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The Origins of Wittgenstein's VerificationismAuthor(s): Michael WrigleySource: Synthese , Vol. 78, No. 3 (Mar., 1989), pp. 265-290Published by: SpringerStable URL: http://www.jstor.org/stable/20116622Accessed: 21-05-2016 19:37 UTC

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MICH EL WRIGLEY

THE ORIGINS OF WITTGENSTEINS

VERIFICATIONISM

ABSTRACT. The question is raised of the source of the extreme verificationist views

which Wittgenstein put forward immediately after his return to philosophy in 1929. Since

these views appear to be radically different from the ideas put forward in the Tractatus

some explanation of this dramatic new turn in Wittgenstein's thought certainly seems to

be called for. Wittgenstein's very low level of interest in philosophy between 1918 and

shortly before his return to philosophy is documented. Attention then focuses on the

crucial period immediately before Wittgenstein's return to Cambridge, and it is shown

that in this period he encountered only two new philosophical influences. These were the

ideas of Brouwer and the ideas of the Vienna Circle. Each of these is examined and

neither is found capable of providing an explanation of the source of Wittgenstein's

verificationism. This leads to a reconsideration of the underlying assumption that

Wittgenstein's verificationism does represent the radical departure from the ideas of the

Tractatus which it appears to. It is argued that the only way we can account for

Wittgenstein's evident approval of the reading of the Tractatus which he must have

encountered in his meetings with members of the Vienna Circle is by concluding that,

far from being incompatible with his earlier ideas, some form of verificationism must

always have been implicit in the Tractatus.

Few positions seem further removed from the ideas of the later

Wittgenstein than the verificationist theory of meaning. Indeed if there

is one position which the later Wittgenstein would have regarded as

committing about every possible philosophical mistake this is surely it.

So it comes as something of a surprise to discover that in the period

immediately after his return to philosophy in 1929 Wittgenstein him

self held views about the relation of meaning and verification which

could have come straight out of the writings of the Vienna Circle. Yet

even the most cursory examination of the texts which he wrote in the

early Thirties leaves little room for doubt that this was indeed the

case, and that at that time Wittgenstein was whole-heartedly com

mitted to a verificationism of the most extreme kind.

1. THE IMPORTANCE OF WITTGENSTEIN'S VERIFICATIONISM

Not surprisingly it did not take Wittgenstein long to appreciate the

implausibility of this position and his period of radical verificationism

was as short-lived as it was extreme. Nonetheless the fact that Witt

Synthese 78: 265-290, 1989.

? 1989 Kluwer Academic Publishers. Printed in the Netherlands.


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MICH EL WRIGLEY

genstein accepted such views, even if only very briefly, raises one very

important question. Why did he ever accept them in the first place?

This question needs to be answered not merely because it would be

interesting to know what it was that attracted Wittgenstein to such

manifestly implausible views, but, more importantly, because the views

he had held before adopting these views appear to have been

diametrically opposed to any form of verificationism. Certainly there is

no explicit reference to verificationism in the Tractatus, and one of the

principal conclusions of recent work on the Tractatus has been that

this is no accident, since any form of verificationism is incompatible

with some of the most fundamental ideas of the Tractatus. If this is

right then Wittgenstein's rejection of his earlier view of meaning in

favour of verificationism marks nothing less than one of the crucial

turning points in the development of his thought. And in that case if

we want to understand any of his subsequent ideas we obviously need

to understand what brought about this radical transformation. Unless

we can answer this question we are running the risk of seeing all his

subsequent views in a completely mistaken perspective. So it is this

question that I shall be focusing on in this paper. I hope to show that

answering it will indeed have far-reaching implications for the under

standing of Wittgenstein's ideas beyond his brief period of explicit

verificationism, although in rather a different way from what might be

expected.

Before going any further let me dispel any doubts that Wittgenstein

really did hold such extreme verificationist views by quoting a few

representative passages from texts which he wrote in the early Thir

ties:1

Every proposition is a signpost for a verification.

The verification is not one token of the truth, it is the sense of the proposition.

In order to determine the sense of a proposition, I should have to know a very specific

procedure for when to count the proposition as verified. In this respect ordinary

language oscillates very much, much more so than scientific language ... this means that

the symbols of ordinary language are not unambiguously defined.

Where there are different verifications there are also different meanings.

The sense of a proposition is the method of its verification.

If someone familiar only with Wittgenstein's later writings were

presented with these remarks I think he would almost certainly assume

that they came from the writings of Carnap, Schlick or some other


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THE ORIGINS OF WITTGENSTEIN'S VERIFICATIONISM 267

member of the Vienna Circle. Yet in fact they are all from Witt

genstein. Nor are these a few isolated aberrations taken out of context.

