding everywhere.  The expansion of space causes light to stretch out as it travels, which decreases its frequency.  Visible light that travels a very long distance through expanding space will eventually be shifted below the threshold of human detection – into the infrared.  So even if the Universe were infinitely old, the well-documented expansion of space would ensure that stars beyond a certain distance would be invisible to us.

To re-emphasize: Olbers did not prove that the Universe is finite in volume.  He argued that the Universe cannot be infinitely large, infinitely old, and unchanging.

Before we move on, I’d like to point out that nobody knows for sure whether the Universe is infinitely huge or not.  It seems clear that the Universe is much, much larger than the portion we can observe; however, what happens beyond our Observable Horizon will always be a mystery to us.  Recent experiments, notably WMAP and BOOMERanG, strongly suggest that the Universe is flat.  A flat Universe is consistent with an infinite Universe, but it is by no means a slam-dunk proof.  While I personally favor the notion of an infinitely large Universe, I know that my preference is more conjecture than fact.  So it is for anybody with an opinion regarding the compactness of the Universe, for now, and perhaps for always.


Is this a paradox?  No, this is a philosophical thought experiment.  As the meme correctly states, it was posed by Avicenna to justify his belief in the soul.  It does not lead to contradictory conclusions.  If you answer yes, you are not logically led to answer no, or vice versa.

According to Avicenna, the ability of a man to know himself, even in the absence of sensory experience, proves that there is a self above and beyond the senses.  Our awareness of self is therefore evidence of some being that does not directly depend on input from the external world – in Avicenna’s view, a soul.  Rene Descartes would later crystalize the link between consciousness and existence in his pithy statement “Cogito ergo sum” – “I think, therefore I am.”

A criticism of Avicenna’s position is that it is not proven that such a man would be self-aware.  Even if he were, that does not prove that his consciousness arises from anywhere but a functioning brain.  Self awareness, even in the absence of sensory input, need not be inextricably linked to the supernatural.


Is this a paradox?  Here is another situation where, in my opinion, arguments could be made on either side.  I will hesitantly allow that this is a true paradox, with the following explanation:  A present object is identical to a past object if the two objects share a continuous history – in other words, if there is no point in time where you can definitely say that they are not the same object.  For example, if the original ship of Theseus had been completely destroyed by fire and rebuilt from scratch, you might reasonably argue that the old and new ships do not have a continuous history; ergo, they are not the same object.  But in this case, the original ship never ceased to exist, even as it was replaced piece by piece.  From that perspective, then, it is the same ship.

On the other hand, the current ship of Theseus is not identical to the original because they share no common components.

On the gripping hand, the ship’s purpose and idea have existed continuously, so what difference does it make if the components of the ship have been replaced?

This paradox has many iterations.  Thomas Hobbes wondered what would happen if you took the planks you removed from the original ship and used them to construct an identical ship.  Which one would truly be the ship of Theseus in that case?

You might also apply the paradox to living beings.  We continuously replace cells as they die.  Even our personalities – our selves – change over time.  Can it truly be said that we are the same person now that we were a decade ago, or two, or three?  For legal purposes, we are, of course, but philosophically…are we really?

Is there a resolution?  Depends on whom you ask.  Heraclitus, who lived long before Plutarch, wrestled with similar paradoxes and concluded that even as things change, they can maintain their identity; in fact, Heraclitus seems to have been convinced that the only constancy is change.

In Japan, Shinto shrines are torn down and rebuilt periodically using new wood.  In doing so, locals have preserved the original architects’ designs, which may be up to two millennia old.  In some ways, then, the modern incarnation of a shrine is more similar to the original form than it would be if it had been left to decay.

Given the difficulty associated with defining sameness and identity, it may be that only a personal resolution is possible.  You may choose which side of the conundrum you agree with, then plant your feet firmly and refuse to be moved.  But who knows?  Perhaps as  your mind evolves, bit by bit, you may someday find yourself on the other side.


Is this a paradox?  No, but it’s an amazing story!  It was indeed invented by Don Mills for a speech given during a 1987 banquet.  Amusingly, the case has often been misreported as having actually happened; ergo, it has attained the status of urban legend.

The story has been adapted and retold many times, including here, but let’s take a step-by-step look at the events leading up to the death of this remarkably unfortunate young man, originally named Ronald Opus in Mills’s speech.

In the original story, Ronald does indeed jump from the top of a ten-story building with the intention of killing himself.  He has left a note indicating his intent, so there can be no doubt.  As he passes the 9th floor, however, a shotgun blast through an open window hits Ronald in the head and kills him.  Neither the shooter nor Ronald knows that a safety net has been set up at the 8th floor level to protect some window washers, and that if Ronald had not been shot, he most likely would have survived his fall.

Ordinarily, a man who intentionally sets events in motion that lead to his own death is said to have committed suicide, even if the exact mechanism of his death is not what he intended.  However, in this case, Ronald’s suicide attempt would have been unsuccessful.  Had it not been for the gun shot, Ronald would still be alive.  The medical examiner decides that Ronald’s death is a homicide (albeit a negligent homicide, perhaps).

As it turns out, the operator of the shotgun was an elderly man living on the 9th floor.  Just prior to Ronald’s death, the old man had been involved in a fight with his wife.  He threatened her with the shotgun (and that is not okay!), but was so upset that he could not hold it straight.  When he pulled he trigger, then, the pellets missed his wife and struck the luckless Ronald.  Because the old man was intending to kill his wife, but accidentally killed Ronald instead, the law holds that he is indeed guilty of the murder of Ronald.

