Let us ask the question, “Should we say that the arrows ⟶ and ⟵ point in the same direction or in different directions?” ‒ ‒ At first sight you might be inclined to say, “Of course, in different directions.” But look at it this way: If I look into a looking glass and see the reflection of my face, I can take this as a criterion for seeing my own head. If on the other hand, I saw in it the back of a head I might say, “It can't be my own head I am seeing, but a head looking in the opposite direction.” Now this could lead me on to say that an arrow and the reflection of an arrow in a glass have the same direction when they point

towards
at

each other, and opposite directions when the head of the one points to the tail end of the other. Imagine the case that a man had been taught the ordinary use of the word “the same” in the cases of “the same colour”, & “the same shape”, “the same length.” He had also been taught the use of the word “to point to” in such contexts as, “The arrow points to the tree.” Now we shew him two arrows facing each other, and two arrows one following the other, and ask him in which of these two cases he'd apply the phrase, “The arrows point the same way.” Isn't it easy to imagine that if certain applications were uppermost in his mind, he would be inclined to say that the arrows ⟶ ⟵ point “the same way”?

(2015–) Wittgenstein Source Bergen Nachlass Edition (WS-BNE). Edited by the Wittgenstein Archives at the University of Bergen under the direction of Alois Pichler. In: Wittgenstein Source, curated by Alois Pichler (2009–) and Joseph Wang-Kathrein (2020–). (N) Bergen: WAB.