Peirce often refers to time as a prototype of continuity and hence of Thirdness. On the other hand, he also points out that temporal continuity is imperfect. The continuity of time evinces “topical singularities, or places of lower dimensionality where it is interrupted or divides” (CP 4.642, 1908) so that “we have no reason to think that [...] time is quite perfectly continuous and uniform in its flow” (CP 1.412, c.1890). Peirce argues that there is pseudo-continuity in time. The continuity of time is imperfect because the present interrupts the flow of time from the past to the future and “the actual instant differs from all other instants”. In our consciousness, “the past is broken off from the future” (CP 6.86, 1898). Furthermore, there is discontinuity in time because the change of objects considered in time "makes their self-identity discontinuous" (cf. CP 1.492, 1893). The contribution discusses this paradox with special reference to a paper of 1908, in which Peirce describes the scenario of a traveler "somehow, in a situation like that of sailing along a coast in the cabin of a steamboat in a dark night illumined by frequent flashes of lightning, and looking out of the windows" (CP 4.642). Session proposal: “Timetrajectories: Limits of time, the Time of Limits”