Abstract
Despite the fact that at the time Russell believed himself to be a neo-Hegelian, ‘the most direct philosophical influences on him in the period from 1895 to 1898 were Kant, Bradley, and Ward’ (Griffin 1991, p. 299), and also Lotze,1 not Hegel. It was his devotion to Kant and to neo-Kantians that led him to choose exact philosophy as a type of investigation. The latter, called the ‘Logic of the Sciences’2 by Russell, was to be developed like the other exact academic disciplines: mathematics and the natural sciences.
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Reference
On Lotze’s influence on Russell see Milkov 2000.
Apparently, Russell was negatively motivated to embrace scientific philosophy. This was because of the example of Herbert Spencer, from whom he wanted to keep as far away as possible. See on this Cunningham 1994.
A collaborative method of working was typical for Russell. Thus in 1912–13 he had a joint philosophical programme with Wittgenstein (see Milkov 1988, 2002b). In 1903–10 he had a joint programme with Whitehead in symbolic logic.
This was also the first idea which the young Wittgenstein accepted from Russell: `There is nothing in the world except asserted propositions’ (Letter of Russell to O. Morrell, 13 November 1911).
See Griffin 1991, p. 305. On Russell’s transcendental arguments before 1898 see Grayling 1996.
A implies B’ cannot mean `A’s truth implies B’s truth’; for here a simpler case of implication is explained by one which is more complex. `A implies B’ implies `A’s truth implies B’s truth’ and also implies `B’s falsehood implies A’s falsehood’. But `A implies B’ applies to A and B simply as propositions, and quite independently of their truth or falsehood.’ (1899c, p. 292)
See Milkov 1997a, i, pp. 82–3.
On this account, it is important to note that `[o]nly after the paper 1 [`Draft’] is abandoned and Russell begins a new draft of the Principles in October 1900 does Cantor’s influence become central [for Russell], along with Peano’s’ (G. H. Moore 1993a, p. 9).
This had incidentally already been accepted by Husserl in 1894 (see Coffa 1991, pp. 101–2).
In fact, it is from here that the principle of contextual definition also entered the Theory of Descriptions (see § 3, (i)). On Russell’s contextual definitions see Makin 2000, pp. 68–9.
It is of importance that already before the Paris Congress, Russell was conscious that the problem of totality, where all and any describe various forms of the permutations in a set, is indeed `intimately connected’ but nevertheless different from that of whole and part. `All cannot be defined numerically’; but it nevertheless means a perfectly specified notion (see 1900b, pp. 39–44).
This analysis of compositionality is a good example of Russell using ordinary language as a compass in philosophy. Ironically, in the 1950s he was strongly against this approach.
Besides aggregates and units, there is a relation between subordinate aggregates (not between an aggregate and a term), which can be called a relation of whole and part proper.
Since Russell accepts that it is aggregates that are the subject of analysis, this acceptance is clearly anti-analytical.
Later Russell apotheosised this idea in his Ramified Theory of Types, which divides functions into types according to whether they do, or do not, involve reference to all functions of their type.
In this section I shall speak of `Russell’s Peano—Fregean turn’ only metaphorically. In fact, until 1902 Russell had as good as no knowledge of Frege. I have two reasons for using this metaphor: (a) The gist of Russell’s turn from August 1900 was the assimilation of the philosophical consequences of Peano’s theory of quantification. Today, however, it is widely accepted that the theory of quantification was Frege’s main contribution to logic. Now, although different from it, this theory was in many respects similar to that of Peano (see Gillies 1982). This partly explains why after assimilating the ideas of Peano, Russell so easily embraced the ideas of Frege. (b) Russell was also impressed by Peano’s elegant symbolism, which was developed `partly under Frege’s influence’ (G. H. Moore 1998, p. 732).
The procedure here is similar to the minima philosophia approach of Moore, already discussed in ch.
Wittgenstein put this matter in similar, yet clearly different, terms. The problem of infinity, as well as other, similar problems, is a product of certain (grammatical) misunderstandings which are to be removed from the calculation (see Wittgenstein 1956, IV, § 6).
The banishment of the infinitesimal has all sorts of odd consequences, to which one has to become gradually accustomed. For example, there is no such thing as the next moment’ (1901a, p. 371).
