Chapter 2 - Scientific inference

An inference is an act or process of reaching a conclusion from a set of premises, which can express, for instance, known facts or evidence.

Conjunction: Two propositions joined by the logical operator AND. The conjunction is true if and only if both propositions are true.

Example:

Premise 1: I am walking to school.

Premise 2: It is raining.

Conclusion: I am walking to school and it is raining.

Inductive inferences amplify knowledge and hence are fallible.

Deductive inferences are explicative and therefore are truth-preserving.

1. Direct Inference:

"I enjoy hiking and have explored many forests around Germany. In my observations, 70% of the forests I visited were primarily made up of spruce trees. Therefore, I infer that 70% of all forests in Germany consist of spruce trees."

2. Generalization:

"I have observed that spruce, pine, and fir trees (all coniferous trees) keep their needles during winter. From this, I infer that all coniferous trees retain their needles in winter."

3. Projection:

"It has rained for the past 5 days. Therefore, I predict that it will rain again tomorrow."

1. A: It is sunny.

2. Therefore, B: we will go to the park.

1. If A: Crystals improve sleep quality then B: sleep quality improves if crystals are placed under the bed.

Hume's view of foundationalism held that justification requires an ultimate foundation. According to this view, claims are justified by tracing them back to a set of basic propositions that require no further justification. These foundational propositions serve as the bedrock from which other claims are derived.

In contrast, coherentism rejects the need for an ultimate foundation. Instead, it holds that a claim is justified not because it rests on foundational propositions, but because it fits well within a coherent system of other claims.

The asymmetry between falsification and confirmation lies in the fact that falsification can be inferred from a single false consequence, whereas confirmation only increases confidence in a hypothesis, but never conclusively proves it. This asymmetry is generally accepted by scientists. However, the Duhem-Quine thesis complicates this by suggesting that even falsification is not always straightforward in practice. If a consequence turns out to be false, it may not directly falsify the hypothesis itself, but instead point to a problem with an auxiliary hypothesis.

Karl Popper believed that the most important characteristic of science is falsifiability. If a theory cannot be falsified, Popper said, it is not scientific.

He thought that science should progress by making falsifiable hypotheses and then testing them to see if they can be falsified. If a hypothesis is falsified, it should be rejected. For Popper, confirmation plays no role in science; scientists should never conclude that a hypothesis is true, even if its predictions are correct. Instead, they should focus on whether or not a hypothesis has been falsified.

A auxiliary hypothesis is a secondary hypothesis that is used when testing a main hypothesis. It's not the hypothesis you're directly testing, but it's needed to help you interpret the results. For example, it could be a background assumption that helps you draw conclusions from the experiment.

The Duhem/Quine problem is that we never test a single hypothesis by itself, but always in conjunction with various auxiliary hypotheses. This makes it difficult to falsify a hypothesis when an observable consequence is false because the failure could be due to one of the auxiliary hypotheses being incorrect, rather than the primary hypothesis under investigation.

An ad hoc modification is made only to prevent a theory from being falsified, without generating any new important scientific knowledge.

The premise "someone feels heartburn" can lead to several possible conclusions, such as exercising too much or having a heart attack, not just stomach cancer. Therefore, even though the observation (heartburn) is true, we cannot increase confidence in the hypothesis of stomach cancer, as the heartburn could also result from other conditions, like a heart attack or something else with similar symptoms.

A better hypothesis would be: I am sick.

The observation "Adam has not called me today" is not a severe test of the hypothesis "Adam does not want to be my friend anymore" because many hypothesis are compartible with the observation such as “Adam is busy”, “Adam has lost his phone”, or “Adam forgot to call me”. Thus, this observation could still occur even if the hypothesis is false, meaning it’s not a severe test.

A severe test requires that the consequence should be unlikely if the hypothesis is false. A better severe test would be the observation "Adam has not contacted me in a year." If the hypothesis is false (Adam still wants to be friends), it is unlikely that he wouldn’t reach out for an entire year, as most friends would contact each other within that time frame. This makes it a more severe test.

The base rate fallacy happens when someone makes a decision or judgment based on specific information (like a test result) without properly considering the overall probability of the situation (the base rate). Essentially, they focus too much on the immediate evidence and ignore the broader context.