On the contrary, they are entirely typical of the statements linking

meaning and verification in the closest possible way which are to be

found throughout the texts which Wittgenstein wrote during the early

Thirties. His degree of commitment to these ideas is illustrated parti

cularly strikingly by the fact that he did not hesitate to accept one of

the most controversial and radical consequences of this view of

meaning, its implications for the status of evaluative language. Yet

Wittgenstein made it quite clear that he did accept them when he

remarked in his 1930/1931 lectures that 'ethical and aesthetic judge

ments are not propositions because they cannot be verified'2 (my

emphasis). So, even though he was later somewhat coy about admit

ting it,3 there can, I think, be little room for serious doubt that in the

early Thirties Wittgenstein was whole-heartedly committed to a form

of verificationism which was every bit as radical as anything put

forward by the Vienna Circle. The question is why?

At the moment all we know is that in 1918 when he completed the

Tractatus Wittgenstein appears to have been anything but a

verificationist. But by 1929 when he returned to Cambridge and

resumed philosophical research he most definitely was. Clearly the key

to discovering what brought about this change in Wittgenstein's views

must lie in something which happened during those intervening years.

So the first thing we must do is to look at what was and was not

happening to Wittgenstein intellectually during this long period away

from the world of academic philosophy.

2. THE FALLOW YEARS, 1918-1929

By 1918 the Tractatus was complete and Wittgenstein's interests

turned to matters far removed from philosophy. It is clear that in the

years immediately following he continued to remain convinced that

the ideas of the Tractatus contained in essence the definitive solutions

to the problems of philosophy, and all that remained to be done was to

work out the details, although this was a task for which Wittgenstein

himself obviously had little enthusiasm. As a result Wittgenstein's

degree of interest in philosophical matters sank to a very low level and

remained there for some time. That this was so is shown very clearly

by the testimony of Frank Ramsey. In 1923 Ramsey visited Witt

genstein in the remote Austrian villages where he was working as a


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a clue as to the source of the radical transformation in his views which

was soon to take place.

3. WITTGENSTEIN'S ENCOUNTER WITH THE VIENNA CIRCLE

The first new ideas which Wittgenstein encountered during this period

were none other than those of Moritz Schlick and the group of his

colleagues and students who were to become known as the Vienna

Circle. Wittgenstein first met Schlick towards the end of 1927 and

attended discussions with Schlick and some members of his group for

several years.8 Once we know this much it might seem that we need

look no further for the explanation of the radical transformation which

Wittgenstein's ideas had undergone by the time he resumed intensive

philosophical research in January 1929. Schlick and his circle were, of

course, all committed radical empiricists for whom verificationism was

an absolutely central doctrine. The fact that only a very short time

after being exposed to their ideas for the first time Wittgenstein

himself began to put forward almost identical ideas about the relation

of meaning and verification can, surely, only be explained in one way.

It was through the sustained and persuasive advocacy of the Vienna

Circle that Wittgenstein was made to realise the immense im

plausibility of the total exclusion of epistemological considerations

from his earlier account of meaning, and how much more plausible a

verificationist approach was. In short, Wittgenstein owed his con

version to verificationism to the Vienna Circle.

This explanation is attractively simple, and, it might seem, must

obviously be correct. For surely it is too implausible to suggest that

despite his discussions with the Vienna Circle just prior to his explicit

acceptance of verificationism Wittgenstein in fact arrived at these

views by some other quite different route and that this change in his

views had nothing to do with the Vienna Circle. For one thing, what

other possible explanation is there for the source of Wittgenstein's

verificationism, and for another, if it was not their advocacy of

verificationism which held Wittgenstein's interest in what the Vienna

Circle had to say what was it? It seems obvious that something they

had to say must have interested him or he would not have kept on

going to their discussions. And if it was not their advocacy of

verificationism what was it?

However, if we look a little more closely at Wittgenstein's inter

action with the Vienna Circle, the picture that emerges is one that


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MICH EL WRIGLEY

does strongly suggest that this apparently implausible possibility was in

fact exactly what did happen, and that the Vienna Circle had nothing

to do with Wittgenstein's conversion to verificationism. Although little

is known about what was said in these discussions during the crucial

period between 1927 and 1929, enough is known to decisively rule out

this attempted explanation of the origins of Wittgenstein's

verificationism. For if the Vienna Circle really had the kind of effect

on Wittgenstein that it is being suggested, then they did nothing less

than bring about a fundamental transformation in Wittgenstein's

views. And if that were the case we would expect to find that

Wittgenstein participated in these discussions eagerly and enthusias

tically as he began to explore the full implications of the new and very

different philosophical perspective whose merits he now appreciated

for the first time. And in that case the other participants in these

discussions could hardly have been unaware of the fact. Yet in fact it

is abundantly clear from the reports that have been given by other

participants in these discussions that nothing of the kind took place.

