A logical counterexample refers to an instance that contradicts a given statement, argument, or hypothesis, indicating that the initial claim is not universally valid. This term is predominantly used in discussions involving logic, mathematics, philosophy, and critical thinking.
In terms of frequency, the term is more frequently used in written contexts such as textbooks, scholarly articles, and educational materials. It is utilized often when discussing logical reasoning and argument validation, especially in academic settings.
"Студент привел логический контрпример, чтобы продемонстрировать недостатки аргумента профессора."
"To refute the claim, we need to come up with a logical counterexample."
"Чтобы опровергнуть утверждение, нам нужно придумать логический контрпример."
"Seeing a logical counterexample can help clarify why certain assumptions are invalid."
While "logical counterexample" itself is not commonly featured in idiomatic expressions, it is relevant in the context of critical thinking and argument analysis. Here are some related phrases that encompass the concept:
"Этот логический контрпример противоречит общепринятому мнению, раскрывая правду за мифом."
Put to the test
"Any theory should be put to the test with a logical counterexample to ensure its validity."
"Любая теория должна быть проверена с помощью логического контрпримера, чтобы гарантировать ее действительность."
Challenge the assumption
"The discussion helped us to challenge the assumption by presenting a logical counterexample."
The term "logical counterexample" is derived from two components: - "Logical" comes from the Greek word "logikos," meaning "of reason" and related to the study of formal logic. - "Counterexample" combines "counter," from the Latin "contra," meaning "against," and "example," from the Latin "exemplum," which refers to a typical instance or model.
Thus, a "logical counterexample" literally refers to an example that goes against reasoning or an established claim.