Cf. the title of his paper `My Debt to German Learning’ (1955).
Some authors have justly noted that `in a neo-Hegelian vein—he [Russell] collected as many paradoxes as he could’ (Grattan-Guinness 1986, p. 108).
The terminology of collective and distributive classes was borrowed by Legniewski from Kotarbinski much later.
A seen in (ii), (a), Russell’s turn of 1900 had two forms that run in parallel: (a) apophantism; (ß) intensionalism.
It is of importance that Russell himself insisted on the nationality of different schools in mathematics and logic (see, for example, his 1901b). What I mean by German-Italian influence in logic can be seen in this passage from Ray Monk’s biography of Russell: ‘Peano was the head of a group of Italian mathematicians whose aim was to further the progress made by the earlier generation of German mathematicians in founding mathematics upon rigorous foundations’ (Monk 1996b, p. 129).
For an investigation which partly supports this view see Hager 1994.
A point often discussed in the newer literature. See, for example, Mayer 1996, p. 135. See also § 5, (ii).
If we compare the development of Russell’s philosophy at that time with that of other philosophers of the same period, it is striking that, in contrast, Husserl, for example, was aware that the new mereology (not Frege’s technique of quantification, with which he was quite well acquainted), or the logic of terms, was the new achievement in the logic of the fin-de-siècle period, and one which was to have radical consequences for philosophy too.
In a letter to Jourdain of 14 March 1906 Russell wrote: `In April 1904 I began working at the Contradiction again, and continued at it, with few intermissions, till January 1905. I was throughout much occupied by the question of Denoting, which I thought was probably relevant, as it proved to be’ (quoted according to Grattan-Guinness 1977, p. 79).
On the forms of Russell’s logical atomism see § 8, (v)—(vi).
Frege was helped in this solution by the fact that his logic was crypto-intuitive from the very beginning. Indeed, his foremost assumption was that we know logical objects only via geometrical intuition (see on this Milkov 1999b).
The first being the Theory of Denoting of 1903, discussed in § 2, (ii), (b).
Exactly this point was challenged later by Kripke, who assumed that names are rigid designators also historically, in the stream of time (see Kripke 1980, p. 5).
In this sense David Kaplan noted that `Russell’s article is about logical form’ (Kaplan 1972, p. 230).
Some authors put this point thus: ‘On Denoting’ ’makes no overt use of the notion of denoting, or of denoting concept’, but is concerned rather with picking out an unique object (Hylton 1990, p. 238).
On this change see Milkov 2001d.
Presumably, its ideological basis was the common Bloomsberrian emphasis on individual experience, already mentioned in ch. 1, § 2, (i). For the striking similarity between Russell’s epistemology and the `philosophical realism’ of Virginia Woolf see Hintikka 1979.
The notion of scaffolding is central to this—constructional—type of logic. It is well known that it also plays a central role in Wittgenstein’s philosophy (see Wittgenstein 1922, 3.42, 6.124). See ch. 3, § 3, (iii).
This understanding was accepted under the influence of Moore. See on this § 5, (ii), (b).
See ch. 1, § 3, (iv).
To be discussed in § 4, (iii).
On this argument see Riska 1980.
It can be successfully shown that the criticism on Russell’s Theory of Descriptions suggested in Straw-son 1950a, Donnellan 1966 and Kripke 1980 is of such limited validity (see Milkov 1997a, pp. 286–8).
Also discussed in § 8, (v)-(vi).
Criticised by Wittgenstein in the Tractatus 5.631–41.
According to this, `if we do not put the meaning in an entity-position, we merely mean it, and do not say anything about it; if, on the contrary, we put it in an entity-position, it stands for its denotation.’ (1905b, p. 382)
Italics mine. In this note Russell points out that Frege’s criticism of psychologism is not anti-psychological enough. Today it is widely accepted that in his works after 1891 Frege `transformed his thesis that all knowledge is propositional into a psychological hypothesis according to which thinking is the mind’s grasping of an abstract Thought or proposition’ (Curry, 1982, p. 192; italics mine).
It is supported, for example, by Michael Kremer, according to whom `the PoA [Principle of Acquaintance] is a primary factor influencing Russell to abandon the theory of denoting concepts’ (Kremer 1994, p. 291).
