minds, machines and economic agents: cambridge receptions of boole and babbage

Studies in History

Stud. Hist. Phil. Sci. 36 (2005) 331–350

and Philosophyof Science

www.elsevier.com/locate/shpsa

Minds, machines and economic agents:Cambridge receptions of Boole and Babbage

Simon Cook

UWP, Duke University, Bell Tower/East Campus, Box 90025, Durham, NC 27708-0025, USA

Received 24 June 2004; received in revised form 30 December 2004

Abstract

In the 1860s and 1870s the logic of Boole and the calculating machines of Babbage were key

resources in W. S. Jevons�s attempt to construct a mechanical model of the mind, and both

therefore played an important role in Jevons�s attempted revolution in economic theory. In

this same period both Boole and Babbage were studied within the Cambridge Moral Sciences

Tripos, but the Cambridge reading of Boole and Babbage was much more circumspect.

Implicitly following the division of the moral sciences into material and �real� as establishedby the Rev. Grote, John Venn treated Boole�s logic as a purely formal science, while Alfred

Marshall based his psychological model of the mechanical part of the human mind upon Bab-

bage�s two-level machine. From the different perspectives of logic and psychology, Venn and

Marshall did not simply incorporate their readings of Boole and Babbage, but also attempted

to establish the limits to any mechanical explanation of the mind. This comparison of the atti-

tudes to mental science of Jevons and Marshall provides a foundation from which the differing

conceptions of economic theory of the two men can be established.

� 2005 Elsevier Ltd. All rights reserved.

Keywords: Alfred Marshall; Charles Babbage; George Boole; John Venn; Logic; Psychology.

0039-3681/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.shpsa.2005.04.001

E-mail address: [email protected] (S.J. Cook).

mailto:[email protected]

332 S. Cook / Stud. Hist. Phil. Sci. 36 (2005) 331–350

And like an Engine moved with wheel and waight,

1 Wh

�consorelatio

explan

ninetee

His principles ceased, he ended straight.

John Milton, Another on the same

1. Introduction

If the history of political economy is still on the whole an internalist enterprise,

written by economists for economists about economists, an emerging body of liter-

ature in this field has nevertheless demonstrated the rewards which can be expected

from the attempt to connect developments in political economy to the broader intel-

lectual context of a period. For example, the emergence of the �marginal economics�of William Stanley Jevons may now, following important work by two historians of

economics, be understood in light of contemporary work in physiology, practical

engineering, and logic. Michael White has argued that, following Richard Jennings,

Jevons drew upon physiological psychology in order to present �natural laws� of eco-nomic behaviour in terms of nervous reflexes. Harro Maas, in this journal, has ar-

gued that both Babbage�s Difference Engine and his reception of Boole�s formal

logic provided Jevons with a mechanical view of the mind, a conception of the mind

which formed �a watershed between Jevons�s and Mill�s notions of economics�.1 Gi-ven that all three of these resources (simply put, Babbage, Boole, and Bain) were

available to Jevons�s slightly younger contemporary, the Cambridge economist

Alfred Marshall, the question arises as to whether Marshall�s innovations in eco-

nomic science can be placed within a similar framework.

Some time around 1872 Marshall, at this time a lecturer in the Cambridge Moral

Sciences Tripos, made the decision to dedicate his life to the study of economics. For

a few years prior to this, however, Marshall had thought that psychology would pro-

vide his life�s work. As we shall see, in his early development of a theory of psychol-ogy the calculating engines of Charles Babbage provided for Marshall a crucial

resource. Marshall was not, however, particularly interested in the formal study of

logic, and there is little evidence to suggest that he ever seriously studied Boole�sLaws of thought (although it is not impossible because he did lecture on logic for

a year or two—before managing to hive off this responsibility onto his younger col-

league Foxwell). Marshall�s colleague in the Moral Sciences Tripos, John Venn, did

however read Boole, and indeed devoted a considerable amount of time to develop-

ing what he called �symbolic logic�. Venn�s views are important here because Mar-shall�s views on the nature and province of logic were broadly similar to those of

ite (1994), and Maas (1999), p. 590. Maas claims that Jevons�s interest in psychophysiology was

nant with his work on a mechanical representation of human reasoning�, but it must be said that the

nship between psychophysiology and Boole�s logic is not obvious and really merits an explicit

ation. Indeed the arguments of this paper should serve to show that in the latter part of the

nth century more than one way of conceiving of the relations between the two fields was possible.

S. Cook / Stud. Hist. Phil. Sci. 36 (2005) 331–350 333

Venn, and broadly opposed, it can be said, to those of Jevons and Jevons�s former

teacher, Augustus De Morgan.

In this paper, then, I propose to survey the reception in Cambridge in the late

1860s and the early 1870s, of the logic of Boole and the interpretation accorded to

the calculating engines of Babbage. I begin, however, with a discussion of the philos-ophy of John Grote, professor of moral philosophy at Cambridge between 1855 and

1866. Grote�s dualistic treatment of the moral sciences provides the context in which

to understand the logical and psychological work of Venn and Marshall, and indeed

also the relationship between these two disciplines as it was conceived of in Cam-

bridge in this period. I next turn to Venn�s views on logic as a whole, and on Boole

in particular, and then to Marshall�s early psychological paper �Ye machine�, inwhich we will find an eclectic mixture of Bain, Carpenter, and Babbage. Venn�s viewson logic are interesting in their own right, for the reception of Boole�s system has notyet been fully explored.2 Nevertheless, my primary interest in outlining Venn�s posi-tion is to provide the material necessary for a complete picture of Marshall�s views ofthe mind. As this paper will show, Marshall and Venn shared similar views as to the

respective domains of logic and psychology, and also as to the inherent limitations in

any purely mechanistic account of the mind. Thus this paper will show that the views

of Venn and Marshall on, respectively logic and psychology, when taken together

and understood in relationship to John Grote�s overall conception of the moral sci-

ences, can provide the first part at least of an explanation as to how and why, when itcame to political economy, Marshall developed an approach quite distinct from that

of Jevons.

2. The Rev. John Grote

The common ground that unites Venn�s views on logic and Marshall�s views onpsychology is to be found in John Grote�s Exploratio philosophica (1865). Grote re-placed William Whewell as Knightbridge Professor of Moral Philosophy in 1855,

and through his efforts the Moral Sciences Tripos was significantly reorganized.

