Propositions and Facts in the Early Philosophy of Bertrand Russell

By Russell Wahl

It has been said that Bertrand Russell adopted at some time or other during his life every philosophical point of view that has ever been held by anyone. While this is without doubt an overstatement, it is certainly true that he held dramatically differing views on propositions and propositional functions during the years of this study 1900-1920. During this time Russell moved from a view that propositions were among the objects in the world to the view that “propositions are nothing” and oscillated back and forth on the subject of the “separableness” of propositional functions. The sharp changes in these positions are often ignored by current authors, especially those interested in the logical atomism of 1918. This is regrettable, since Russell concentrated a lot of effort on his difficulties with propositions and propositional functions and propositions played a central role in his philosophy and many of his insights were a result of work he did on propositions. Russell’s changing positions on propositions and propositional functions were not arbitrary: they were a consequence of some of the most concentrated philosophical thinking he ever did, and fit in well with many of his philosophical views. These problems with propositions and propositional functions have not been adequately studied. Indeed, in a recent work on Russell they were by and large ignored.

This book discusses Russell’s difficulties with the notions of proposition, propositional function, and (somewhat later) fact, particularly the role of propositions in Russell’s philosophy and in Russell’s reasons for thinking propositions unnecessary, and, in fact, an unwelcome addition to ontology.

• Language: English
• Publisher: Society for Philosophy & Culture
• Release date: Aug 30, 2013
• ISBN: 9781301142330

Russell Wahl

I began my career working primarily in the history of analytic philosophy and logic. I was particularly interested in the theory of logic found in Russell’s and Wittgenstein’s work. I am still working in this area, but for the last twenty years I have done more of my research in early modern philosophy, particularly the rationalists of the seventeenth century. Mostly I have worked on the theories of ideas, perception and causation developed in this period. While my research has been primarily in the history of these areas, I am interested in contemporary theories in all these areas as well. My main teaching areas are logic, philosophy of science, and early modern philosophy. In the past I frequently taught epistemology and twentieth-century philosophy and I hope to be able to do that again. Most of my teaching at Idaho State has been in introductory courses. In these courses we often find students who have never had any exposure to philosophy and are then quite taken by the richness of the field and the benefits that come with careful thinking. I did my graduate work at Indiana University under Romane Clark. Nino Cocchiarella, Mike Dunn and Alberto Coffa were also members of my committee and people from which I learned a great deal. I taught at Wabash College in Indiana for five years before coming to Idaho State University in 1985. Since 1995 I have been director of the Philosophy Program here

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Published by Society for Philosophy & Culture at Smashwords

Copyright 2013 Russell Wahl

Propositions and Facts in the Early Philosophy of Bertrand Russell

Russell Wahl

Society for Philosophy & Culture

Wellington

2013

Published by

Society for Philosophy & Culture

Wellington, NZ

2013

[e-mail]

© Author

ISBN: 978-1-3011423-3-0

Cover Design by Miku Yasui

Contents

Acknowledgments

Introduction

Chapter I: Propositions and Propositional Functions in the Principles of Mathematics

Chapter II: Meaning and Denotation

Chapter III: The Rejection of the Theory of Denoting

Chapter IV: Propositional Functions

Chapter V: Russell’s Rejection of PropositionsW

Chapter VI: Propositions and Facts

Vita

Acknowledgments

I would like to thank Professor Romane Clark for accepting the task of directing this thesis. Without his patience and good philosophical sense, it is unlikely that I would have finished this thesis. I owe much to Nino Cocchiarella who first introduced me to the complexity of Russell’s thought, and whose classes on Russell and Logical Atomism inspired me to write this thesis. I have also learned a great deal from Michael Dunn, Alberto Coffa and Paul Spade.

I am greatly indebted to Mr. Kenneth Blackwell of the Bertrand Russell Archives at McMaster University, who made many of Russell’s unpublished manuscripts available to me, and to Indiana University for a grant which enabled me to do research at the Russell Archives during the summer of 1979.

Catherine Albrecht read the entire draft and offered many helpful criticisms. My debt to her is very great.

