This blog contains some random thoughts about Pearl’s The Book of Why Kant’s Critique of Pure Reason. The former is about probability reasoning, and the latter about metaphysics. Nevertheless many ideas fit into each other.
- Correlation vs. causation
- The structure of reasoning
- Deconfounding as transcendental illusion
Correlation and Causation
According to Pearl, only correlation exists in data, whereas the causation is produced while human construct the structured probabilistic diagrams.
According to Kant, knowledge does not only come from experience — experience provide analytic information — the synthetic component plays a crucial role in transforming experience into knowledge. We can say the correlation is an analytic information, while the causality between factors are synthetic a priori.
As another illustration, experience render the accessible, sensible world, while understanding enables us to conjecture the true world, consisting of things-as-in-themselves. Correlation is a phenomenon, and causation resides in the world of neumenon.
The structure of reasoning
According to Pearl, causation relationships can be represented by structural causal models (SGM). Models like Bayesian Networks are constructed following certain rules. For example, a factor is a node while a relation is an edge. A node can be causally related to another one, or another several nodes. Regardless of the structures, there is a basic law that inferences in Bayesian Networks are based on: the Bayes rule, which computes the posterior as the product of the prior, the conditional, and the inverse of the evidence.
According to Kant, synthetic a priori knowledge follow certain categories. For example, the feeling of time, space, singular, multiplicity, cause and effect. He didn’t specify the numerical rules but provided a compatible framework. The posterior knowledge comes from the synthetic a prior, and the knowledge acquired from experience.
Deconfounding as transcendental illusion
According to Pearl, mediation analysis is vital to removing confounding factors. If not done properly, multiple different interpretations could be drawn from the same dataset.
According to Kant, objects and events in the world do not ‘tell us’ their absolute, complete truths. Instead, what people can do is to infer their truth based on limited experience. During the stepping from solid ground towards the world of things-as-in-themselves, we could be trapped into transcendental illusions. There are a large set of topics where you can argue reasonably for both sides. Several examples of these antimonies include, whether time has its starting point, whether space has its boundary, whether causality exists, and whether god exists.
In early ages (when there were not enough controlled experiment data), whether smoking caused lung cancer is also an antinomy. If you agree, the correlation from smoking and lung cancer support you statistically. If you disagree, however, you can argue that certain genes might cause unexpected confounding and that such correlation does not lead to causation.
Can they disagree with each other?
I feel that Kant provided a framework where scientific theories can fit in by providing spceific computational rules. Metaphysical theories probably can defeated by metaphysical rebuttals. I will read more about the works after Kant later.
References