An alternative view of confirmation is rooted in a widely-employed method of scientific inquiry known as the hypothetico-deductive (H-D) method. The H-D method itself is not a theory of confirmation, but a procedure for testing hypotheses. The procedure can be summarized as follows:

  1. The scientist begins by observing and collecting data about some phenomenon.
  2. Next, she formulates a hypothesis to explain the data she has collected.
  3. Then, she logically deduces from the hypothesis a prediction about what to expect in some other situation that has not yet been observed.
  4. Finally, she tests the hypothesis either by producing the relevant situation in an experiment or by finding the relevant situation in nature, and she observes whether the prediction was correct. If the prediction was wrong, the scientist discards that hypothesis and tries a new one; if the prediction was correct, she deduces another prediction and tests the hypothesis again.

This procedure is called the hypothetico-deductive method because it involves deductive reasoning (deducing predictions) from hypotheses.

A philosophical view called hypothetico-deductivism holds that the hypothetico-deductive method is the key to inductive confirmation. According to hypothetico-deductivism, a hypothesis or theory is confirmed by its successful predictions. More precisely, a theory is confirmed whenever a prediction deducible from the theory—or deducible from the theory in conjunction with relevant background knowledge and information about the experimental setup—is observed to be true. (As with Hempel’s theory, the term ‘confirmed’ doesn’t mean that the hypothesis is proven correct. In this context, it means that the hypothesis is supported—perhaps only to a small degree—when its predictions come true.)

Hypothetico-deductivism has some advantages over Hempel’s theory of confirmation. For one, it allows hypotheses of any logical form, whereas Hempel’s theory only applied to hypotheses that can be expressed as universal categorical propositions (All A’s are B’s). Another advantage is that hypothetico-deductivism avoids the ravens paradox. Since the hypothesis that all ravens are black does not logically entail the existence of non-black things that aren’t ravens, you can’t deduce the existence of such things from the hypothesis. Therefore, non-black non-ravens (white shoes, etc.) don’t confirm the hypothesis, so the paradox doesn’t arise.

Unfortunately, hypothetico-deductivism leads to paradoxes of its own. An especially troubling one is the irrelevant conjunction paradox. Consider the compound hypothesis that unicorns exist and all emeralds are green. From this hypothesis, we can deduce the prediction that the next emerald we see will be green. According to hypothetico-deductivism, therefore, the discovery of another green emerald confirms the hypothesis that unicorns exist and all emeralds are green. That surely isn’t right. We shouldn’t be able to confirm the existence of unicorns by finding green emeralds!

A closely related challenge is the Quine-Duhem problem, first noticed by physicist Pierre Duhem and later clarified by philosopher Willard Van Orman Quine. The problem arises from the fact that most scientific hypotheses don’t yield testable predictions on their own. In order to deduce a testable prediction, typically, you must add information about the system you are measuring (e.g. its initial condition) and you must also invoke numerous “auxiliary hypotheses” (e.g. background theories about how your measuring apparatus works).

What kinds of background information and auxiliary hypotheses are we allowed to use when deducing predictions? Without an answer to this question, hypothetico-deductivism is useless as a theory of confirmation, because any hypothesis can yield practically any prediction when conjoined with sufficiently hokey auxiliary hypotheses. For example, we can deduce a prediction about the color of emeralds from the hypothesis that unicorns exist, simply by adding the following auxiliary hypothesis: If unicorns exist, then emeralds are green. Since the prediction that emeralds are green was deduced from the hypothesis that unicorns exist (along with an auxiliary hypothesis), the discovery of a green emerald confirms that unicorns exist! Thus, with a clever selection of auxiliary hypotheses, any observation can be said to “confirm” any hypothesis whatsoever, provided the hypothesis is at least logically compatible with the observation.

Perhaps the aforementioned problems could be solved by restricting, in various ways, the kinds of hypotheses that are allowed in the hypothetico-deductive method. Even so, hypothetico-deductivism has a further shortcoming in regard to its epistemic usefulness: it doesn’t give us the most important information we want from a theory of confirmation. It doesn’t tell us how much a hypothesis is confirmed by successful predictions, and it doesn’t explain why some successful predictions seem to provide stronger confirmation than others. Philosophers of science have long recognized that successful predictions that are surprising or unexpected provide stronger support for a hypothesis than successful predictions that are unsurprising. Hypothetico-deductivism gives no hint of why that should be the case, nor does it provide any way to determine the strength of confirmation.

For solutions to these problems, we’ll turn to another theory of confirmation: the Bayesian theory, which is by far the most popular view among contemporary epistemologists and philosophers of science. Since Bayesian confirmation theory is a probabilistic theory, it will be necessary first to introduce some fundamental concepts and terminology related to probability.