# Logical Content Reference Vaden Masrani podcast (probability, episode 4). The content of a statement is the set of all **logical consequences** of that statement. The content of "today is Monday" is the set of all things derivable from that statement: * "today is not Tuesday" * "today is not Wednesday" * ... The content of the statement "it is raining outside" would be: * "it is not sunny outside" * "there are clouds in the sky" * ... There are different kinds of content. There is **empirical content** and **metaphysical content**. Empirical content is a subset of all the content. These are things that are derivable that are empirically falsifiable. For example, the content of the statement "all swans are white" has a derivable conclusion "there is not a black swan in Times Square on Wednesday 2024". This is an empirically derivable claim. The content of a metaphysical claim would be "the arc of progress bends towards justice"—the content of this would be "the future will be more just than the past". We can then ask: how do you compare the content of different kinds of statements? With the exception of [Tautology](Tautology.md), everything has infinite content. This is because you can derive an infinite number of statements from, for example, "today is not Monday". However, you can do class-subclass relations. The content of Einsteins theory is strictly greater than Newtons because you can derive Newton from Einstein. Einstein contains newton. Note that you cannot compare the content of Einstein and Darwin—they are just infinite sets that cannot be compared. We can then talk about the content of a conjunction. We have two statements "today is Monday" and "it is raining". The conjunction "today is Monday and it is raining" will have a content that is strictly greater than or equal to the statements on their own. The content of a [Tautology](Tautology.md) is $0$ because nothing can be derived from a tautology. The content of a contradiction is $1$ because anything can be derived from a contradiction ([Principle of Explosion](Principle%20of%20Explosion.md)). However, you can immediately derive an empirical falsifier that shows that the content of the contradiction is false. Now what about the probability of a conjunction? It is strictly *less than or equal to* the probability of the individual statements. The probability of a tautology is $1$, the probability of a contradiction is $0$. If you want—in science and thought—to have high content, you must necessarily have low probability. If you want your theories to be bold and risky, then they have to have low probability. The project of science is to have high content theories that are bold and risky. This necessarily means they have low probability. We want *high content* which means*low probability*. This means that Bayesianism is wrong --- Date: 20250410 Links to: [Logic](Logic.md) Tags: References: * [Is P(Doom) Meaningful? Epistemology Debate with Vaden Masrani and Ben Chugg - YouTube](https://youtu.be/zKz-t_l5yHg?t=5021)