Whewell had initially conceived of a tripos in which history and secular jurispru-

dence were to be harmonized with Anglican moral philosophy.3 Under Grote�s stew-ardship history and jurisprudence were ejected from the tripos, and two new sciences,

mental science (or psychology) and logic, were introduced. From this foundation

Grote proceeded to significantly shift the orientation and emphasis of Cambridge

2 See Maas (1999), p. 597 n. 27, for references.3 See Palfrey (2003). Palfrey notes that for Whewell, in both ethics and in science, there was a reciprocal

dependence between ideal and fact. Thus whilst it is not incorrect to describe Whewell�s philosophy of

science as �Kantian�, as a moralist Whewell was a pre-Kantian (as indeed Maine in his Ancient law pointed

out). Grote�s revision of Whewell�s moral philosophy thus entailed not simply according a new legitimacy

to such �positivist� thinkers as Mill and Bain, but also the rejection of the idea that jurisprudence was of

relevance to moral philosophy. I am indebted to David Palfrey for helping me understand Whewell�s viewsas to the relationship between moral philosophy and law.


philosophy. While his philosophical position was presented as—and in many ways

was—a continuation of Whewell�s Anglican idealism, Grote now emphasized Des-

cartes in place of Kant, and advanced a dualistic conception of the mind and, sub-

sequently, a bifurcated vision of the moral sciences. For Grote the materialist logic

of J. S. Mill, and the associationist psychology of A. Bain, provided credible in-stances of what he regarded as �phenomenological� logic and psychology. Grote

was happy to see such studies both taught and developed within his tripos by other

members of the faculty. He considered his own role, however, to consist in articulat-

ing what he called the �higher philosophy�, or �real logic�. Real logic was developed by

way of a reflection upon the movement of the subjective mind or soul in the processes

by which positive knowledge was advanced.4

Crucially, Grote argued that the positive moral sciences could not stand alone

without the support of real logic, and furthermore that real logic could lead toknowledge of God. Mill�s proposed science of character, for example, was regarded

by Grote as a quite sensible project; but while it �is all very well to know what cir-

cumstances will produce this and that character�,5 it does not take us a step towards

knowing what kind of character we actually want to create by means of any partic-

ular regime of education. In short, �the logic of the moral sciences, or what Mr Mill

considers such, will not at all in the same degree [as the physical sciences] stand alone

without Teleology�.6 Such teleology was, of course, to be provided by real logic. Real

logic began from the introspective observation of self-consciousness, but developedby way of the observation of the meeting of that consciousness with the sensations

generated by way of interaction with the material world. Here Grote�s arguments be-

came almost mystical. He claimed that this meeting of consciousness with sensation

advanced the �Self� into the void of the �non-Self�, and he identified this �non-Self�with God. Hence reflection upon the advance of positive knowledge leads to real

knowledge of God.

This theological dimension of Grote�s philosophy reveals the deeper context that

lies behind Grote�s revision of Whewell�s philosophical legacy. Whewell�s Cambridgecareer can be read as a sustained campaign against philosophical and scientific rad-

icalism, in which Ricardo, Bentham, Babbage and J. S. Mill were each in turn held

up as �godless� and �irreligious� enemies, to be combated by the development of a

nativist Anglican philosophy. But from mid-century onwards Cambridge divines be-

gan to detect that the theological and scientific ground of recent debate had shifted.

Spencer and Huxley were more radical and outspoken opponents of Anglicanism

4 On Grote�s proposed bifurcation of the moral sciences, see especially Grote (1865), pp. ix–xiii, and

Cook (2004). For his discussion of positivist moral science (e.g. Mill), see Grote (1865), pp. 153–200; for

his discussion of Ferrier see pp. 67–80; and for his own relating of self-consciousness to theological

knowledge of God, pp. 87–91. Grote�s revision of Whewell�s philosophy in light of the threat posed by

Mansel led him to argue, firstly, that the �semi-Kantist or Kantiodic doctrine . . . with its almost inevitable

results of notionalism and relativism, does not properly belong to the right proportion of Dr Whewell�sviews� (Grote, 1865, p. 240), and secondly, that, contrary to Whewell�s own insistence, there was as much

of Descartes as of Bacon in Whewell�s Organon.5 Grote (1965), p. 198.6 Ibid., p. 200.


than J. S. Mill had ever been; yet for Cambridge divines the philosophical framework

of the emerging new creed of �agnosticism� was understood to have been derived

from Dean Mansel�s theological rendering of William Hamilton�s philosophy of

the Absolute. Mansel�s theological �relativism� (the term is Grote�s) was designed

to defend orthodox Evangelical Anglicanism from the attacks of liberal theologianssuch as F. D. Maurice and B. Jowett.7 These latter theologians charged that the

Evangelical conception of Divine providence implied a rather unpleasant and even

immoral Deity to be at work in the world. Mansel�s defence, constructed in the terms

of Hamilton�s version of Kantianism, countered with the argument that the finite hu-

man mind could not hope to understand the morality of the Divinity; in other words,

that God was not knowable. But in Cambridge it was perceived that Mansel�s con-clusion destroyed the very foundation of natural theology, and opened the door

to the secularism of the scientific naturalists. As Leslie Stephen would later put it,the �whole substance� of Mansel�s argument �was simply and solely the assertion of

the first principles of Agnosticism�.8

Grote�sExploratio philosophica can in fact be read as, from first to last, an argument

against Mansel�s �relativism�. In so redirecting the underlying target of Cambridge

philosophical thought, Grote was now quite willing to accord a place within his tripos

to the study of those whom he regarded as reasonable positivist thinkers, in particular

Bain andMill. Indeed, given thatMill was known to beworking on an entire book ded-

icated to the refutation of William Hamilton�s philosophy, the old philosophical rad-ical could even appear as a potential ally. The most critical parts of the Exploratio are

therefore directed, not against Mill�s Logic, but against Hamilton�s �notionalism�.9 By�notionalism� Grote meant the tendency to �realize� abstract logical concepts, a ten-

dency which he saw as being at the heart of Hamilton�s (and hence Mansel�s) entirephilosophical endeavour. Against Hamilton�s Kantianism, Grote constructed a vision

of moral science as a two-fold enterprise consisting of, on the one hand, the positive

study ofmaterial logic and psychology, and on the other that reflection upon themove-

ment of consciousness to which he gave the name �real logic�.As young dons in the Cambridge Moral Sciences Tripos, Venn and Marshall can

be seen to have set about the study of these two separate departments of positivist or

material moral science. Here it is important to appreciate that �real logic� combined,

on the idealist side, both logic and psychology; on the materialist side, however,

these became two distinct sciences. Psychology treated of the actual behaviour of

the material mechanisms of the mind, while logic dealt with the set of formal tools

by means of which positivist science was augmented. Venn had apparently already

lost his faith by the time he began teaching for the tripos, while Marshall underwenthis own �crisis of faith� in the midst of his studies in psychology.10 But loss of faith,