Introduction

It has been said that Bertrand Russell adopted at some time or other during his life every philosophical point of view that has ever been held by anyone. While this is without doubt an overstatement, it is certainly true that he held dramatically differing views on propositions and propositional functions during the years of this study 1900-1920. During this time Russell moved from a view that propositions were among the objects in the world to the view that propositions are nothing[1] and oscillated back and forth on the subject of the separableness of propositional functions. The sharp changes in these positions are often ignored by current authors, especially those interested in the logical atomism of 1918. This is regrettable, since Russell concentrated a lot of effort on his difficulties with propositions and propositional functions and propositions played a central role in his philosophy and many of his insights were a result of work he did on propositions. Russell’s changing positions on propositions and propositional functions were not arbitrary: they were a consequence of some of the most concentrated philosophical thinking he ever did, and fit in well with many of his philosophical views. These problems with propositions and propositional functions have not been adequately studied. Indeed, in a recent work on Russell they were by and large ignored.[2]

My topic, then, is Russell’s difficulties with the notions of proposition, propositional function, and (somewhat later) fact. I am particularly interested in the role of propositions in Russell’s philosophy and in Russell’s reasons for thinking propositions unnecessary, and, in fact, an unwelcome addition to ontology. While I will not comment directly on contemporary developments, it should be mentioned that some of Russell’s earlier views are again coming into fashion, and so Russell’s own problems and alternatives to his earlier views may well be of interest to people who are not just interested in Russell scholarship. This thesis is primarily historical in that it examines Russell’s views on propositions primarily with an eye on his own reasons for holding certain positions and for rejecting them. It is also critical in that it contains a critique not only of various views Russell held, but also of commentators’ works on Russell. Nevertheless., I will stick as closely as I can to the views Russell actually held, with all the problems that were involved with these views. Thus I spend a good deal of time on Russell’s theory of meaning and on his problems with denoting, and on his ontological views as they relate to the theory of types. These diversions are necessary to an understanding of Russell’s changing solutions to the problems he associated with propositions and functions.

Chapter I: Propositions and Propositional Functions in the Principles of Mathematics

Russell’s position concerning propositions in the Principles of Mathematics can best be understood in relation to his realism and his theory of meaning. For Russell, a proposition was (a) the objective correlate of a sentence, that piece of the world which was the meaning of a sentence, and (b) the object of a belief or judgment. This notion of a proposition can be traced to earlier positions of Brentano, Bradley, Meinong (who called them ‘objectives’) and Moore, as well as others. According to Prior,[3] this use of the word ‘proposition’ is comparatively recent and traditionally propositions have been taken to be sentences which were capable of being true or false, the verbal expressions of beliefs rather than the objects of beliefs.

The realist view toward propositions fits in with Russell’s extreme realism which he inherited from Moore roughly around the turn of the century. In the Principles of Mathematics, Russell acknowledged a debt to Moore, even attributing all the chief features of what is philosophical in the work to his influence.[4] While there is actually quite a bit of philosophical material in the Principles which cannot be found in Moore, it is probably true that the basic realist view of the world Russell got from Moore, including the realist view of propositions.

Moore and Russell had both embraced the idealism of McTaggart and Bradley until 1898, when first Moore and then Russell rejected idealism in favour of an extreme realism. In My Mental Development Russell described this change:[5]

[Moore] took the lead in the rebellion, and I followed, with a sense of emancipation. Bradley argued that everything common sense believes in is mere appearance; we reverted to the opposite extreme, and thought that everything is real that common sense, uninfluenced by philosophy or theology, supposes real. With a sense of escaping from prison, we allowed ourselves to think that grass is green, that the sun and stars would exist if no one was aware of them, and also that there is a pluralistic timeless world of Platonic ideas.

This realism included propositions among those things which exist independent of minds. In one of the early articles of this new realism, The Nature of Judgment, G.E. Moore followed Bradley in taking a proposition (the idea in judgment) to be a universal meaning or concept.[6] But concepts, for the realist Moore, were not ideas or mental entities: A proposition is composed not of words, nor yet of thoughts, but concepts... concepts are possible objects of thought.[7] It is clear from the context of the article that Moore’s ‘concepts’ are not mind dependent entities, and not even mental, for the world itself is made up of concepts.[8]

Moore and Russell held that propositions are non-linguistic, since they are composed of concepts, not words. Concepts are the meanings of words, and propositions are the meanings of sentences. They are apprehended by the mind, but are not dependent on the mind for their existence. They are in a basic sense objective, for they are the objects of beliefs, and two or more people are capable of believing the same thing.

