Evidence vs Logical Implication
A valid implication makes a conclusion follow when its premise is true. Evidence can change how plausible a claim is without proving it, and selected confirming examples do not establish a universal statement.
THE IDEA
EVIDENCE
A valid logical implication makes a conclusion follow if its premise holds. Evidence can support or undermine a claim without establishing it by deduction. In particular, collecting confirming examples does not by itself prove a universal statement.
For example, suppose you think all Chinese people are good at maths. Perhaps every time you see a Chinese-looking maths person (like me) you think this adds to your theory. You are thinking of the implication
Being of Chinese origin implies being good at maths.
Every time you meet a Chinese-looking mathematician you store this up as evidence. One issue is that you might be succumbing to confirmation bias, where you only notice evidence that backs up your theory. However, another issue is simply that evidence doesn’t contribute to logic. With our new power in dealing with contrapositive statements, we can perhaps see this more clearly. The contrapositive of the statement is
Not being good at maths implies not being Chinese.
Working by the idea that “evidence contributes to logic”, this means that every time you see a non-Chinese non-mathematician this should also add to your theory. For example, every time you see a Canadian goose, or a French macaron, this should add to your theory that all Chinese people are good at maths. You might object that we’re only thinking about people here, not animals or food. But that still means that if you meet an American singer or a British football player, that should add to your theory that all Chinese people are good at maths.
Intuitively this might seem much more bizarre than adding to your theory every time you meet a Chinese mathematician, but logically speaking both cases make equally little sense.
When to use it
Evaluating the strength of arguments in debates or discussions by distinguishing evidence from logical proof.
Recognizing when personal biases (like confirmation bias) lead to overvaluing evidence that supports a preexisting belief.
Teaching critical thinking skills to students, especially the difference between inductive and deductive reasoning.
FROM THEORY TO EVERYDAY LIFE
In practice
Stereotyping Chinese people as good at math
Meeting a Chinese mathematician does not prove that all Chinese people are good at mathematics. The proposed claim’s contrapositive is that anyone not good at mathematics is not Chinese; it is not a statement about whether someone works as a mathematician. The source’s goose and macaron examples show how remote confirming cases can seem relevant under a purely formal reading without supplying a proof of the stereotype.
A MOMENT TO REFLECT
Put it to work.
Think of a strong belief you hold. What evidence supports it, how reliable is that evidence, and does it warrant the breadth of the claim?
Consider a stereotype you've encountered. How could the contrapositive reveal the weakness of the evidence supporting it?
When evaluating an argument, ask: does the evidence actually imply the conclusion, or does it only make it more likely?
Often confused with
CONTINUE THE CONVERSATION
Source texts
- The Art of Logic How to Make Sense in a World that Doesn’t (Eugenia Cheng)