56 pages • 1 hour read
David HumeA Treatise of Human Nature
Nonfiction | Book | Adult | Published in 1739A modern alternative to SparkNotes and CliffsNotes, SuperSummary offers high-quality Study Guides with detailed chapter summaries and analysis of major themes, characters, and more.
Book 1, Part 2Chapter Summaries & Analyses
Book 1, Part 2 Summary
Hume turns to other philosophers’ arguments about the limits of human understanding. He discusses the idea of “infinite divisibility,” the concept that any measurement of space or time can be broken down into smaller parts infinitely. Hume considers the example of “the thousandth and ten thousandth part of a grain of sand” (76). He can hold the idea of the number itself and the idea of a grain of sand, even if he cannot envision what such a microscopic piece of sand would look and feel like. Likewise, Hume points out that if you drew a spot of ink on a piece of paper and walked away from it, there will be a point when you can no longer see it. All this suggests that a person’s impression of the image itself cannot be divided into smaller parts of itself past a certain point (76-77). For Hume, these observations prove the limitations of the human mind in forming ideas about the infinitely small or the infinitely vast. Plus, Hume argues a person can have an abstract idea of a “unity” that can include any number of subjects, including the entire world or even the universe (79).
As for time being infinitely divisible, Hume also considers that impossible. Infinite divisibility cannot be proven through an actual demonstration, so it cannot be perceived through the five senses and, as a result, we cannot know about it. Nor can it be imagined. Hume compares imagining infinite divisibility to imagining a golden mountain and a mountain without a valley (81). It is possible to imagine a mountain made of gold, even though one does not exist in reality, because we have the impression of gold and the idea of a mountain. However, it is impossible to imagine a mountain without a valley because any idea of a mountain depends on the concept of a valley. Likewise, we can imagine different lengths of space and time, even ones we have not experienced, but we cannot imagine space and time as infinitely divisible.
In contrast, Hume can use the imagination to change the characteristics of the objects he perceives. For example, Hume considers the table he is writing on. He can imagine the length of the table getting longer, but his imagination depends on the perceptions of the table he gained through sight and touch. He can also imagine the table in different colors. Hume concludes that, through the imagination, abstract ideas can represent many diverse variations of different objects (82-83). Even something as intangible as time is understood or imagined through our perceptions. We perceive time through objects changing in some way or something like the sound of five musical notes on a flute (84).
Next, Hume rebuts some arguments for the infinite divisibility of space and time. Hume argues that attempts by philosophers to visualize an infinite series of mathematical points or tiny atoms destroying each other do not prove infinite divisibility. Such mathematical points are still something we visualize in some way. Hume instead imagines these atoms combining, rather than breaking through each other. He notes that one cannot add up an infinite number of mathematical points that represent nothing—zero—without giving “a colour or solidity on these points” (89). For Hume, this proves the “natural infirmity and unsteadiness of our imagination and senses” (90), which still cannot truly envision infinitely-divisible points.
Hume rejects the mathematical arguments for infinite divisibility. Even if such infinite points did exist, we cannot perceive them the same way a painter can tell the difference between colors, an engineer between different speeds, or a musician between musical notes (97). In fact, the lines and angles drawn on paper are just representations of the ideas in our mind. According to Hume, even our understanding of geometry depends on the imagination. After all, we need scientific instruments like a ruler or a compass to make up for our limited understanding (99-101). That understanding cannot imagine or even represent something like an infinite series of points in time or space.
Then there is the idea of the vacuum, which philosophers have also argued over. Like infinitely divisible points, Hume argues this does not truly exist. A true vacuum would be space without any matter. Since darkness is just the absence of light and objects can still exist in darkness even when we cannot perceive them, Hume argues a totally black space is not a true vacuum (104). Even if a person was suspended in the air or there was a vast space between objects, there can still be a perception of color, a feeling of motion, or an idea of the distance (113). However, if a vacuum does not exist, how can we have an idea of it, according to Hume’s own logic about experience, impressions, and ideas? Hume would counter that we do not even really have an idea of a true vacuum because it does not come out of a sensation or reflection. Instead, Hume compares the idea of a vacuum to the idea of an existence that lasts through time but never changes. We can broadly conceive of it through our imagination using related ideas, like any kind of imaginary place or creature, but it does not seem to exist (113-14).
