Albert Einstein on Bertrand Russell

 

Remarks on Bertrand Russell's Theory of Knowledge

By Albert Einstein

When the editor asked me to write something about Bertrand Russell, my admiration and respect for that author at once induced me to say yes. I owe innumerable happy hours to the reading of Russell's works, something which I cannot say of any other contemporary scientific writer, with the exception of Thorstein Veblen. Soon, however, I discovered that it is easier to give such a promise than to fulfill it. I had promised to say something about Russell as philosopher and epistemologist. After having in full confidence begun with it, I quickly recognized what a slippery field I had ventured upon, having, due to lack of experience, until now cautiously limited myself to the field of physics. The present difficulties of his science force the physicist to come to grips with philosophical problems to a greater degree than was the case with earlier generations. Although I shall not speak here of those difficulties, it was my concern with them, more than anything else, which led me to the position outlined in this essay. 

In the evolution of philosophic thought through the centuries the following question has played a major role: What knowledge is pure thought able to supply independently of sense perception? Is there any such knowledge? If not, what precisely is the relation between our knowledge and the raw material furnished by sense-impressions? An almost boundless chaos of philosophical opinions corresponds to these questions and to a few others intimately connected with them. Nevertheless there is visible in this process of relatively fruitless but heroic endeavours a systematic trend of development, namely an increasing scepticism concerning every attempt by means of pure thought to learn something about the "objective world,"· about the world of "things" in contrast to the world of mere "concepts and ideas." Be it said parenthetically that, just as on the part of a real philosopher, quotation-marks are used here to introduce an illegitimate concept, which the reader is asked to permit for the moment, although the concept is suspect in the eyes of the philosophical police. 

During philosophy's childhood it was rather generally believed that it is possible to find everything which can be known by means of mere reflection. It was an illusion which any one can easily understand if, for a moment, he dismisses what he has learned from later philosophy and from natural science; he will not be surprised to find that Plato ascribed a higher reality to "Ideas" than to empirically experienceable things. Even in Spinoza and as late as in Hegel this prejudice was the vitalizing force which seems still to have played the major role. Someone, indeed, might even raise the question whether, without something of this illusion, anything really great can be achieved in the realm of philosophic thought-but we do not wish to ask this question. 

This more aristocratic illusion concerning the unlimited penetrative power of thought has as its counterpart the more plebeian illusion of na1ve realism, according to which things "are" as they are perceived by us through our senses. This illusion dominates the daily life of men and of animals; it is also the point of departure in all of the sciences, especially of the natural sciences. The effort to overcome these two illusions is not independent the one of the other. The overcoming of na1ve realism has been relatively simple. In his introduction to his volume, An Inquiry Into Meaning and Truth, Russell has characterized this process in a marvellously pregnant fashion:

We all start from "naive realism," i.e., the doctrine that things are what they seem. We think that grass is green, that stones are hard, and that snow is cold. But physics assures us that the greenness of grass, the hardness of stones, and the coldness of snow, are not the greenness, hardness, and coldness that we know in our own experience, but something very different. The observer, when he seems to himself to be observing a stone, is really, if physics is to be believed, observing the effects of the stone upon himself. Thus science seems to be at war with itself: when it most means to be objective, it finds itself plunged into subjectivity against its will. Naive realism leads to physics, and physics, if true, shows that naive realism is false. Therefore naive realism, if true, is false; therefore it is false. 

Apart from their masterful formulation these lines say something which had never previously occurred to me. For, superficially considered, the mode of thought in Berkeley and Hume seems to stand in contrast to the mode of thought in the natural sciences. However, Russell's just cited remark uncovers a connection: If Berkeley relies upon the fact that we do not directly grasp the "things" of the external world through our senses, but that only events causally connected with the presence of "things" reach our sense-organs, then this is a consideration which gets its persuasive character from our confidence in the physical mode of thought. For, if one doubts the physical mode of thought in even its most general features, there is no necessity to interpolate between the object and the act of vision anything which separates the object from the subject and makes the "existence of the object" problematical.

