What is the nature of scientific interference? - Chapter 2

Scientists arrive at beliefs by a thorough process of reasoning or inference: for example, Darwin never saw two species evolve from each other, he got there by a process. 

There is deductive and inductive inference. Deduction is:

All Frenchmen like red wine. Pierre is a Frenchman. Therefore, Pierre likes red wine.

The first two statements are the premises of the inference, and the last one is the conclusion. Deduction means that if the premises are true, then the conclusion must be true. The truth of the premises guarantees the truth of the conclusion. 

Induction is:

The first five eggs in the box were good. All the eggs have the same best-before date. Therefore, the sixth egg will be good. Here, the premises do not entail the conclusion. It's possible for the premises to be true and yet the conclusion false. So in induction, we move from premises about objects that we have examined, to conclusions about objects of the same kind that we have not examined. Induction is riskier than deduction, but we use it a lot in our daily lives: like when you turn on your computer, you think it won't explode, because it never did: but it is possible that it will so this is inductive reasoning. And you expect the sun to rise, because it always does. So we have faith in induction. Scientists also reason inductively, as they move from limited data to a general conclusion. But with induction you should not truly speak of "proof", as you never know for sure, unless it's deduction. So in this strict sense, scientific hypotheses can rarely if ever be truly proved. 

Popper said scientists only need to use deduction, because a scientific theory can not be proved true but can be proved false, and this is then by the process of deduction. But the goal of science is not just to refute theories but to find true, or probably true, theories, and for that, induction is needed.

Hume said that using induction cannot be rationally justified. He said yes, we use it all the time, but it's just like a brute animal habit, and there's no way of giving a good, satisfactory reason for using it. So why did Hume think this? He noted that as we use induction, we seem to presuppose the uniformity of nature: the assumption that objects we haven't examined will be similar to objects we have examined of the same kind. But we cannot prove if that's really true, because it's not a logical impossibility that there is no uniformity of nature. Hume's problem of induction means that if Hume is right and we believe in him, the foundations on which science is built basically fall apart. 

Strawson came up with this analogy to react to Hume: when someone doesn't know if something is legal, they will read a lawbook. You cannot worry if the law itself is legal, as this is the standard against which legality is judged: it makes no sense to worry if the standard is legal. He then says that induction is also a standard we use to decide whether someone's beliefs about the world are justified, and it then makes no sense to ask if induction itself is justified. 

What is inference to the best explanation (IBE)?

So previously, the inferences took us from examined to unexamined. But there is another type of inferencing:

The cheese has disappeared, apart from a few crumbs. Scratching noises were heard last night. Therefore, the cheese was eaten by a mouse.

This inference is non-deductive: the premises do not entail the conclusion. Still, the inference is reasonable, as this hypothesis is a better explanation than any other explanation (usually because it's the most simple, yet sufficient, one). Some say this IBE is a type of inductive inference, and others say it's a different thing. IBE, thus basically meaning: reasoning from specific data to a theory or hypothesis that explains the data, is frequently used by scientists as well. However, then the simplicity rule is not always liked: this is still up for debate. 

How does causal inference work?

An important goal of science is to find out the causes of natural phenomena. And since causal connections are not directly observable, some inferring must occur. There is a distinction between inferring the cause of a specific event, versus inferring a general causal principle; on which we will focus. 

First, a correlation should be found. But when there is correlation, this does not always mean causation, for example due to the common cause scenario (something else, found in both things, is actually the cause). A possible other variable should be controlled.  

Some say only controlled experiments can reliably show causality. However, the technique of statistical control can also work to show causality in observational data. 

A randomized controlled trial (RCT) contains a control group, and goes with random assignment to the groups. Lots of people say random assignment is necessary to find true causality, because it eliminates the effect of other factors, since the randomization makes sure these are unlikely to be over-represented in either group. But RCTS are not always possible, and valid causality can be established in other ways too. 

What is the concept of probability in scientific inference?

Probability has both an objective and subjective side. The objective side is about how often things tend to happen, for example when someone says: the probability that the coin will land on heads is half, you know what that means. Statements about probability are then objectively true or false. Then, the subjective side is about probability being a measure of rational degree of belief. For example, a scientist says that the probability of finding life on Mars is very low. Ultimately, there is life or there isn't, but talking about probability in this context reflects that we don't know for certain which one it is. However, the evidence we have, makes the rational degree of belief that there is life on Mars very low. Thus, a rational degree of belief in a scientific hypothesis, also called the scientist's credence, shows the probability. It is a number between zero and one. The credence can increase or decrease with new information (depending on if the information supports or contradicts the hypothesis.

The general rule for updating your credence, after new information, has to do with conditionalization. This means: when there is new, true evidence, your new credence should be set equal to your initial credence conditional on the assumption of this evidence. 

Shown in symbols:

- H: particular hypothesis. - P(H): credence in H. - P-new-(H): updated credence after new evidence. - E = evidence. - P(H/E): credence in H conditional on the assumption that E is true. - P(H and E): credence that both H and E are true. - P(E): possibility of what the evidence is actually happening. 

The rule of conditionalization then is: Upon learning evidence E, P-new-(H) should equal P(H/E). 

And: P(H/E) is equal to the ratio: P(H and E) divided by P(E). 

The conditionalization rule was discovered by Bayes, and the branch of statistics known as Bayesian statistics uses updating by conditionalization a lot. And though the rule sounds complicated, we often obey it without thinking. This Bayesian view of scientific interference sheds light on aspects of the scientific method. But not all scientific interference can come from Bayesian reasoning, since Bayesian reasoning does not explain coming up with new theories, as happens often. And another limitation is about the source of the initial credence. the initial credence then purely subjective?