In the hopes of clarifying his empiricist philosophy and expanding on the work of John Locke, David Hume published An Enquiry Concerning Human Understanding in 1748. I will present Hume’s distinction between relations of ideas and matters of fact, his claim that matters of fact can only be learned from experience, and how we tend to come to conclusions about matters of fact based on our experiences. In his arguments, Hume outlines the problem of induction and why he believes the method of reasoning is not rationally justified or really reasoning at all. I will then present an objection to this problem from a probabilistic view and another from a skeptical view, and then I will argue for Hume’s response. Although the probabilistic objection fails to prove that induction is rationally justified, Hume’s conclusion about our formation of beliefs in matters of fact is not a skeptical one. Rather, he defines a natural limit on human knowledge regarding matters of fact and leaves room for the pragmatic acquisition of knowledge through experience.
Hume partitions all of human knowledge into two categories: relations of ideas and matters of fact. Relations of ideas are logical necessities, such as the principles of arithmetic and geometry, or that all bachelors are unmarried. These facts are implied from the definitions of their components. Because relations of ideas can be understood through thought and reasoning alone, they can be proven certain through logical demonstration and, importantly, their contrary must be a contradiction. Matters of fact, however, are ideas that can plausibly take another form, meaning it is not impossible (and often quite easy), to conceive them differently. For example, most humans believe that the sun will rise tomorrow, but it is not logically impossible for the sun to fail to rise tomorrow morning and leave us in darkness. To understand these ideas, Hume claims, we need to experience them: there is nothing that inherently necessitates their truth. It is easy to conclude that the sun rises everyday after watching it do so your entire life, but without ever experiencing the sun, who could come to know the way in which the sun moves?
Hume posits that in processing this experience and in the formation of beliefs in matters of fact, we observe a series of causes and their subsequent effects and begin to associate certain conjunctions of the two. It is important to note that although we may catalogue these conjunctions as “cause-effect” pairs, Hume argues that we do not perceive the necessary connection itself: we merely know we have observed them in conjunction. For example, we notice that fire seems to be hot when touched or stood next to, and we associate future interactions with bright orange matter to align with our past experiences of heat. Hume is adamant about the dependence of our beliefs in matters of fact on experience, arguing that no human could reason, the first time they observe fire, that it must produce high heat.
Although Hume has asserted that our conclusions about matters of fact are based on cause-effect relationships from past experience, he raises a serious problem about the justification of our causal conclusions. Commonly referred to as the problem of induction, or making general conclusions from specific examples, Hume argues that there is no logical chain of reasoning that implies past events should continue in the same way in the future. We all seem to assume this in our everyday lives, extremely confident that gravity will continue to hold us down on the ground or that food will continue to provide the nutrition we need. Our belief in this continuation of past events or properties is called the Principle of Uniformity of Nature, which states that the laws of nature are consistent across time and space. Hume explains that justification of this inference must depend on the fact that past events will continue in the same way in the future, meaning any argument must be circular and assume the very principle trying to be proven.
Hume suggests that this inductive “reasoning” must be explained by something other than rational justification. He presents his principle of custom, claiming that our observation of repeated cause-effect conjunctions naturally influences our expectation of future events. He uses an example of a billiard ball rolling towards another. In our imagination, we can just as easily conceive the entire set of possibilities regarding the outcome of their collision, yet there is something different about the conception that aligns with our past experience. There is a unique strength with which we are drawn to conceive the effects that have accompanied this specific cause in previous observations. This aspect of human nature is not a supposed innate idea, but rather a natural ability or inclination to learn from experience.
In a world that depends so heavily on scientific and probabilistic frameworks to describe and analyze natural events, Hume’s claim that predictions and reasoning based on induction are not rationally justified is worrying. To clarify the strength of Hume’s argument about the circularity of rational justification regarding the Principle of Uniformity of Nature, I will present an objection based on Bayesian inference, which updates estimated probabilities with new experiences, allowing for a more dynamic, and arguably more flexible, assessment of the world, and then I will explore Hume’s conclusion on this objection. Take, for example, the belief that a ball will fall towards the ground when dropped. As a matter of fact, we could conceive of the ball moving in any direction when released, yet we are very confident it will tend towards the ground, or more accurately, the center of the Earth, because we have seen it happen so many times. Bayesian inferrers don’t claim to truly know based on past probability, but rather they guess with greater and greater confidence as their past experience raises the estimated probability of the ball dropping. Philosophers and mathematicians have tried to represent and justify the way humans form beliefs in matters of fact based on optimality, either utilizing modern machine learning techniques or Bayesian reasoning.
The argument is predicated on an important claim: if a method of prediction or expectation can be shown optimal, then it is rationally justified. The argument for this optimality, specifically, comes from a maximization of correctness when predicting outcomes, measured by so-called proper scoring rules. A scoring rule is considered proper if it is optimized when a predictor chooses the true outcome every time. There are variations on exactly how a scoring system is calculated, but it is most important that they are proper and reward truth. The goal of a predictor is to minimize total score, and predictions are penalized in proportion to their confidence. That is, predicting incorrectly with high confidence adds to your score more than predicting incorrectly with less certainty. These rules reward predictors that estimate with probabilities that most closely reflect the underlying distribution. It can be shown mathematically that Bayesian inference is optimal and cannot be outperformed, in terms of expected score, by any other prediction system with the same reasonably limited and experiential information to which a predictor has access.
