Qualifica Autore: University “Federico II” of Naples, Italy

I claim that there exists an exact relationship between politics and logic provided that to classical logic one adds intuitionist logic.

i) If politics is intended as a war (see e.g. Schmitt, Foucault, etc.) K. von Clausewitz’ book about war (1832) presents both an „absolute war“, performed according to dichotomic laws of classical logic (eg win/lose) and a „real war“, which he describes through several doubly negated propositions (DNPs) of intuitionist logic; e.g. „War is nothing but a continuation of political intercourse”(Cap. VI B). (Two other celebrated strategists, Sun Tzu (VI-V Century B.C.) and Lazare Carnot (1753-1823) illustrated their strategies through DNPs). Clausewitz’ book also presents ad absurdum arguments pertaining to intuitionist logic. ii) If politics is intended as an exercise of social power, Machiavelli and Hobbes illustrate it through classical logic of yes-or-not propositions; e.g. “The enemies of my enemies are my friends.” Instead, Arendt: “to be political… mean[s to decide].. not through violence.”. Gandhi was the champion of this kind of politics, based on the DNP “non-violence”. Also Gandhi reasoned through ad absurdum arguments whose I offer some instances; eg “[ØTs] An eye for an eye [┴] only ends up making the whole world blind”. As a logical conseuence, [Ø ØTs] “No eye for an eye”, a proposition leading him to act through “Non-violence”. The last step is recognized as the application of the principle of sufficient reason, which results to be the inverse translation of the GKG double negation translation. iii) Similar results are obtained if politics is intended as an activity of conflict resolution in the interpersonal rlationships.

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