Herbert Feigl attended many of these discussions and this is how he

described them:9

Wittgenstein ... emphatically told the few of us ... with whom he occasionally met

[between 1927 and 1929]... that he was no longer interested in philosophy. He felt that

he had said all he could in the Tractatus. Moreover, only on relatively rare occasions

could we get him to clarify one or another of the puzzling or obscure passages in his

work. He seemed himself rather unclear on the ideas he had developed during the First

World War.

This is very clearly not the picture of a man in the throes of a radical

transformation involving some of his most fundamental ideas. But this

is very much the picture given by other participants in these dis

cussions. Far from taking a keen interest in the proceedings it was

more often than not difficult to get Wittgenstein to discuss philoso

phical questions at all. Sometimes all he would do was to read poetry

aloud.10 When he could be prevailed upon to consider philosophical

questions his contributions seem to have been limited to giving

explanations of the Tractatus. There is certainly no sign of his having

radically changed his views nor of his having rejected any fundamen

tal aspect of the ideas he had expounded ten years earlier. So, far from

a radical transformation having taken place as a result of Witt

genstein's encounter with the Vienna Circle, things seem to have

changed very little from the state of affairs a few years earlier when he

wrote to Keynes. If pressed Wittgenstein could sometime be prevailed


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upon to explain bits of the Tractatus, as he had to Ramsey, but that

was about all. Certainly the one thing Wittgenstein seems not to have

done was to seize on the ideas of the Vienna Circle as a basis for

making far-reaching modifications in his earlier views. So, surprising

though it may seem, I think this attempt to explain the source of

Wittgenstein's verificationism does have to be rejected.

This conclusion means that we are going to have to find answers to

those two questions mentioned earlier. Firstly, and most obviously, if it

was not by this route that Wittgenstein arrived at his own

verificationism, where did it originate? Secondly, if it was not because

they had won him over to verificationism what was it that interested

Wittgenstein sufficiently for him to keep coming to these discussions?

A reply to this second question is needed, and we will come back to it

later. But for the moment I want to concentrate on the first and most

fundamental question of the source of Wittgenstein's verificationism.

By answering this question we will also be able to answer the second.

It seems that in order to find out what motivated Wittgenstein's

adoption of verificationism we need to locate some powerful influence

which affected Wittgenstein during the crucial period just before his

return to Cambridge, and which was capable of leading him in the

direction of verificationism. In fact there is an obvious candidate

which, in one respect, seems to be just what we are looking for. This is

the impact made on Wittgenstein by the ideas of Brouwer.

4. THE IMPACT OF BROUWER

In March 1928 Wittgenstein attended a lecture given by Brouwer in

Vienna. Brouwer's ideas evidently made a considerable impression on

him. Once again Feigl provides an eyewitness account:11

When the Dutch mathematician Luitzen Jan Egbertus Brouwer was scheduled to lecture

on intuitionist mathematics in Vienna, Waismann and I managed to coax Wittgenstein,

after much resistance, to join us in attending the lecture. When, afterwards, Witt

genstein went to a caf? with us, a great event took place. Suddenly and very volubly

Wittgenstein began talking philosophy - at great length.

Quite clearly something Wittgenstein heard struck a chord which had

not happened during his discussions with the Vienna Circle. What is

more Wittgenstein's excitement was not something that quickly

faded away. He was sufficiently interested to go back and hear

Brouwer's second lecture a few days later,12 and the story circulates (it

seems to have originated with Waismann) that he even travelled to


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MICH EL WRIGLEY

Holland to have discussions with Brouwer. Less than a year later

Wittgenstein was back in Cambridge at work on philosophy as in

tensively as ever. So the purely circumstantial evidence, that it was

here in the ideas of Brouwer that Wittgenstein found the crucial new

inspiration for the views he began to expound in 1929, looks quite

persuasive.

However when we try to explain in more detail just how the ideas of

Brouwer could have had this effect on Wittgenstein we encounter an

obvious problem. In fact there are two distinct but related problems.

Firstly, it is not at all obvious how anyone could have been led to

adopt radical verificationism by exposure to the ideas of Brouwer.