It was, however, the very same physical mode of thought and its practical successes which have shaken the confidence in the possibility of understanding things and their relations by means of purely speculative thought. Gradually the conviction gained recognition that all knowledge about things is exclusively a working-over of the raw-material furnished by the senses. In this general (and intentionally somewhat vaguely stated) form this sentence is probably today commonly accepted. But this conviction does not rest on the supposition that anyone haactually proved the impossibility of gaining knowledge of reality by means of pure speculation, but rather upon the fact that the empirical (in the above mentioned sense) procedure alone has shown its capacity to be the source of knowledge. Galileo and Hume first upheld this principle with full clarity and decisiveness. 

Hume saw that concepts which we must regard as essential, such as, for example, causal connection, cannot be gained from material given to us by the senses. This insight led him to a sceptical attitude as concerns knowledge of any kind. If one reads Hume's books, one is amazed that many and sometimes even highly esteemed philosophers after him have been able to write so much obscure stuff and even find grateful readers for it. Hume has permanently influenced the development of the best of philosophers who came after him. One senses him in the reading of Russell's philosophical analyses, whose acumen and simplicity of expression have often reminded me of Hume.

Man has an intense desire for assured knowledge. That is why Hume's clear message seemed crushing: The sensory raw material, the only source of our knowledge, through habit may lead us to belief and expectation but not to the knowledge and still less to the understanding of law-abiding relations. Then Kant took the stage with an idea which, though certainly untenable in the form in which he put it, signified a step towards the solution of Hume's dilemma: Whatever in knowledge is of empirical origin is never certain (Hume). If, therefore, we have definitely assured knowledge, it must be grounded in reason itself. This is held to be the case, for example, in the propositions of geometry and in the principle of causality. These and certain other types of knowledge are, so to speak, a part of the. instrumentality of thinking and therefore do not previously have to be gained from sense data (i.e., they are a priori knowledge). Today everyone knows of course that the mentioned concepts contain nothing of the certainty, of the inherent necessity, which Kant had attributed to them. The following, however, appears to me to be correct in Kant's statement of the problem: in thinking we use, with a certain "right," concepts to which there is no access from the materials of sensory experience, if the situation is viewed from the logical point of view.

As a matter of fact, I am convinced that even much more is to be asserted: the concepts which arise in our thought and in our linguistic expressions are all-when viewed logically-the free creations of thought which cannot inductively be gained from sense-experiences. This is not so easily noticed only because we have the habit of combining certain concepts and conceptual relations (propositions) so definitely with certain sense-experiences that we do not become conscious of the gulf-logically unbridgeable--which separates the world of sensory experiences from the world of concepts and propositions.

Thus, for example, the series of integers is obviously an invention of the human mind, a self-created tool which simplifies the ordering of certain sensory experiences. But there is no way in which this concept could be made to grow, as it were, directly out of sense experiences. It is deliberately that I choose here the concept of number, because it belongs to pre-scientific thinking and because, in spite of that fact, its constructive character is still easily recognizable. The more, however, we turn to the most primitive concepts of everyday life, the more difficult it becomes amidst the mass of inveterate habits to recognize the concept as an independent creation of thinking. It was thus that the fateful conception-fateful, that is to say, for an. understanding of the here existing conditions-could arise, according to which the concepts originate from experience by way of "abstraction," i.e., through omission of a part of its content. I want to indicate now why this conception appears to me to be so fateful. As soon as one is at home in Hume's critique one is easily led to believe that all those concepts and propositions which cannot be deduced from the sensory raw-material are, on account of their "metaphysical" character, to be removed from thinking. For all thought acquires material content only through its relationship with that sensory material. This latter proposition I take to be entirely true; but I hold the prescription for thinking which is grounded on this proposition to be false. For this claim-if only carried through consistently absolutely excludes thinking of any kind as "metaphysical."

