Abstract
I distinguish three periods in Russell’s philosophical development: the Moorean period, following his break with Idealism around 1899 through his attending the Paris conference in August 1900 at which he saw Peano; the period following the Paris conference through his prison stay in 1918; and his post-prison period, in which he becomes concerned with the nature of language as such. I argue that while the topic of vagueness becomes an explicit theme in his post-1918 writings, his view that ordinary language is vague plays a central role in his post-Peano practice and characterization of analysis. On the Moorean view, analysis is intended to make explicit what is already “present to the mind” of anyone who understands the relevant sentence prior to analysis; post-Peano and pre-prison, Russell presents analysis as making precise what was previously vague; post-prison, he denies that any language is precise, so that analysis involves a transition only from the more to the less vague. I argue that the failure to recognize the character of Russell’s post-Peano conception of analysis reflects a broader misunderstanding of the character of Russell’s philosophy and of his place in the history of analytic philosophy.
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- 1.
I attempt a fuller account (which overlaps with, but also differs in some respects from, claims I make here), in Levine (2009).
- 2.
See, for example, Williamson (1994, p. 37), who indicates that in Russell’s (1923), “the problem of vagueness is systematically presented for the first time in something close to its current form”. See also Keefe and Smith (1997, p. 1), who write that after antiquity, “there seems to have been relatively little further discussion of vagueness before Bertrand Russell’s seminal paper”, and include his (1923) as the first modern discussion of vagueness in their reader.
- 3.
Griffin (2003, p. 35, note 45) is one of the few to suggest that Russell’s views of meaning and understanding in The Analysis of Mind had a positive influence on Wittgenstein: “It seems quite possible that The Analysis of Mind was the original source of Wittgenstein’s view that meaning is use.”
- 4.
- 5.
By 1910, in accepting his multiple-relation theory of judgment (MRTJ), Russell no longer holds that there are entities that are propositions. The sense in which he then accepts (PoA) is that he holds that “whenever a relation of supposing or judging occurs, the terms to which the supposing or judging mind is related by the relation of supposing or judging must be terms with which the mind in question is acquainted” (Russell 1911a, p. 155). Here, as I discuss in more detail below, “the terms to which the supposing or judging mind is related” are (in general) non-linguistic entities, entities that as Russell writes in his 1910 paper “The Theory of Logical Types” (where he first endorses the MRTJ) “are called the constituents of the proposition” (Russell 1910, pp. 10–1).
- 6.
Thus the Moorean conception of analysis invites the so-called “paradox of analysis” as to how, or in what sense, the analysis of a proposition expressed by a sentence we understand can be informative, if it can reveal nothing with which we were not already acquainted in our original understanding of that sentence (see Moore 1942, 665f). What I point out here, in effect, is that in applying the Moorean conception of analysis, the early Moore and Russell are often not attempting to provide apparently “informative” analyses of familiar concepts, but rather argue against apparently “informative” analyses provided by others, on the basis that such analyses conflict with what is “present to the mind” of one who understands the words in question.
- 7.
Although here, unlike the relative theory of number he considered during his Moorean period, similarity is not indefinable but is rather defined in terms of one-to-one correspondence.
- 8.
“More” perspicuously, because a fully perspicuous representation of that proposition would have to take into account the definition of “similarity” in terms of one-to-one correspondence.
- 9.
The technical difficulty in defining moments and points is that since the “events” in terms of which they are to be defined “have a finite extent”, events can be “overlapping” without being entirely simultaneous, so that moments (and points) will have to be “constructed” out of “overlapping”, rather than “simultaneous” events. Russell credits Whitehead with the solution of this problem (see, for example, Russell 1915, pp. 114ff, 1924, p. 166).
- 10.
By Principia Mathematica, Russell dispenses with classes by accepting “no classes” theory, according to which sentences containing class symbols are interpreted so that there is no reference to any entities that are classes; however, in the passage I have quoted from Our Knowledge of the External World, Russell makes no allusion to his dispensing with classes and instead reflects the understanding of the “principle of abstraction” he had at the time of The Principles of Mathematics. Thus, as early as December 1903, Russell writes to Couturat that once he proves his earlier “axiom of abstraction” by substituting an equivalence class of objects for the “hypothical quality common to all these objects” (“substítuer la classe même des objects dont il est question à la qualité hypothétique commune à tous ces objects”), it would be better to call the “principle of abstraction” the “principle replacing abstraction” (“princípe remplaçant l’abstraction”). See Schmid (2001, p. 346).
- 11.
Thus, for example, Russell (1903, Chap. 10) calls “the contradiction” what others typically call “Russell’s paradox”.