But wait…there’s more!  The old man claims not to have known that the gun was loaded; apparently he has a long-time habit of waving an unloaded shotgun at his wife when they quarrel (and that is still not okay!)  So it appears the gun was accidentally loaded, which means that Ronald’s death is an accident.  A horrible, negligent accident.

And who loaded the gun, you might ask?  A witness reports that he saw the old man’s son loading the shotgun six weeks prior to the fatal shooting.  Apparently, the old lady had cut off her son, financially speaking, and knowing his father’s worrisome penchant for waving unloaded shotguns in his mother’s face, the vengeful son decided to put an end to her.  So now the son is guilty of the murder of Ronald Opus (and the attempted murder of the old lady, come to think of it).

Now for a twist worthy of M. Night Shyamalan: the identity of the murderous son was…Ronald Opus himself!  (Actually, I’m quite sure you saw that coming.)  Apparently, a period of peace had erupted in the elder Opuses’ household, during which Mr. Opus had blessedly declined from threatening his wife.  Despondent that his murder plan had failed, Ronald decided to kill himself, and was ultimately struck by the ammunition he had loaded into the gun himself.  Since Ronald was ultimately responsible for the death of Ronald, the medical examiner decides that Ronald Opus committed suicide.  Case closed!

Some might argue that the case is a paradox because Mr. Opus was responsible for the death of his son.  I agree that Mr. Opus ought to be looked into, legally speaking, but ultimately, it was not his intention to kill anyone, and he had no good reason to believe that the gun was loaded.  With the clarity of hindsight, we can say that Mr. Opus should have checked the gun anyway.  I suppose Mr. Opus’s legal culpability in the death of his son will vary from one jurisdiction to the next, depending on local laws.  In any case, this story is not a paradox.  It appears to have been carefully engineered by Don Mills to avoid running into a paradox.


Is this a paradox?  Yes, I believe so.

Intention is a tricky beast.  You might be thinking “Tonight, I will intend to drink the poison so I can collect the million dollars, then change my mind once I have the money.”  But in that case, you aren’t really intending to drink the poison, only to try to trick the billionaire into thinking you intend to drink the poison.  Assuming that the billionaire really has a fool-proof way to measure your intentions, he will surely detect your deception.

The only way to collect the million dollars is to actually intend to drink the poison.  But how can you convince yourself to intend to do something that will lead to 24 hours of excruciating suffering, particularly if you know you don’t have to follow through?  You might tell yourself that 24 hours of pain is not a large price to pay for a cool million, but it must be constantly at the back of your mind that no pain at all is an even lower price, and is entirely within your reach.

Perhaps you could hire a hypnotist to implant a subconscious suggestion that would make you willing – eager, even – to drink the poison, then have him remove the suggestion after you collect the money?  Even if that were truly how hypnosis worked, some versions of the toxin puzzle prohibit outside interference; you must intend to drink the poison all on your own.

Let’s examine the pay-offs and risks associated with each probable scenario.

  1. You intend to drink the poison and then actually drink it.  You make a million dollars, but you endure a day of horrible pain.  It’s a victory, but not one without cost.
  2. You intend to drink the poison but do not drink it.  You make a million dollars with no suffering.  Hooray!
  3. You do not intend to drink the poison, and you do not drink it.  No suffering, but no million dollars either.  You’re pretty much right where you started.
  4. You do not intend to drink the poison, but you do drink it.  You have horrible pain and no money.  What kind of idiot are you?

Here is the paradox: It is rational for you to intend to drink the poison, since you will be rewarded handsomely.  However, once you have collected your reward, it is no longer rational to actually drink the poison, since you will collect no further reward for doing so; indeed, you will be harmed.  By the first argument, a rational person intends to drink the poison, but by the second argument, anybody who intends to drink the poison isn’t rational.

Is there a resolution?  Maybe, but once again, the nature of the resolution depends on whom you ask.

Kavka believed that it was impossible to intend to drink the poison, because any rational person would know that he was not going to drink the poison after getting paid.  The billionaire’s fool-proof intention detection tool would identify cheaters – i.e. rational people – and prevent them from getting paid.  According to Kavka, Options 3 and 4 are the only realistic options, and Option 4 is insane.

David Gauthier proposes a slightly different approach: he believes that the only rational action is to intend to drink the poison, but since you cannot legitimately intend one thing while intending to change your mind later, you must consequently drink the poison.  In other words, Option 2 is impossible and Option 1 is the only option that yields a pay-out suitable to compensate you for your suffering.

For what it’s worth, I think the billionaire is bluffing; it isn’t possible to determine your intentions before you act on them.  Tell the billionaire you intend to drink the poison, making a good show of it.  Then collect your million dollars and say “So long, chump!”  You’re welcome.

So that’s it, folks.  Today’s tally of actual paradoxes: 3/5.  Final tally: 10.5 (maybe 11.5) / 20.  Of the 20 so-called paradoxes presented in the article, fewer than 60% of them were actual paradoxes…according to me (and I cannot emphasize this enough: I am not a professional philosopher, so I submit that my interpretations are subject to correction).  I don’t blame the writers at, however.  As we have seen, it can be difficult to determine what is a paradox and what isn’t.  Even some classic paradoxes are still open to academic debate.

Next time, I’ll get back to the business of trashing hateful, fact-free, terrible memes.  See you then!

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