Secondly, it is particularly difficult to see how Wittgenstein could have

got verificationism, or indeed anything else, out of Brouwer. These

problems arise because, although Brouwer was primarily a philosopher

of mathematics, his account of mathematics was part of a general

metaphysical view which amounted to a solipsistic form of transcen

dental idealism strongly influenced by Schopenhauer. Such an outlook

is obviously far removed from the radical empiricism which forms the

basis for verificationism. It is for this reason that there is a problem in

seeing how anyone could have been led to adopt verificationism by

exposure to the ideas of Brouwer. Furthermore, Brouwer's ideas also

provide an almost perfect example of the psychologism which had

been attacked by Frege as one of the worst errors any philosophical

account of mathematics could commit, and it is this feature of

Brouwer in particular which makes it so difficult to understand how

Wittgenstein could have responded in such a positive way to

Brouwer's ideas. For on the question of psychologism Wittgenstein

was a loyal follower of Frege,13 and so we would expect him to have

found views like Brouwer's as much of an anathema as Frege himself

would have. Certainly the last thing we would expect to find is

Wittgenstein reacting enthusiastically to such ideas. Yet, despite this

apparent obstacle, it seems quite clear that something in Brouwer's

ideas nevertheless did strike a deep chord in Wittgenstein.

In order to discover what it might have been we must obviously

take a closer look at both Brouwer's ideas and Wittgenstein's response

to them. Despite the many differences there is one obvious point of

contact between Brouwer and Wittgenstein, which has already been

mentioned, and this is the influence of Schopenhauer. The strongly

Schopenhauerian tone of Brouwer's general metaphysical outlook can


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hardly have failed to find a sympathetic response in Wittgenstein. But

while this is likely enough, there is an obvious reason why it cannot

have been this aspect of Brouwer which was responsible for bringing

about a change in Wittgenstein's attitude towards verificationism. For,

quite apart from the difficulty in seeing how Schopenhauer could have

been the source of radical verificationism, we need only remember

that this was not Wittgenstein's first encounter with the ideas of

Schopenhauer. On the contrary, Schopenhauer was one of the very

earliest influences on Wittgenstein's philosophical development.14 So

by the time he encountered Brouwer Wittgenstein had long ago

absorbed all those aspects of Schopenhauer's ideas which he thought

were of value. By 1928 there was nothing new which he had to learn

from Schopenhauer, and so it cannot have been this aspect of

Brouwer's thought which struck Wittgenstein and which, apparently,

led him to modify his views in such a radical way.

In order to try and locate what it might have been in Brouwer which

Wittgenstein responded to, we need only notice one very striking fact

about the ideas which he began putting forward immediately after his

return to philosophy in 1929. Although one very conspicuous feature

of his thought during this period is his new-found radical veri

ficationism, there is another equally conspicuous new feature - his

intense interest in the philosophy of mathematics. This area was, of

course, precisely the one which was at the centre of Brouwer's

interests and, for good measure, it was the subject to which he

devoted the bulk of his Vienna lectures. The fact that within only a

few months of encountering Brouwer's ideas for the first time Witt

genstein himself developed an intense interest in this very area can

hardly be a mere coincidence. What this suggests is that something in

what Brouwer said struck Wittgenstein as containing a major new

insight into the nature of mathematics which revealed the fundament

ally mistaken nature of his own earlier views.

When we look at the details of the new ideas about mathematics

which Wittgenstein began to develop in 1929 we find that many of his

ideas bear a striking resemblance to key ideas of Brouwer. A rejection

of the completed infinite, criticism of the Law of the Excluded Middle,

and an insistence that the content of a mathematical sentence is

determined by its proof, all these are central features of an intuitionist

account of mathematics which Wittgenstein appears to echo. Witt

genstein's discussions of mathematics even contain explicit references


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274 MICH EL WRIGLEY

to Brouwer. In view of all this we might seem both to have well nigh

conclusive evidence that it was here in Brouwer's account of mathe

matics that the crucial inspiration for Wittgenstein's return to

philosophy is to be found, and also to have pinpointed the precise

aspect of Brouwer which Wittgenstein was so struck by.

If this is right then the answer to our central question must be that

Wittgenstein was led to adopt a radically verificationist account of

meaning not in the very direct way that the previous attempted

explanation suggested, but by a much more roundabout route which

began with certain new ideas about mathematics. However it is one

thing to conclude that this must provide the explanation of Witt

genstein's conversion to verificationism, quite another to show how he

found himself led to verificationism by adopting an account of

mathematics modelled on Brouwer's intuitionism. In fact not only do

we need to explain the nature of the connection which it appears must

exist between Wittgenstein's new account of mathematics and his

equally new verificationism, but we also need to explain how he even

arrived at this account of mathematics in the first place.

