In the second half of the eighteen century, Immanuel Kant challenged the supporters of the relational account of space with his famous argument, in which he took advantage of the existence of incongruent counterparts. This reasoning generated a great deal of heated debate that has lasted until nowadays. As it turns out, one of the most popular types of responses these days refers to the notion of non-orientable spacetimes, for which the Kantian argument fails. I shall take this as a motivation to pay more attention to the issue of orientability in the philosophy of spacetime. In particular, I will examine some possible tests for the orientability of our spacetime and answer whether they are able to provide reliable results.
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