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Bertrand Russell

Bertrand Russell on Something

Landon D.C. Elkind explains why Russell believed logic can set thought free.

Using Bertrand Russell’s remarks on something as a foil, I shall try to explain why he thought studying logic and philosophy is valuable.

As almost any Russellian knows, Russell abhorred teaching Aristotelian logic, also called traditional logic. To take two quotes:

“If you wish to become a logician, there is one piece of advice which I cannot urge too strongly, and that is: Do NOT learn the traditional formal logic. In Aristotle’s day, it was a creditable effort, but so was Ptolemaic astronomy. To teach either in the present day is a ridiculous piece of antiquarianism.”
(The Art of Philosophizing, and Other Essays, 1990, p.38)

“I conclude that the Aristotelian doctrines with which we have been concerned in this chapter are wholly false, with the exception of the formal theory of the syllogism, which is unimportant. Any person in the present day who wishes to learn logic will be wasting his time if he reads Aristotle or any of his disciples.”
(The Basic Writings of Bertrand Russell, 2009, p.257)

Russell’s criticism was tempered by praise for Aristotle’s achievement in advancing logic beyond what his predecessors had achieved (p.251). But I am not concerned with delivering justice to Aristotle. I want to consider what Russell believed about modern logic that so sets it apart from the logic of Aristotle, and about philosophy itself. And an apt illustration of the value of modern logic is Russell’s treatment of something.

Doubts about Something In Logic

In their monumental Principia Mathematica, Russell and his co-author Alfred North Whitehead attempted to create a logically sound basis for mathematics. In it their primitive proposition ∗9.1 implies that at least one individual thing exists. It follows that the universal class of things is not empty. This is stated explicitly in proposition ∗24.52. Whitehead and Russell then remark: “This would not hold if there were no instances of anything; hence it implies the existence of something.” (Principia Mathematica, Volume I, 1910, ∗24). Here then, logic seems committed to the existence of something.

By 1919 Russell took a different view. From his prison cell he wrote: “The primitive propositions in Principia Mathematica are such as to allow the inference that at least one individual exists. But I now view this as a defect in logical purity” (The Basic Writings of Bertrand Russell, p.156). Now Russell views the logical proof that something exists quite negatively.

It may seem curious that Russell held that the existence of something, even of just one something, was too bold a commitment for a logician. That at least one thing exists seems manifestly true, even obvious, to most any of us. There appears no difficulty in presuming what is patently true, even in logic. So why does Russell object to the primitive propositions of logic proving that there is something? Why hesitate over the obvious?

Russell’s Concept of Logic

Russell objected to the apparent logical implication in his earlier work that something exists because it is antithetical to his conception of logic. For him, logic stands apart from the blithe acceptance of the intuitively obvious, even the innocent-seeming thesis that something exists.

Consider Russell’s take on another ‘obvious’ truth: that all humans are mortal:

“…there is nothing self-contradictory about an immortal man. We believe the proposition [‘All men are mortal’] on the basis of induction, because there is no well-authenticated case of a man living more than (say) one hundred and fifty years; but this only makes the proposition probable, not certain. It cannot be certain so long as living men exist.” (ibid., p.253)

For Russell, certifying the obvious is not the task of logic. Logic should not dogmatize about the ‘obvious’ because this runs the terrible risk of mistaking the obvious for the true. As Russell wrote in Our Knowledge of the External World (1914), “The logic which thus arises is not quite disinterested or candid… Such an attitude naturally does not tend to the best results” (p.56).

For earlier logicians the function of logic is to exclude all possibilities save for one and then declare that the world must be in whatever way remains (p.18). The modern logic Russell advocates can instead show us new possibilities:

“Modern logic… has the effect of enlarging our abstract imagination, and providing an infinite number of possible hypotheses to be applied in the analysis of any complex fact. In this respect it is the exact opposite of the logic practised by the classical tradition. In that logic, hypotheses which seem prima facie possible are professedly proved impossible, and it is decreed in advance that reality must have a certain character. In modern logic, on the contrary, while the prima facie hypotheses as a rule remain admissible, others, which only logic would have suggested, are added to our stock, and are very often found indispensable if a right analysis of the facts is to be obtained. The old logic put thought in fetters, while the new logic gives it wings.”
(p.68, emphasis added).

