According to Hume, there are problems present in moral philosophy that stand to bring it to an intellectual level below that of the mathematical sciences. Largely analytical works such as those based on mathematics are founded on the relations between our ideas, and are generally extremely precise in their statements and proofs. These are intuitively true in a sense that do not require any external information, as their legitimacy is not dependant on anything found in nature, and in fact their falsehood is generally thought to be logically inconceivable. For example, how could it ever be that two plus two does not equal four, and furthermore, what is ‘two’ but a construct of our minds, rather than something actually out there in the world? In many cases we will believe certain things to come in pairs, but this is only a matter of applying our understanding of previous experiences to the situation: unexamined they are simply interconnected pieces of what we observe to be external reality, but with no more relation to one another than to any other part of it. If this were not the case, then would a person who was never taught the mathematical concept of ‘two’, be able to consider two things as a pair? On the other hand, the terms found in moral philosophy, like ‘justice’ and ‘virtue’, are incredibly complicated, by the fact that many people have differing conceptions of them, and will even contradict their own beliefs given the same circumstances twice over. This is related to Hume’s problem with knowledge founded on prior human experience, like that of moral philosophy, in that although we often believe it to be based on matters of fact resulting from external reality, really we are only able to reflect on our own flawed conceptions of it.

When in mathematics one conceives of a certain term once over again, or even repeatedly, what we are really considering is the same exact construct in each situation. For example, in geometry a circle will always be a circle, as it is defined by an exactly precise definition, which is not dependant on the circumstances of any real world phenomena. In this idea, Hume goes so far as to say that the mind is able to readily replace the term with its definition, as they are in fact one in the same, and so when we think of a circle, we immediately conceive of the meaning of the circle in itself. On the other hand, when we experience a series of events in the external world, what we are experiencing is not the actual events in themselves. Instead, we are experiencing discrete perceptions of external reality, impressions of the events constricted by what our senses are able to tell us and our ever diminishing memories of them. There is no question that we are often confused in our ideas, so often the case, and so it is not inconceivable then for ambiguity to deteriorate the ability of the senses. How easy is it to see or hear something that was not actually there? It is also quite clear that there are certain limitations on the human mind, as Hume notes, it seems not to be wholly original in its ideas, but rather only works to combine and augment previously encountered ones. In this way, we can conceive of a unicorn, even though it likely does not exist, simply because we are able to combine our previous experiences of horses and horns. Despite all of these shortcomings, he also believes that there is one advantage to moral philosophy, in that in light of the obvious inadequacies of the mind, we can come to comparatively brief conclusions on its nature, as opposed to the generally verbose and extensive proofs in mathematics. In this matter then, we must only set out to make our terms as clear as those in mathematics, so that there is little to no ambiguity to be found in the few narrow premises held by moral philosophy.

Hume believes that cause and effect can be narrowed down as the basis for all of our apparent understanding of the external world. It is only through the construction of relations between separate events in time, due to our notions of cause and effect, that we can attempt to reason beyond our present experience and our memories of the past. Otherwise, it would seem that each event remains entirely separate from one another, without any order or further meaning for us to derive between them. If this is the case then we should probably be clear in our definition of what cause and effect actually entails, which was previously to Hume obscured by the egoism of the Renaissance philosophers and their Classical idols, namely in regard to the sheer extent of reason. Let us consider again that all of our ideas are not of actual things in the world, but rather secondary impressions of those things, obscured by our imperfect senses and shallow understanding. This being the case, it would appear that in the same way, our own notions of cause and effect are not actual emergent phenomena taking place in the natural world, but rather are constructions of the mind. Why then would we even hold such concepts to exist in the external world, should it be conceivable that they are entirely fabricated? It is simply that we all have countless previous experiences wherein cause and effect seem to have taken place, and so by virtue of these previous experiences, and notably without ever definitive proof, we continue to believe this pattern of cause and effect will hold true. Note that it could even be the case that cause and effect is a real phenomenon in nature, but we would still never be able to ascertain this as a matter of fact through mere sensual observation. The human condition is such that the most we can really say is that one event happens to follow another, and each of these events are connected through the sequence of time, but our belief that one event has caused another is simply a relational construction of the mind.

We have no problem imagining different things happening from what really has taken place in the past. Why then should one event have necessarily caused another, when it is distinctively conceivable that a number of different events could have followed? More importantly, it seems to also hold that whatever our present circumstance may be, we can never be absolutely certain of what will take place in the future. It may even be the case that previous experiences are able to help us narrow down the probable outcomes of a certain event, but this still can not give us a precise explanation as to what must follow next. This is the ultimate downfall of human understanding, as no matter how many times we observe a specific sequence of events to take place, it can never follow that the same sequence of events must take place again in the future. Even worse, even though time and time again we experience our very notions of cause and effect to be taking place, it is at least conceivable that they are mere fabrications of the mind, and might never hold again in the future.

At one point in the paper Hume makes the statement that, “[T]he necessary conclusion seems to be, that we have no idea of connection or power at all.” Hume phrases this almost sarcastically, in that he does not ever want to give an entirely definitive statement, knowing himself to be grounded in nature and constricted by his imperfect senses and understanding. Seemingly he puts an emphasis on the inability to ever come to exact conclusions about reality, and this is something that pervades and in my opinion empowers all of his philosophy. Up until his time and especially amongst many of the major philosophers immediately preceding him, it was common to give mankind and reason a certain egotistical level of merit above that of other life forms, and even above that of the entire material world. Like his contemporary Empiricists, Hume worked to ground us in the reality that we are severely bounded by the limitations of a physical mind fixed in the natural world. However, Hume amongst all of them is defined by his very distinct Skepticism, in which he examines the human mind with the same experimental approach we do all forms of science, and similarly as something that must be bound by natural laws.