7 Hilton (1988), pp. 289–290.8 Quoted in Maurice (1884), Vol. II, p. 328.9 Grote accuses Hamilton of conflating philosophy and phenomenalism and goes so far as to describe

Hamilton�s position as �the master-confusion, the ‘‘temporis partus maximus’’ of mis-psychology� (Grote,

1865, p. 125).10 Venn (ca. 1903).


and rejection of at least some of what Grote meant by �real logic� does not seem to

have altered the way in which both men understood the materialist side of Grote�sbifurcated moral science. In his Logic of chance of 1866, for example, Venn referred

to Grote�s ‘‘admirable and suggestive’’ Exploratio philosophica, and his acknowl-

edged use of Grote�s term �Phenomenalist Logic� as a designation for the �MaterialLogic� practiced by Mill and developed by himself, was evidently intended as a trib-

ute to Grote�s help and influence on his own work.11

3. Venn on logic

In his approach to logic, Venn described himself as a follower of J. S. Mill: �With

what may be called the Materialist view of Logic as opposed to the Formal or Con-ceptualist,—with that which regards it as taking cognisance of laws of things and not

the laws of our minds in thinking about things,—I am in entire accordance�.12 As we

shall see below, this statement from the preface of the 1866 Logic of chance provides

the key to the very different reception of Boole in Cambridge as opposed to London

or Liverpool. In this preface Venn explicitly stated that almost �the only writer to

have expressed a just view of the nature and foundation of the rules of Probability

is Mr. Mill, in his System of logic�. Furthermore, Venn emphasized the divergence

of his own view of probability from that of both De Morgan and Boole, both ofwhom regarded probability �very much from the conceptualist point-of-view�, thatis considering probability to be �concerned with formal inferences in which the pre-

mises are entertained with a conviction short of absolute certainty�. Hence the whole

issue of the quantification of the predicate, which for De Morgan and Jevons pro-

vided the connecting link between logic and probability was for Venn, concerning

the logic of chance at least, immaterial; the logic of probability was a branch of

inductive reasoning and so grounded, not on any supposed laws of uncertain infer-

ence, but rather upon evidence, specifically, statistics.Yet Venn�s rejection of the views of De Morgan demonstrates not only his agree-

ment with Mill, but also his partial allegiance with Grote. To define logic as dealing

with the laws of things not of mind was of course to follow Grote�s distinction be-

tween real and phenomenological logic. For Grote, material logic treated of the for-

mal techniques of scientific inference, material psychology treated of the

phenomenological mind, and real logic with the laws of mental advance; and to

regard material logic as describing the laws of thought was to conflate the laws of

11 Venn (1866), p. 171. A letter from Venn to J. B. Mayor, written shortly after Grote�s death, describedhow this book was �full of memories of our meetings at Trumpington. A good deal of the substance of it

was read there�. The last time that Venn had met with Grote, he recalled, �was to talk with him about one

of the chapters which he had looked over when in type, and the last letter I had from him was on the same

subject; full of sympathy and encouragement, as everything was that came from him� (J. Venn, Letter toJ. B. Mayor, Mayor Papers, 4 November, 1866, B16/135; quoted in Gibbins, 1998, p. 453).12 Venn (1866), p. xii. For a more detailed account of his view on the nature of logic, see Venn�s article inthe first ever issue of Mind, �Consistency and real inference� (Venn, 1876a).


the natural world with the workings of the human mind. Where Grote on this score

accused Hamilton of �notionalism�, that is the �realizing� of abstract logical concepts�,so Venn argued that De Morgan�s whole treatment of the logic of probability rested

on the assumption that the operation of our minds was in harmony with the laws of

nature; an assumption that bordered on what Venn described as the error of �real-ism�.13 Realism, a doctrine �which after being banished elsewhere still manages to lin-

ger in the remote province of probability�, was the �tendency to objectify our

conceptions even in cases where the conceptions had no right to exist at all�.14 Real-

ism was the sin of the conceptualist, and whilst Venn described De Morgan and

Boole as �Conceptualists� in the Logic of chance, in his �Consistency and real infer-

ence� (1876a), published in the first edition of Mind, it was Hamilton and Mansel

who were held up as representatives of the Conceptualist point of view.15 In Venn�sview, De Morgan�s attempt to quantify the gradations of belief should not be con-sidered as an exercise in logic; to engage in such an exercise was �to trespass into

the province of Psychology�.16

Given his rejection of the view that logic treats of the laws of thought not of

things, it would be expected that Venn, like Mill, would pay no attention to Boole�sbook The laws of thought. The fact is, however, that Boole�s system seems to have

occupied his attention, both as a lecturer and a writer, more than any other branch

of logic. As Venn later recalled in an autobiographical manuscript, in 1861 he had

been offered the post of catechist at his old Cambridge college Gonville and Cauis,with the duty of �teaching logic and political economy to such of the Indian Civil Ser-

vice candidates as might be in residence:—the Moral Science Tripos was scarcely ta-

ken into account at this time�.17 It was, according to these autobiographical notes, in

1863 that he began work on The logic of chance, but it was already in 1861, having

13 For Venn�s criticisms of De Morgan, see Venn (1866), pp. 60–75 (especially pp. 72–73). It must be

emphasized here that Venn�s allegiance with Grote was only partial. That is to say, while Venn and Grote

could agree as to the nature of material logic, and could also agree as to the sins of Hamilton and De

Morgan, Venn would most certainly have regarded Grote�s real logic as an instance, albeit a sophisticated

one, of realism. We might note also that Grote regarded Mill as at times guilty of �notionalism�, althoughon this point, at least with regard to probability, it seems that Venn followed Grote. That is to say, Venn

revised Mill�s notion of natural kinds as the basis of probability, insisting on the transitory nature of any

form in a world governed by evolution and historical change. On �realism� in probability, and Venn�sevolutionary logic of chance see Kilinc (1999, 2000, 2001).14 Venn (1866), p. 36.15 It is to be noted that, in setting down the Conceptualist position in this article in Mind, Venn observed

that �in a question of consistency it is, of course, to Mansel rather than to Hamilton that we turn� (astatement, we may note, that is very much in accord with Grote�s complaints in the Exploratio as to the

utterly confusing nature of Hamilton�s writing). Venn (1876a), p. 45. On the relationship between

Hamilton and De Morgan see Maas (1999), pp. 598–603. For a contextual account of De Morgan�s secularapproach to mathematics, see Richards (2002).16 Venn (1866), p. 104.17 Venn (ca. 1903). Venn added: �Of course the device was not new then, but it was so obviously

representative of the way in which any one who approached the subject from the mathematical side, would

attempt to visualise propositions, that it was forced upon me almost at once�. In general, Venn�s work on

symbolic logic struck contemporary logicians by its emphasis upon historical precursors (see for example

the review of Venn�s Symbolic logic, Munro, 1881, p. 574).


