Abstract
In the Principles of Mathematics, Russell presents his famous ontology of terms. Terms, he says, are anything that can be an object of thought, occur in any true or false proposition, or be counted as one; what is more, every term has some sort of being. ‘Term,’ then, is presented as the widest word of the philosophical vocabulary – but only together with ‘unit’ and ‘entity’. In this paper, the Russellian equivalence between ‘terms’, ‘units’ and ‘entities’ will be thoroughly examined, and its roots will be shown to be retraceable to the Platonic passage – known and discussed by Russell, though often overlooked by commentators – from τι (something) to ἕν (one) and to ὄν (being) as it appears in many dialogues and notably in the Sophist (237c7-e6). Some philosophical conclusions will then be extracted from this connection, in particular the conclusion that the traditional picture of Russell’s early Platonism as a somewhat naïve commitment to abstract objects must be revised, or at least enrichened; and that this Platonism should rather be looked for in the very concern with accounting for the reference of discourse, a concern of which the commitment to both entities and unities/multiplicities (i.e., to both realism and pluralism) are equally important consequences.
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Notes
- 1.
In the context of the Principles, reasonably enough, Russell will focus on terms as logical subjects more than as objects of thought. The ‘object of thought’ criterion, by its turn, is directly borrowed from Moore’s The Nature of Judgment, p. 179: “Concepts are possible objects of thought; but that is no definition of them. It merely states that they may come into relation with a thinker”. As is well-known, and as will be briefly discussed later, the story of Moore’s critique of idealism and of his innovations in logic and metaphysics runs parallel to – or, we could even say, as a basis of – that of Russell.
- 2.
As Hylton also shows, and as it is clear for anyone who has read both the Principles of Mathematics and Moore’s work from this period – the Principia Ethica (1903) but, most of all, The Nature of Judgment (1899) –, Russell’s and Moore’s thoughts are indissolubly intertwined in that moment, with Moore taking a slight lead in the charge against the Idealists.
- 3.
Moore’s ‘concept’, by turn, corresponds to one specific sense in which Bradley employs the word ‘idea’, namely: the ‘idea as meaning’, the idea as it is present in judgment. Moore’s paper is concerned precisely with showing that an ‘idea’, in this sense of Bradley, is completely independent from any action of our minds, and he thus calls ‘ideas’ by a different name – ‘concepts’ –, so as to dispel any remaining ambiguities and avoid any confusion (Moore, 1899, p. 177). Still, if one were to understand ‘idea’ in the strict sense of ‘logical idea’ which Moore is discussing here, then it could just as well apply to his notion of ‘concept’ as to its cognate, namely Russell’s ‘term’.
- 4.
In his The Philosophy of Leibniz, Russell had argued that “one of the main sources of novelty” (PL, p. 47) in Leibniz’s thought was the full recognition of this “logical reduction” of the concept of substance, as well as its assumption as a basic premiss of his philosophy: “[t]he distinctive feature of substance, when used as the basis of a dogmatic metaphysic, is the belief that certain terms are only and essentially subjects. When several predicates can be attributed to a subject, and this in turn cannot be attributed to any other subject, then, Leibniz says, we call the subject an individual substance.” (PL, p. 50) Russell is here emphasizing the freshness of the Leibnizian logical conception of substance against the then-dominant conceptions of the Cartesians and of Locke, though one could also read it as a way of going back to the Aristotelian characterization of substances as, first and foremost, “that which is neither said of a subject nor in a subject” (Cat. 5, 2a12–13; but cf. also Met. Δ 8, 1017b10–26).
Another important point we see here is that the talk of ‘terms’ is already present in the quote of PL, and actually stems from Leibniz himself. Indeed, throughout his book, Russell adopts the Leibnizian terminology of ‘terms’ when he wants to talk about the constituents of propositions. Cf. for instance, the passage he quotes from Leibniz’s letters to Arnauld (Leibniz, 1978, p. 62), which reads, in Russell’s translation: “[I suppose] that nothing is without a reason, or that every truth has its a priori proof, drawn from the notion of the terms [la notion des termes], although it is not always in our power to make this analysis” (PL, p. 38). Leibniz’s French ‘terme’ corresponds to what Leibniz himself calls in Latin ‘terminus,’ a common term in Medieval logic.
Now, one would suppose that this Leibnizian engagement is the reason why, in the Principles, when Russell refers to the constituents of propositions, he continues to call them ‘terms’, even if – and this makes all the difference – these constituents of propositions are no longer either mental contents or their spoken or written signs, as terms had come to be understood, through their successive transformations.
