Taking Aim with the Cartesian Canon

Call the Cartesian Canon the principle that whatever one has reason to doubt should be rejected as false. This is a useful principle, perhaps, when one is engaged in foundational epistemology, but its appropriateness elsewhere is disputable.

Now my question is: Do KRS rely on the Cartesian Canon in their conclusion about how far the fragment of Anaximander extends in the passage from Simplicius?

Their view, which I believe is the most widely accepted view, is that the fragment consists only of the words in bold:

ἐξ ὧν δὲ ἡ γένεσίς ἐστι τοῖς οὖσι, καὶ τὴν φθορὰν εἰς ταῦτα γίνεσθαι κατὰ τὸ χρεών. διδόναι γὰρ αὐτὰ δίκην καὶ τίσιν ἀλλήλοις τῆς ἀδικίας κατὰ τὴν τοῦ χρόνου τάξιν, ποιητικωτέροις οὕτως ὀνόμασιν αὐτὰ λέγων·

"And the source of coming-to-be for existing things is that into which destruction, too, happens 'according to necessity; for they pay penalty and retribution to each other for their injustice according to the assessment of Time', as he describes it in these rather poetical terms" (KRS).

Using the Cartesian Canon, one might reason about the passage thus:

The words "as he describes it in these rather poetical terms" mark the end of a quotation, surely. But then how far back should the fragment be counted as going (since obviously it does not go back to the beginning)? It goes back only as far as we are certain that it is a quotation. The words γένεσις and φθορά are stock Peripatetic terms; the thought expressed by ἐξ ὧν δὲ ἡ γένεσίς ἐστι τοῖς οὖσι, καὶ τὴν φθορὰν εἰς ταῦτα γίνεσθαι is also endorsed by Peripatetics (see Arist. Phys. 204b33). Thus that might have been written by a Peripatetic (Theophrastus). Thus we should not count it as part of the fragment.

Now is this how KRS argue, or is their view, rather, simply that it is most plausible (all things considered) that the quotation extends thus far? After all, one might consider it possible that ἐξ ὧν δὲ ἡ γένεσίς ἐστι τοῖς οὖσι, καὶ τὴν φθορὰν εἰς ταῦτα γίνεσθαι were the words of a Peripatetic historian, but still ascribe them to Anaximander, all things considered.

To be continued.