been offered the post of catechist, and starting to prepare his lectures, that he �first hitupon the diagrammatical device of representing propositions by inclusive and exclu-

sive circles�. But Boole�s system proved a far harder nut to crack than the logic of

probability. Venn had in fact first become acquainted with The laws of thought in

1858, through his Cambridge tutor Todhunter: �I read the book with care, and couldfollow the mere mechanism of his processes. But to rationalise them was a far other

business, and I did not see my way to do this till after the third or fourth study of

the book, in 1878–9�. Venn appears to have lectured on Boole�s logic consistently

over these years, publishing various articles on the subject in Mind and other jour-

nals, and eventually publishing his own book on Boole�s system, Symbolic logic, in

1881.18

What, then, did a Materialist logician and follower of J. S. Mill have to say about

Boole�s system of logic? The title of Venn�s book on Boole�s logic is enough to informus that, where Boole himself, as did Jevons after him, saw his system as describing

the operations of the human mind, Venn viewed Boole as having simply contributed

a symbolic logical calculus to the study of formal logic. Formal logic, for Venn, had

previously been constituted by the Aristotelian syllogism (which he referred to as �theCommon Logic�). Symbolic logic was a development, or rather a generalization of,

the Common Logic (albeit �not a generalisation of the Common Logic in all direc-

tions alike�).19 In other words, symbolic logic was a generalisation, �of which syllo-

gism is a special case�. Moreover, the common logic of the syllogism should �be nomore regarded as superseded by the generalisations of the Symbolic System than

is Euclid by those of Analytical Geometry�.20 Thus where De Morgan, and following

him Jevons, regarded Boole�s system as superseding the syllogism, and where Boole

and Jevons regarded this logic as describing the operations of the mind, Venn pre-

sented it as a purely �formal science� with no substantive implications for either

the problems of induction, the principles of science or a model of the mind.

Venn was also at pains to stress the distance between symbolic logic and mathe-

matics. As Maas points out, through his �true revolution� in logic, that is quantifica-tion of the predicate, De Morgan was able to connect logic and probability. The

reversibility of the copula established by De Morgan suggested to Boole its expres-

sion by the mathematical sign of equation �=�; as Maas puts it, �Boole�s logical system

18 Venn published an article on �Boole�s logical system� in Mind in 1876 (Venn, 1876b), which made

reference to Jevons�s work on the subject, and also gave an example of Boole�s system by translating into

symbolic notation Senior�s definition of wealth; he reviewed Alexander MacFarlane�s Principles of the

algebra of logic in Mind in 1879 (Venn, 1879); and in the Philosophical Magazine and Journal of Science of

1880 he wrote �On the diagrammatic and mechanical representations of propositions and reasonings�(Venn, 1880), this latter is discussed in the main text below.19 Venn (1894), p. 35 and p. xv. It should be noted that while Maas appears to regard formal logic as

synonymous with Boolean logic, and its emergence therefore defined purely by the reception of Boole�stheory, for Venn at least the term �formal logic� had a much wider reference: �Whately, for instance, is a

thorough formalist� (Venn, 1876a, p. 47). Note also that Grote characterized J. S. Mill�s System of logic, as

�a Phenomenalist Logic, with a starting point from the Aristotelian or formal Logic� (Grote, 1865, p. 157).

In short, �formal logic� before Boole was, at least in Cambridge, identified with the Aristotelian syllogism.20 Venn (1894), p. xxvii.


essentially reduced logic to a branch of mathematics�.21 As noted above, because

Venn viewed probability as a branch of inductive logic, he regarded the quantifica-

tion of the predicate as irrelevant to the logic of chance. Further, in the preface to

The logic of chance Venn took care to declare as �erroneous� the �opinion that Prob-

ability, instead of being a branch of the general science of evidence which happens tomake much use of mathematics, is a portion of mathematics�. These views provide

the background to why, nearly three decades later, in the preface to the second edi-

tion of his Symbolic logic, Venn explained how an �explanation of the principles of

the logical calculus, in entire independence of those of the mathematical calculus,

is one of the main objects which I have had before me in writing this book�.22 For

Venn, the use of symbols such as �+�, �-�, and the like resulted from the �accidental�fact that, to date, symbolic languages had been developed principally by mathema-

ticians.23 In fact, he argued, symbolic language and mathematics may be regarded �asbeing branches of one language of symbols which possess some, though very few,

laws of combination in common�.24

In keeping with the Cambridge tradition of preferring visual to symbolic represen-

tation, Venn�s interpretation of Boole�s system extensively utilized diagrams. This

preference, at least as it was justified by Venn, owed less to William Whewell�s ide-alistic ideas on the nature of a liberal education, and more to a desire to provide

proper demonstration when teaching moral science to Cambridge students. As I

have argued elsewhere, Venn evidently viewed his diagrammatic presentation ofsymbolic logic as providing for the moral sciences lecture room what the Cavendish

�demonstrators� were able to provide for students reading mathematics and natural

sciences. Because each form of propositional statement �has a corresponding dia-

gram which illustrates its exact signification with the demonstrative power of an ac-

tual experiment�, therefore, if �any sluggish imagination did not at once realize that

from ‘‘All A is some B’’, ‘‘No B is any C,’’ we could infer that ‘‘No A is any C,’’ he

has only to trace the circles, and he sees it as clearly as anyone sees the results of a

physical experiment�.25 Thus if the distinctive feature of Jevons�s version of Boole�ssystem was a mechanical representation—the logical abacus—the distinctive feature

of Venn�s version of Boole was diagrammatic representation.

21 Mass (1999), pp. 598–599.22 Venn (1894), pp. xiii–xiv. Venn further paid tribute to J. N. Keynes�s Formal logic for demonstrating

that �the most complicated problems can be solved with much less of the symbolic apparatus than had

previously been supposed�. In his review of Keynes�s work Venn described it as �a decided advance� overJevons�s Studies in deductive logic (Venn, 1884, p. 301).23 Venn (1894), p. ix.24 Ibid., p. xv. Venn states that Boole�s own conception of mathematics was very �broad�, basicallyincluding any language of pure symbols.25 Venn (1880a), p. 344. See my �Late Victorian visual reasoning� (forthcoming in the British Journal for

the History of Science) for further discussion. It is worth noting, in this context, Charles Dodgson�s small

book on symbolic logic (Dodgson, 1896) in which a square grid is used to represent syllogistic argument.