Hume concludes by discussing the nature of existence. Anything we can conceive of in our minds can be said to exist. At the same time, external existence only exists in our own minds through our perceptions or impressions and ideas (115).
Book 1, Part 2 Analysis
Hume has two main goals in this part. The first is continuing his arguments about Empiricism Versus Rationalism by exploring the fundamentals of how humans learn and know about things. As Hume puts it, “Wherever ideas are adequate representations of objects, the relations, contradictions and agreements of the ideas are all applicable to the objects; and this we may in general observe to be the foundation of all human knowledge” (78). Here, Hume emphasizes more on how our senses lead us to comprehend things we normally consider abstract, like geometry or time. For a modern example of what Hume is arguing, when an astronomer today calculates the distance between our solar system and another one, they clearly can only represent through numbers and geometrical lines the distance involved. In fact, Hume would argue that even an astronomer would struggle to adequately imagine the 96 million miles between Earth and Mars, much less the 6 trillion miles between Earth and the nearest known Earth-like planet, Alpha Centauri B. This is because, as Hume would argue, our knowledge of space comes from things like the distance between our home and the grocery store. It is extremely difficult, if not impossible, to use that experience to form an accurate idea of massive astronomical distances or, for that matter, the infinitesimal distance between atoms.
It is the same with time. Based on just our impressions and ideas of minutes, hours, years, and even centuries, we cannot truly imagine a billion years or a zeptosecond, the time it takes for light to cross a hydrogen molecule, which is a trillionth of a billionth of a second. The best we can do is represent such things beyond our experience with representations like numbers, equations, and lines. Besides explaining The Limits of Knowledge, this idea supports Hume’s argument for empiricism: Even our concepts of space and time are formed and limited by our personal experience.
Hume’s second goal is to debunk two concepts from philosophy: space and time as infinitely divisible, and the concept of a vacuum. The idea of infinitely divisible points comes from Zeno’s paradoxes. The fifth-century BCE Greek philosopher Zeno of Elea was said to have come up with a number of paradoxes. In one, Zeno asks if the mythological heroine Atlanta wants to cross a certain distance, then when is she halfway to her destination. Then, he asks when is she a quarter of the way there, an eighth of the way there, a sixteenth of the way there, and so on. Another paradox is that of Zeno’s arrow. If an arrow is fired, the time the arrow takes to hit its target can be broken down indefinitely into a practically infinite series of nows. Hume rejects these paradoxes, even though he does not describe them specifically. Even with the help of representations like points on a graph, we cannot map out or visualize the infinite indivisibility of space or time. This is not to say that Hume is arguing against the concept that infinity stretches infinitely outward or inward in space and time. Instead, he is saying that our experience is too limited to allow us to know, even with the aid of our imagination or with mathematical and geometrical representations, so most if not all questions about the infinity of space and time are basically pointless. In Hume’s own words, it is “almost impossible to answer in an intelligible manner” (90).
Likewise, our knowledge does not allow us to envision a true vacuum or nothingness, something else debated by philosophers from the ancient Greek philosopher Aristotle to Descartes. As with infinite divisibility, Hume does not consider the question worth considering since our experience does not allow us to form more than a broad imagining of it. It is basically no different than imagining a unicorn or an immortal human being, since our imagination just forms the idea of a vacuum from an idea of an absence of things like light and matter. However, it is worth pointing out that 18th-century science was not aware of outer space, although even then, if Hume were around today he might argue that outer space is still not a true vacuum, since cosmic dust and light rays are still there.
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