- 12.
During his Moorean period, Russell regards numbers as properties of plural subjects (see, for example, Russell 1900a, p. 12). This is opposed to the Fregean view Russell later came to accept that “statements of number” are about properties, not objects (see, for example, Russell 1915, pp. 201–2). See Byrd (1987, pp. 65–6) for some discussion of how this change in view is reflected in late additions Russell made to The Principles of Mathematics.
- 13.
In The Principles of Mathematics, Russell (1903, p. 315, see also p. 123) claims that their definitions of finite and infinite numbers “may be easily shown to be equivalent”; however, he later recognizes that their definitions are equivalent only assuming the axiom of choice (or what he and Whitehead call the multiplicative axiom). See (Russell 1903, “Introduction to the Second Edition”, pp. viii–ix).
- 14.
Similarly, in discussion following his 1911 presentation of his paper “Analytic Realism”, Russell says: “[W]e already have an idea in us of the continuum. But this idea, hitherto vague and unanalyzed, has become precise and analyzed.” (Russell 1911b, p. 143). Again, in his Introduction to Mathematical Philosophy, Russell writes: “The word ‘continuity’ had been used for a long time, but had remained without any precise definition until the time of Dedekind and Cantor.” (Russell 1919a, p. 100; see also pp. 105–6).
- 15.
Thus, for Russell (1903, p. 270), the class of all rationals less than 1/2 is the real number 1/2 (which he thereby distinguishes from rational number 1/2); and the class of rational numbers which are such that their squares are less than 2 is the real number √2.
- 16.
Convergent in the sense that the difference between consecutive members of that sequence becomes as small as we like, if they are sufficiently far out in the series (see Russell 1903, p. 281, for this sense of convergence).
- 17.
Later, he would claim that Dedekind’s “method of ‘postulating’ what we want has many advantages; they are the same as the advantages of theft over honest toil” (Russell 1919a, p. 71).
- 18.
This despite indicating in the Preface to The Principles of Mathematics that, as a result of his “contradiction”, he has “failed to perceive any concept requisite for the notion of class” (Russell 1903, pp. xv–xvi), and despite introducing, and tentatively, advocating in his reply to Hobson a “no class” theory (see Russell 1905–6, pp. 80–2).
- 19.
She here uses “nothing” as an example of a one-word sentence, because in a previous letter she questions Russell’s claim in “On Denoting” that words like “everything”, “nothing”, and “something” “are not assumed to have any meaning in isolation” (Russell 1905, 416). In particular, she claims that “such words can be used by themselves”, as, for example, when in response to the question “What did you give Smith?”, one replies “Nothing” (see Petrilli 2009, 321). In reply, Russell wrote that “such words used alone are mere abbreviations for propositions” (ibid., 322).
- 20.
- 21.
See Footnote 5 above.
- 22.
Already, by in his pre-prison 1918 lectures “The Philosophy of Logical Atomism”, Russell (1918, pp. 165–6) had indicated—as a result, I believe, of in following Wittgenstein in holding that there are no entities that are “logical constants”—that “for the purposes of logic”, the sentence should be regarded as the “typical vehicle of truth and falsehood”, but he also indicates there that “for the purposes of the theory of knowledge”, judgments should be so regarded (where judgments are not regarded as containing symbols, such as images, among their constituents). By 1919, Russell has changed his view of judgment and unequivocally holds that all truth–bearers contain symbols.
- 23.
As a number of commentators have discussed (see, for example, Faulkner (2008–9), and others she cites there), in thus presenting Wittgenstein as concerned with “a logically perfect language” as opposed to any actual language, Russell appears to misinterpret Wittgenstein, who writes, for example, in the Tractatus that “all the propositions of our everyday language, just as they stand are in perfect logical order” (Wittgenstein 1921, 5.5563). Further, in a 1922 letter to Ogden, Wittgenstein explains this remark by writing:
By this I meant to say that the prop[osition]s of our ordinary language are not in any way logically less correct or less exact or more confused than prop[osition]s written down, say, in Russell[’]s symbolism or any other “Begriffsschrift”. (Only it is easier for us to gather their logical form when they are expressed in an appropriate symbolism.) (Wittgenstein 1973, 50)
From this remark, at any rate, it would appear that Wittgenstein’s early conception of analysis, unlike Russell’s, is in accord with the Moorean view.
- 24.
It might be noted, however, that two paragraphs following the passage that Hylton quotes, Russell writes: “When we, who did not know Bismarck, make a judgment about him, the description in our minds will probably be some more or less vague mass of historical knowledge ….” (Russell 1912, p. 55). For some further discussion of what sort of “analysis” Russell intends his theory of descriptions as providing, see Footnote 27 below.
