Deductive and Inductive Logic in Scientific Hypothesis Testing

Asymmetry Between Hypothesis Justification and Refutation

Arguments used to justify and refute a hypothesis ($H$) often appear symmetrical. Both typically involve two conditions and an experiment resulting from the premises. However, this symmetry is broken when the argument for justification further demands that Condition 1 be fulfilled.

The reason for this asymmetry is crucial: arguments of type (**) — refutation — are all deductively valid. In contrast, arguments of type (*) — explanation — are only inductively valid, meaning the conclusion is only probable.

We can find counterexamples: cases of the form (*) — justification — where the truth of the premises does not make the conclusion highly probable. That is, the hypothesis might be false, yet the prediction is satisfied. In all these cases, however, Condition 1 is not met (the prediction is not consistent with the hypothesis). Therefore, we demand that justification fulfill both conditions.

Originating Experiments and Effective Contrasting

Experiments that lead to the formulation of a theory constitute a poor test of a hypothesis based on that theory. Similarly, experiments that lead to the formulation of a hypothesis are poor tests of that hypothesis.

In these cases, the issue is that the hypothesis was formulated to explain already known facts (Hechos Ocurridos). These known facts cannot be compared with the same facts as a prediction. A prediction requires forecasting what will happen next. Recall that effective contrasts rely on the predictive nature of the hypothesis.

The Necessity of Multiple Contrasts

A single successful contrast is not sufficient to fully justify a hypothesis. The reason is that, despite the success, the result could have occurred by chance, and the hypothesis might still be false, even if the prediction proved true and both conditions were met.

Thus, science usually requires performing several tests of a hypothesis. If only one successful contrast has been carried out, the justification of the hypothesis is weaker. The more positive contrasts performed, the greater the likelihood and justification of the hypothesis.