John Corcoran

(1937 - 2021)

As noted in 1962 by Timothy Smiley, if Aristotle’s logic is faithfully translated into modern symbolic logic, the fit is exact. If categorical sentences are translated into many-sorted logic MSL according to Smiley’s method or the two other methods presented here, an argument with arbitrarily many premises is valid according to Aristotle’s system if and only if its translation is valid according to modern standard many-sorted logic. As William Parry observed in 1973, this result can be proved using my 1972 proof of the completeness of Aristotle’s syllogistic.

Contrary to dictionaries, a non sequitur isn’t “any statement that doesn’t follow logically from previous statements”. Otherwise, every opening statement would be a non sequitur: a non sequitur is a statement claimed to follow from previous statements but that doesn’t follow. If the sentence making a given statement doesn’t contain ‘thus’, ‘so’, ‘hence’, ‘therefore’, or something else indicating an implication claim, the statement isn’t a non sequitur in this sense. But this is only one of several senses of that expression, which, contrary to appearances, is a unitary common noun more properly written as one word: non-sequitur or nonsequitur. Above a nonsequitur was, roughly speaking, a conclusion of an invalid premise- conclusion argument, but not every such, only those that were stated to follow from premises that had been stated. Every informative proposition is the conclusion of an invalid argument. Anyway, nonsequiturs were not arguments. However, the expression ‘nonsequitur’ also means “invalid premise- conclusion argument”. It also means something like “fallacious reasoning” as in ‘Abe’s proof of the big-bang hypothesis is a nonsequitur’. The English noun is also used for an irrelevancy, an abrupt change of topic, or for any of many other expressions that are gratuitous, inappropriate, incongruous, or in some other way out of place. The English noun is derived from the Latin expression ‘non sequitur’, which is not a common noun but a sentence variously meaning “it isn’t in sequence ”, “it doesn’t follow”, “it is out of order”, etc. A statement that begins ‘in the second place’ is a nonsequitur if the previous sentence lacked implication of something like ‘in the first place’ or if it contained something similar to ‘in the third place’. In fact, a true implication claim can be a nonsequitur if there is no reason for making it. If Ben says ‘Hence, Abe swims and Abe swims’ in reply to Carl’s statement ‘Abe swims‘, then Ben may well be committing a nonsequitur. Many conversation stoppers are nonsequiturs. This lecture surveys and analyses a wide selection of uses of ‘nonsequitur’ in logic and logic-related literature. -/- END OF DRAFT 4 -/- NOTE 091215: When Rick Perry was discussing possible withdrawal from the race—unfortunately not the human race but the Republican race—a reporter reminded him that just last week Donald Trump predicted the Perry withdrawal. Perry interrupted with “A broken clock is right once a day”. -/- If you did not know Perry you might think his reply was a brilliant diversionary nonsequitur. If you know Perry you might think his reply was a stupid nonsequitur. -/- For the record, he did say ‘once a day’, not ‘twice a day’. BTW, my interjection ‘unfortunately not the human race but the Republican race’ was also a nonsequitur