Our Knowledge of the External World as a Field for Scientific Method in Philosophy Informative Summary


In this collection of lectures, Bertrand Russell tackles the long-standing philosophical problem of how our sensory experiences connect to the objective reality described by physics. He criticizes the dominant philosophical schools of his time – the classical tradition, descended from Kant and Hegel, and evolutionism, popularized by thinkers like Bergson. Russell finds both schools lacking in their reliance on untested generalities and their failure to employ rigorous logical analysis.

He proposes a new approach, which he terms “logical atomism,” as a more scientifically grounded way to understand the relationship between our sense perceptions and the world of physics. By constructing a hypothetical universe based on individual perspectives, he demonstrates that concepts like permanent objects, space, and time can be logically derived from our sensory experiences without needing to assume the existence of any metaphysical entities. Russell argues that this approach, while yielding a less ambitious picture of reality than classical or evolutionary philosophies, offers a more reliable and verifiable understanding of the world.

Key Findings:

  • Logic as the foundation of philosophy: Russell posits that every philosophical problem, when rigorously analyzed, either proves to be not truly philosophical or ultimately reduces to a problem of logic.
  • The inadequacy of traditional logic: He critiques traditional logic, particularly its emphasis on the subject-predicate form, for its inability to account for the reality of relations, a crucial aspect of the world of science and daily life.
  • Redefining “things”: Russell proposes that “things” be defined as series of appearances connected by continuity and causal laws, dispensing with the need for the metaphysical assumption of permanent substances.
  • Sense-data as the basis of knowledge: He argues that objects of sense, even in dreams, are the most indubitably real objects we know, and that a scientifically valid understanding of the physical world should be interpretable in terms of sense-data alone.
  • The principle of abstraction: This principle allows us to use classes of similar objects to replace the assumption of shared qualities, thereby avoiding the introduction of unnecessary metaphysical entities.
  • Constructing space and time: Russell explains how points and instants, concepts central to mathematical physics, can be logically constructed from sense-data, bridging the gap between the worlds of physics and sense perception.
  • A new approach to infinity: He champions Cantor’s theory of infinity, demonstrating how infinite numbers, despite their paradoxical qualities, can be understood without contradiction and can help resolve the challenges of continuity.
  • The limits of induction: Russell emphasizes that induction, the principle underlying inferences about the unobserved, cannot itself be justified empirically and, if valid, must be an a priori logical law.
  • Rethinking causality: He argues that a scientifically valid concept of cause, based on constant relations between events, dispenses with the anthropomorphic notion of volition and compulsion.
  • Free will redefined: Russell reconciles free will with determinism by defining freedom as the absence of external compulsion and the presence of volitional actions that are the result of our own desires.


  • The importance of logical analysis: The reader will learn how rigorous logical analysis can clarify philosophical problems, expose the flaws in traditional arguments, and pave the way for more scientifically grounded solutions.
  • The nature of mathematical continuity: Russell provides a clear explanation of what mathematical continuity entails, disentangling it from common misconceptions related to infinitesimals and consecutive points. He shows how this concept can be applied to understanding the continuity of change in the world of sense.
  • The reality of relations: The reader will learn how the concept of relations, particularly asymmetrical relations, helps to overcome the limitations of traditional logic and provides a more accurate account of the world of science and daily life.
  • A new understanding of the infinite: The lectures introduce Cantor’s revolutionary theory of infinity, freeing it from the contradictions that plagued earlier philosophical attempts and demonstrating its power to solve long-standing problems of continuity and infinite divisibility.
  • The limits of empirical knowledge: Russell highlights the crucial role of a priori logical principles, such as induction, in justifying inferences that go beyond the immediate data of sense experience, while emphasizing the limits of what can be known with certainty through empirical evidence alone.
  • A scientific approach to causality: The reader will learn how to understand causality in terms of constant relations between events, shedding the anthropomorphic baggage of volition and compulsion that often accompanies traditional notions of cause.
  • Reconciling free will and determinism: Russell offers a nuanced perspective on the free will debate, arguing that a valuable sense of freedom is compatible with determinism, as long as our volitions are determined by our own desires and not by external compulsion.

Historical Context:

Russell’s lectures were delivered in 1914, a time of significant intellectual ferment. The scientific revolution, initiated centuries earlier, was reaching a new crescendo with groundbreaking discoveries in physics, such as Einstein’s theory of relativity. This was also a period of intense philosophical debate, with the classical tradition facing challenges from new schools of thought like pragmatism and evolutionism. Russell’s work, informed by the burgeoning field of mathematical logic, sought to carve a new path for philosophy, one that embraced the rigor of scientific methods while tackling traditional philosophical problems with fresh insights and a critical eye towards untested assumptions.