In order that thinking might not degenerate into "metaphysics,'' or into empty talk, it is only necessary that enough propositions of the conceptual system be firmly enough connected. with sensory experiences and that the conceptual system, in view of its task of ordering and surveying sense-experience, should show as much unity and parsimony as possible. Beyond that, however, the "system" is (as regards logic) a free play with symbols according to (logical) arbitrarily given rules of the game. All this applies as much (and in the same manner) to the thinking in daily life as to the more consciously and systematically constructed thought in the sciences.

It will now be clear what is meant if I make the following statement: By his clear critique Hume did not only advance philosophy in a decisive way but also-though through no fault of his-created a danger for philosophy in that, following his critique, a fateful "fear of metaphysics" arose which has come to be a malady of contemporary empiricistic philosophizing; this malady is the counterpart to that earlier philosophizing in the clouds, which thought it could neglect and dispense with what was given by the senses.

No matter how much one may admire the acute analysis which Russell has given us in his latest book on Meaning and Truth, it still seems to me that even there the spectre of the metaphysical fear has caused some damage. For this fear seems to me, for example, to be the cause for conceiving of the "thing" as a "bundle of qualities," such that the "qualities" are to be taken from the sensory raw-material. Now the fact that two things are said to be one and the same thing, if they coincide in all qualities, forces one to consider the geometrical relations between things as belonging to their qualities. (Otherwise one is forced to look upon the Eiffel Tower in Paris and that in New York as "the same thing.") 1 Over against that I see no "metaphysical' danger in taking the thing (the object in the sense of physics) as an independent concept into the system together with the proper spatio-temporal structure.

In view of these endeavours I am particularly pleased to note that, in the last chapter of the book, it finally crops out that one can, after all, not get along without "metaphysics." The only thing to which I take exception there is the bad intellectual conscience which shines through between the lines.

ALBERT EINSTEIN 

SCHOOL OF MATHEMATICS 

THE INSTITUTE of ADVANCED STUDY

PRINCETON 

1 Compare Russell's An Inquiry Into Meaning and Truth, 119-12.01 chapter on "Proper Names."

From The Philosophy of Bertrand Russell, Vol. V of "The Library of Living Philosophers," edited by Paul Arthur Schilpp, 1944. Translated from the original German by Paul Arthur Schilpp. Tudor Publishers.

Related reading: What Albert Einstein Thought of Christianity; Einstein Was Right About Education

Pioneers of Logic

Alice C. Linsley


Ancient logic

Plato’s view of reality was based on his belief that pattern can be seen in the order of nature and that we recognize pattern because it reflects the pattern intuitively grasped by the soul or inner person. The observable patterns in nature include the binary sets uniformly applied in the logic of the ancient world.

In mathematical terms, a binary set would be 1a+1b = {1} (binary set) in which the two entities are not equal. An example is male + female = human, but the male is larger and stronger than the female. The paradoxical nature of this is evident. This paradox was rejected as logical by modern pioneers in logic who, like Frege, insisted that 1+1 = a set of 2 and 2 = 1+1, a set of equals.

The anthropologist Levi-Strauss has demonstrated how binary logic is reflected in the thought of primitive peoples, and Jacques Derrida has shown how binary thinking is inescapable even in modern logic. This is because in a binary set we have more than one thing. Through disclosure or deconstruction, we find there are sets within sets.

Derrida saw the middle as a function by which binary opposites acquire extended meaning as merisms and reversals. These thinkers discovered in analysis of primitive myths that there are some universal ideas related to the most fundamental of human experiences such as birth, the Sun, and nourishment. This suggests weakness in nominalism, the view that there are no universal essences; that no abstract entities, essences, classes, or propositions have real existence.


Syllogistic reasoning

Aristotle (384-322 BC) is often credited with being the "father" of logic. He taught his students syllogistic logic. A syllogism attempts inference of one proposition from two premises. Each premise has one term in common with the conclusion. If (1)A = B, and (2)B = C, then (3)A = C. A standard-form categorical syllogism meets the following four conditions:

1. All three statements are categorical propositions.
2. The two occurrences of each term are identical.
3. Each term is used in the same sense throughout the argument.
4. The major premise is listed first, the minor premise second, and the conclusion is last.

