Plato, attempting to explain why mirrors reverse left–right, in the Timaeus Place a clock in front of a mirror and join the numbers with imaginary lines. The lines do not cross top to bottom or left to right.
would be oriented if you were rotated to stand across from yourself, and how mirrors actually refl ect an image of you, we take something for granted. This is the axis about which we rotate you when we imagine you behind the mirror.
TURNING IT AROUND When we turn something around, we rotate it on an axis. A spinning top, for example, rotates around a vertical axis.
A car wheel rotates around a horizontal axis. When we imagine you over there in the position your mirror-self seems to be in, we mentally put you there by rotating you on a vertical axis, as in the above diagram. But what if we were to place you over there by rotating you around a horizontal axis instead? Then you would be standing on your head. And, compared to your mirror image, your left and right sides would not then be switched around.
Your left hand (the one that is pointing in the diagram) would remain to the left.
Which is where your right hand would appear if it were refl ected in a mirror.
But top and bottom are now reversed.
Your head appears where your feet are in the image.
It seems the reason we say mirrors reverse left and right but not top and bottom is due to the fact that we take for granted a particular axis of rotation. But we could just as easily choose a horizontal axis. Then it would be true to say that a mirror reverses top to bottom but not left
to right. So yes, it is true to say mirrors reverse left to right, but only if we choose a vertical axis of rotation. Choose a horizontal axis and they then reverse top to bottom instead.
OVERLOOKING THE OBVIOUS Of course, this explanation of why people perceive there to be something puzzling about mirrors raises the question of why we take the vertical axis for granted. The answer, presumably, is that we are not in the habit of somersaulting through the air and landing on our heads. We stand upright (most of the time), and when we rotate, it is almost always on a vertical axis. So this puzzle about why mirrors do what they do is generated by our not noticing what has been taken for granted.
Rotated on a vertical axis (above) it is as if the man stands behind the glass, facing himself: his left hand is now on the right, and vice versa. Rotating him around a horizontal axis (above right), top and bottom are reversed, but not left and right.
WHEN ONLY PHILOSOPHY WILL DO Notice that if this solution (or part solution) to the mirror puzzle is correct, we certainly didn’t have to conduct any scientifi c research into how light and mirrors behave.
Nor did we have to investigate how our brains work. Even if we had done that sort of scientifi c research, it still wouldn’t have solved the puzzle. In order to solve this puzzle, we need to stop doing science and start doing philosophy. It is a puzzle that is solved by thinking. People sometimes assume all questions can be answered by science. They would assume that the mirror puzzle must have a scientifi c solution.
But it turns out that the mirror puzzle is a puzzle that science cannot solve. It seems that, sometimes, only philosophy will do.
MIND-DEPENDENCE 99
Here is a conundrum related to the mirror puzzle. Walk through a door that opens on your left and turn around to come back through it, and the door now opens on your right. But pass through a door that opens at the top (like a cat flap) and turn to come back through it and the door still opens at the top. Why does passing through a door reverse the way it opens from left to right, but not top to bottom?
THE DOOR PUZZLE
reversed but not top and bottom only because we take for granted a particular axis of rotation. In the weightless environment of space, you could just as easily spin on a horizontal axis instead. So, after years in space, it might seem as natural to you to say that a door that opens at the top opens at the bottom when you come back through it, as it does to say that a door that opens on the left opens on the right when you return through it.
For creatures that live in a weightless environment, where it is as easy to rotate on one axis as on the other, perhaps neither the mirror puzzle nor the door puzzle would even be puzzles.
SOLVING THE MYSTERY The solution to the door puzzle is much the same as for the mirror puzzle.
When you pass through a left-opening door and turn around to come back through it, you would normally rotate on a vertical axis. But what if you were to rotate on a horizontal axis, and you floated back through upside down? Then the
door that opened on the left would still open on the left on the way back through it, but a door that opened at the bottom would now open at the top. We say that left and right are
For astronauts in a weightless environment, it is as easy to rotate on a horizontal axis as it is to rotate on a vertical one.
Pass through this door, and it opens to the right. Return, and it now opens to the left.
here are three different ways in which we can think about morals. First, we can think about whether a particular action or type of action is right or wrong. Are abortion or euthanasia right or wrong? When is lying permissible, if ever? This type of thinking is called practical ethics, and anyone who has ever argued the case for or against a certain action on the basis of morality has engaged in it.
How are we to fi nd the answers to these types of questions? Normative ethics, the second way to think about right and wrong, good and bad, develops general theories about what is right and what is good that we can use in practical cases. We can try to understand these ideas by looking at our actions themselves;
or through examining the consequences of our actions; or by looking at the types of people we can be or become.
The third way to think critically and refl ectively about morality is metaethics (“meta-” is a Greek word that means
MORAL