Dodgson regarded his visual system as superior to that of Venn, not because of the differing logical system

represented, but because his grid method allowed the addition of ever more propositions to the argument

without the diagrammatic representation becoming too cluttered to be useful.


Given that, in Maas�s view, Jevons�s logical abacus constitutes the defining mo-

ment of a new discourse on mechanical reasoning, it is interesting to note Venn�s takeon logical machines. In an article of 1880 entitled �On the diagrammatic and mechan-

ical representations of propositions and reasonings�, by far the larger first part of

which was devoted to the former, Venn noted at the close of his essay how such dia-grammatical methods as he had treated �readily lend themselves to mechanical per-

formance�, but immediately commented that he himself had �no high estimate of

what are sometimes called logical machines�. One reason for this was the practical

consideration that intricate logical calculations are necessary in life only within the

lecture room; hence logical machines �stand in marked contrast with those of math-

ematics, where economical devices of any kind may subserve a really useful purpose

by enabling us to avoid otherwise inevitable labour�. In other words, Venn did not so

much deny Jevons�s equation of logical thought with routine labour, and declaredthat such labour was not a part of ordinary life.26 Venn�s second point, however,

did concern the nature of the labour involved in logical work. Such labour, he stated,

involves four �tolerably distinct steps�: the statement of the data in accurate logical

language, the putting of these statements into a form fit for an �engine to work with�,thirdly the combination or further treatment of our premises after such a reduction,

and finally the interpretation of the results. In Venn�s view, only the third of these

steps could be aided by an engine, and so it �seems doubtful� whether any such con-

trivance as Jevons�s logical abacus �really deserves the name of a logical engine�. Log-ical reasoning, for Venn, was thus more than a matter of operating on symbols, it

was an act of the mind that involved �judgment�, �sagacity�, �skill� and

�interpretation�.27

In conclusion we may state that if Jevons considered Boole�s logical system as a

contribution to our knowledge of the mind, this was not at all how Boole was read

in Cambridge. Venn�s work as a logician may be said to have began with his reading

of Boole�s logic, and the interpretation of this logical system occupied his attention,

albeit not exclusively, for the next two decades. At no point, however, did Venn everregard symbolic logic as providing insight into the nature of the mind. This negative

conclusion, when read in light of Grote�s philosophical legacy, provides the contex-

tual clue as to why, when in the late 1860s, Venn�s colleague in the moral sciences,

Alfred Marshall, became interested in constructing a mechanical model of the mind,

it apparently never even occurred to him to look to Boole�s work for guidance. In

terms of the disciplinary divisions of the moral sciences in Cambridge at this period,

both Venn and Marshall accepted a clear cut distinction between logic and psychol-

ogy. This division, if supported by Grote, was ultimately inherited from J. S. Mill.Logic dealt with how we know facts and things, psychology dealt with the mind

in and of itself. Venn, as a logician, was interested in Boole. Marshall, in the early

26 Here Venn may be observed to have been articulating the Cambridge concern with �ordinary language�,a concern shared by Marshall and to be found in several later Cambridge philosophers such as Moore.

This emphasis upon ordinary language was a further aspect of Grote�s legacy (see Gibbins, 1998, for a

discussion of Grote and �ordinary language�).27 Venn (1880b), pp. 15–16.


stage of his academic career during which he studied psychology, was neither inter-

ested in logic in general, nor Boole in particular; as a neophyte psychologist Mar-

shall�s resources were rather Bain, Carpenter, and Babbage.

4. Marshall�s machine

Our evidence of Marshall�s early development of a theory of psychology comes

primarily from four surviving manuscripts, almost certainly written in the late

1860s to be presented to the Grote Club, the weekly gathering in Cambridge of those

either lecturing on or otherwise interested in the moral sciences. The first three of

these Grote Club papers constitute the core of our information; taken together they

constitute a continuous project, intended to clear methodological and philosophicalground, and then begin the development of a �general theory of psychology . . . capa-ble of being developed into the true one�.28

The first two papers rehearse familiar arguments from Mill, Spencer, Hamilton,

Mansel and Bain. The second paper, �Ferrier�s proposition one� argues that no con-

ceivable mechanical analogy can account for self-consciousness. In other words,

Marshall was taking his cue from Grote�s Exploratio; and not simply in his defence

of Ferrier�s idealist postulate, for the range of authorities discussed in these two pa-

pers is precisely the same spectrum of thinkers whose views Grote held up for exam-ination in the Exploratio. In his third paper, �Ye machine�, Marshall turned to Bain�sassociationist psychology in order to construct a hypothetical thinking machine.

There is a common misconception amongst historians of economics that in this third

paper Marshall was explicitly rejecting Grote�s philosophy.29 A close reading of the

second and third papers, however, reveals that this was far from the case. These two

papers are not contradictory; rather, they mutually delineate a division of mental la-

bour, between spiritual and mechanical agencies. This is indicated in the several ref-

erences to �Ye machine� in �Ferrier�s proposition one�, and by the fact that the twopapers were clearly read at two consecutive weekly meetings of what was called

the Grote Club (a fact which hardly supports the claim that Marshall changed his

views between his second and third paper).30 In other words, Marshall�s �Ye machine�is to be understood as an attempt to develop the materialist side of Grote�sbifurcated vision of psychology, and this attempt went hand-in-hand with a recogni-

28 Raffaelli (1994), p. 67.29 This view was first suggested by Raffaelli in his initial commentaries upon Marshall�s four papers

(Raffaelli, 1994, and see also Raffaelli, 1991). Nevertheless, he here stated clearly that Marshall never

explicitly abandoned the postulate of self-consciousness, and in his later work (e.g. Raffaelli, 1995).

Raffaelli has moved away from this position; emphasizing now, in addition to mechanical routines, also

the �spontaneous� and �creative� dimension of Marshall�s model of the mind. In Cook (2004) I have shown

the extent to which Marshall�s writings on education in the early 1870s do not support the view of

Marshall as a materialist, and indeed anyone who consults Marshall�s early notes on Hegel (ca. 1871–1873;

to be found in the Marshall Library, Cambridge) cannot fail to realize the extent to which idealism in some

form at least remained an entrenched part of Marshall�s thought.30 Raffaelli (1994), pp. 57, 64–65, 67.


tion of the validity of the idealist approach to the mind in terms of self-

consciousness.