Thus, it is not without some irony that, once they are freed from their attachment to subject-predicate logic, and once they are duly de-mentalized (as Moore had done with his ‘concepts’), it is precisely these originally Aristotelian terms that will become the almost caricatural Platonic entities of the Principles of Mathematics.
- 5.
Denoting concepts, however, immediately complicate the issue. Russell acknowledges the difficulty, as we can see in the footnote to PoM, p. 46. Hylton also shows how Russell could have sidestepped the logical subject argument – though he seems not to have realized it – using the tools of his own theory of denotation, as was developed in the Principles, Hylton, 1990, p. 212.
- 6.
In 1899, Russell began to work on a book that was to be called The Fundamental Ideas and Axioms of Mathematics. He eventually abandoned the project, but the manuscripts that remain somehow pave the way to the Principles of Mathematics (see CP II, pp. 261–4) and, thus, provide us with some early takes on problems that would reappear in the 1903 book. In these manuscripts, regarding terms and units, Russell suggests that “‘A is one’ is a true proposition whatever A may be, unless A is many as such. ‘2 men are one’ is false, but ‘a pair of men is one’ is true. […] ‘A is one’ seems almost like an analytic judgment, since it is involved in ‘A is a concept’, which means ‘A is one concept’”. (CP II, p. 273).
- 7.
There are two versions of this passage: the first is in a paper published in Mind in 1901, where Russell criticizes the relational theory of time and space, and where he thus argues against Lotze’s positions on the matter. The second is in chapter LI of the Principles, published in 1903, where he used some of the material of that paper. In this second version, however, he suppresses the expression in brackets, i.e., the equation of logical concepts and Platonic ideas.
- 8.
The attempt to articulate terms, units and entities also appears in other passages of the Principles. In those cases, the articulation is even less detailed than in the discussion of terms in §47. What is interesting, though, is that, in some of them, Russell suggests different articulations, different paths connecting terms, units and entities. Cf., for instance, this breakdown of a passage in §427 of the Principles: [Term → entity] “Being is that which belongs to every conceivable term, to every possible object of thought – in short to everything that can possibly occur in any proposition, true or false, and to all such propositions themselves. [Unit → entity] Being belongs to whatever can be counted. [Unit → term → entity] If A be any term that can be counted, it is plain that A is something, and therefore that A is. [Term → entity] “A is not” must always be either false or meaningless. For if A were nothing, it could not be said not to be; “A is not” implies that there is a term A whose being is denied, and hence that A is. [Term → entity] Numbers, the Homeric gods, relations, chimaeras, and four-dimensional spaces all have being, for if they were not entities of a kind, we could make not propositions about them” (PoM, p. 449).
And also: [Term → entity] “Whatever can be thought of has being, and its being is a pre-condition, not a result, of its being thought.” (PoM, p. 451) [Unit → term and entity] “What can be counted must be something, and must certainly be, though it need by no means be possessed of the further privilege of existence. Thus, what we demand of the terms of our collection is merely that each should be an entity.” (PoM, p. 71).
- 9.
Many translators assume that this follows from what came before – in Cornford’s translation, for instance, the Visitor’s line reads “[s]o it seems to follow necessarily that to speak of what is not ‘something’ is to speak of nothing at all” (1935, p. 204, emphasis mine) and in Rowe’s “[b]ut then it seems there will be no escape […]” (2015, p. 130). This seems to suppose that, if ‘something’ is a sign for ‘one thing’, then to speak of what is not ‘something’ (reading τι as being mentioned) is to speak of what is not ‘one thing’ (μηδ-έν) at all. But it is not obvious that this should follow. Crivelli, who himself defends that e1–2 is “a new independent claim” and that “it is not a consequence of what comes before” (2012, p. 39), provides a more prudent translation, that I adopt here out of cautiousness.
- 10.
On this, see for instance Cornford 1935, p. 308: the “assertion [in e5] that ‘every statement is about something’ indicates that one element in the complex statement is the name of the agent or (to use the later term) subject, and the agent itself is one element in the existing fact.”
One should be careful, however, to distinguish, on the one hand, the expression ‘λόγος τινός’ from another, ‘λόγος περί τινος’. As Francesco Fronterotta has recently shown, ‘λόγος τινός’ has indeed that very specific function of expressing the fact that speech must be about some logical subject, without which the weaving of names and verbs that is proper to speech cannot happen. It is to be distinguished from what is conveyed by the expression, employed in the same passage, of ‘λόγος περί τινος’, which already supposes the speech to be about a subject but, additionally, purports to convey the many possibilities of predication of the logical subject. See Fronterotta 2019, especially the second section.
- 11.