Aristotle also deserves credit for modal logic because his evaluation of involves concepts like possibility, necessity, belief and doubt. He also identified several common fallacies

Aristotle dealt with the logical constants and, or, if ... then ..., not, and some and all. This is referred to as Naïve Set Theory because it relies on natural language to describe sets and the words and, or, if ... then, not, for some, for every are not subject to rigorous definition. Syllogisms may be useful in training young minds to reason according to a pattern, but they do not lead to discovery of anything new.

Naive sets are common in informal logic, but the 19th and 20th centuries saw the rise and refinement of formal logic, initiated by John Stuart Mill (1806-1873) and the brilliant mathematician Gottlob Frege (1848–1925).

John Stuart Mill

Mill was a British empiricist who formulated five principles of inductive reasoning in his A System of Logic, Ratiocinative and Inductive (1843). These are 1 Direct method of agreement; 2 Method of difference; 3 Joint method of agreement and difference; 4 Method of residue and 5 Method of concomitant variations.

John Stuart Mill

As an empiricist, Mill insisted that there is no metaphysical necessity. All necessity is conveyed in language and a matter of propositions. The world we describe propositionally is the world of our ordinary experience and observation. The ontology of the world is reflected in the language we use. Knowing the meaning of terms enables us to evaluate the importance of propositions.


Mill's Nominalism

Mill believed that the early versions of nominalism held that "there is nothing general except names." He was mistaken in this, as anthropologists subsequently demonstrated.

The earliest nominalism, as reflected in ancient lexemes, involved general names and complex related experiences including attributes and related ideas. Lexemes are the basis for early scripts such as Thamudic. A solar lexeme such as Y or T or O represented a deified or divinely appointed ruler, his territory, his people, and all his resources such as water and gold. The Horite rulers are identified with the solar symbol Y: Yaqtan, Yishmael, Yitzak, Yisbak, Yacob, Yosef, Yeshua, etc. Other ancient lexemes include V, W and X.

Mill was correct that names of entities (nouns) have levels of meaning, or connotative variables. He showed that names denote either individuals or the attributes of individuals. A general name - white, for example - connotes an attribute and denotes all individuals that have that attribute. White connotes the attribute whiteness, and denotes all things that have that attribute.

Mill explored the variability of names through analysis of syllogisms. Here is one he used to illustrate that there is a connection between attributes connoted by terms, but the attributes are logically independent.

Consider the syllogism:

Man is mortal.
Socrates is a man.
Ergo, Socrates is mortal.

In the syllogism "man" and "mortal" are attributes. Given Mill's claim that attributes are logically independent, the major premise - Man is mortal - adds nothing to the truth of the propositions concerning Socrates. What matters is the particulars - Socrates and the attributes man and mortal. In other words, deductive inference cannot advance knowledge. There is nothing new discovered by the syllogism.

George Boole

George Boole (1815-1864) was an English mathematician and philosopher who developed some of Leibniz's ideas about the relationship between mathematics and logic in his book The Mathematical Analysis of Logic (1847). His later work An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic (1854) presents a more complete system of symbolic reasoning.

Boolean logic is easy to understand. Begin with the idea that some statement (P) is either true or false. (He applies the law of the excluded middle). Then other statements can be formed, which are true or false, by combining these initial statements together using the fundamental operators And, Or and Not.

Boole's syllogistic reasoning did not place importance on the existential question, as happened with Aristotle. For Aristotle any proposition involving unicorns or satyrs, for example, would render an argument invalid. In Boole's view, anything named in a proposition does not imply that it in fact exists.

Consider the difference in their views:

Aristotle
All men are humans.  This implies the existence of men.
No maple trees are oaks.  This implies the existence of maple trees.
All unicorns are grand creatures.  This does not imply the existence of unicorns.

Boole
All men are humans.  This does not imply the existence of men. (Heidegger would love this!)
No maple trees are oaks.  This does not imply the existence of maple trees.
All unicorns/satyrs are grand creatures.  This does not imply the existence of unicorns/satyrs.

