Negation in Science
The negation of a claim that evidence is sufficient is that the evidence is insufficient. That does not, by itself, establish that the underlying hypothesis is false. Keep this logical distinction separate from the statistical question of how evidence is measured.
THE IDEA
NEGATION IN SCIENCE
While we’re thinking about evidence, it is just as well to think about what evidence does do for us in scientific experiments, and how it interacts with negation. After all science, like mathematics and all fields, has a framework for showing that things are not true as well as for showing that they are true.
Scientific experiments usually proceed by starting with a hypothesis, that is, a statement that a scientist thinks might be true, but whose truth value is currently unknown. In school science experiments it usually has to be something rather simple that scientists have in reality known for a very long time. This always made me feel that science experiments at school were contrived. Because of my lack of motivation for doing the experiments, I was not very good at them. I wish they had been presented more as a way of exploring the scientific method and learning how to verify things that have been told to us as facts.
One experiment that I remember actually going well was the one about Hooke’s law. The hypothesis is: the extension of a spring is proportional to the load that is hanging from it.
Scientists (or school pupils) will then look for evidence to support the hypothesis. In this case, an experiment would involve selecting various different springs and measuring them with various different loads hanging from them, and then analysing the data. The field of statistics deals with what sort of data you need to back up various types of hypotheses. If you find you have the right kind of data then you make a logical conclusion of this form:
There is sufficient evidence to suggest that this hypothesis is true, to within 95 per cent certainty (for example).
If you find you do not have the right data then your logical conclusion should be the negation of this statement, which is:
There is not sufficient evidence to suggest that this hypothesis is true, to within 95 per cent certainty.
Here the negation concerns the sufficiency of the evidence, not the truth of the hypothesis itself. The quoted statements use certainty informally: a statistical confidence level is not, by itself, the probability that a hypothesis is true.
Insufficient support alone does not establish falsehood. We may need more data or a better experiment; evidence may also reveal that the hypothesis needs limits. For the spring example, consider a refined hypothesis:
The extension of a spring is proportional to the load hanging from it, within a maximum load limit.
This is the proportional relationship described by Hooke’s law, within its range of applicability. A hypothesis does not simply get “promoted” to a law once enough evidence accumulates. Laws describe regularities; theories explain phenomena. Both depend on empirical evidence. Logic then lets us ask what follows if a law and its conditions apply.
Calling an account “only a theory” misunderstands what a scientific theory is. Quantified uncertainty also needs careful interpretation. If an analysis genuinely assigns a hypothesis a probability of 50 per cent, that model treats truth and falsehood as equally likely. If it assigns a probability of 95 per cent, it treats truth as much more likely. These are statements about probabilities assigned within a model, not what a frequentist confidence level means.
The evidence needed for a decision also depends on the consequences of error. Would it be worse to accept a false claim or reject a true one? A high-stakes decision may require stronger evidence, but that does not supply a universal probability threshold. Empirical conclusions generally do not offer 100 per cent certainty. If we demanded 100 per cent certainty before acting, we would rarely do anything at all.
Likewise, a model that assigns a hypothesis a probability of 1 per cent treats it as unlikely, without ruling it out. That is different from a significance test’s error rate. My excellent maths teacher, Mr Muddle, taught us that when you work as a professional statistician, if you do not have the right data to support your hypothesis the correct negation is “There is insufficient evidence to support this hypothesis and therefore we need more funding in order to pursue the matter further.”
[1] The source’s optical-illusion note refers to a diagram not included here and draws an analogy with perceived racial boundaries.
[2] Cisgendered: your personal gender identity matches the sex you were assigned at birth.
When to use it
Evaluating scientific studies: understanding that a study failing to prove an effect does not prove no effect exists.
Business decisions: distinguish an inconclusive test of a strategy from evidence against it before deciding whether to collect more data, revise it, or stop.
Legal reasoning: distinguish 'not guilty' from a finding of factual innocence; the prosecution has not established guilt to the required standard.
Personal beliefs: when you encounter a claim that is not well-supported, avoid jumping to the opposite conclusion without further investigation.
FROM THEORY TO EVERYDAY LIFE
In practice
Hooke's Law Experiment
Compare a spring’s extension under different loads. If proportionality breaks down beyond a certain load, that can count against an unrestricted hypothesis and suggest a more precise one with a limit. A merely inconclusive experiment, however, does not establish that proportionality is false.
An Illustrative Evidence Threshold
Suppose a decision rule requires a 99.9% confidence level for a specified analysis. Failing to meet it means that this rule’s evidence requirement has not been met; it does not settle the underlying safety question. This is an illustration, not a general threshold for drug trials.
A MOMENT TO REFLECT
Put it to work.
Think of a claim you hear often. What kind of evidence would be needed to support it? How would you distinguish 'insufficient evidence' from 'the claim is false'?
Consider a time when you misinterpreted a lack of evidence as proof of falsehood. How might reinterpreting it as a need for more information change your conclusion?
How does the concept of negation in science apply to everyday decision-making when you have incomplete information?
Often confused with
CONTINUE THE CONVERSATION
Source texts
- The Art of Logic How to Make Sense in a World that Doesn’t (Eugenia Cheng)