 Peirce was both aware and untroubled by infinite semiosis. In part, this is due to the anti-Cartesian project carried out in Peirce’s work in the 1860s. A significant part of this project for Peirce is the denial of intuitions, something that Peirce took as a key assumption of Cartesian philosophical method. Given that Peirce defines “intuition” as “a cognition not determined by a previous cognition of the same object” (W2. 193), it seems clear that the infinite procession of thought-signs generated by earlier thought-signs and in turn generating further thought-signs is part and parcel of the denial of intuitions. However, in later developments to his sign theory, despite never explicitly relinquishing infinite semiosis, many of the concepts that lead to it are replaced or revised, and the concept becomes less prominent in Peirce’s work. (See Atkin 2015, 132–135) for more on the anti-Cartesian motivation of Peirce’s early account of signs).