This view should be distinguished from that of Frege. While Frege thought of propositions as the objects of beliefs, he thought of these as intensional entities, or thoughts. Propositions, for Frege, were the senses of sentences, what sentences express. While Frege also thought of facts as intensional entities (unlike Russell) and equated facts with true propositions (like Russell), variations of the Fregean view would put propositions as a sort of intermediary between language and the world. They are the meanings of sentences, and if we speak truly, they correspond to, but are discrete from, the facts in the world.[9]

The Russell-Moore view of propositions differs sharply from this view. For while, like Frege, they took the proposition to be the meaning of a sentence, they thought of this in terms of what a sentence refers to. That is, they thought of propositions as complexes composed of the references of words. For Frege, propositions were a function of the senses of the parts of sentences, rather than the references. Thus, it is the sense of Mont Blanc which is a constituent of the proposition Mont Blanc is over 4,000 meters high. For Russell, it is the referent of the word Mont Blanc which is a constituent, the actual mountain. The proposition of which it is a constituent is really just the state of affairs of Mont Blanc’s being over 4,000 meters high.[10] One important difference between Russell’s early view of propositions and a more contemporary view is that since facts are also complexes whose constituents are the references of words of a sentence, facts are identical with true propositions. Rather than a three-level hierarchy of sentences, propositions and states of affairs, Russell had just two levels – sentences and propositions.[11] For this use of the word ‘proposition’ in Russell’s work I will use the expression ‘propositionW’. Unfortunately, sometimes in Russell’s writings, and particularly in the works written after 1907, the word ‘proposition’ is used as a synonym for ‘indicative sentence’. For these usages, I will use the expression ‘propositionL’. It is not surprising that most of the things one could say about propositionsL (e.g., that they are true or false, that they occur in other propositions, etc.) Russell would say about these propositionsW for there is an indication that Russell thought that any property one could attribute to a piece of language had an analogous property which one could attribute to the objective correlate of that piece of language.

Russell’s propositions are composed of terms. He replaced Moore’s word concept with term and used the word concept in a narrower sense. He made it very clear that terms are not words, and propositions not sentences when he said that a term was whatever may be an object of thought, or may occur in any true or false propositions... a man, a moment, a number, a class, a relation, a chimaera, or anything else that can be mentioned.[12] Further on he said A proposition, unless it happens to be linguistic, does not itself contain words: it contains the entities indicated by words.[13]

Russell presented this view earlier in his unpublished work An Analysis of Mathematical Reasoning (finished July, 1898). This is interesting, because the bulk of this work was written before Russell’s rejection of idealism. In this work it is clear that properties, relations, etc. are terms, but that self-contradictory things are not. Discussing the elements of a judgment (by which he means the object of a judgment, or a proposition), he said that whatever may be a logical subject, I call a term,[14] and that every predicate may be a logical subject. It is clear from other passages that predicate is not used to indicate a linguistic entity, but something indicated by one.[15] Later on he said that everything imaginable, may, if not self-contradictory, be a subject... every predicate may be a subject.[16] Thus properties, chimaeras and the present king of France will all be terms, but the round square will not. All terms have being, on this view, and some are existent.

Given this definition of a term, one would think that the proposition Socrates is human contains two terms, or perhaps three, an object joined to a property by a copula. This is not the way Russell saw it. for although such properties as humanity may be terms, that is, they may be logical subjects, they are not always so. Socrates is human has only one term; Socrates has humanity and Humanity belongs to Socrates each have two.[17]

In An Analysis of Mathematical Reasoning, Russell distinguished two sorts of elements in propositions, subjects and predicates. Since on his view predicates can also occur as subjects, he was careful to state that this is a distinction in aspect. The view is that humanity occurs differently in the two propositions Socrates is human and Humanity belongs to Socrates, although it is in some sense the same entity.[18]

This position was reiterated in the Principles of Mathematics, where such terms which can occur both as subjects and as predicates were called concepts, while those that can only occur as subjects are called things. Concepts which occur as predicates are called assertions.[19] Russell sometimes called these predicates which occur as predicates or verbs which occur as verbs. For example, in the proposition Caesar died,... died is asserted of Caesar. In the proposition Dying is not painful, the same concept occurs, but here as a term, not as an assertion. Russell’s reason for maintaining that the same concept is involved, even though there is a grammatical difference, is that a contradiction ensues if we maintain that they are different on the grounds that one of them cannot be put in subject place.[20]

...suppose that one as adjective [i.e., predicate] differed from 1 as term. In the statement, one as adjective has been made into a term; hence either it has become 1, in which case the supposition is self-contradictory; or there is some other difference between one and 1 in addition to the fact that the first denotes a concept not a term while the second denotes a concept which is a term. But in this latter hypothesis, there must be propositions concerning one as adjective as opposed to one as term; yet all such propositions must be false, since a proposition about one as adjective makes one the subject, and is therefore really about one as term.