We need to do this because, while there is little room for doubt that

Wittgenstein's new view of mathematics was in some way directly

inspired by Brouwer, there is still an obvious problem of explaining

how Wittgenstein could have responded so positively to Brouwer's

ideas about mathematics. The thoroughly psychologistic nature of

Brouwer's ideas about mathematics has already been pointed out. It

has also been pointed out that Wittgenstein would have been un

sympathetic in the extreme to this aspect of Brouwer. And in case

there is any doubt about this, we do indeed find him emphatically

rejecting such psychologism in his discussions of mathematics after

1929, and, what is more, singling out Brouwer for criticism on this

score.15 But this creates an acute problem for the following reason. All

the striking theses about mathematics which intuitionism is notorious

for, its rejection of the completed infinite, and other characteristically

constructivist claims, are, in Brouwer's view, justified only on the basis

of his underlying metaphysical view. What Wittgenstein vehemently

rejects as psychologism constitutes for Brouwer not some optional

extra but the very essence of his whole account of mathematics. But if

this is right then by taking his uncompromisingly anti-psychologistic

stance Wittgenstein is depriving all the other aspects of intuitionism of

their sole justification. Yet in fact he seems to be quite happy to


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accept those other aspects. Such a position seems on the face of it to

be blatantly inconsistent. So if this attempt to explain the origins of

Wittgenstein's verificationism is going to get anywhere it has got to

find some way of showing that this inconsistency is only apparent and

that Wittgenstein's selective attitude to Brouwer is a tenable position.

I now want to consider a way that has been suggested of solving both

these problems at a single stroke.

5. A POSSIBLE ROUTE FROM INTUITIONISM

TO VERIFIC TIONISM

The starting-point of this suggested solution is a proposal that has

been made by Michael Dummett concerning the interpretation of

Brouwer's account of mathematics. What Dummett claims is that

despite the prominence given to it by Brouwer himself, the psy

chologistic dimension of intuitionism is actually completely irrelevant

to, and indeed, actually in conflict with, the genuine insight at the

heart of intuitionism. According to Dummett what is really at the core

of the intuitionist approach to mathematics, and what provides the real

motivation for all the familiar intuitionist claims about mathematics, is

not some murky idealist metaphysical picture, but something quite

different, namely a radically innovatory theory of meaning for

mathematical sentences.16

What intuitionism is implicitly claiming, Dummett suggests, is that

instead of regarding the meaning of a mathematical sentence as

determined by its truth-conditions, we should recognise that it is

determined by something quite different, namely its proof-conditions.

The principal argument in favour of this interpretation of Brouwer is

that when the implications of such an account of meaning for mathe

matical sentences are worked out in detail, they match exactly those

that Brouwer was led to advocate on the basis of his more metaphysi

cal formulation of intuitionism. I shall not pursue the question of

whether or not Dummett's interpretation really does justice to

Brouwer's account of mathematics,17 but if so it is clear that Dum

mett's proposal is of immediate relevance to our problem of under

standing how Wittgenstein could have consistently reacted to Brouwer

in the selective way he did.18 For all we need to do is to suppose that,

like Dummett, Wittgenstein also recognised the possibility of separat

ing the semantic core of intuitionism from the purely psychologistic


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MICH EL WRIGLEY

setting in which Brouwer had embedded it. In that case we would

expect to find Wittgenstein endorsing all the substantial claims about

mathematical practice which are characteristic of intuitionism, while

at the same time rejecting its psychologism. And this, apparently, is

exactly what we do find. So the mystery of how Wittgenstein could

have responded so enthusiastically to Brouwer's ideas is dispelled.

If this is right then we have disposed of one of the problems raised

by the suggestion that Brouwer provided the crucial inspiration behind

Wittgenstein's revival of interest in philosophy after 1929. They key

inspiration was in the philosophy of mathematics and Wittgenstein's

revival of interest in other areas is to be seen as in some way the result

of this. But the obvious question is how? In particular, what about the

problem of explaining how Wittgenstein's verificationism could also

have originated in his encounter with Brouwer? It is one of the great

attractions of this interpretation of Brouwer that it offers an equally

neat and elegant solution to this problem too. Again the crucial point

has been clarified by Dummett. For, he has argued, if a case can be

made at all for replacing an account of meaning for mathematical

sentences in terms of truth-conditions by one in terms of proof

conditions, then it has potentially global application and is not restric

ted only to the domain of mathematics. When such a generalisation of

the intuitionists' implicit account of meaning is carried out the ap

propriate analogue of proof-conditions turns out, Dummett argues, to

be none other than the concept of ueri/icaiiott-conditions.19 Hence, to

explain how Wittgenstein's conversion to verificationism was the out

come of his encounter with Brouwer, we need only suppose that he

too grasped the implicitly global implications of the new conception of

meaning which provided the underlying motivation for the intuitionist

account of mathematics.