Marshall�s hypothetical machine is able to receive sensations from the outer

world, associate those sensations by way of connecting rotating wheels correspond-

ing to such associations, and follow trains of ideas of those associations in a circuitwhich leads from initial idea of incoming sensation through to a subsequent idea of

action, upon which the �body� of the machine then acts. Tiziano Raffaelli has pro-

vided an almost exhaustive account of the resources which Marshall used in his third

Grote Club paper.31 In addition to the associationist psychology of Alexander Bain,

Raffaelli also points to the ways in which the physiological research of William Car-

penter can be seen to inform Marshall�s model. Marshall in fact labels the basic cir-

cuit of the �brain� of his machine, its �cerebrum�, and the higher level circuit that we

shall discuss shortly, the �cerebellum�, and his description of voluntary action interms of these circuits is from one point of view an attempt to extend Carpenter�saccount of reflex or involuntary action to �higher levels� of human behaviour. But

Marshall�s account of the relationship between his machine�s �cerebrum� and �cerebel-lum� in fact reveals a crucial, if hitherto little noted, third resource for Marshall�s �Ye

machine�: the calculating engines of Charles Babbage.32 To appreciate the signifi-

cance of Babbage�s engines to Marshall�s model of the mind it is however necessary

to examine more closely the model set out in �Ye machine�.The project of �Ye machine� had in fact been announced in the first page of Mar-

shall�s previous manuscript, �Ferrier�s proposition one�. Following an initial dis-

claimer, Marshall had begun this earlier paper by announcing �I wish to

investigate what operations can, and what cannot, be performed by pure mecha-

nism—mechanism, that is, such as is the subject of the daily occupation of the prac-

tical Engineer�. He then went on to explain that there is �no class of actions

performed by brute animals, which we cannot conceive to be governed and directed

by purely mechanical agencies; while there is no race of men which is not known to

perform actions which are incapable of being referred to such an origin�.33 The taskof �Ferrier�s proposition one� was to demonstrate this latter statement, that is, the

irreducibility of self-consciousness to mechanical agency. �Ye machine�, then, consistsof an attempt to describe just how the actions of brute animals can be explained in

terms of mechanical agencies, and to specify just what actions of humans are not

attributable to self-consciousness and so may also be explained in terms of mechan-

ical agency. Thus in the first part of �Ye machine� Marshall proceeded to outline the

workings of a machine that would be capable of performing all the actions of �bruteanimals�. This initial machine contains only a �cerebrum�. By then adding a �cerebel-lum� to the machine Marshall was able to delineate those higher level human activ-

ities which, whilst still below the highest levels of human agency (that is those

31 Raffaelli (1994); see also Raffaelli (1991).32 Groenewegen notes the few explicit references to Babbage in �Ye machine� (Groenewegen, 1995, p. 120)

but does not comment upon them. Raffaelli however goes considerably further, but does not arrive at the

precise relationship between the Analytical Engine and Marshall�s machine (Raffaelli, 2003, pp. 25–26).33 Raffaelli (1994), p. 57.


activities that could only be attributed to the activity of self-consciousness), were be-

yond the range of mere brutes, yet nevertheless explicable in terms of mechanism.

Marshall begins his paper �Ye machine� by describing a machine consisting of �anindefinite number of wheels�. These wheels are connected by physical bands, and the

interactions of which, one with another, and of the whole with the outer world con-stitute a circuit which proceeds from sensation, to idea of sensation, to idea of action,

to action. This circuit is called the machine�s �cerebrum�. When any two wheels that

correspond to ideas are moving together they become associated one with the other

because �the Machine itself connects them by a light band�.34 In this way the machine

can come to �know� that any one particular action will alter the external world in the

same manner, and thus this initial circuit is seen to generate �expectations� (that isideas of sensation that will follow from a particular action). After classifying various

states of the environment and resulting sensations as either �painful� or �pleasurable�Marshall introduces the thought that the machine might find itself in a painful situ-

ation such that no known action will alter the world in a way that is pleasurable. The

result is that certain wheels of the machine continue to rotate until by some chance

another wheel is set in motion, that wheel corresponding to some idea of action, the

consequent performance resulting from which so alters the external world as to make

the initially desired action possible. What Marshall has described in this first part of

his paper is the mind of a �brute�, capable of expectation, and even of low level voli-

tion, and further capable of evolving what Marshall calls �contrivances� or �the germsof instinct� according to a form of Darwinian evolution.35

It is at this point in his manuscript, as he moves from brute to human intelligence,

that Marshall introduces a second level to his machine. With but one circuit Mar-

shall�s machine can form �expectations�, but it cannot �anticipate, in any sense, or rep-

resent to itself beforehand the consequences of its actions* so as to readjust them to

the circumstances�.36 Marshall therefore announces that he will now enable his ma-

chine to anticipate the future, and he proceeds to do so by introducing a second cir-

cuit, the �cerebellum� of the machine. This cerebellum also consists of wheels andbands and it replicates the lower level cerebrum such that each lower level idea

has a corresponding higher level idea. The crucial difference between the circuits,

however, is that the turning of the wheels in the cerebellum allows the machine to

follow through in thought the consequences of any actual action exactly correspond-

ing to that which would have been produced if the action* had been carried out and

34 Repetition of this double motion tightens the band. This is the association of contiguity; wheels can

also be associated due to similarity. These two kinds of mechanical connection are analogies for the

principles of association in Bain�s association psychology.35 Raffaelli (1994), pp. 72–77. Immediately after this mention of �instinct� Marshall offers the thought that

his machine, �like Paley�s watch�, might make others like itself, thus giving rise to �hereditary and

accumulated instincts�. Due to accidental circumstances the �descendents�, however, would vary slightly,

and those most suited to their environment would survive longer: �The principle of natural selection, whichinvolves only purely mechanical agencies, would thus be in full operation� (ibid., pp. 76–77). For a useful

discussion of the role of �contrivances� in Marshall�s thought, see Raffaelli (1991), pp. 41–42.36 Raffaelli (1994), p. 77. Throughout his manuscript Marshall marks various terms (in this case �action�)to indicate that he is referring to a machine and not a real human being.


the corresponding change in the environment had produced its effect on the sensa-

tions*. �In this way�, concludes Marshall, �the Machine will have gone through,

whether rightly or wrongly, what I shall call a chain of reasoning ** with regard

to the effects of any actions�.37 This higher level circuit to a large measure replaces

the chance generation of contrivances, which is Marshall�s way of saying that in hu-man beings a higher level of reasoning takes the place of instincts.

What have these distinctions, between mechanical �cerebrum� and �cerebellum�, be-tween, that is, mechanical analogies of animal and human intelligence, to do with the

calculating engines of Charles Babbage? In a nutshell, Marshall�s two-circuit ma-

chine appears to be modeled upon the ability of Babbage�s Analytical Engine to

�eat its own tail�. Both practical engine and psychological model of the human ma-

chine are equipped with the property of �foresight�, and in both cases the mechanism

of such foresight is the same. Using more recent terminology, we could say that bothcalculating engine and two-level psychological model work in terms of a �feedback�mechanism, such that standard operations give rise to subroutines that, depending

upon where they lead, feed back into, and in doing so redirect to the required extent,

the initial operation.

