Counterexamples to "All"

Since "All" means "every single one without any exceptions" then it is hard for "All" statements to be true and easy for them to be false. Indeed it only takes one example to prove it false. "All Americans drive cars" can be disproven by a single American. Find one who doesn't drive and the sentence is false. However, finding one, two or even hundreds of examples of Americans who do drive cars will not be sufficient to prove the "All" statement true.

We call examples which disprove universal statements counterexamples. A counterexample to an A Form statement is a member of the subject category that is not also a member of the predicate category. So to find a counterexample to "All swans are white" we must find a member of the subject category a swan that is not a member of the predicate category white. So a black swan would be a counterexample. Notice that finding a member of the predicate category that is not a member of the subject category is not a counterexample. So if you find a white duck that will not be a counterexample to "All swans are white." The statement doesn't say anything about what color ducks are. It only makes a claim about swans.

While positive examples of A Form categorical statements do not provide proof, they do provide confirmation. Suppose I say "All birds have feathers" and someone challenges me to provide a reason. I would naturally point out positive instances of my claim "Robins have feathers. Blue jays have feathers. Eagles have feathers." While each falls short of proof, each example does provide relevant evidence that supports my claim. Such positive evidence that falls short of proof is called confirmation.

This is easy to see with such concrete categories as birds and colors, but it is surprising how many mistakes people make with regard to counterexamples when the categories are abstract and hard to visualize in the imagination. But logic is about forms and patterns. It does not matter if we can visualize the objects talked about or not.

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