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===On Intuitive Knowledge===
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===Truth and Falsehood===

Revision as of 21:03, 30 April 2013

The Problems of Philosophy
Author Bertrand Russell
Language English
Publisher Williams and Norgate, London
Released 1912
Pages 192

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Executive Summary

This book is an introduction to philosophy. In it the eminent British philosopher, Bertrand Russell explores what we can know, and how philosphy helps us to identify and classify knowledge and uncertainty. The book also argues for the value of philosophy both as an enriching study for individuals as well as an asset to society. The entire text is available at

Chapter Summaries


In the four sentence preface Russell commits to saying something constructive and therefore confining himself primarily to epistemology. He credits G. E. Moore, J. M. Keynes and Gilbert Murray for their contributions.

Appearance and Reality

In seeking certainty, we discover vagueness and confusion in many common ideas. The search for certainty launches us into the study of philosophy.

One area that seems to grant us certainty is our immediate experience. Russell describes his immediate experience as he sits in a sunny room at his desk. He focuses on the sensations he experiences of the table before him. In a precise description of its visual appearance Russell notes that although he believes the table to be all one color, that part of the table appears almost white due to the reflected light. He knows that if he moves that the apparent whiteness of the part of the table will move, too. Although this difference in appearance is unimportant for most practical purposes, the artist must learn to see and portray things as they appear, rather than as they "really" are. Philosophy too, guides us to examine closely what we experience.

Examining the color of the table, we are lead to the conclusion that there is no color which is preeminently the color of the table. The color depends on the presence and kind of artificial light, the time of day and the condition of the viewers eyes, among many other factors.

The texture of the table presents a similar result. Although to the unaided eye the table appears smooth, with a magnifying glass, ridges and rough spots become evident. More powerful magnification would reveal an even more elaborate texture. Which is the true texture? There is no reason to pick one over the other.

The sense of touch does not give us any more certainty about the real nature of the table. Examining the sensations we experience about the table we must conclude that we only know about its appearance. "The real table, if there is one, is not immediately known to us at all, but must be an inference from what is immediately known."

Russell then introduces us to Bishop Berkley, who showed that matter can be denied without absurdity. He concludes the chapter by pointing out that philosophy guides us to from the common place to the amazing in quick order. Our inquiry into the certainty provided by our immediate experience leads us to realize that the appearance of matter can not be the same as its reality. The next question Russell addresses is does matter exist?

The Existence of Matter

Since our immediate experience gives us no certainty about the existence of matter and since it is possible to deny the existence of matter without logical fallacy, should we assume that matter does not exist? Russell answers no. The existence of matter is the simplest explanation of our experience.

Russell asks us to consider a cat. He asks to imagine that he sees a cat at one moment in one part of the room and in another somewhere else. Our simplest assumption is that the cat has moved. But if there is no matter and nothing but Russell's sensations, then the cat can not have been anywhere he did not see it. It must have ceased to exist when it passed out of his view and reappeared when he saw it in its new location. Now imagine that his cat is acting hungry. How could this be accounted for? No hunger can exist except his own sensation of hunger. Any explanation of this behavior that does not suppose the existence of a real cat is bound to be more complicated than assuming that the cat does exist outside the sensations Russell is experiencing.

But the problem of the cat is minor compared to the problem of explaining other people. When some one speaks and we hear sounds we associated with ideas and we see the persons face, it is difficult to imagine that they are not expressing a thought, as we would be if we were to make similar sounds.

We are certain of our sensations regarding matter and those sensations seem to have agreement with each other about objects of our experience. Common sense tells us that there is a source of these sensation external to us. We would never have doubted that matter existed if we had not begun an analysis of appearance and reality. Although this argument is not convincing, taken with the argument for the existence of matter as the simplest explanation, it does urge us to accept we previously naturally believed.

The argument for the existence of matter is not decisive. There is room for doubt. This is the nature of philosophical knowledge. Such knowledge is built up from instinctive beliefs that we hold most strongly. "...each as much isolated and as free from irrelevant additions as possible. It should take care to show that, in the form in which they are finally set forth, our instinctive beliefs do not clash, but form a harmonious system." Such a harmonious system, though it may contain error, is less likely to be incorrect, because of the interrelationship of the parts and the scrutiny given to each part.

