Mills` methods can only reveal evidence of probable causes; they don`t really offer an explanation. The discovery of causalities is an important step towards understanding the world, but it is only part of what we need. We also need to understand how and why some cases of causation work the way they do. The answers to these questions lead us to the possibility of identifying cause-and-effect relationships. We need to develop theories and hypotheses that underpin the scientific argument. This situation is an example of Mills` common method of agreement and difference: the first four students are proof that all those who got sick had eaten coleslaw, and the four matching couples are proof that only those who fell ill had eaten coleslaw. This is a strong combination of the first two methods, as it tends to support our idea that real causes are necessary and that the conditions for their effects are sufficient. Mills` rule of understanding states that if, in all cases where an effect occurs, there is a single prior C factor common to all of these cases, then C is the cause of the effect. According to the table in this example, the only thing you ate was oysters. Therefore, if we apply the rule of concordance, we conclude that the consumption of oysters is the cause of the disease. Although Mills` methods are an important part of the serious study of natural phenomena, they have significant constraints. These methods can only be applied with care if all relevant pre-gonal circumstances are taken into account, which cannot be guaranteed in advance. Symbolically, the common method of concordance and difference can be presented as: so far, I have talked a lot about observations and how we can improve them, but we often observe to learn something about causal contexts, which depends on what? I will conclude our discussion of observations by introducing a framework that we can use to understand how scientists draw conclusions based on their observations, experiences and simulations.
The logic of observation is based on conclusions was described by John Stuart Mill, a philosopher best known for writing about freedom, but who also has many contributions on how we think about science. Mill was interested in how we can use observations and experiences to determine the causes or what depends on them. He introduced a series of methods to reflect on the empirical data that we now call Mills` methods. I will talk about the first two of his methods; what we now call the method of agreement and the method of disagreement.