[16ff] Now Kant says "I do not approve of the rule that if the use of pure reason has proved something this result should later no longer be doubted, as though it were a solid axiom." And he said "I do not share the opinion that one should not doubt once one has convinced one's self of something. In pure philosophy this is impossible. Our mind has a natural aversion against it. From which it seems to follow that the business of thinking is like the veil of Penelope. It undoes every morning what it has finished the night before."
If it is true that the ability to think and even certain habits and the ability to engage in so profitless an enterprise must be ascribed by everybody -- to the many and not to the few -- then we find ourselves in a curiously difficult and paradoxical situation. For this everybody writes notebooks to tell us about his experiences, yet much more urgent business... And the few who do write books can hardly [make a coherent explanation(?)].
Wikipedia explains the Penelope reference.
Penelope is married to the main character, the king of Ithaca, Odysseus (Ulysses in Roman mythology), and daughter of Icarius of Sparta and Periboea (or Polycaste). She only has one son with Odysseus, Telemachus, who was born just before Odysseus was called to fight in the Trojan War. She waits twenty years for Odysseus' return, during which time she devises various cunning strategies to delay marrying any of the 108 suitors.
On Odysseus's return, disguised as an old beggar, he finds that Penelope has remained faithful. She has devised cunning tricks to delay the suitors, one of which is to pretend to be weaving a burial shroud for Odysseus's elderly father Laertes and claiming that she will choose a suitor when she has finished. Every night for three years, she undoes part of the shroud, until Melantho, a slave, discovers her chicanery and reveals it to the suitors.
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