In his autobiography Babbage emphasized how the Analytical Engine was de-

signed as an advance upon the earlier Difference Engine precisely because the new

engine would have the ability to anticipate the future: �Nothing but teaching the En-

gine to foresee and then to act upon that foresight could ever lead me to the object Idesired�.38 This foresight was to be the product of precisely the same two-level mech-

anism that Marshall would subsequently introduce into his model of the human

mind. Babbage initially planned that the new engine would consist of two main units,

a store and a mill. In the store were held the numbers derived from the mill, while in

the mill, using numbers brought from the store, were carried out the various numer-

ical operations such as addition, subtraction, and so on.39 This division of calculat-

ing labour had vast potential, for the results of calculations in the mill could be fed

back into the beginning of new calculations—the �engine eating its own tail�. In theAnalytical Engine this feature was, after 1836, developed by way of programmable

cards. Babbage now drew upon the principle of the Jacquard loom, in which the pat-

terns woven were controlled by the patterns of holes in a set of punched cards strung

together in the sequence in which they were to be used. The key here is that the en-

gine can print new cards as it goes along, and new cards can in turn instruct the en-

gine to print other new cards. Marshall�s two levels of circuit can be seen to perform,

in theory, exactly the same division of labour that Babbage�s engine was designed to

perform in practice.

37 Ibid., pp. 78, 79 (emphasis in original; the double �**� indicates that it is the second circuit that is being

referred to).38 Babbage (1864), p. 114; see also pp. 59–63, 114–116.39 Hyman notes that Babbage was here making an analogy with the cotton mills: �numbers were held in

store, like materials in the storehouse, until they were required for processing in the mill or dispatched to

the customer� (Hyman, 1982, pp. 164–173).


It is therefore no coincidence that directly after Marshall has introduced this sec-

ond circuit, and outlined its working, he makes reference to Babbage�s autobiogra-phy. Having established the structure of his two-circuit mechanical model of human

intelligence, Marshall now wants to put it into the world and watch it perform. He

therefore turns his machine loose at the chess-board, envisaging his machine as anexample of a chess automaton of the kind �proposed by Babbage, though he does

not give any indication of the way in which it could be made�.40 The subsequent dis-cussion is particularly interesting. Marshall imagines a machine that could always

play a winning hand of chess:

40 Ra41 Ra

passag42 Sch

Analyt

in his 1

the pro

calcula

Engine

say, th

numbe

add tw

time�.43 Bab

If the wheels of the machine be sufficiently numerous, it must of course have infi-

nite power. And if its character is such that distance does not tell at all (i.e. if the

tightenings . . . take place in an infinitely short space of time), its desire* to win

the game would always prevail over every other desire*; and it would always win,

if it were possible to do so under the given circumstances.41

Now, if we turn to Babbage�s autobiography, and examine Babbage�s discussionof the difficulties he faced in providing the Analytical Engine with foresight, we find

that in the above passage Marshall has curiously inverted Babbage�s practical solu-tion. In order to redesign the original Difference Engine in order to be able to foresee

the future Babbage was forced to dramatically improve the calculating efficiency of

the engine.42 Babbage�s solution was in fact precisely the two-level programming de-scribed above, for by means of a division of labour—for example between store and

mill—and a connecting link between these two parts of the engine, any particular cal-

culation can be broken down into component parts that are more easily dealt with by

the machine�s parts. In his autobiography Babbage explained how this solution

translated from the �infinity of space, which was required by the conditions of the

problem, into the infinity of time�. In the programmable cards version of the Analyt-

ical Engine, for example, the �infinity of time� would be occupied by printing cards

for the mill and in the printer itself, however long it be used, �the force to be exertedalways remains the same�.43 In describing an ideal chess player, Marshall can be seen

to have reversed Babbage�s translation of space into time.

ffaelli (1994), p. 89; see Babbage (1864), pp. 465–491.

ffaelli (1994), p. 81; see Raffaelli (1991), pp. 29–30, for a useful commentary on other aspects of this

e.

affer (1994). As recent commentators have noted (e.g. Hyman, 1982, pp. 164–173), this aspect of the

ical Engine was already prefigured in the Difference Engine; a fact which W. K. Clifford emphasized

872 talk on Babbage�s Engines (see Clifford, ca. 1872). Essentially, in both engines Babbage faced

blem of having to design his engine such that a necessarily finite number of wheels could perform

tions involving a potentially unlimited series of numbers. This solution embodied in the Analytical

was an advance upon the feature of the original Difference Engine whereby a connection between,

e ninth figure wheel and the difference wheel would cause the difference wheel to turn once the

r one hundred million was arrived at—from originally adding ones the machine might now begin to

os. In Clifford�s words, Babbage�s machine �possesses the power of changing its law at a prearranged

bage (1864), pp. 123–129.


Marshall�s word choice has had the perhaps rather predictable effect of sowing

confusion in the minds of early twentieth-first century commentators upon �Ye ma-

chine�; yet not only is his meaning really quite simple, but also its obvious connection

to Babbage�s discussion relatively straightforward.44 In his autobiography Babbage

was describing how he had solved a practical engineering problem; in �Ye machine�Marshall was describing a hypothetical mechanical model of the human mind. The

workings of the two machines were indeed similar, but the contrivances developed by

human design were necessary because of the distinctly crude form of material that

the human designer had to work with; crude, that is, in comparison to the material

organs that had naturally evolved within the human body. Thus while in the work-

shop it was possible to connect together only a finite number of wheels, within the

human body problems of space were unimportant; as Marshall�s close friend of this

period, W. K. Clifford, wrote with regard to human voluntary action, within the hu-man nervous system there �seems plenty of room for the requisite mechanism on the

physical side�.45 Again, in �Ye machine� Marshall used the analogy of physical bands

to describe the connections between the various wheels of the mechanical �brain�.Such bands were of course an analogy for nerves; and if Helmholtz had recently

demonstrated that nervous transmission was not instantaneous, nevertheless, such

human �bands� could still be regarded by Marshall as tightening �in an infinitely short

space of time�.46

In short, because Marshall�s concern was not with designing a practical calculat-ing machine, but with using the mechanisms of practical engineering in order to out-

line in theory a mechanical psychology, he was able to reverse the conditions of

Babbage�s practical problem in order to arrive at an ideal limit of mechanical intel-

ligence—a machine with almost infinite wheels and instantaneous connections be-

tween such wheels. The description of a machine with infinite wheels is in fact the

logical limit of Marshall�s project. In �Ferrier�s proposition one� Marshall had drawn

a distinction between mechanical action, and action that manifested self-conscious-

ness. In �Ye machine� Marshall proceeded to work out the different levels and poten-tial of a mechanical intelligence. From the lower level brutes, equipped with but one

mental circuit, Marshall proceeded to move to humans, whose two level circuits

operated in the same way as Babbage�s Analytical Engine. Finally, Marshall looked

to the most developed form such a human machine could take, where the number of

�wheels� and �bands� has no limit.47 Such an ideal human-machine could always play

a winning hand of chess; but beyond this it could not go; and by implication, beyond

this point self-consciousness must take over from mechanical agency.