Making use of Dummett's work in this way we are able to demon

strate the existence of a very natural route which leads from Witt

genstein's encounter with the ideas of Brouwer to his apparently

totally unconnected conversion to verificationism. Granted that this is

a possible route from intuitionism to verificationism the question we

must now ask is whether this was a route which Wittgenstein travelled.

In fact, despite its great ingenuity and considerable initial plausibility,

I think that this attempted explanation of the origins of Wittgenstein's

verificationism is open to decisive objections and is in the end no more


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successful than the attempt to trace these ideas back to Wittgenstein's

contact with the Vienna Circle.

6. DUMMETT'S INTERPRETATION REJECTED

Although I shall argue that it cannot adequately explain the origin of

Wittgenstein's verificationism this perspective does nonetheless have a

number of things to recommend it and there are some important

things to be learned from it. Quite apart from the intrinsic interest of

this new approach to questions in the theory of meaning, this inter

pretation quite rightly draws attention to the fact that any adequate

account of Wittgenstein's ideas in the early Thirties has got to take

account of the central place which the philosophy of mathematics

occupied in his thought at that time, and why it was that it was this

particular area he became so preoccupied with at this time. It also

highlights the need to give an account of the connections which must

surely exist between Wittgenstein's ideas on mathematics and the rest

of his thought. Finally it also draws attention to the need to give some

explanation of why Wittgenstein responded with such enthusiasm to

Brouwer's ideas. I think this interpretation is absolutely right to raise

all these points, and that all these questions are of great importance.

What is more, I think that the answers which this interpretation

proposes to these questions do contain at least an important grain of

truth. For I think that it is quite right to suggest that there are

important connections between Wittgenstein's new ideas about

mathematics and his other new ideas. I think it is right again to

suggest that Brouwer did play a role in shaping these new ideas, both

in the philosophy of mathematics and elsewhere. However it is when it

comes to the proposed explanation of precisely how Brouwer

influenced Wittgenstein that his interpretation goes astray, and as a

result its attempted explanation of the origins of Wittgenstein's

verificationism is wholly mistaken.

Let us now see why it is mistaken. The core of this interpretation

consists in the claim that Brouwer's intuitionism provided Wittgen

stein with a model for a new account of meaning for mathematical

sentences. It was then suggested that his verificationism is to be

explained as the result of generalising this new account of meaning


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MICH EL WRIGLEY

outside mathematics. Clearly if the first claim about the nature of

Brouwer's influence on Wittgenstein's account of mathematics is in

correct then the proposed explanation of Wittgenstein's conversion to

verificationism must also be incorrect. Yet I think that it can be

conclusively established that this first claim is indeed incorrect. The

key to showing this is to look a little more closely at Wittgenstein's

philosophy of mathematics.

The starting-point of this whole interpretation was the discovery

that the new account of mathematics which Wittgenstein began to

expound after 1929 exhibited a number of very striking points of

resemblance to Brouwer's intuitionism. However, while there un

doubtedly do appear to be some very striking resemblances between

what Wittgenstein says and what Brouwer says, by no means every

thing Wittgenstein says about mathematics fits so smoothly with this

interpretation. In fact it is not difficult to find aspects of his account of

mathematics which are not merely very different from any account of

mathematics modelled on intuitionism but are clearly inconsistent with

it. Nor is this a matter of a few minor discrepancies which might

perhaps be brushed under the carpet. On the contrary, Wittgenstein's

points of disagreement with intuitionism concern absolutely central

issues and go to the very heart of his account of mathematics.

The crucial issue is what view Wittgenstein took of the role of

mathematical sentences. Intuitionism in common with most other

philosophical accounts of mathematics assumes that the function of

mathematical sentences is to describe, truly or falsely, a certain

domain of facts. To say that a mathematical sentence has a meaning

really amounts to nothing more than the claim that it has descriptive

content. Now if the explanation we are considering of the origins of

Wittgenstein's verificationism is correct then Wittgenstein too must

have accepted this assumption. Yet it- is clear from many quite

unequivocal remarks that Wittgenstein did not accept it. Not only did

he reject the idea that mathematical sentences have a descriptive

meaning, but his rejection is fundamental to his whole vision of

mathematics. In complete contrast with intuitionism (in either its

original psychologistic form or the refurbished semantic form pro

posed by Dummett) Wittgenstein emphatically rejects the whole idea

that mathematical sentences are properly construed as having de

scriptive content or being 'about' anything. 'When we talk about the


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sense of mathematical sentences, or what they are about ', Witt