As we can see in our world today, we have believed in the past that certain phenomena would continue, and for many matters of fact, we have been proven correct over and over. Modern artificial intelligence systems rely entirely on inductive reasoning, and their capacity to predict outcomes and model the world grows as data availability and computational power expand exponentially. Fortified by the precision and mechanical repeatability of computers in addition to the optimality of Bayesian reasoning, it is evident that these systems have the potential to observe patterns that we may never have without their help, which could point towards underlying principles. With this much repeated confirmation of our beliefs and an argument for the optimality of Bayesian reasoning, it should seem we are justified to expect these beliefs to hold true in the future.
In a Humean response, it can be conceded that this argument does identify an optimal way of making predictions. Hume responds, however, by identifying the true pattern this objector is expecting to continue, and it is not so much the individual beliefs themselves that are being argued rational because of optimality. Rather, this objector is claiming that humans are justified in present inductive reasoning because we have been correct through inductive reasoning in the past, meaning we are expecting this abstracted pattern of correctness to continue. However, that depends on an assumption that past events will continue (most importantly, that induction was correct), exactly what the objector was hoping to prove. This argument redefines what it means to be rationally justified, claiming that choosing optimality, even from a set of options that are all supposedly unjustified, is itself justified. Hume, however, still requires a necessary and logical demonstration without any circular dependence of inductive reasoning, so correctness in the past does not supply the desired justification for why any event is going to continue similarly in the future.
Hume is unfazed by his own conclusion that our induction is both irrational and inevitable. Although he has made it clear that he believes our inductive tendency is sufficiently accurate for all human intents and purposes, there remains a worry as to just how accurate it is. Hume’s grounding of our beliefs in psychological custom rather than reason feels like a skeptical conclusion, and it is easy to side with this line of thinking. What is there to make us confident that our experience aligns with the truth? If we can’t justify our conclusions, what are they worth? We as humans seek causal relationships, which we hold in higher regard than correlations, to describe the world. Hume argues that we can’t perceive underlying, necessary connections, or causal relationships, directly. Our senses limit us to observing only repeated conjunctions that we believe are constant. We claim that shark attacks and ice cream sales on the beach are not causally related and only correlated, but what leads us to believe there exists a stronger relationship between the two is founded on further correlative inference about other experiences. We can imagine, for example, that were all the sharks removed from the ocean, ice cream sales would not be affected (provided that the weather was still nice enough). How can we know that? This knowledge stems from other observations of similarly correlated instances regarding ice cream shops and their independence from the activity of sharks. The strength of our beliefs in matters of fact is necessarily dependent on prior established beliefs regarding other cause-effect pairs. Therefore, all relationships that we regard as causal cannot be guaranteed to be more than strong correlations.
If this premise regarding the contingency of our belief in matters of fact is accepted, the possibility that we are completely wrong about the laws of nature persists. What if everything we have come to believe has been and continues to be confirmed by our experience on Earth but there exist counterexamples that escape our experience or perceptive ability? If we were to stumble on such a counterexample, it could throw a wrench in everything we believe. For example, Isaac Newton presented his laws of motion and explanation of universal gravitation in 1687, positing revolutionary ideas including F = ma and that time is absolute for all observers. However, in 1905, Albert Einstein realized that space and time are neither absolute nor independent entities, proving that they are an interconnected, four-dimensional structure he called spacetime. We look back on historic thinkers like Newton and applaud them for their insight but acknowledge that they just couldn’t figure out the underlying principle in the way more recent scientists are able to. However, there is a worry that there could never be enough evidence to completely quell skeptical doubts. Aren’t the scientists of today just going to be somebody’s Newton in the future? How do we know that future counterexamples won’t fundamentally disrupt the basis of our scientific beliefs and completely disprove that which we depend on most? If that is going to happen, do we presently understand the world at a dangerously low level?
Hume isn’t as much skeptically declaring that scientific and probabilistic endeavors are meaningless or illegitimized because of their dependence on induction. He is offering the idea that they are inherently limited by the nature of their formation. It is not a problem that these schools of thought are not grounded in logical demonstration and rational justification—how could they be? We exist in a world that doesn’t tell us its secrets, meaning we are left to question it and figure out how it works through nothing more than observation. Hume references the fact that we discovered the functionality of our limbs and were able to sufficiently use them long before knowledge of the underlying biology was established. It is through this inductive abstraction that we have developed all of our understanding of the world, and we would be nowhere, maybe not even still alive, without it.
There is a natural desire to understand specific relationships in the world with complete certainty, but that desire misinterprets the scope of every matter of fact: it could very well be otherwise. Hume’s psychological conclusion regarding the problem of induction leaves many unsatisfied in terms of skeptical worries, lacking trust towards this mysterious, natural propensity. I think that his conclusions can be furthered by emphasizing a pragmatic surrender of the necessity and possibility of absolute reason regarding matters of fact. What are we to do other than make use of the experience available to us? If what we glean from his arguments is that all forms of prediction are incapable of being rationally justified, then he is correct that denigrating what seems to be the best method among them is unproductive. Choosing optimally, as in Bayesian reasoning, is not completely misguided on the basis that its inductive nature is logically circular. In rationalizing our inductive nature, Hume argues that we do it because it is natural, and I add that it is simply the best we as humans can do. In this way, our unjustified but natural conclusions regarding matters of fact are all we can come to have and all we need to exist.