There is a lot of very interesting medieval work on epistemic modalities, usually found in treatises De scire et dubitare, and whenever I present on this material at conferences, contemporary logicians always want to know whether they considered iterated modalities.
The answer is, it’s not always clear. Certainly the frameworks that they construct are more than apt for iterating, and there are some contexts in which you can find explicit denials of positive introspection () and multi-agent epistemic statements (e.g., ). But I have certainly never found any explicit discussion of unrestricted iteration, or even any clear examples of triple iteration.
Which is why this sophism caught my eye earlier today when reading (D’Ors 2015):
Sortes scit an Plato sciat an Sortes sciat an Plato sciat aliquid de eo.
This sophism is number three in a list of sophisms that “were taken as the ‘topical sophisms’ in connection to the syncategorem ‘an‘ (p. 142), and unfortunately the rest of the paper focuses on the first two, and doesn’t discuss this one further. There isn’t even a translation given, and I have to admit, I’m not entirely confident how to translate it myself; but it certainly does look like it should read something like:
Socrates knows whether Plato knows whether Socrates knows whether Plato knows something of him.
I haven’t been able to find any explicit discussion of this sophism by modern commentators; the closest I’ve found, other than its reference in (D’Ors 2015), is in (Streveler 1993), where it appears in the list of sophisms in the Magister Abstractionum(p. 145). I don’t have access to that text, but the sophism also occurs in Richard the Sophister:
Item, dubitet Plato utrum Sortes sciat aliquid de eo et similiter Sortes dubitet utrum Plato sciat aliquid de eo et proponatur: SORTES SCIT AN PLATO SCIAT AN SORTES SCIAT AN PLATO SCIAT ALIQUID DE EO. Et probatur sic: Sortem scire an Plato sciat aliquid de eo, scilicet de Sorte, est quoddam falsum; et Sortes scit quod nullum falsum scitur, ergo Sortes scit Platonem non scire Sortem // scire an Plato sciat aliquid de eo; ergo // Sortes scit an Plato sciat an Plato sciat etc.
Sed contra: Sortes neque scit Platonem scire neque non scire aliquid de eo; non ergo Sortes scit an Plato sciat an Sortes sciat an Plato sciat aliquid de eo.
I will not attempt a rendering of this at this point; instead, let’s look at a simplified version of the sophism that appears in the Abstractiones of Herveus the Sophister:
Item. In rei veratete Sor scit multa de Platone, Plato multa de Sorte, sed uterque dubitat, utrum reliquus sciat aliquid de se; inde sic: SOR SCIT, AN PLATO SCIAT ALIQUID DE EO. Probatio. Sor scire, an Plato sciat aliquid de eo, est falsum, et Sor scit, quod nullum falsum scitur; ergo Sor scit Platonem non scire hoc; ergo scit Sor, an Plato sciat, etc. Vel sic: Sor scit, an Plato sciat aliquid de eo, quoniam scit se ipsum scire; similiter scit Platonem scire aliquid de Plato; ergo Sor scit, an Plato sciat aliquid de eo. Contra. Ergo Sor scit Platonem scire vel non scire aliquid de eo. Quod falsum est: dubitat enim ipsum scire et ipsum non scire, etc.
Let’s give a stab at translating this:
The truth of things is that Socrates knows many things concerning Plato and Plato many things concerning Socrates, but one of them is uncertain whether the other knows something about him, hence thus: SOCRATES KNOWS WHETHER PLATO KNOWS SOMETHING ABOUT HIM. Proof: That Socrates knows whether Plato knows something about him is false, and Socrates knows that nothing false is known, therefore Socrates knows that Plato does not know this, therefore Socrates knows whether Plato knows, etc. Or so: Socrates knows whether Plato knows something about him, because he [Socrates] knows that he knows something about himself, similarly, he knows that Plato knows something about Plato, therefore Socrates knows whether Plato knows something about him. Contra: Therefore Socrates knows that Plato knows or does not know something about him, which is false: For he is doubtful that he himself knows and that he himself does not know.
I have to say, I’m not entirely sure what to make of this, but maybe I’ll come back to Richard’s version at some point and see if working through that one sheds any light!
- D’Ors, Angel. 2015. “Tu scis an de mentiente sit falsum Sortem esse illum: On the Syncategorem ‘an‘”, in P. Pérez-Ilzarbe & M. Cerezo, eds., History of Logic and Semantics: Studies on the Aristotelian and Terminist Traditions (Brill): 128-151.
- Streveler, Paul A. 1993. “A Comparative Analysis of the Treatment of Sophisms in MSS Digby 2 and Royal 12 of the Magister Abstractionum“, in S. Read, ed., Sophisms in Medieval Logic and Grammar. Nijhoff International Philosophy Series, vol 48. (Springer).