Ad Hominem Logic: Logic between Aristotle and Boole
The aim of this study is to contrast Aristotelian essentialism with Boolean extensionalism and to discuss the aftermath. This precludes discussion of much interesting material and of many interesting periods in the history of logic. Megarian and Stoic logic are mentioned now only in passing and to a very limited end. Significant works of Aristotle’s followers (Greek, Roman, Arabic and scholastic) are ignored here. We are about to leap forward in time, then: from the time of Aristotle’s to that of Leibniz. The next two chapters should cushion the landing.
Some formal limitations of Aristotle’s system of logic were well known at least since the Stoics worded new rules of inference (such as the ones known today as the modus ponens and tollens). This suffices as a rather straightforward refutation of the claim that the Aristotelian system is complete: it does not describe all valid reasoning. As it was well known, since antiquity, how did this knowledge influence the history of logic? I expand a bit on the formal limitations of Aristotle’s logic in this chapter.
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