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42 pages 1 hour read

Bertrand Russell

The Problems of Philosophy

Nonfiction | Book | Adult | Published in 1912

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Chapters 7-9Chapter Summaries & Analyses

Chapter 7 Summary: “On Our Knowledge of General Principles”

In the previous chapter, Russell explored the principle of induction, showing both its necessity for validating arguments and its limitations. The principle can never be proved by experience because the possibility of an alternative may challenge an assumption’s validity. Russell explains that there are other principles that work similarly, including the principle of inference. Humans draw inferences based on a strategy of logic. For example, the knowledge that yesterday was the 15th leads to the logical inference that today is the 16th. Philosophers recognize an important quality in principles like inference and induction: Human knowledge is derived from other places besides direct sensory experience.

Russell outlines three laws of thought that permeate philosophical tradition. First, the law of identity asserts that whatever exists must truly exist. Second, the law of contradiction states that an object cannot both be and not be. Third, the law of excluded middle suggests that an object must be one or the other: existing or not existing. Russell argues that these principles have nothing to do with thought; instead, they are related to priori knowledge.

Russell’s epistemological theory combines both priori knowledge, which suggests that all knowledge is innate, and posteriori knowledge, which is built upon the idea that all knowledge comes through experience. In Russell’s philosophy, both are intrinsically linked. Knowledge that is independent of experience is still informed by experience. For example, a person’s understanding that the Eiffel Tower exists, even if that person has never seen it, is a combination of both the priori understanding that objects can exist even if a person has never seen them and the posteriori understanding of sense data derived from descriptions of the Eiffel Tower. Priori knowledge is often logical, indicating that because one thing exists, something else must exist too. However, it can also be non-logical, such as priori knowledge of ethical value. For instance, humans innately understand that happiness is preferable to misery.

Chapter 8 Summary: “How a Priori Knowledge Is Possible”

Russell turns his attention to Kantian philosophy, which seeks to merge empiricist and rationalist thought. Before Russell, many philosophers believed that priori knowledge was strictly analytical. To say that a tall man is a man is an example of this type of analysis. This ideology asserts that priori knowledge is inherently logical. For example, 2+2=4 is an example of something that is logically deduced. The philosopher David Hume challenged this idea, arguing that some types of knowledge are not built upon a logical cause and effect. Kantian philosophy combines rationalism and empiricism by proposing that the simple equation above both extends knowledge by adding something new to human understanding and is innate.

For Russell, these arguments ignore important contradictions: “The problem arises through the fact that such knowledge is general, whereas all experience is particular” (50). Kantian philosophy asserts that knowledge is formed by the interaction between sense data derived from comparison and analysis and priori knowledge of concepts like space and time. The philosopher Immanuel Kant referred to the physical object as a “thing-in-itself.” The nature of the thing-in-itself is unknowable except through personal experience, called the “phenomenon.”

Russell criticizes Kant’s assumption that knowledge always conforms to a constant set of rules. The simple equation above appears to be concrete, but the slippery nature of physical objects may one day reveal that this equation is not true in every case. Furthermore, viewing this equation as exclusively priori knowledge does not account for humans’ ability to apply it across experiences. Russell proposes that principles, like the law of contradiction, occur within psychological reflection on experience. Therefore, the connections, or relations, that humans draw are different from physical objects, thoughts, or sense data.

Chapter 9 Summary: “The World of Universals”

Russell makes a case for a new form of knowledge that utilizes connections. He establishes that this knowledge is neither strictly priori nor posteriori. Instead, it is a combination of the two. For example, the concept of justice is understood through the discovery of connections between multiple scenarios. A person draws on both experience and innate understanding. The commonality among the scenarios forms the concept of justice. Plato called this through-line a form, or idea, but Russell uses the term “universal.” Universals are different from particulars. They are derived from connections and do not stand for concrete objects.

Russell argues that all sentences must contain a universal and that all truth relies on universals. Some philosophers have sought to reduce universals to concrete understandings. Colors, for example, have been used by rationalists to support this idea. Imagining the concept of “whiteness” may lead to the recollection of a specific white object. However, Russell argues that the application of a color across physical objects reveals its universal nature.

Despite the discovery of universals through psychological reflection, they are not strictly within the mind. In the example of one city being north of another, “north” is a universal. However, it also has a direct connection to the physical realm. Although “north” is not a physical object that exists in a tangible way, it has a relationship with the external world. Therefore, a universal is something else entirely: “It is neither in space nor in time, neither material nor mental; yet it is something” (59).

Chapters 7-9 Analysis

In Chapters 7-9, Russell unpacks two epistemological viewpoints. Knowledge is often divided into opposing camps: innate or experiential. These two modes of thinking about knowledge help contextualize The Relationship Between Perception and Reality. Russell follows the often-used equation 2+2=4 to unpack priori knowledge and its contradictions. While Russell often uses accessible words or phrases, in this case, he distills his ideas into simple numbers. This equation becomes a motif that Russell uses to represent different philosophical schools of thought. For idealists, the equation is a logical analysis that can be understood without concrete examples. Empiricists argue that priori knowledge is independent of experience. Rationalists propose that all knowledge is derived from experience. The equation 2+2=4 is only understood by seeing the principle play out in real life.

Russell offers a challenge to the simple equation of 2+2=4. This equation, taken by many philosophers and mathematicians in history to be indicative of priori knowledge, appears to be universally true. However, Russell argues that probability does not guarantee the truth of a concept. It is possible for a person who has only ever seen white swans to see a black one. Just because the equation has been proven true repeatedly does not mean that it will always be proven true. By shaking the foundations of a seemingly simple equation, Russell conveys that knowledge shouldn’t be simply taken for granted, reinforcing the textual aim to explore “problems” instead of immutable solutions. The equation is understood both through experience and innately. Because humans can apply equations and other concepts across contexts, their knowledge is not and cannot be limited to mere direct experience. Russell did not yet know that the equation would one day be challenged by quantum mechanics and modulo arithmetic.

Russell explores several philosophical theories in this section, further presenting himself as an authoritative figure by exploring the limits of each one. He argues that adhering to one philosophical theory means ignoring The Nature and Limits of Human Knowledge. To assume that all knowledge is strictly empirical is to ignore the way humans develop understandings about the world around them by interacting with it. To believe that all knowledge is rational, or experiential, is to disregard the many ways in which humans develop their own internal belief systems. Russell proposes that knowledge is often formed by the interaction of both priori and posteriori knowledge.

Relatedly, Russell suggests that The Value of Philosophy is in its relentless pursuit of truth. While exploring several philosophical schools of thought, this is the common thread that he finds between each one, thus presenting his own arguments while constructing a narrative of the development of philosophical thought through time. Russell maintains that sound philosophy requires a combination of empirical and rationalist approaches.

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