No one answered the classical Chinese puzzle or its metaversion? That’s a shame. It does seem to show that brainteasers are popular in many places. Or as they might have said, xin teasers. Much classical Chinese thought held the organ of cognition as being the heart, mind you (brain you?) — an odd convergence with Aristotle.
My take on it is that if one interprets it as “White horse is not a horse” then it is meant to remind us that a class is not an individual. This emphasis of the article is necessary for the explanation of the puzzle; it has no counterpart in classical Chinese and thus gives rise to a puzzle. The metapuzzle, via the charity idea is: Why is this a puzzle anyway? That’s an interesting metaquestion, because it is unclear that it was even meant to be a puzzle. So you were asked to interpret it as one and that seemed plausible enough (presumably) because you’re reading a column about puzzles.
To make up for the flop that was, I’ve gathered 15 tiny conundrums taken from more contemporary sources.
Most of these are adapted from Remarks on the Philosophy of Psychology, Remarks on the Foundations of Mathematics, and On Certainty, all by Wittgenstein. I have also included a few from Dennett along the same lines, and one or two by me alone. I have put the puzzle in bold and then produced some comments to get you started. If you want specific references I can dig them out if you contact me privately. There are items related to the philosophies of mathematics, language, art, and computing, as well as logic and epistemology. Something for everyone!
1. Why is it odd to say that a rose has no teeth but not odd to say that a goose has no teeth?
a. Is the claim even true? b. Is it merely because a goose is an animal? If so, why does that matter?
2. Imagine a cow. Now imagine a purple cow. What’s the difference?
a. Is each cow looking at you head on? Can you see her feet?
3. Does a calculating machine calculate?
a. Wittgenstein likely thought not, because it could not take part in the social system involved in calculating, like being corrected for errors. b. Bunge thought similarly — oddly, given his antipathy to Wittgenstein. Yet he also added the idea that because the calculating machine is only finite precision and range, it does not calculate, but rather “obey” laws that allow a human to read off approximations to the ‘+’ function. [Hint to the hint: Is there a difference between a calculator and computer here? Does it matter? Mathematician Ian Stewart thought not in the appendix of his calculus textbook, which he called “Lies my calculator or computer told me.”]
4. I go to the National Portrait Gallery of some country and see a painting of that country’s first leader. What makes the painting of her?
a. Could one paint a painting of someone by accident?
5. Can one depict “wanting an apple” in a painting? Does one have to depict an apple to do so? Can one do it in music (without lyrics)?
a. If one can do it without the apple depiction, what makes it about an apple?
6. What would a painting depicting “Goethe composing Beethoven’s 9th symphony” look like? Would it be any different from one of “Goethe composing ‘Think of Me’” (from Phantom of the Opera)? Or different from him composing “Bolero,” by Ravel?
a. I have expanded, greatly, Wittgesntein’s idea here. Note carefully the timeline! b. Historical note: Wittgenstein the philosopher is the brother of Paul Wittgenstein,the “one handed” composer, and came from a very musical family beyond that.
7. Can one consider something (e.g., what to eat) mechanically?
a. Why is this different from calculating mechanically?
8. Can one imagine calculating in one’s head?
9. Thoughts can be care-laden but not toothache-laden. Why?
a. Really? I dare say Wittgenstein is wrong.
10. How does one know that one has successfully obeyed the order “Imagine Ms. X!”
a. Suppose you were given the order by a drill sergeant. How will he check for obedience?
11. How do we learn to infer?
a. I dare say we don’t. Empiricists might struggle with this one.
12. What would change if we suddenly discovered that we had always gotten 12×12 wrong?
a. Does it matter if the multiplication was instead 34523987x234973928?
13. You encounter an intelligent creature of a kind unknown to science. Somehow, you manage to communicate in a natural language. It does not know what following a rule is; there’s no such practice in its life. How do you teach it this?
a. Is this situation self-contradictory? HINT: AI.
14. Following on 13, you encounter another such creature, of a different species, who has no notion of games. How do you teach it? What psychosocial prerequisites are needed?
15. How do you know the class of all cats is not a cat?
a. Frege also asked a similar question: How do you know that Julius Caesar is not a number?