The Nature of Matter

Having established, at least to some degree of certainty, that matter exists, what can we know of its nature? The physical sciences tells us that matter is wave-motion in space. This wave-motion is not identical to our experience but corresponds to it. For example, if we see a red object and a blue object we know that there is some corresponding difference between the two objects that give rise to the different sensations. Likewise, if we see two blue objects we may assume that there is some common property in the two objects that gives us the sensation of blueness.

We experience space through our sense of touch and our sense of sight. We learn in infancy how to associate these two sensations to create an internal sense of the space we perceive. Science and common sense assume that there is a public space in which objects exist. "It is this physical space which is dealt with in geometry and assumed in physics and astronomy." As with our experience of matter, our experience of space is one of correspondence. We do not experience the intrinsic nature of space.

Some philosophers contend that we can know something of the intrinsic nature of matter. They make this claim because although our sensations do point to something that exists independently of us, that something is mental. These philosophers are called idealists.


Idealism is a widely held doctrine in philosophy and so demands some attention. Russell defines idealism as "the doctrine that whatever exists, or at any rate whatever can be known to exist, must be in some sense mental." This doctrine is presented in the context of discussions about what is required for something to be known.

The first philosopher to argue for idealism was Bishop Berkley, who Russell introduced in Chapter 1 "Appearance and Reality". Berkley's argument is that our sensations must be in our minds and do not have any existence apart from us. Our sensations are all that we can know and to be known is to be in a mind. The conclusion of Berkley's argument is that nothing can be known except that it is some mind, and whatever is known without being in my mind must be in some other mind.

Russell presents a critique of Berkley's argument, starting with Berkley's notion of idea. Berkley defines an idea as something that is immediately known. Sensations are ideas; things we see and sounds we hear and so forth. Things we remember or imagine are also immediately known and so are also ideas. Berkley maintains that we can only know of objects in the world by perceiving them, that being is being perceived. Objects continue to exist when no one else perceives them because they remain in the mind of God.

Such a view of idea confuses the notion of being "in a mind". The thought of the object is in the mind but the thing itself is not. It seems like too simple a mistake to be made, but there are circumstances that led Berkley down this path.

Berkley does successfully demonstrate that sensation of physical objects is subjective. Without the observer, there would be no sensations. The sensations of an object therefore exist only in the mind of the observer. This is a step towards showing that to be known things must be mental. However, Berkley's idea conflates the thing apprehended with the apprehension itself. Because the perception is mental does not imply or require the thing being perceived to be mental. As Russell puts it:

...we readily assent to the view that ideas must be in the mind. Then, forgetting that this was only true when ideas were taken as acts of apprehension, we transfer the proposition that 'ideas are in the mind' to ideas in the other sense, i.e. to the things apprehended by our acts of apprehension. Thus, by an unconscious equivocation, we arrive at the conclusion that whatever we can apprehend must be in our minds.

Russell then turns his attention to a related notion in idealism, that of "we cannot know that anything exists which we do not know." Know is used in two different ways in the sentence and when this ambiguity is handled the sentence becomes clearly false. The "know" used in "we cannot know that anything exists..." is the know that means recognizing as true. This kind of knowledge is also called called judgement. The "know" in the second case is knowing about things, and is called acquaintance. The statement is then rendered as "we cannot make judgements about anything with which we are not acquainted." This is false, for, although we are not acquainted with Bertrand Russell or Bishop Berkley, we can certainly make judgements about them.

When something is not known by direct experience, or, in Russell's terminology, by acquaintance, it is known by description.

Knowledge by Acquaintance and Knowledge by Description

We know from the previous discussion of judgements and acquaintance, that there are two kinds of knowledge: knowledge of truths and knowledge of things. Knowledge of things is further partitioned into knowledge by acquaintance and knowledge by description. Knowledge by acquaintance is the simplest kind of knowledge. It is without reference to any truths and accessed by direct experience.

To given an example of knowledge by acquaintance Russell returns to the example of the table. The experience of the color of the table, is an experience of knowledge by acquaintance. There is nothing that can be added to the experience of the "brownness" of the table. It is immediately accessible and complete.