This sort of passage could be used to show Russell’s use-mention problems. I think that such a criticism of this passage would miss the mark, however. It is clear that the words adjective and term are used in this instance for non-linguistic entities. What is wrong with this passage is not that quotes are missing from all the occurrences of ‘one’ and ‘1’, but rather that the word ‘statement’ in the second line should be ‘proposition’ in the sense of ‘propositionW’ discussed above. We can then see that what Russell said here is correct: that if in fact one as adjective cannot be put in subject place, there can be no true propositionW. One as adjective cannot be put in subject place. If we think of statements or sentences as being true or false (as well as propositionsW) then we have not shown that the statement is false or self-contradictory, but only that if it is true, what makes it true is not the existence of this particular propositionW. As we shall see, Russell’s original position was that propositionsW are the bearers of truth or falsehood, and that if a statement like One as a predicate cannot occur in subject place is meaningful, its meaning was just the propositionW. One as predicate cannot occur in subject place.[21]

Since Russell thought of predicates, i.e., properties, as capable of being terms, one might think that Russell held a Bergmannian view of propositions where such propositions as Socrates is human should be best represented as

E(S, H).

Where the E stands for the relation of nexus of exemplification, and the S stands for Socrates, the H for humanity.

This was not Russell’s view though. The element of binding in a proposition or judgment is included in the predicate or property when it occurs as a predicate. So the propositionW above should better be represented, on Russell’s view, as

H(S).

It is just that this same H can occur in propositions of the sort

X(H)

as well. In this proposition the element of assertion – that which binds the proposition – is absent from the H, and is in the X. As we shall see, Russell was to change his views on this matter when he introduced the theory of types.

In Appendix B of the Principles of Mathematics Russell did introduce the theory of types in terms of the range of significance of a propositional function.[22] While he was primarily concerned with distinguishing propositional functions which could be asserted of classes, it would seem to follow from his discussion, that while there may be propositions of the sort

X(H)

the ‘X’ would have to be of a different type from the ‘H’. Such a position makes it impossible to formulate Russell’s objection given above that One as predicate cannot differ from one.

To summarise Russell’s realist theory of meaning then, propositionsL which are composed of words indicate propositionsW which are composed of terms, at least one of which is a concept which does not occur as a term. The propositionsW are the meanings of the propositionsL, just as the terms are the meanings of the words. At this time Russell did not want to make an ontological distinction between concepts, propositionsW, and terms; although he did distinguish a concept occurring as a concept from one occurring as a term, he did not make it clear whether this was an ontological distinction. As we shall see in the next chapter, there is quite a bit more to Russell’s theory of meaning than this, including not only his theory of denoting, but a changing position on the nature of concepts which occur as concepts, or functions. Nevertheless, the later positions do seem to share this basic feature, that words are meaningful if they stand for entities, and complexes of words (including propositionsL) have for their meanings complexes of the corresponding entities. If there is such a complex of entities, the complex phrase will be meaningful, if there is not, it won’t.

Truth and Falsehood

Both Moore and Russell thought of propositions as the bearers of truth and falsehood, and both of them rejected the correspondence theory of truth, where truth is considered a correspondence of ideas with reality, or propositions with facts. In The Nature of Judgment G.E. Moore said, When I say this rose is red... what I am asserting is a specific connexion of certain concepts forming the total concept rose with the concepts this and rose and red". If the judgment is false, that is not because my ideas do not correspond to reality, but because such a conjunction of concepts is not to be found among existents."[23] In the article on truth in Baldwin’s Dictionary of Philosophy and Psychology, Moore said:[24]

it seems plain that a truth differs in no respect from the reality to which it was supposed merely to correspond: e.g., the truth that I exist differs in no respect from the corresponding reality – my existence.

A true proposition then is just identified with the fact.

In the Principles Russell adopted a slightly different approach: he linked the notion of truth to the notion of assertion. Since his remarks in the Principles on assertion are quite confusing, they will be outlined here.

We have already seen that Russell thought that concepts could occur in propositions either as terms, or as assertions (this is in fact what distinguished concepts from things). The difference was shown in language by a grammatical distinction, as between, for example, died and dying. There is another sense of assertion in the Principles which is somewhat related to this one.[25] This is the sense in which a proposition can be said to be asserted or not. If the verb (or predicate) in a proposition is replaced by a verbal noun, or an unasserted concept (Russell seems to use these as synonyms), the whole proposition is capable of being a logical subject. Thus, the proposition Caesar died is an asserted proposition, but if the concept is replaced by the unasserted concept, we obtain the unasserted proposition the death of Caesar (or: Caesar’s dying; Russell didn’t seem to allow for a distinction between these two). Russell occasionally called these unasserted propositions propositional concepts. He did not characterise this distinction much further, but he did make the following claims:

(a) The proposition involved in these two is in some sense the same.[26]

(b) The asserted proposition contains its own truth or falsehood, while the other does not.[27]

(c) Only true propositions are asserted ones.[28]

Several things appear to be involved in this discussion of assertion, which I will attempt to