Did Peirce hold that, when stripped to its absolute core, Descartes’ cogito could be summarized as: ‘There is an Idea’?

Question

In ‘The Simplest Mathematics’ (1933), C.S. peirce elaborated:

It is a fundamental mistake to suppose that an idea which stands isolated can be otherwise than perfectly blind. He professes to doubt the testimony of his memory; and in that case all that is left is a vague indescribable idea. There is no warrant for putting it into the first person singular. "I think" begs the question. "There is an idea: therefore, I am," it may be contended represents a compulsion of thought; but it is not a rational compulsion. There is nothing clear in it. Here is a man who utterly disbelieves and almost denies the dicta of memory.

He notices an idea, and then he thinks he exists. The ego of which he thinks is nothing but a holder together of ideas.

But if memory lies there may be only one idea. If that one idea suggests a holder-together of ideas, how it can do so is a mystery.

Much has been published on this site regarding the cogito. Notably, I’ve seen in my surfing that users such as Conifold and Alexander S. King, as well as others, make note of minds who objected to the cogito with the likes of Kant and Nietzsche, who argued against the unity of the I, or the self, but didn’t object as hard to the proposition (or conclusion) that “there is thinking”, or that “thinking is occurring” as a base epistemological certainty.

Did Peirce come to the same conclusion as they did when he said “there is an idea?” … “A vague, indescribable idea?” Despite not giving any credence to the idea of the ‘I’, as many others have done in dissecting Descartes’ cogito?

Answer 1

Q: Did Peirce come to the same conclusion as they did when he said “there is an idea?”

Pierce distinguishes himself by addressing the dimension of time as memory, albeit in passing. Heidegger develops the theme significantly in that time is understood as structurally incorporated in the 'holder-together': i.e. the self is temporal.

From The Principle of Reason (1957) p.12

It is well known that Descartes wanted to bring all human knowing to an unshakable ground (fundamentum inconcussum) by first doubting everything and acknowledging only what presented itself clearly and distinctly as secure knowledge. Leibniz remarked that Descartes’ procedure neglected to specify what was entailed in the clarity and distinctness of cognition that count as his leading principles. According to Leibniz, Descartes had at this point doubted too little. Concerning this, Leibniz said in a letter to Johann Bernoulli on August 23, 1696: sed ille dupliciter peccavit, nimis dubitando et nimis facile a dubitatione discedendo; “but he (Descartes) failed in a two-fold manner, by his doubting too much and by too easily desisting from doubting.”4

and Being & Time (1927) p.45-46

Kant took over Descartes' position quite dogmatically, notwith­standing all the essential respects in which he had gone beyond him. Furthermore, in spite of the fact that he was bringing the phenomenon of time back into the subject again, his analysis of it remained oriented towards the traditional way in which time had been ordinarily under­stood; in the long run this kept him from working out the phenomenon of a 'transcendental determination of time' in its own structure and function. Because of this double effect of tradition the decisive connection between time and the 'I think' was shrouded in utter darkness; it did not even become a problem.

In taking over Descartes' ontological position Kant made an essential omission: he failed to provide an ontology of Dasein. This omission was a decisive one in the spirit [im Sinne] of Descartes' ownmost Tendencies. With the 'cogito sum' Descartes had claimed that he was putting philo­sophy on a new and firm footing. But what he left undetermined when he began in this 'radical' way, was the kind of Being which belongs to the res cogitans, or—more precisely—the meaning of the Being of the 'sum'.1 By working out the unexpressed ontological foundations of the 'cogito sum', we shall complete our sojourn at the second station along the path of our destructive retrospect of the history of ontology. Our Interpretation will not only prove that Descartes had to neglect the question of Being altogether; it will also show why he came to suppose that the absolute 'Being­-certain' ["Gewisssein"] of the cogito exempted him from raising the ques­tion of the meaning of the Being which this entity possesses.