Here, like in Russell’s double criterion of terms (logical subject/intentional object), there is a parallel between the requirement of a logical subject of propositions – i.e., that speech be about something – and the requirement of objects of belief (in Rep. 478b6-c2 above) and of sight, hearing and touch (in Tht. 188e6-a9) – i.e., that one believes or sees or touches something.
- 12.
Cf., on this, Mary McCabe’s thorough investigation of individuation in Plato (especially ch. 8, 221ff.): “Being one (or a something), therefore, is determined in two different ways, made explicit here for the first time. The first is absolute (being the same as itself, being ‘itself by itself,’ Soph. 255b12); the second is relative (being different from the others, being ‘with relation to something else,’ 255c13). So, to be one/an individual/countable, each something is one in itself (by virtue of being the same as itself) and in the context of others (by virtue of being different from them). If both ‘same as itself’ and ‘different from the others’ are true of the item, then it is conceded to be one.” (McCabe, 1994, pp. 233–4). Cf. as well Christine Thomas’s discussion of the importance of this general account of individuation in the context of the articulation of τι, ἕν and ὄν: “Change is not alone in sharing in being, sameness, and difference. Everything that is participates in being and is some one self-identical something that is different from every other being. […] According to Plato’s metaphysics of somethings, then, a something is a being, some one countable thing that is self-identical, different from every other being and capable of being affected by or itself affecting other beings. […] The metaphysics of somethings is a metaphysics of complex, unified, countable, interactive beings.” (Thomas, 2008, pp. 643–5). Thomas’s summary of Plato’s “metaphysics of somethings” could well be, mutatis mutandis, a summary of Russell’s “metaphysics of terms” – with the notable and important exception, that is, of the interactive aspect, the account of which, in Russell, would require special attention.
- 13.
This means that Plato must explain how it is that we can speak about fictional objects without their being somethings, in apparent defiance to step (i) of the path. This is the main issue of Thomas, 2008; and, among others, of Durrant 1998 on Plato’s Quinean Beard.
- 14.
It is important to note: this youthful Platonism was not simply a retrospective projection. At the time of writing the Principles, Russell was quite aware of the Platonic elements of his – and Moore’s – position. As he wrote to Couturat on May fifth, 1900: “En éthique théorique je ne suis nullement kantien, mais plutôt platonicien (comme en logique) que quoi que ce soit de moderne” (CP III, p. 216).
- 15.
“Great difficulties are associated with the null-class, and generally with the idea of nothing. It is plain that there is such a concept as nothing, and that in some sense nothing is something. In fact, the proposition “nothing is not nothing” is undoubtedly capable of an interpretation which makes it true – a point which gives rise to the contradictions discussed in Plato’s Sophist.” (PoM, p. 73).
We know for a fact that Russell was engaged in serious study of Plato’s works at the time he wrote the drafts of the Principles and the manuscripts for Fundamental Ideas (where he explores already the concept of “terms”). Russell read widely and variedly, and the reading list of his earlier years is fortunately available to us.
There is a noticeable anomaly in it: having read only the Theaetetus and the Symposium as a young man (Nov. 1892), and after an isolated reading of the Phaedo (May 1896), Russell suddenly and consistently read through the Parmenides (Jan. 1899), Gorgias, Protagoras, Theaetetus and Sophist (!) (Mar. 1899), the Timaeus and Phaedrus (Apr. 1899). Not much later, he continued his studies by reading the Parmenides again (Jan. 1901) and then the Laches, Charmides and Euthydemus (Oct. 1901).
All of the dialogues were in Jowett’s translation and most of them were read together with his wife Alys, with whom he also read Milton, Austen and copious amounts of Shakespeare. There are, however, some notable exceptions, such as the Theaetetus and the Sophist, which he read alone – maybe indication of a more thorough study. (Cf. CP I, pp. 345–65).
- 16.
Russell was, of course, aware of this being a Parmenidean strand inside Plato’s thought. Cf. HWP, p. 122, when he is discussing Plato’s theory of ideas: “The man who has knowledge has knowledge of something, that is to say, of something that exists, for what does not exist is nothing. (This is reminiscent of Parmenides).”
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This study, both in its conception and in its development, owes much to Claudio Majolino, to whom I am deeply grateful. It also benefitted greatly from my constant exchanges with Raimundo Henriques. Neither of them, however, was aware of – or is responsible for – the many flaws of this final redaction.
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Riscali, G. (2022). Russell on the Widest Words in the Philosophical Vocabulary: A Platonic Path Through Terms, Units and Entities. In: Mariani Zini, F. (eds) The Meaning of Something. Logic, Argumentation & Reasoning, vol 29. Springer, Cham. https://doi.org/10.1007/978-3-031-09610-5_4
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