genstein insists, 'we are using a false picture'.20 Just how fundamental

this idea is to Wittgenstein's view of the nature of mathematics is

illustrated very clearly by his warning that 'nothing is more fatal to

philosophical understanding [of mathematics] than the notion of proof

and experience as two different but comparable methods of

verification',21 since this implies nothing less than that almost all errors

in philosophy of mathematics stem from failing to grasp this fun

damental fact about the distinctive role of mathematical sentences.

Such errors can be avoided, in Wittgenstein's view, only if we con

stantly bear in mind that in mathematics, in sharp contrast with the rest

of language, 'nothing [is] meaning... even when it doesn't look like

that because we seem to be using words to talk about mathematics'.22

It emerges, then, that where intuitionism sees an identity of function

between mathematics and the rest of language Wittgenstein wishes to

make the sharpest possible distinction. This point is clearly fatal to the

whole idea that Wittgenstein reacted to Brouwer in the way that has

been suggested, that is by taking intuitionism as the starting-point for

a new theory of meaning for mathematical sentences. Wittgenstein

cannot have reacted in this way because he had no account of

meaning for mathematical sentences since he did not think that

mathematical sentences had a meaning of which some account needed

to be given. But in that case Wittgenstein's verificationism cannot

have been arrived at by a process of generalisation from his new

account of meaning for mathematical sentences because there is no

such account to generalise from. So whatever it was that Wittgenstein

got from his contact with the ideas of Brouwer his radical

verificationism was not it, and while there may be a possible route

from an account of mathematics modelled on intuitionism of the kind

Dummett has described to a general verificationism it was not a route

which Wittgenstein followed.

Before we consider what alternative explanation might be available

of the source of Wittgenstein's verificationism, however, there are a

number of other obvious questions which the conclusion we have just

reached raises and which call for at least brief comment. And in fact

this will turn out not to be a complete digression from our central

question, since in answering these questions some unexpected light

will be thrown on the way to answer our central question.


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7. EXPLAINING AWAY APPARENT RESEMBLANCES

TO INTUITIONISM

Perhaps the most obvious question raised by the argument of the

previous section is that of what alternative account Wittgenstein had

of the role of mathematical sentences if he rejected the usual view that

they have a descriptive function. Does this denial of descriptive

meaning to mathematical sentences leave him with no option but to

say that mathematics consists only of empty marks on paper? If this

were his position then it would no more deserve to be taken seriously

than the naive nineteenth century formalist accounts of mathematics

which Frege criticised so devastatingly. So if Wittgenstein's philoso

phy of mathematics is to be taken at all seriously then it needs to be

shown that his position was clearly quite distinct from anything so

crude and implausible. The only account of mathematics which shares

with Wittgenstein a rejection of the descriptive meaningfulness of

mathematical sentences is the more recent and much more sophisti

cated version of formalism of which Hubert was the most committed

advocate.23

However it is important to realise that Wittgenstein's reasons for

taking this position are quite different from Hubert's. Wittgenstein's

account in fact offers a radically new picture of mathematics which is

quite different from any of the familiar positions. The key idea in

Wittgenstein's approach is that mathematical sentences instead of

having a descriptive role have a prescriptive or normative role. Rather

than describing anything themselves they constitute a framework with

in which any description must take place. The importance and interest

of Wittgenstein's account of mathematics stems from the question of

whether or not he succeeded in giving cogent reasons for thinking that

this is the correct way to regard mathematics and in meeting the

obvious objections to which this position appears to be open. Whether

or not he did succeed should still, I think, be regarded as an open

question. This question is obviously a large and complex one and

further discussion of it would take us too far afield from our central

question. However I have mentioned this facet of Wittgenstein's

account of mathematics not merely because it is so central. I do so

also because it throws light in an unexpected way on the central

question of this paper, namely the origin of Wittgenstein's

verificationism. To see how it does this we need to consider one of the


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other questions raised by the rejection of Dummett's interpretation.

