Every exception to a rule works as a counterexample.
The notion of counterexample refers to an example that is used to deny or refute what another tried to explain. A counterexample, therefore, works in opposition to a first example.
Before continuing, it is important to mention that examples are propositions , expressions or facts that are cited with the intention of illustrating or demonstrating something . If a person wants to contradict what has been stated, they can resort to a counterexample.
Possible situations
Suppose someone, in a conversation, says: “All children like to play soccer, my son Raúl can spend hours kicking a ball.” Faced with this comment, another subject proposes a counterexample to show that what was said is not true: “My son Bautista doesn't like soccer, he prefers to play tennis.” As you can see, given that Raúl and Bautista are children and that Bautista does not enjoy playing soccer, it cannot be said that all children love this sport . With a counterexample it is evident that the generalization is not correct.
Let's look at another case. An individual may state: “All the countries in Oceania are highly developed, like Australia and New Zealand.” These two nations, according to the United Nations Development Program ( UNDP ), have a “very high” human development index. However, it is possible to maintain that this reality is very different in other States in the region and appeal to the counterexample of Papua New Guinea or the Solomon Islands , with a "low" human development index according to the UNDP .
For logic
Everything said so far can be applied to the definition that logic gives to the concept of counterexample. However, below we will see it in more technical terms and with some more abstract cases. This is an exception to a given general rule; in other words, to a specific case of falsity that we can detect and reproduce in a proposition according to which all the elements of a set satisfy it. In this context, we must mention the symbol known as the universal quantifier , which is read as "for everything."
This occurs especially when logic is applied to philosophy and mathematics. Take the following proposition as an example: "all plants have only green leaves." In this case, there are several counterexamples, which are those plants whose leaves are of other colors, or combine green with another.
On the other hand, if we position ourselves in the field of mathematics , certain apparently correct statements fall apart in the face of a small exception, which can be understood as a counterexample. Such is the case of the proposition "there is no even prime number" ; This is a common mistake, since there is only one even prime number, 2.
Ignored possibility
The concept of counterexample can also be found in everyday life, in countless trivial conversations, in which it is presented as an opposition to a statement. In this case, unlike its scientific application, it often leads to unpleasant confrontations, instead of serving a purely informative purpose.
A counterexample is an example that opposes another and invalidates it.
Let's start by remembering that arguing is not fighting, but rather analyzing or comparing results based on possible or real data. In its original definition, it serves to grow, to rethink supposed truths. In everyday life, on the other hand, human beings tend to be reluctant to be contradicted, to have our errors pointed out, so we give the discussion a negative tone.
In the best of cases, a counterexample could help us solve a problem : if someone says that "there are no rentals that fit your budget" but your interlocutor presents a counterexample, you may finally get a house that suits your needs. .