I don't think it's vindictive to point out that a man would never say such a supercilious thing, and I don't think it's excessive to conclude that, for every instance in which women's rights are better served by a woman, there is a counter-instance in which they are better served by a man.
But as we add further instances \(b\), \(c\), etc., it becomes stronger (provided we discover no counter-instances, of course).
The problem with this at the time was, firstly, that some atomic weights needed to be known independently to establish the truth of the rule, and, secondly, there were known counter-instances.
These observations suggest a proposal due to Nicod (1930) and famously examined by Hempel (1945): Nicod's Criterion A universal generalization is confirmed by its positive instances (as long as no counter-instances are discovered): \(\forall x(Fx \supset Gx)\) is confirmed by \(Fa \wedge Ga\), by \ Fb \wedge Gb\), etc.
Observation counts against a theoretical claim if the conjunction entails a counter-instance.
The only counter-instance to this rule is prior absence, which has occasional existence but being beginningless has no cause.
It would not be acceptable if the only evidence for the existence of the disturbing factor were the counter-instance we started with.
Richard Swinburne (1970) has suggested that a miracle might be defined as a non-repeatable counter-instance to a law of nature.
Every genuine test of a scientific theory, then, is logically an attempt to refute or to falsify it, and one genuine counter-instance falsifies the whole theory.
Both of these theories spring from purely logical roots, confirmationism from Carnap's work on inductive logic, and falsificationism from Popper's rejection of inductive logic coupled with his assertion that universals can be falsified by a single counter-instance.
Yet, if one supposes that the law is to be formalized as a universally quantified conditional sentence, then one counter-instance (due to a disturbing factor) to the universally quantified sentence means that it is false.
