Scientific Thinking (2)Inference patterns for hypothesis testing

Scientific Thinking (2)Inference patterns for hypothesis testing

The method of tracing relationships among various facts (reasoning pattern) mentioned in the previous section includes deduction, which is a method of deriving a proposition from a set of statements or propositions, and four non-deductive methods: induction, projection, analogy, and abduction.

Lessons in Scientific Thinking

Here, the deductive method goes from the premise that “all fishes have gills” and “eels are fishes” to the conclusion that “therefore eels have gills” (the truth or falsity of the premise is carried over to the conclusion and the overall amount of information is not increased), and the inductive method goes from the premise that “all fishes have gills” and “eels are fishes” to the conclusion that “therefore eels have gills” (the truth or falsity of the premise is carried over to the conclusion and the overall amount of information is not increased).

Induction, for example, draws the conclusion “Therefore, every cell in the human body has a nucleus” closely from the premises “White blood cells have nuclei,” “Nerve cells have nuclei,” and “Epithelial cells have nuclei.

The projection method is based on the premise that “white blood cells have nuclei,” “nerve cells have nuclei,” and “epithelial cells have nuclei,” and leads to the conclusion that “therefore, red blood cells have nuclei.

From the premise that “the force of attraction between two masses is inversely proportional to the square of the distance” and “the force of attraction between a positive and a negative charge is inversely proportional to the square of the distance,” analogy leads to the inference that “mass and charge are subject to the same law.

Abduction is an explanation based on the assumption that the orbit of Uranus does not fit well with Newtonian mechanics, and the hypothesis that the calculation will fit well if there is another celestial body nearby.

The common denominator of all four types of non-deductive reasoning is “probable,” the opposite of “necessary,” which means that even if the premises are correct, the conclusion is not necessarily correct. (Deductive reasoning is inevitable; if the premises are correct, it will always be correct.) This means that non-deductive reasoning increases the amount of information in the conclusion.

In other words, by using non-deductive reasoning, humans create new information from the information they have taken in, and this is the act of “thinking.

Why is deduction, which does not increase the amount of information, used here? The reason is that as reasoning becomes more complex, it becomes more difficult to see through the information that is originally included, and deduction makes it possible to find it mechanically. This can be seen, for example, in the case of the ZF axiom system in set theory, where various theorems about sets can be deduced, but it is difficult to see what propositions are included in the ZF axioms and what are not.

In summary, the advantage of using non-deductive reasoning is that it can be used in hypothetical thinking about what is unseen or invisible in light of what is seen, whereas deductive reasoning can be used to make explicit information that is hidden within certain premises but which is not immediately noticeable intuitively. It can be said that deductive reasoning is used to make explicit information that is hidden within certain premises but not immediately noticeable intuitively.

In scientific considerations, we can combine these two methods to draw out a hypothesis from non-deductive reasoning (e.g., abduction), and then apply deductive reasoning to the hypothesis to predict the actual events hidden in the hypothesis, an approach called “hypothetico-deductive reasoning.

There are also approaches that use computation to perform these inferences.

Here, even if the prediction (P) deduced from the hypothesis (H) by the hypothetico-deductive method comes true, the hypothesis (H) can be said to be certain, but it is still a non-deductive, probabilistic inference, and it cannot be said 100% that H is certain. This can be confirmed, for example, by the fact that even if there is a fact that “the square of a is 4” for the inference “if a is 2, then the square of a is 4,” it does not necessarily mean that “a is 2” (a can also be -2).

A hypothesis is always a hypothesis, and it is accepted as “the hypothesis is certain” when the following conditions are satisfied. Translated with www.DeepL.com/Translator (free version)

• It explains a lot of things that are already known.
• The various predictions that can be made from it are all true
• It does not contradict other accepted hypotheses
• It does not contain any ad hoc elements.
• There are no equally valid hypotheses to explain the same thing.

In the next article, we will discuss how to test the hypotheses that have been deduced.