First Premise Second Premise ConclusionAnd we consider the best known example of it:
All men are mortal. Socrates is a man. Therefore, Socrates is mortal.This is correct logic since
But one of our corny ancestors turned this syllogism into the following:
The Apostles are twelve. Peter was an Apostle. Therefore, Peter was twelve.Yak! Yak! But, firstly, we clear up the langabuse in the First Premise of this second form: "The Apostles are twelve." You do not, do not, do not say, "Two plus three are five" -- rather, "Two plus three is five". Each addend ("two", "three") is "absorbed into" the sum ("five"). So, the articulation of the "First Premise" is: "The count of the set of Apostles is twelve". That is, "twelveness" is predicated about "Apostles". It requires all members of the set of Apostles to provide eligibility for twelveness. (Get it? Each member must "cosign" for this "loan".) Hence, the illogic of the "First Premise" invalidates the entire argument .
For this reason, I vehemently urge parents and teachers to teach small children to count fingers of the hand as follows: count by ORDINAL NAMES, "First, second, third, fourth, fifth", then (gesturing around all the fingers of that hand) state the CARDINAL NAME , "Five". (Get it? ORDINALITY MEASURES CARDINALITY!) Otherwise, the previous argument can be rephrased:
The hand's fingers are five. Thumb is a finger. Therefore, thumb is five.After doing the ordinality-into-cardinality form a sufficiency of times, we can permit the langbuse of counting: "One, two, three, four, five".
The great American logician, WillardOrman Quine (x-y) advised us: "We can permit the abuse of language whereby we confuse a singleton set with its only member".
Elsewhere I've defined "education" as "knowing where to find a knowable when you need it". Travel light, but secure your inventory! Especially that involving Logic and Truth. If you're challenged about paying a bill, be able to produce the cancelled check for your payment. If challenged about your reasoning, be able to "flesh out the ellipsis" correctly! Or get expert help to do so.