Consider next the case of Frege. Although deceptively similar, his use of analyticity and his logicism must be distinguished from the logical empiricist versions. Although Frege has much to say about analyticity – reducibility to logic via explicit definitions – he has, apparently anyway, next to nothing to say about our knowledge of logic.19 It is true that he claims that his intention is not to assign any new meaning to the terms “analytic” and “synthetic” but that he only wants to state precisely what earlier authors, Kant in particular, had had in mind (1884, §3). Yet, it is no less true that Frege was largely insensitive to
18 “Partial” since it has to be complemented by an account of the nature of language and our knowledge of it that can be deemed acceptable by the logical empiricists’ standards. But here they could refer to conventionalism and behaviourism.
19 See, however, section 5.5 for a more accurate description of Frege’s situation.
the epistemological problems that had exercised Kant and were to exercise logical empiricists.20 As far as Frege is concerned, the crucial point can be put briefly by saying that he was – most of the time, anyway – content with the assumption that there is knowledge that is apriori, without bothering to provide an explanation of what this knowledge is like.21
Consider finally Russell’s early logicism. There are, of course, conspicuous differences between Russell’s and Frege’s logicisms.
Nevertheless, when it comes to the issue of analyticity, their views bear an important similarity to one another. Above all, as in Frege’s case, the motives that Russell had for his logicism must be distanced from the epistemological underpinnings of logical empiricism. As several scholars have pointed out, Russell has in fact very little use for the notion of analyticity.22 The notion of analytic truth, or the distinc-tion between analyticity and syntheticity, is afforded absolutely no role in the Principles. It receives no extended discussion and is not put into any use. Indeed, he almost fails to mention it, and when he once mentions it, he does so only to put it aside as being of no concern to him. Moreover, what little he says seems to distinguish him firmly from logical empiricism. This is what Russell has to say about the notion:
Kant never doubted for a moment that the propositions of logic are ana-lytic, whereas he rightly perceived that those of mathematics are syn-thetic. It has since appeared that logic is just as synthetic as all other kinds of truths: but this is a purely philosophical question, which I shall here pass by. (Russell 1903a, §434)
Taking this passage into account prevents us from applying the standard characterisation of logicism to the early Russell: if logic,
20 See, for example, Skorupski (1984, pp. 239-40).
21 See Skorupski (1993, pp. 142-3; 1995). This view may be a little too simple as a complete characterisation of Frege’s views (see, again, section 5.5), but it will do for now.
22 See Taylor (1981), Coffa (1982), Hylton (1990a, p. 197; 1990b, p. 204).
according to Russell, has turned out to be synthetic, we can hardly say that the point of his logicism was to show that mathematics is ana-lytic. On the other hand, saying it is synthetic is something that seems to have little interest for him.
In thus rejecting the terminology of “analytic” and “synthetic”, Russell also seems to be deviating from Frege. However, it is worth pointing out – and this is something that has not been widely recog-nised – that Russell was ready to express agreement with Louis Couturat when the latter proposed a definition of analyticity that was exactly like the one that Frege had given in Grundlagen:
We may usefully define as analytic those propositions which are deducible from the laws of logic; and this definition is conformable in spirit, though not in the letter, to the pre-Kantian usage. Certainly Kant, in urg-ing that pure mathematics consists of synthetic propositions, was urgurg-ing, among other things, that pure mathematics cannot be deduced from the laws of logic alone. In this we now know that he was wrong and Leibniz was right: to call pure mathematics analytic is therefore an appropriate way of mark-ing dissent from Kant on this point (Russell 1905a, p. 516; italics added).
In the end, then, Russell did not object to applying the notion of analyticity to “pure mathematics”. But as we saw above, this sense which Russell was ready to accept – the Fregean one – is in a crucial respect different from what Kant and logical empiricists had in mind.
The following quotation from Warren Goldfarb gives a succinct formulation of this conclusion: “In fact, no real role is played by any distinction between analytic and synthetic in early logicism. The central and basic distinction for both authors [sc. Frege and Russell]
is that between logical truth and extralogical truth. The question, then, is that of discerning those features of the new logic which enabled it to work so effectively against Kant” (1982, p. 693). The point is this. Even though it is a trivial consequence of Frege’s defini-tion of analyticity that logic is analytic, the definidefini-tion does not as such deliver any further characterisation of logic that would explain the importance of the purported reduction.
When it comes to analyticity and syntheticity, we must distinguish Frege’s and Russell’s use of these concepts from Kant, for whom analyticity is spelled out by dint of the notion of conceptual contain-ment, as well as from logical empiricists, who resorted to “truth in virtue of meaning”. This difference can be expressed as follows.
Neither the notion of conceptual containment nor that of truth in virtue of meaning contain reference to logic. It follows that for Kant and the logical empiricists it is, as it were, a further discovery that the discipline one calls “logic” is one to which analyticity applies, whereas Frege’s – and, on occasion, Russell’s – procedure is the exact oppo-site. For this reason Frege and Russell cannot use analyticity for any explanatory purposes (and do not intend so to use it). As Goldfarb says, for them the crucial distinction is that between logical and extra-logical truth. This point is seen clearly by reflecting on the above quotation from Russell. He did not dispute Kant’s claim that pure mathematics is not “deducible from the laws of logic”, if logic is understood in the way Kant understood it. If he had disputed this, there would have been no need for reform in logic. Hence the slogan
“pure mathematics is reducible to logic” is “an appropriate way of marking dissent from Kant” only when it is conjoined with an articu-lation of what distinguishes logical truth from non-logical truth and how this undermines Kant’s theory of mathematics.23
This being said, we can conclude that the analytic-synthetic dis-tinction had no important role to play in the early Russell’s logicism.
