###### Consequences, Content and Explanatory Power In order to explain *why* Moravec's argument is wrong, and *why* it was so hard to argue against, we need to continue our deep dive into the world of logical content and explanations. First let us explore the concept of a *logical consequence*. This is a specific *implication* (consequence) that follows from a statement. When you make a statement about the world, you are simultaneously ruling out a potentially infinite number of alternatives. For example, stating "today is April 28th 2025", implies that it is not April 27th or April 29th in any year, and it is not April 28th in any other year besides 2025. It also implies "it is not prior to the rise of Alexander the Great"—that is another implication of our statement. We can see that language carries an implicit richness: even saying a little can logically entail quite a lot. The set of all logical consequences of a statement make up it's *logical content*. In our example above—"today is April 28th 2025"—this would be the class of all statements such as: "today is not April 27", "today is not April 29", "today is not the day that Julius Caesar was assassinated", and so on. Now this will then bring us to *empirical content*. This is the class of the all empirical statements logically entailed by a statement. The empirical content forms the set of potential falsifiers of a statement. %%TODO: almost definitely need to flesh this out%% Consequences and content can be visualized quite nicely within our arguments structure: %%TODO: show argument in black, consequences in grey%% Just as we previously showed that we can analyze an argument based on it's internal structure to see if it is consistent, we can analyze arguments based on their consequences and content. It is table stakes that an argument is internally consistent. The main entry point into criticizing non-empirical theories is via their intrinsic structure. This can of course be used to criticize empirical theories as well, but we often move straight to criticizing them via their *empirical consequences*. It is the goal of science and problem solving more broadly to seek theories with *high content*. This stems from a deep principle of knowledge creation: that we do not generate knowledge via induction—collecting many observations and having truth flow to a general theory—but rather, we guess a theory, deduce it's logical consequences, and then check if they are falsified by some form of criticism (experiment, argument, proof, etc). Thus, the more content our theory has, the more ways it can be falsified. The more ways that we can falsify it, the more exposed it is to be rejected, allowing us to correct errors in our guesses. However, if even while being very exposed it manages to survive falsification, we say that it has been corroborated. This is not quite the same as saying "we have evidence for our theory". Rather, it is saying "our theory has successfully managed to avoid refutation". We can summarize this as follows. The mechanism of knowledge creation is guessing some theory and then subjecting it to criticism. The more content our theory has, the more forms of criticism it can be subjected to. In other words it has a larger surface error that we can attack it from. If it survives those attacks (while all of it's rivals fail to do so), we tentatively can accept it. Given this process, you can start to see the danger of *removing content* from a theory—updating it to have fewer implications and consequences. We are now able to address the notion of *explanatory power*. A theory's explanatory power comes from it's success in empirically accounting for phenomena and its ability to provide a descriptive account of the underlying structure of the world that makes these phenomena and predictions understandable in terms of cause and effect or governing laws. Thus for our present purposes we can say that the explanatory power of a theory is based on two main components: 1. It's empirical content and predictive power. 2. It's description of the underlying structure of reality—the *how* and the *why*. A theory explains phenomena by successfully accounting for them, which often means making predictions that are confirmed by observation. The more specific and risky the predictions a theory makes (and are successfully corroborated—survive attempted falsification), the higher it's empirical content and, consequently, it's potential to explain the phenomena it predicts. This refers to proposing a model or description of the underlying reality or structural properties of the world that *cause* the observed phenomena and allows for the deduction of the predictions. A good explanatory theory will describe the world in such a way that we there is empirical content—consequences—that we can then criticize. For example, consider a theory such as The Law of Supply and Demand. This describes mechanism for how the price of a good will vary based on the amount of it available (supply) and the desire for that good (demand). One consequence of this theory is that "if we have very few bananas, and everyone wants bananas, then bananas will become more expensive". If we then observe that this does not happen, we have evidence that our theory does not always hold—as stated it is false. Notice that this is just one little element from the theories empirical content. Because it nicely describes what will happen to price in a very broad, general set of situations, it has high empirical content. In this way the *how* and the *why* portion of explanatory power are directly connected to generating more empirical content, and thus explaining more. An example should help make this clear. Consider two theories, $A$ and $B$. $A$ is stated as "the variability of life that we observe is due to natural selection, which is the process by which replicators (like genes) produce variants, and the environment selects those that are better at being replicated". $A$ specifically talks about the mechanism by which we observe variability. This has incredibly high empirical content that is ripe for falsification. For instance we could ask: what about massive increases in variability that occurred during a small window of time—often referred to as punctuated equilibrium—does the theory predict that? Or we could design an experiment where we manually ensured that a gene was held constant for 1000 reproductive cycles in a changing environment, and then check to see that no variability had been introduced. Now consider $B$, which is stated as "the variability of life is due to natural selection, which introduces variability at a rate of $v(t) = \alpha \times t^2$ which increases over time". Notice that $B$ effectively says nothing of the *how* or *why* we observe variability. It tells us that variability will increase over time—that life will get more diverse. And it tries to quantify the degree of this increase via a basic equation. But it doesn't tell us anything more. Thus it's empirical content is rather low. Sure, if we observed that the variability plateaued we would have a falsification of the theory, but that is basically the end of our options for empirical criticism. Compare this to a theory that speaks of the mechanism—that massively increases its empirical content, and opens it up to far more criticism. It also opens it up to be able to *explain more*. For our purposes the details are not critical. The big idea that we must internalize is that by talking about the mechanism we increase a theory's explanatory power. We increase the amount that a theory explains, and we increase it's empirical content. Let us now see how this can be used in the context of Moravec's argument.