Had I not stumbled upon the mnemonic chart of syllogisms, as used by the Renaissance masters for their students at that time, I would have been utterly lost in this chapter. I honestly could not figure out, why in the world Aristotle would provide all these different examples of invalid syllogisms, and not provide one demonstration of a valid one with predefined terms from natural philosophy. I was trying to understand the point and purpose of this. Every example he provided did not make any sense to me and felt very absurd to even reason with: “Some horse is no white, no crow is a horse, therefore no crow is white.” I kept asking myself, “So what? That, ‘no crow is a horse, while some horse is not white?’ What does that have to with a crow not being white? It has nothing to with it; these things are irrelevant and prove nothing about each other.”
Learning of Barbara, Celarent, Darii, and Ferio shed light on this question. It was such a huge breakthrough for me. Once I learned their propositional order, then it became a piece of cake to simply diagram out each syllogism in my notes and see why these were not working. In fact, I was able to quickly recognize what was universal, particular, privative, categoric, and the quick determination of the validity of each demonstration. I also noticed a commonality between the four perfect first figure syllogisms: viz. B A, C B, C A. Coming back to my original conundrum of not understanding why he demonstrates these as he did: it seems that he is showing us examples that are wrong, in order to make what is true more apparent to us.
Aristotle, Prior Analytics. Book I, Chapter 4.
EAR