  1. Objects of sense are the most indubitably real objects we know: This is based on the fact that our senses provide us with direct, immediate experiences that do not require any further justification.
  2. Traditional logic is inadequate for understanding the world of science and daily life: The subject-predicate form favored by traditional logic fails to account for the reality of relations, a crucial aspect of scientific and everyday experiences.
  3. The concept of “things” can be reconstructed without assuming permanent substances: Russell defines “things” as series of appearances connected by continuity and causal laws, dispensing with the need for metaphysical entities.
  4. There are no “illusions of sense”: Objects of sense, even in dreams, are real in the sense that they are genuine experiences. They become “illusory” only when we draw inferences from them that turn out to be incompatible with other experiences.
  5. The world of physics can be interpreted in terms of sense-data alone: This means that the concepts and laws of physics should, in principle, be relatable to the kinds of experiences we have through our senses.
  6. Different senses have different spaces: The spaces of sight, touch, hearing, etc., are not given to us as unified, but are correlated through experience.
  7. Points and instants are not among the data of experience: These are logical constructions, defined as classes of sensible qualities or groups of events, rather than independently existing entities.
  8. The series of fractions in order of magnitude is compact: This means that between any two fractions, there are always infinitely many other fractions.
  9. A continuous motion does not consist in occupying consecutive positions at consecutive times: There are no “next” positions or “next” instants in a continuous series.
  10. Infinite divisibility does not imply infinitesimal distances or times: Any distance or time interval, no matter how small, can be further divided, but it will always remain finite.
  11. There are no empirical grounds for deciding whether sense-data are composed of mutually external units: This is a question of logical analysis, not of direct experience.
  12. Complexity implies constituents: The complexity of our experiences, such as the visual field, suggests that they are composed of simpler elements.
  13. Mathematical space and time are formally absolute: This means that mathematics assumes the existence of points and instants as distinct entities, but this assumption is not empirically verifiable.
  14. The relational theory of space and time is more economical: This theory dispenses with the assumption of points and instants as independent entities, while still allowing us to define them as logical constructions.
  15. There is no empirical evidence to demonstrate the continuity of the sensible world: Our senses have limited discrimination, so we cannot rule out the possibility that the world is composed of a large but finite number of discrete elements.
  16. Infinite numbers have the property of reflexiveness: This means that an infinite number is not increased by adding one to it or by doubling it, a property that initially seems paradoxical but is logically consistent.
  17. Infinite numbers do not have the property of inductiveness: This means that proofs based on the principle of mathematical induction, which rely on a step-by-step process from one number to the next, are not applicable to infinite numbers.
  18. Numbers are properties of classes, not of physical things: We ascribe a number to a class of objects that share a defining property.
  19. Two collections have the same number of terms when there is a one-one relation between their members: This provides a logically sound way to compare the size of collections, even infinite ones.
  20. The law of universal causation is an ideal, not an empirically proven fact: There is empirical evidence for causal laws within certain domains, but no guarantee that they apply universally and without exception.


  1. Logical atomism: A philosophical approach that analyzes complex entities and concepts into their simplest, most fundamental components, which are often taken to be logically independent “atoms” of meaning.
  2. Sense-data: The immediate objects of perception, such as patches of color, sounds, smells, and tactile sensations.
  3. Perspective: A view of the universe from a particular point of view, encompassing all the sense-data available to an individual observer at a given moment.
  4. Thing: A series of appearances connected by continuity and causal laws, dispensing with the assumption of a permanent substance underlying those appearances.
  5. Point: A logical construction defined as a class of spatial objects that enclose one another in a specific way, capturing the geometrical properties of points without assuming their independent existence.
  6. Instant: A logical construction defined as a group of events that are simultaneous with each other and not all simultaneous with any event outside the group.
  7. Compact series: A series in which no two terms are consecutive, and where between any two terms, there are infinitely many other terms.
  8. Infinite divisibility: The property of a quantity that can be divided into smaller and smaller parts without ever reaching a limit.
  9. Reflexive number: An infinite number that is not increased by adding one to it or by doubling it.
  10. Non-inductive number: An infinite number to which proofs by mathematical induction cannot be applied.


  1. Walking around a table: Russell uses this example to illustrate how the appearance of a single object can change with the point of view, challenging the common-sense assumption of permanent objects with changing appearances.
  2. Blue spectacles: This example demonstrates how the interposition of a transparent object can affect the perceived color of other objects, without needing to assume the continued existence of the transparent object when not being touched.
  3. The “Comedy of Errors”: This Shakespearean play, featuring mistaken identities due to the close resemblance of twins, is used to illustrate that similarity alone is not a sufficient criterion for identifying “things.”
  4. A fading wallpaper: This example showcases how a “thing” can be understood as a series of continuously changing appearances (colors in this case) connected by causal laws, without needing to posit a permanent substance.
  5. Drops in the sea: This example shows that continuity alone is not enough to define a “thing,” as any two drops of water in the sea can be connected by a continuous path.
  6. The series of fractions less than 1: This serves as a concrete example of a compact series, where between any two fractions, there are always infinitely many others.
  7. A speck of light moving along a scale: This example helps to illustrate the concept of continuous motion as a series of instantaneous states, where the moving object occupies different positions at different instants without jumping or having periods of rest.
  8. The hour-hand and the second-hand of a watch: Both hands are in motion, but the second-hand’s motion is readily perceived while the hour-hand’s motion is only known by inference, illustrating the distinction between perceived and inferred motion.
  9. Adding small weights to a hand holding a weight: This example demonstrates the existence of imperceptible differences between sense-data, challenging the notion that immediate data must be directly perceived as different if they are in fact different.
  10. The story of the grouse in the gun-room: Russell uses this humorous anecdote to illustrate the predictability of human actions based on knowledge of someone’s habits and character, while acknowledging that complete particularity of an act may not be foreseeable.


Russell’s lectures offer a compelling case for a scientifically inspired approach to philosophy, one grounded in logical analysis and attentive to the findings of empirical science. While this approach may not satisfy our desires for grand pronouncements about the ultimate nature of reality or the destiny of humankind, it promises a more reliable and verifiable understanding of the world around us. By carefully analyzing our sensory experiences and constructing logical frameworks for interpreting them, Russell demonstrates how we can bridge the gap between the world of sense and the world of physics, address the challenges of infinity and continuity, and develop a more nuanced understanding of causality and free will. His work stands as a testament to the power of logical analysis to illuminate philosophical problems and to guide us towards a more scientific and grounded understanding of our place in the universe.

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