Case Study 2
Logical Proof and Factual Proof
At this stage, we can begin to introduce rudimentary logical concepts and distinctions. In everyday conversation, children have already begun using what we might call “natural logic.” They may, for example, get in arguments, like the one below, in which they draw conclusions based on premises. When children present these types of arguments, parents can intervene to teach basic logical concepts and ask children how a given conclusion might be proven or disproven.
One distinction appropriate to teach at this age is that between logical proof (proof that draws logical conclusions from certain premises) and factual proof (proof that uses actual facts to prove or disprove a given statement). The following anecdote provides the opportunity for such a lesson.
William and Eve, two children walking their dog in the park, are having a conversation about Labradors:
— “There are two kinds of Labradors—black and golden,” declares William.
— “That’s not true; there are also chocolate Labradors,” replies Eve. “My friend Adam has one.”
— “Well, his dog must not be a Labrador then,” William says.
How might we interpret this conversation?
In terms of logical proof, if Labradors are either black or golden, Adam’s chocolate “Labrador” cannot be a Labrador. That is a logically formulated proof. The reasoning is valid. It is the basic premise, William’s initial declaration that there are only two kinds of Labradors, that is false. It is, therefore, possible for William to draw a false conclusion even though his logic is technically correct.
In terms of factual proof, if we can prove that the chocolate-colored dog has two Labrador parents, we can factually prove that William’s premise is wrong: there are at least three types of Labrador.
There are many opportunities like this one to begin to make explicit the logical steps involved in everyday conversations with your children and to show them that they are already using logic, even if they may not know it. This serves to get them thinking about their own thinking, and it makes the topics of logic and reasoning less intimidating.