Gottlob Frege

Gottlob Frege

Friedrich Ludwig Gottlob Frege is considered another founder of modern logic and the father of analytic philosophy. Frege's logic is now known as second-order logic.

His first major work was Begriffsschrift, published in 1879. In 1884, The Foundations of Arithmetic appeared, and this was followed by two volumes known by the German title Grundgesetze.

Frege's writings were largely ignored when first published, partly because the English philosophers were not capable of reading the original German. That would change with Bertrand Russell (1872–1970), whose knowledge of German made it possible for him to understand Frege and even to refute him.

Russell was introduced to the significance of Frege's work in logic through Giuseppe Peano (1858–1932), who he met at a conference in Paris in and both of whom saw the merit of his work.

In 1903, Russell wrote an appendix to The Principles of Mathematics in which he presented deficiencies in the assumptions that Frege made in Grundgesetze, which Russell recognized led to paradox or contradiction. Russell communicated this to Frege by letter and Frege's response was to accuse Russell of undermining the whole of mathematics.

Others influenced by Frege's work include Alfred North Whitehead (1861–1947), Ludwig Wittgenstein (1889–1951), Willard van Orman Quine (1908-2000), and the Logical Positivist Rudolf Carnap (1891–1970). In his Der logische Aufbau der Welt, Carnap attempted to apply the concepts of Principia Mathematica to his discourse about sense data, the external world and logic. Quine would go beyond the Vienna Circle’s position that philosophy is properly defined as the philosophic study of the language of science. Though Quine was not a scientist, he saw his philosophy as science.


Proper Names and Cognitive Value

Leibniz developed an approach to questions of necessity, possibility, contingency that served an important function within his metaphysics and epistemology. This is called modal metaphysics and it has important implications for logic. Carnap thought one could give a possible world semantics for the modalities of necessity and possibility by giving the valuation function a parameter that ranges over Leibniz's possible worlds. We will explore this under "Modal Logic."

Frege agreed with Leibniz that natural language is unsuited to formal logic. This led Frege to create a symbolic language in which logical relations and possible inferences would be clear and unambiguous.

Frege’s term for such a language -“Begriffsschrift” - may have been borrowed from a paper on Leibniz written by Adolf Trendelenburg, considered by Søren Kierkegaard "one of the most sober philosophical philologists I know."

Leibniz’s Problem: Why doesn’t ‘2+3 = 5’ reduce to ‘5 = 5’? Frege does not address this problem, but instead recasts it. Frege’s Puzzle is about the semantics of proper names.

(1) Hesperus is Hesperus. (Hesperus is a proper name for the planet Venus.)
(2) Hesperus is Phosphorus. (Phosphorus is a personification of the planet Venus.)

Each of these sentences is true. 'Hesperus' refers to the same object as 'Phosphorus' (the planet Venus). Nonetheless, (1) and (2), though synonymous, differ in what Frege called "cognitive value." Frege thus rejects John Stuart Mill's view that a proper name has no meaning above and beyond the object to which it refers. Frege develops this in his book Sense and Reference.

David Kaplan demonstrates how it is rationally possible to believe one while denying the other with this:


"I am David Kaplan", spoken by David Kaplan.
"He is David Kaplan", spoken by someone pointing at David Kaplan.
"David Kaplan is David Kaplan", spoken by anyone.

All express the same content and refer to the same individual. Yet each has a different cognitive value. Kaplan explains this by associating cognitive value with character rather than content, thus providing what seems a remedy to Frege's problem.

Frege's Concept-Writing

Frege's most famous work is Begriffsschrift (Concept-Writing: A Formal Language for Pure Thought Modeled on that of Arithmetic). It marked a turning point in logic. Here Frege demonstrates that true contents do not follow directly from other true contents. This requires a mediating system or what has come to be called axiomatic predicate logic. The book includes a rigorous treatment of functions and variables.

