On widespread disagreement

In his 1978 book "What Is the Name of This Book?," Raymond M. Smullyan repeats a riddle from his childhood:

4. Whose Picture Am I Looking At?

This puzzle was extremely popular during my childhood, but today it seems less widely known.  The remarkable thing about this problem is that most people get the wrong answer but insist (despite all argument) that they are right.  I recall one occasion about 50 years ago when we had some company and had an argument about this problem which seemed to last hours, and in which those who had the right answer just could not convince the others that they were right.  The problem is this.

A man was looking at a portrait.  Someone asked him, "Whose picture are you looking at?"  He replied:  "Brothers and sisters have I none, but this man's father is my father's son." ("This man's father" means, of course, the father of the man in the picture.)

Whose picture was the man looking at?

Often, when I get in long arguments about politics or science or the internet or any number of other things that people strongly differ on, someone (usually someone butting in, who wasn't listening, but occasionally the person I'm arguing with) says, "There is no right answer, people have different opinions and that's that."

Now, these people are clearly wrong.  A system can be complicated, and it can be easy to come to incorrect conclusions when trying to understand that system.  People can over-or-under-emphasize the importance of certain details, or fail to imagine certain actors in the system complexly, or for any number of other reasons become firmly convinced that their conclusion is right, even if it's not.

Lately, it's been reminding me of this riddle.  I have a lot of trouble with this one.  I've known it for years, and I still have trouble holding the whole thing in my head firmly enough to produce the correct answer.  I might have even defended that wrong answer, when I first heard the riddle.

But the wrong answer is definitely wrong.  There can be no difference of opinion about it, only people getting it right or wrong.

In real life, problems are more complicated than that.  Some people may be more right or wrong than others, or disagree about how to act on the knowledge of the correct answer.  People may be bitterly divided over small or large issues.  But in real life, like in this riddle, even if the wrong answer is really persuasive, and has a lot of very vocal supporters, it's still wrong.

Here's the solution to the riddle:


From the book:

A remarkably large number of people arrive at the wrong answer that the man is looking at his own picture.  They put themselves in the place of the man looking at the picture, and reason as follows: "Since I have no brothers or sisters, then my father's son must be me.  Therefore I am looking at a picture of myself."

The first statement of this reasoning is absolutely correct; if I have neither brothers nor sisters, then my father's son is indeed myself.  But it doesn't follow that "myself" is the answer to the problem.  If the second clause of the problem had been, "this man is my father's son," then the answer to the problem would have been "myself."  But the problem didn't say that; it said "this man's father is my father's son."  From which it follows that this man's father is myself (since my father's son is myself).  Since this man's father is myself, then I am this man's father, hence this man must be my son.  Thus the correct answer to the problem is that the man is looking at a picture of his son.

If the skeptical reader is still not convinced (and I'm sure many of you are not!) it might help if you look at the matter a bit more graphically as follows:

(1) This man's father is my father's son.

Substituting the word "myself" for the more cumbersome phrase "my father's son" we get

(2) This man's father is myself.

Now are you convinced?


Opinion vs. fact

There's an article on Theconversation.edu.au called No, you're not entitled to your opinion. It's a great piece, and I recommend all of it. But this part in particular stuck out to me, and I want to talk about it.

Plato distinguished between opinion or common belief (doxa) and certain knowledge, and that’s still a workable distinction today: unlike “1+1=2” or “there are no square circles,” an opinion has a degree of subjectivity and uncertainty to it. But “opinion” ranges from tastes or preferences, through views about questions that concern most people such as prudence or politics, to views grounded in technical expertise, such as legal or scientific opinions.

First of all, it's a well-established fact that I strongly dislike Plato.  But moving on from that,

I don't think that the fact/opinion dichotomy is as worthy of dichotomy status as we treat it.  I think, rather, that opinions are a type of fact.  Specifically, opinions are facts about an individual's preferences.  Opinions have truth-value, just like every other kind of fact.  The problem is, most of the time we phrase statements that should be opinion statements as metaphysical claims.

If I say "Strawberry ice cream is good," I'm wrong.  I'm not saying I'm wrong because there's no one who likes strawberry ice cream.  I like strawberry ice cream.  I'm wrong because strawberry ice cream does not posses intrinsic metaphysical value.  It is not good, people just like it.

If I say "I dislike strawberry ice cream," I'm still wrong.  Or, I'm lying.  This time it's phrased as an opinion statement, but the statement I'm making is a lie about the fact of my experience.

To use a more common manifestation of this argument, let's try this with God.

  • "God is real" is not an opinion.  It's a fact-claim.  Its truth or falsehood is external to individual beliefs.  (Unless you believe in a fairly complicated metaphysics, but it's still not an opinion.)
  • "I believe in God" is not an opinion.  It's a statement about your internal set of presumed fact-claims.
  • "I love God" is an opinion.  Now, we're talking about your emotional relationship to something external. Just like I can say "I love Batman" as easily as I can say "I love Terry Pratchett," whether God is real or not doesn't affect your ability to have feelings relating to that concept.

So, yeah.  That's how I feel about all that.