I am a beginner philosopher and I have to explain Hume's "Doubts concerning the operations of the understanding" as part of a short exercise for my class. Would anyone be willing to give their honest opinion on my explanation and try to correct the parts that are wrong or to point out what I might have misunderstood? I have to explain it as clearly as possible, in such a way that a person who has never heard of this passage or even a person who is unfamiliar with philosophy would get a clear sense of what Hume's tried to argue for. Do not hesitate to also criticize my sentence structures or the vocabulary I use (in short, you might find English mistakes or weirdnesses and it would help me to know what they are to improve my explanation). Anyways, here is my work so far:

In this passage, David Hume starts by stating that the objects of human reason are divided into two kinds: Relation of ideas and Matters of fact. The first kind, relation of ideas, is constituted of everything that can be demonstrated or intuitively proven by the human mind, such as mathematics. The mind in itself is sufficient to unravel the truth about these objects. For instance, there is no doubt about the exact result of a calculation following natural operations, like 2+2=4, as there is no way to prove otherwise(very unsure about this example). Another example would be to say that 2x2=5. This proposition is necessarily false as it is impossible to conceive that it can be true and its falsehood can be demonstrated since the relationship between numbers is immutable and can be grasped by reason alone- it does not involved sensations. The logic chain that mathematicians form from a property to a conclusion does not leave any space for doubt.

As for matters of fact, they are products of inductive reasoning (or induction). Hume distinguishes them using the particularity that the contrary of these facts is conceivable. Such is the case with the proposition “The sun will rise tomorrow morning”. It is possible for the mind to imagine the sun not rising the following day, and thinking it could be true does not lead to any contradiction. In other words, the certainty of these facts is not asserted through a demonstration unlike it is with relation of ideas. Hume shows that inferences relative to matters of fact are based on causal relations, with direct, indirect or collateral effects. It is using this relation -which seems to dominate most of our reasoning regarding matters of fact-, that Hume aims to investigate on the truthfulness of these facts. To him, it is only experience that allows someone to predict the pattern of a familiar object. If the object is unknown, then its cause and its effect will remain unknown to the subject until he has an experience with the object. For instance, humans were surely unaware of fire’s burning power until they came in contact with it for the first time and realized the damages fire can cause. Now that humans have had experiences with fire, they would expect any similar object to have the same effects. In other words, we tend to associate the unknown to known patterns in order to establish conclusions on these unfamiliar objects. This is what Hume calls custom. To illustrate Hume's claim on human's associative way of reasoning, it may be relevant to mention Pavlov's experiment conducted on dogs. While studying the salivation of dogs, Pavlov noticed that after having been used to hearing a bell ring whenever their food was coming, the dogs would start salivating whenever they would hear the bell ring, without having the certainty of having food served to them following the ring. Dogs associated the bell ring with the food coming because they became accustomed to the event of being fed right after their master had rang the bell. This phenomenon was named Classical Conditioning and it is analogous to the way humans associate effects to objects due to the habit of witnessing familiar events taking place, as Hume describes. The sun is known to rise every morning and so we assume that it will rise tomorrow, the future being the unknown object in this particular case. In short, we base our certainties about some facts solely on what we have been used to through experience of the world. This is what induction is. Hume questions the reliability of induction as a way to establish certainties. Indeed, nothing proves that the future is what we predict it to be: by some unexpected events, the sun could not rise one morning and so what we had taken as a certainty was in fact wrong. Similarly, it is not a given that an object will follow the same causal pattern as a similar one.

Voilà.