44 See, for example, Mirowski (2002), pp. 41–42, for a failure to grasp Marshall�s meaning.45 Clifford (1879), Vol. II, p. 156; emphasis added.46 On the standard view of nervous transmission as instantaneous, see Morus (2000), pp. 456–458.47 It is therefore not accidental that directly following the discussion of �Babbage�s chess player� Marshall

proceeds to comments upon the fact that whereas his machine can engage upon several trains of thought at

the same time, humans can follow but one. Following this brief shift of focus and discussion of a human

mind, Marshall is now, in other words, in the process of bringing the focus of his paper back to his

machine.


John Venn, it will be recalled, would describe the limitations of any �logical ma-

chine�. For Venn, such an external contrivance could indeed engage in the combina-

tion of initial premises, but was no help at all in terms of those acts of the mind

involving �judgment�, �sagacity�, �skill� and �interpretation�. Marshall�s model of

mechanical intelligence showed that some—but by no means all—judgments couldbe conceived of in mechanical terms, and, in terms of the build up of routine circuits,

a mechanical model could also account for skill. Thus a mechanical mind, operating

a logical machine could indeed go some steps towards completing a circuit of purely

mechanical thought. Nevertheless, purely mechanical agencies would come unstuck

whenever such logical work called for either �sagacity� or �interpretation�. In other

words, while members of the Cambridge Moral Sciences Tripos were by no means

oblivious to either the work of Boole or of Babbage, and in the case of Marshall

at least, were by no means uninterested in exploring the nature of mechanical reason-ing, their approach to such matters was quite distinct from that taken by Jevons, and

their conclusions as to the significance of mechanical reasoning were not only con-

ducted upon quite different lines (psychological routines rather than logical opera-

tion), but were also a good deal more qualified.

5. Conclusion

Maas regards Jevons�s conception of the mind as mechanism as marking a

�watershed� between Mill and the British economic science of the later nineteenth

century. With regard to identifying the pivotal point on which Jevons broke with

J. S. Mill, this is surely correct. But although the main focus of his arguments con-

cern Jevons, it is nevertheless clear that Maas considers Jevons to have inaugurated a

general revolution in political economy. �For Edgeworth and then, shortly after, for

Marshall,� he writes, �it was completely unproblematical to speak about this agent

[economic man] as a machine�.48 But with regard to Marshall at least, the situationis not in fact quite so straightforward. At first sight the very existence of a psycho-

logical paper by Marshall entitled �Ye machine� suggests that Marshall too had

crossed the same ontological bridge as Jevons, and of course to some degree he

had indeed done so. Nevertheless, not only was Marshall far more circumspect than

Jevons as to the domain of human thought and activity that could fall under the

category of mechanical reasoning, but furthermore the two men actually attached

quite distinct meanings to the term �mechanical� when applied to intelligence.

That Marshall took a different route from Jevons with regard to his conception ofmechanical intelligence followed, as this paper has shown, from his initial acceptance

of the philosophical legacy that Grote bequeathed to the Cambridge Moral Sciences

Tripos. Grote not only insisted upon the limitations of any purely materialist ap-

proach to mental science, but also defined the relationship between materialist logic

and psychology in a manner that, whilst wholly compatible with the approaches of

48 Maas (1999), pp. 590, 616.


Mill and Bain, was wholly incompatible with the approaches of De Morgan, Boole

and Jevons. Both Marshall and Venn followed Grote�s definition and delineation of

the materialist branches of mental science and so, to this extent, their approaches to

their respective disciplines are complementary, and in both cases worked to preclude

the kind of relationship between mind and machine upon which Jevons built his rev-olution in logic and political economy. It is thus not surprising to find, in Marshall�spersonal copy of Jevons�s The theory of political economy (1871) the following anno-

tation: �Mill�s language is horribly slipshod but there is nothing stated in this account

which Mill does not state in some form or other at some part of his account�.49 It wouldseem extremely unlikely that Venn, who it will be recalled had begun his career as a

moral scientist lecturing on political economy as well as logic, would have dissented

from Marshall�s opinion.Where Venn and Marshall diverged, however, and therefore where we reach the

limits of fruitful comparison between their respective views on logic and psychology

with regard to Marshall�s later political economy, is in the philosophical ramifica-

tions of their loss of religious faith. As we have seen, for Grote �real logic� providedboth a means of knowing the nature of God, and an epistemological ground for our

positive claims to knowledge. An agnostic position was clearly incompatible with an

acceptance of the theological dimension of �real logic�, and it seems clear that for

both Venn and Marshall it also entailed a rejection of the epistemological dimension

as well. In other words, both of these two moral scientists accepted Grote�s demar-cation and definition of materialist moral science, but rejected his particular idealist

epistemology. But at this point the thought of Venn and Marshall diverged. In reject-

ing �real logic�, Venn was content to occupy the position of a moderate skeptic, con-

vinced that ultimately our knowledge rests upon no firm foundation, and that even

the universal categories of formal logic are suspect in an evolutionary world.50 Mar-

shall, by contrast, continued to search for an alternative ground for our moral and

intellectual convictions and ideas; and his subsequent explorations of the work of

Spencer and Hegel took him into regions that were suspect to Venn, as indeed theywere also to Henry Sidgwick. Ultimately, Marshall�s development of economic sci-

ence can only be fully explained when the philosophical dimension of his evolution-

ary thought is taken into account. Here, of course, Marshall�s economics departed

significantly from that of Jevons. But although Marshall�s evolutionary economics

was developed by way of his reading of Spencer and Hegel, nevertheless its founda-

tion lay in his early biological rendering of Babbage�s calculating engines.

Acknowledgements

I would like to thank David Palfrey and Harro Maas for instructive comments on

earlier drafts of this paper.

49 Jevons (1871), p. 102 (Marshall�s personal copy, Marshall Archive, Marshall Library, Cambridge).50 On Venn�s �historicism� see Kilinc (1999).


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