The table itself though, is not known to us by acquaintance. There are a set of sensations we associate with the table and we can, from these, create a description which only Russell's table will match. Thus the table is known to us by description.

Russell declares:

All our knowledge, both knowledge of things and knowledge of truths, rests upon acquaintance as its foundation.

The following are things we know by acquaintance:

  • direct sensation, as per earlier discussion
  • memory
  • introspection, as in "I am aware of my perception of the brownness of the table"
  • perhaps, although not certainly, the self
  • general ideas, such as motherhood

Having categorized what can be known by acquaintance, Russell turns to knowledge by description. Anything that is referred to a "a so-and-so" is an ambiguous description. Things that are referred to as "the so-and-so" are a definite description. Ambiguous descriptions are problematic and a definition of knowledge by description can be made without going into those problems. So Russell focuses on definite descriptions. A definite description is a set of properties that designate a particular object. Unless the object derives its existence from a logical analysis of the description, such as "the longest living man", some aspect of the description must be known to us by acquaintance. In fact, in the analysis of propositions made up of descriptions, each proposition which can be understood must consist entirely of constituents with which we are acquainted. If there were not the case we could not make any judgment about the proposition. For the words in the proposition must have some meaning and that meaning derives from acquaintance.

We are certain of knowledge we have by acquaintance, but such knowledge is private to us. Knowledge by description allows us to pass beyond the realm of private experience and gain knowledge of things we have not experienced.

On Induction

Given what we can know about things, Russell turns our attention to what we can infer. To do this he presents the judgement, "The sun will rise tomorrow."

What basis do we have to believe this is true? Our immediate answer is because it has always done so in the past, but this does not satisfy us with any certainty. Even if we appeal to science and the laws of motion our desire for certainty is not satisfied, for we should we believe that the laws of motion will continue to operate tomorrow as the have in the past?

The answer is that we do not know "for certain". As a kind of event A occurs together with a kind of event B and these two kinds of events never occur apart, each new occurrence increases the probability that these events will be related in the next occurrence. This probability approaches certainty, without limit.

Russell concludes the chapter by stating:

all knowledge which, on a basis of experience tells us something about what is not experienced, is based upon a belief which experience can neither confirm nor confute, yet which, at least in its more concrete applications, appears to be as firmly rooted in us as many of the facts of experience

The following chapter elaborates on other kinds of knowledge that, like induction, is assumed true but can not be proven true.

On Our Knowledge of General Principles

Russell next brings our attention to implication. The simple argument if A is true then B is true. A is true, so B must be true is generally accepted, but there is nothing in our experience to prove that it is true. Yet, without proof, we are as certain of it as we are of our sensations. In addition to implication, there are other self-evident principles that allow us to reason about propositions. These are called the laws of thought (though Russell finds the title misleading).

They are as follows:
(1) The law of identity: 'Whatever is, is.'
(2) The law of contradiction: 'Nothing can both be and not be.'
(3) The law of excluded middle: 'Everything must either be or not be.'

The title is misleading because it is not that we must think this way, but that when we do think this way, we think correctly.

The Empiricists and Rationalists schools of philosophy each have different views as to how to we come to know these general principles. The Empiricists believe that general principles arise out of experience. The rationalists believe that the general principles are inate ideas.

Russell declares that the rationalist are correct, in that experience can not prove these general principles are true, but that empiricists are correct in that our experience does suggest the principles. It would be ridiculous to suggest that the principles are inate in the sense babies are born knowing them. Experience clearly plays a role in giving us an understanding of these prinicples. Since the term inate has this notion of being born into this knowledge, philosopers use the term a priori.

How A Priori Knowledge is Possible

Immanuel Kant made significant contributions to the understanding of a priori knowledge. He showed that a priori knowledge is can be synthetic, that is, new knowledge can be gained that is not implicit in the a priori proposition. Prior to Kant's work, it was general held that all a priori knowledge was analytic, that is any knowledge recognized from an a priori proposition was some how contained in the proposition and extracted by analysis.