This last sentence aptly expresses what Russell sees as the function of logic. Modern logic does not preclude perfectly respectable possibilities like immortal humans. Modern logic strengthens our critical capacities by forcing us to set aside feelings of obviousness as our guide in critical inquiry. Modern logic thus enables us to see the truth through the haze of the obvious. As Russell writes, “Thus, while it [modern logic] liberates imagination as to what the world may be, it refuses to legislate as to what the world is” (p.19).

Russell’s later view of logic thus explains why he objected to his own earlier proof that something exists. Logic should not be tasked with proving this, because is not self-contradictory to suppose that there is not something. Where logic ‘proves’ that some real possibility cannot be, we know we have regressed into practicing the misguided traditional logic.

The Essence of Philosophy

Chapter II of Russell’s book Our Knowledge of the External World is titled ‘Logic as the Essence of Philosophy’. In it Russell claims “that every philosophical problem, when it is subjected to the necessary analysis and purification, is found either to be not really philosophical at all, or else to be, in the sense in which we are using the word, logical” (p.42).

Let’s focus on one aspect of this fascinating feature of Russell’s thought: he held that the value of philosophy itself is the same as the value of modern logic. Philosophy, too, is valuable, because it can expand our critical capacities and cause us to critically reflect on what seems at first obvious or necessary. The value of philosophy as well as of modern logic is therefore to free our imprisoned thoughts from inherited prejudices and feelings. And the reward of those that study philosophy and modern logic is uncertainty. As Russell writes in The Problems of Philosophy (1959):

“The value of philosophy is, in fact, to be sought largely in its uncertainty. The man who has no tincture of philosophy goes through life imprisoned by the prejudices derived from common sense, from the habitual beliefs of his age or his nation, and from convictions which have grown up in his mind without the co-operation or consent of his deliberate reason. To such a man the world tends to become definite, finite, obvious; common objects rouse no questions, and unfamiliar possibilities are contemptuously rejected. As soon as we begin to philosophize, on the contrary, we find…that even the most everyday things lead to problems to which only very incomplete answers can be given. Philosophy, though unable to tell us with certainty what is the true answer to the doubts which it raises, is able to suggest many possibilities which enlarge our thoughts and free them from the tyranny of custom. Thus, while diminishing our feeling of certainty as to what things are, it greatly increases our knowledge as to what they may be; it removes somewhat the arrogant dogmatism of those who have never travelled into the region of liberating doubt, and it keeps alive our sense of wonder by showing familiar things in an unfamiliar aspect.” (pp.156-157, emphasis added).

This intellectual expansion is the tremendous boon of studying philosophy and modern logic. Such expansion was necessary to generate every idea that anyone has tried to lift off the ground, including a few ideas that Russell himself advocated: a world without nuclear weapons and even without war; a world free from want, with a universal basic income for all; women’s suffrage; an end to retributive punishment for crimes; free university education for all who desire it, and so on. Perhaps immortality will eventually join the ranks of such ideas. But if we’re not prepared to sacrifice our antiquated ideas and customary habits for a bold vision of the possible, we will never know for certain.

There is nothing logically contradictory about a world without war, without sickness, without poverty, without want, without fear, even without death. It is through the study of philosophy and particularly of logic that such possibilities become open to us, that we are startled into critical reflection on what the past has allotted to us; and then startled into action. It was for these reasons that Russell was so strongly opposed to the traditional logic inspired by Aristotle and so ardently devoted to modern logic. Modern logic and philosophy can save us from the unhappy tyranny of uninspired thought, so long as we are willing to question even our most natural suppositions, such as human mortality, or the existence of something.

Landon D.C. Elkind is a doctoral student in philosophy at the University of Iowa. He is also a board member of the Bertrand Russell Society and of the Society for the Study of the History of Analytic Philosophy.