See the note of the editor of Russell 1994, Alasdair Urquhart, p. 491.
The history of `On Denoting’ is also discussed in (ii).
In a letter of 29 December 1904 Russell wrote to Moore that if he wrote on truth, `I should first write an ordinary technical article, and then boil it down’ (Levy 1979, p. 256).
Italics mine. The term `philosophical logic’, as used by Russell, will be discussed presently.
Or `Logic’, or `Philosophy of Mathematics’ (1992a, p. 442), or `Popular Logic’ (p. 458). The content of these plans is set out in 1984, p. 183; see also 1984, p. xxiii.
As just noted (in (ii)), in the beginning Russell accepted that logical forms are in possession above all of indefinables, which are simple.
From this point on, Wittgenstein developed the theory of two types of scaffolding: logical scaffolding and material scaffolding. See ch. 3, § 3, (iii) on this, as well as Milkov 2001a.
The well-known criticism of logical constants made by Wittgenstein beginning from 1912 and explicated in full in the Tractatus (5.4) with the words: `At that point it becomes manifest that there are no `logical objects“ or `logical constants” (in Frege’s and Russell’s sense)’ was, in fact, an assimilation of Russell’s conception of `logical forms’, developed to its logical conclusion.
Wittgenstein developed this understanding further. See ch. 3, § 3, (vi).
The term `logical space’ is used by Wittgenstein for the first time on 23 Nov. 1914 (see Wittgenstein 1979e, p. 31). Already before that, however, Russell spoke (in June 1913) of `logical world’ (1984, p. 138).
The description of philosophical logic as a `zoo’, the task of which is to supply the `nomenclature’ of logical forms, is a biological point in Russell’s thinking. For a logical investigation of (biological) ‘nomenclatures’ (taxonomies) see Simons 1992.
Thus, according to Dummett’s definition of analytical philosophy as investigating the structure of language-meaning (see Dummett 1993, p. 4), Russell (sic!) was not an analytical philosopher. A similar reductio ad absurdum argument against Dummett’s understanding of what analytical philosophy is is suggested in Monk 1996a.
Which was a consequence of the identity theory of truth accepted by both Moore and Russell in the 1900s. See ch. 1, § 3, (i).
An account of these analyses is to be found, for example, in Budd 1989, pp. 10–15.
The same is assumed also in Moore 1909b, p. 47.
The conception of `logical intuiting’ was later developed by Wittgenstein in a theory of intellectual intuition. See on this ch. 3, § 2, (iii).
Sec on this distinction Frege 1882/3, p. 91.
Incidentally, the compatability of the Principia with mereology is well demonstrated in Whitehead’s later mereological analysis of space and time (see Whitehead 1919, pp. 101 ff.).
Incidentally, this statement was strongly criticised by such neo-Fregeans as P. T. Leach (see Geach 1969).
This understanding of Russell’s was obviously motivated by the fact that his very mathematical training was in calculating—it was not theoretical. Some historians go further, noticing that ‘he was the victim of a highly politicised and personalised tutorial system which sacrificed comprehension in favour of computational legerdemain and problem-solving tour de force skills’ (Anellis 1987, p. 153). This tradition was apparently connected with the ’calculus revolution’ which was advanced by mathematicians from Trinity College, Cambridge, in the first decades of the nineteenth century (see Koppelman 1971).
From this point on, it was not difficult for Wittgenstein to arrive at the idea of the deflationary role of logic. According to this understanding, with the help of a `suitable notation we can in fact recognize the formal properties of propositions by mere inspection of the propositions themselves’ (Wittgenstein 1922, 6.122). See on this ch. 3, § 2, (iii).
Thirty-seven years later Russell repeats: `In emphasizing the importance of structure, I still think he was right’ (1959, p. 113).
This project ran parallel to the attempt to replace logical objects with logical forms, already discussed in § 6, (iv).
Which was Russell’s variant of Moore’s minima philosophia, discussed in eh. 1, § 2, (vii).
Ironically, this was nothing but a Kantian appeal to intuition.
This formulation follows almost word by word 1911b, p. 135.
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Russell, B. (2003). The New Method as a Logic. In: A Hundred Years of English Philosophy. Philosophical Studies Series, vol 94. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0177-8_3
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