David Hume, a slightly earlier contemporary of Kant's, had shown that cause could not be logically deduced from effect (contrary to what the rationalist school, in which Kant had studied, believed). Hume went on to propose that no a prior knowledge is possible about cause and effect. Kant countered this proposal by asserting that synthetic a priori knowledge is possible and indeed that all mathematics is synthetic a priori knowledge. Russell explains Kant's assertion by presenting Kant's stock example 7+5 = 12. No amount of analysis of 7 or of 5 will demonstrate the idea of 12. This proposition and all mathematical propostions are synthetic.

Having made and demonstrated this assertion, Russell explores Kant's answer to the question "How is mathematics possible?"

The problem arises through the fact that such knowledge is general, whereas all experience is particular. It seems strange that we should apparently be able to know some truths in advance about particular things of which we have as yet no experience; but it cannot easily be doubted that logic and arithmetic will apply to such things. We do not know who will be the inhabitants of London a hundred years hence; but we know that any two of them and any other two of them will make four of them. This apparent power of anticipating facts about things of which we have no experience is certainly surprising.

Kant distinguishes "the thing in itself", what Russell has called the physical object, and our sense data. Our experience of an object is a combination of our sense data and our own judgements about the sense data. This combination of sense data and judgements Kant refered to as "phenomenon". Since phenomena are a result of sense data and our own judgements and our judgements supply abstract concepts about the sense data, all our experience of the world is subject to reason, because nothing enters our experience which does not include the abstract judgements we supply.

Russell points out that by attributing logic and arithmetic to the observer, the problem of how mathematics is possible is not answered. This is because our own nature is changeable, where as logic and mathematics seems unchanging. If our nature is the source of mathematics, and our nature changes, then it might be possible that tomorrow 2+2 would be 5.

A priori knowledge involves concepts which can not be placed in the physical world. To give and example of a concept not in the physical world, consider the sentence "I am in my room". I am an entity in the physical world and so is my room, but "in" is not, at least not in the same way that "I" and "my room" are. The concept can not be attributed to the mind, either. For if an earwig is in my room, it is in my room whether I know it or not.

In the chapter The World of Universals, Russell then explores what these concepts, being neither mental nor physical, are.

The World of Universals

Plato gave an excellent account of universals in his "Theory of Ideas". When, for example, Plato seeks to define justice, he points out that we notice this or that just act, each of them has something in common and this commonality is justice. Russell clarifies that the idea here is not an idea in the sense that it is a thought, rather it is a pure form, the distillation of individual just acts. So though it is apprehended by minds, it is not a thought. To avoid confusion, Russell uses the term universal.

Universals are distinguished from particulars in that particulars are given by sensation. We experience a white thing or a just act. There is a commonality of white things which gives us the universal white. Proper nouns and pronouns are particulars while other nouns, verbs, adverbs and prepositions are universals. It is remarkable that no sentence can be constructed without the use of at least one universal.

Russell presents the following argument against the empiricists that deny the existence of universals. Suppose that there are no universals and that the idea of whiteness can only conceived of as a particular. Then when we examine how we know that any given thing is white, we discover that it must have a relationship to some other white thing. This relationship is a universal.

Universals have a unique sort of being in that while they are not sensations neither are they thoughts. Given the statement "Edinburgh is north of London". The statement is true whether there is any one who thinks it. The statement's truth does not depend on any ones apprehension of it. Further, if a universal were a thought we would

... rob it of its essential quality of universality. One man's act of thought is necessarily a different thing from another man's; one man's act of thought at one time is necessarily a different thing from the same man's act of thought at another time. Hence, if whiteness were the thought as opposed to its object, no two different men could think of it, and no one man could think of it twice. That which many different thoughts of whiteness have in common is their object, and this object is different from all of them. Thus universals are not thoughts, though when known they are the objects of thoughts.

Thus there are two realms of being, the realm of thoughts and sensations and the realm of universals. Our knowledge of universals relates these two realms.

On Our Knowledge of Universals

<some universals are known by acquaintance>

<all a priori knowledge deals exclusively with the relationship of universals>

<summary of sources of knowledge>

On Intuitive Knowledge

Truth and Falsehood

Knowledge, Error and Probable Opinion

The Limits of Philosophical Knowledge

The Value of Philosophy

Bibliographical Note

Russell recommends reading philosophers directly rather than reading about them in other philosophy texts. His recommendations are all available free on line: