Carroll's Paradox from the viewpoints of Wittgenstein, Ibn Sīnā, and Tūsī

Carroll’s paradox calls the most fundamental concept of logic, namely the concept of inference, into challenge, and appears to convey that one cannot pass, in any inferences, legitimately from premises to conclusion. So as to get hold of any possible solution out of their writings, the current article puts the paradox under three giant thinkers’ (i.e. Wittgenstein, Ibn Sīnā, and Tūsī) views. Wittgenstein puts forward an “inexpressible” but “showable” modus ponens in all inferences that leads ultimately to the distinction between “rule” and “premise”. Ibn Sīnā recognizes the logical principles as criterion (“mikyāl”) not as matter (“mādda”) for which the same exactly holds as the above distinction. Also, Tūsī speaks of the necessity of any syllogism to have an “assistant” and “concomitant” modus ponens that can be considered as the iteration of Wittgenstein’s “inexpressible-but-showable modus ponens” leading as before to the mentioned distinction. As a key solution to Carroll’s paradox, one should make a robust distinction between “rule” and “premise”, and bring inadmissibility to converting the former to the latter.