Frege declared nine of his propositions to be axioms, and justified them by arguing informally that, given their intended meanings, they express self-evident truths. In contemporary notation, these axioms are:

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 


Frege wanted to show that mathematics grows out of logic, and devised techniques that took him beyond syllogistic and propositional logic to symbolic or formal logic. He accomplished this through his invention of quantified variables, which solved the problem of multiple generality.

Frege's symbolic logic was able to move beyond the logical constants and, or, if ... then ..., not, and some and all to more complex inferences. He prepared the way for the analysis of logical concepts by  Bertrand Russell (theory of descriptions), Kurt Gödel's incompleteness theorems, and to Alfred Tarski's (1901–1983) theory of truth. All owe a great debt to Frege's work.

Other philosophers who have responded to Frege's work include Saul Kripe (Naming and Necessity, 1980), David Kaplan, Ruth Barcan Marcus, and Hilary Putnam. (We will look closer at Kripe's contribution when we study Modal Logic.)

Frege's Intention

In his work Frege intended to set forth a system to isolate logical principles of inference. He perceived the need for this because he saw that only formalized logic could be applied to the sciences. No longer would an intuitive element be permitted as an assumption/premise. It would be isolated and represented separately as an axiom. The proof was to be logical and without gaps.

Frege was an important influence on Russell who influenced Quine. Russell's work inspired Quine to pursue logic. Quine wrote, “Russell’s name is inseparable from mathematical logic, which owes him much, and it was above all Russell that made that subject an inspiration to philosophers.” In 1962, Quine wrote to Russell that “Principia Mathematica was what, of all books, has influenced me the most.”

Wittgenstein also studied Frege's work and in 1911, he wrote to Frege concerning his solution to Russell’s paradox (see below). Frege invited him to Jena to discuss his views. The two engaged in a philosophical debate, and Wittgenstein reported that Frege “wiped the floor” with him. However, Frege was impressed with Wittgenstein and suggested that he study with Russell at Cambridge.

Russell's Paradox and Wittgenstein's solution

Russell's paradox Z = {x : x is not a member of x}

If Z is a member of Z how can it not be a member of Z?

Is Z a member of Z? If yes, then by the defining quality of Z, Z is not a member of itself. This forces us to declare that Z is not a member of Z. Then Z is not a member of itself and so, again by definition of Z, Z is a member of Z. What we have here is the following contradiction: Z is a member of Z if and only if Z is not a member of Z.

In 1923, Ludwig Wittgenstein proposed to "dispose" of Russell's paradox as follows:

The reason why a function cannot be its own argument is that the sign for a function already contains the prototype of its argument, and it cannot contain itself. For let us suppose that the function F(fx) could be its own argument: in that case there would be a proposition 'F(F(fx))', in which the outer function F and the inner function F must have different meanings, since the inner one has the form O(f(x)) and the outer one has the form Y(O(fx)). Only the letter 'F' is common to the two functions, but the letter by itself signifies nothing. This immediately becomes clear if instead of 'F(Fu)' we write '(do): F(Ou). Ou = Fu'. That disposes of Russell's paradox. (Tractatus Logico-Philosophicus, 3.333)

Related reading: Student Graphics Illustrate Fallacies; Modal Logic, Introduction to Logic (Fallacies); A Pragmatic Approach to Knowledge; Modal Logic: On the Lighter Side; Naive and Axiomatic Set Theory; Russell's Reasons for Ramification

Socrates: A man in control of himself

Socrates offered prayer facing the rising Sun as was the common practice among the ancients. He spent hours in contemplation and exercised great self-control in every area of his life.

Leo Strauss believed that Socrates' moderation was not merely a concession to political stability and good citizenship, but more importantly, it addresses the question of how we come to truth. Strauss wrote: “Socrates implied that disregarding the opinions about the nature of things would amount to abandoning the most important access to reality which we have, or the most important vestiges of truth which are within our reach” (Natural Right and History, p. 124)

Listen to this YouTube video in which Bertrand Russell discusses Socrates appearance, fortitude and influence.