23 We can now see what Russell meant when he wrote in the Principles of Mathematics that “[i]t has since appeared [sc. after Kant’s days] that logic is just as synthetic as all other kinds of truth”. This means simply that the new logic of Peano, Russell and others was not a body of trifling truths and principles – a view that Kant had applied to the formal logic of his time – and cannot therefore be classified as analytic in Kant’s sense. Russell’s claim that logic is synthetic is not an exciting philosophical thesis but a recognition of what he took to be an undeniable fact. This, however, did not lead Russell to reflect on the epistemological status of this new logic, which shows him to have been an ally of Frege in this respect and distinguishes him clearly from Kant and logical empiricists.
Certainly it had no role comparable to that given to it in logical empiricism. If we draw the distinction within the context of Russell’s logicism at all (and as we have seen, this can certainly be done), then it is essentially identical with Fregean analyticity. This notion, how-ever, does not ascribe to logic any further characteristic which would turn “analyticity” into an explanatory concept. For this reason Rus-sell’s logicism, like Frege’s, must be kept firmly distinct from the later use to which their ideas were put in the hands of someone like Car-nap or Ayer. This means in particular that Russell’s reasons for pursuing logicism cannot be brought to the fore simply by referring to the analytic-synthetic distinction.
It comes as no surprise to hear that Frege’s and Russell’s appro-priation of “logicism” was significantly different from the logical empiricist one. Their opposition to empiricism was indeed quite fundamental and stems from a firm conviction that consistent em-piricism is inconsistent with a viable philosophy of mathematics and logic. First and foremost, they regarded empiricism as being irreme-diably involved in psychologism, and this was for them a sufficient reason for dismissing it as a confused piece of philosophising.24
24 Frege’s opposition to empiricism is evident, for example, from his dismissal of Mill’s attempt to ground arithmetical definitions in observed matters of fact. Frege admits that the idea of grounding a science in defini-tions is sound; nevertheless, Mill’s execution of this idea is flawed “thanks to his preconception that all knowledge is empirical” (1884, §7). It can be seen, then, that Frege’s criticism of Mill was not that the latter’s theory was psychologistic. Yet, Frege thought that at least at the level of logic the Millian preconception results in psychologism with its characteristic confu-sion of what is objective with what is subjective (the subject-matter of logic, or the science of the laws of thought, consists in mental items and their interrelations). Russell is in this respect more sweeping and sees in empiri-cism an immediate commitment to psychologism: “[m]isled by neglect of being, people have supposed that what does not exist is nothing. Seeing that numbers, relations, and many other objects of thought, do not exist outside the mind, they have supposed that the thoughts in which we think of these entities actually create their own objects” (1903, §427). Thus he dismisses the Millian account of numbers offhand and contends that the failure to
Frege’s anti-psychologism is both well-known and extensively dis-cussed in the secondary literature.25 It was also of crucial significance for Russell. He had published his own (short) criticism of psycholo-gism as early as 1895 (Russell 1895, pp. 251-2), while he was still an idealist. In this he was merely following such better-known idealists as F. H. Bradley, whose verdict on empiricist associationism and the resulting psychologism was not only as harsh as Frege’s but also bears important similarities to it.26 While no longer an idealist, the logicist Russell remained every bit as hostile to psychologism. It is true that he now associated psychologism with idealism, rather than empiri-cism.27 This, however, does not signal any change in his attitude towards empiricism; rather, it has to do with the fact that there were not many people in Russell’s intellectual environment at the turn of the century for whom empiricism would have been a live option.28 observe the distinction between being and existence leads immediately to psychologism. Though empiricism is not mentioned here by name, it is clear that Russell’s remark is intended to apply to it as well. According to Moore’s and Russell’s new realism, the characteristic thesis of empiricism, to wit, that
“experience is the origin of all knowledge”, amounts to the view that “all known truths are truths about what exists at one or more moments of time”
(Moore 1902-3, pp. 91-3), thus implying precisely, a failure to observe the distinction between being and existence.
25 See, for example, Notturno (1985) or Baker and Hacker (1989).
26 See Gerrard (1997, sec. VII) f or a discussion of Frege, Bradley, Russell (and Moore) on anti-psychologism.
27 Russell’s criticism of Kant’s transcendental idealism is a prominent example of how idealism was thought to get entangled in psychologism. See below, section 3.6.2.1.
28 It seems also clear that Frege and the early Russell would have seen little reason to revise their appreciation of empiricism even if they had been acquainted with it in some more refined form than that exhibited by Mill; if, for instance, they had been familiar with logical empiricists, who were particularly concerned with bringing the Millian preconception into harmony with the existence of such putatively apriori disciplines as mathematics and logic. Logical empiricists were quite as much opposed to psychologism as were Frege and Russell, so that the latter would have been forced to refine their criticisms. Nevertheless, there is little reason to think that they would