- 25.
See also Russell (1959, p. 133), where he characterizes this view of his “method” as “my strongest and most unshakable prejudice as regards the methods of philosophical investigation”.
- 26.
Thus, for example, he writes: “All analysis is only possible in regard to what is complex, and it always depends, in the last analysis, upon direct acquaintance with the objects which are the meanings of certain simple symbols” (Russell 1918, p. 173).
- 27.
See, for example, (Russell 1918, p. 237), where he makes the point with regard to matter, and (Russell 1919b, p. 294), where he makes the point with regard to minds. In contrast, in Principia Mathematica, Whitehead and Russell distinguish Russell’s theory of descriptions in this regard from their “no class” theory, writing that in “[t]he case of descriptions it was possible to prove that they are incomplete symbols” but that “in the case of classes, we do not know of any equally definite proof” and that “it is not necessary … for our purposes to assert dogmatically that there are no such things as classes” (Whitehead and Russell 1910, p. 75). Again, while Russell consistently presents any of his “logical constructions” as providing one, but not the only possible, interpretation of the discourse in question, in his (1905) he takes himself to present decisive arguments against other proposed analyses of propositions expressed by sentences containing definite descriptions. However, in “On Denoting”, Russell acknowledges that his “interpretation” of propositions expressed by sentences of the form “The F is G” “may seem … somewhat incredible” (Russell 1905, p. 417), thus suggesting that he does not regard his “interpretation” as reflecting what is “present to the mind” of one who understands such a sentence. And in his 1957 reply to Strawson, which he reprints in My Philosophical Development, Russell writes:
I … am persuaded that common speech is full of vagueness and inaccuracy, and that any attempt to be requires modification of common speech both as regards vocabulary and as regards syntax. … My theory of descriptions was never intended as an analysis of the state of mind of those who utter sentences containing descriptions. … I was concerned to find a more accurate and analysed thought to replace the somewhat confused thoughts which most people at most times have in their heads, (Russell 1959, pp. 241–243)
Thus, while there are some significant differences between the way Russell presents his theory of definite descriptions and how he presents his “logical constructions”, here, at least, he presents it as conforming to his post-Peano model of analysis of replacing the “vague” and “confused” with something more “precise and accurate”. For some further discussion of the issues raised here, see Szabo (2005, Sect. 2) and Kripke (2005, 1107, note 28).
- 28.
See, similarly Husserl, who assumes what I have called the Moorean conception of analysis in criticizing an equivalence class definition of faintness of tone:
‘What we mean’ is surely our sense, and can one say even for an instant that the sense of the proposition ‘This tone is faint’ is the same as the sense of the proposition ‘This tone belongs to a group (of whatever sort) of similars’?.… Naturally the utterances ‘A tone is faint’ and ‘A tone belongs to the sum total of objects alike in their faintness’ are semantically equivalent, but equivalence is not identity. (Husserl 1900–1, pp. 303–4).
- 29.
Likewise, Moore criticizes the two definitions of the infinite that Russell (following Dedekind and Cantor) provides in The Principles of Mathematics in favor of a definition that he claims “is far more in accordance with the ordinary use of the word ‘infinity’”(Moore 1905, pp. 30–1) than those presented by Russell.
- 30.
Vann McGee (2004, p. 621) presents Russell’s (1923) account of the vagueness of the name “Ebenezer Wilkes Smith” as a case of “the inscrutability of reference” consistent with “the line of argument of argument of Chapter Two of Word and Object”. I have argued, in effect, that in his earlier account of the vagueness of numerical terms—specifically, in his acknowledging that if there are indefinables of the sort he previously took cardinal numbers to be, then either those indefinables, or classes of similar classes will enable us to sustain the same “formulae of arithmetic”—Russell is likewise arguing for a case of the “inscrutability of reference”.
- 31.
An earlier version of this paper was presented at the 2013 meeting of the Society for the Study of the History of Analytic Philosophy at the University of Indiana, Bloomington. Thanks to the audience there, in particular Kevin Klement, Gregory Landini, Ian Proops, and Thomas Ricketts, for helpful comments. Thanks especially to Sébastien Gandon and Peter Hylton for reading and commenting on that earlier version.
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Levine, J. (2016). The Place of Vagueness in Russell’s Philosophical Development. In: Costreie, S. (eds) Early Analytic Philosophy - New Perspectives on the Tradition. The Western Ontario Series in Philosophy of Science, vol 80. Springer, Cham. https://doi.org/10.1007/978-3-319-24214-9_7
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