Now we can appreciate how different the basis of Wittgenstein's

account of mathematics is from intuitionism we need to say something

about those aspects of it which appeared to provide such convincing

evidence of Wittgenstein's debt to intuitionism. What alternative

explanation are we now to give of these now that it is clear that they

cannot be the manifestations of intuitionist influence which they

appeared to be? There are two outstanding features of Wittgenstein's

views which need fresh explanations. These are his insistence that the

significance of a mathematical sentence is determined by its proof, and

his emphatic rejection of the completed infinite. To explain the first of

these I think we need only grasp one of the lessons of Wittgenstein's

rejection of the idea that mathematical sentences have a descriptive

meaning. Although this idea is one with few parallels in other accounts

of mathematics there is one context from which it ought to be very

familiar, and this is Wittgenstein's own earlier work. It is one of the

most fundamental and innovatory ideas of the Tractatus that the

sentences of mathematics (and logic) had an entirely different status

from sentences of other kinds. Unlike ordinary sentences which had

Sinn, or sense, the sentences of mathematics were sinnlos, or sense

less, although that was not at all to say that they were nonsensical like

empty marks on paper. Rather it was to say that they were normative

in function. So it turns out that one of the central ideas of the account

of mathematics which Wittgenstein was putting forward in the early

Thirties was in fact not anything new at all, but stems directly from the

Tractatus. And I think exactly the same turns out to be true of

Wittgenstein's statements about the connection between a mathema

tical sentence and its proof. This idea too is present, if in an extremely

compressed form, in the Tractatus and has nothing to do with in

tuitionism.24

When we turn to the other apparent point of agreement between

Wittgenstein and intuitionism, his rejection of the completed infinite, I

think that here we do have to admit that the agreement is genuine and

not merely apparent. What is more in this case we must also admit that

this does mark a genuine change in Wittgenstein's views and is not

something that can be traced back to the Tractatus.25 However this

does not mean that we are at a loss to explain how Wittgenstein came

to adopt this view, nor even that we are compelled to deny that it had

anything to do with Brouwer. All that was ruled out by the argument


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of Section 6 was the idea that Wittgenstein came to reject the

completed infinite through his acceptance of a theory of meaning

which was based on intuitionism. But this does not rule out the

possibility that he was influenced by Brouwer's ideas in some quite

different way. Indeed it is a good thing that this is not ruled out,

otherwise we would be in danger of being unable to find any way of

explaining how Brouwer influenced Wittgenstein. But on the strength

of Wittgenstein's reaction to Brouwer's lecture alone, and more im

portantly, in the light of the many explicit references to Brouwer's

ideas in Wittgenstein's writings this is one of the few things we can be

sure of.

Very briefly I think the true picture of what happened was, in

outline, as follows.26 What so struck Wittgenstein was not so much any

particular thesis which Brouwer advanced as the fact that he raised in

a very vivid form the whole problem of the nature of the infinite. This

was something which Wittgenstein had previously regarded as com

pletely unproblematic (there is nothing in the Tractatus to suggest the

opposite). But the form in which the problem of the nature of the

infinite crystallised for Wittgenstein was quite different from the way in

which Brouwer presented it. The crucial question for Brouwer con

cerned the incompletability of infinite mental processes of construc

tion. But for Wittgenstein the question was, rather, one of how can

any rule, which must be finite, determine its infinitely many possible

applications. The concept of a rule had a pervasive role in the

Tractatus, but until he encountered Brouwer its immensely prob

lematic nature had simply never struck Wittgenstein. How Witt

genstein pursued this question need not concern us here. But it is

obvious enough from the subsequent course of Wittgenstein's thought

that this is a problem whose ramifications are perfectly general and are

not confined to the philosophy of mathematics. It is also obvious that

there is nothing inconsistent in Wittgenstein's adopting this new

perspective on the nature of rules while at the same time retaining the

basic framework of his Tractatus account of mathematics.

So it is here, I think, that the explanation is to be found of what it

was that excited Wittgenstein so much in Brouwer. This also explains

how this crucial new inspiration led Wittgenstein to begin exploring

new and very different ideas both in philosophy of mathematics and in

other areas too. This is the grain of truth which I suggested earlier was

to be found in Dummett's interpretation and the attempt to explain

Wittgenstein's verificationism as the outcome of his encounter with


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the ideas of Brouwer. Although it was in a quite different way from

that suggested by the interpretation based on Dummett's inter

pretation of Brouwer, it turns out that Brouwer was the crucial

stimulus behind many of the new ideas which Wittgenstein began

expounding in 1929. However, to return to our main concern, his

verificationism is a very conspicuous exception. Whatever may be true

of the other ideas which are prominent in what Wittgenstein was

saying immediately after 1929, his verificationism is certainly not

something that can be traced back to Brouwer.

But if this is right then what are we to say about the origin of

Wittgenstein's verificationism? We seem to have reached an impasse

since none of the available candidates for the source of these new

ideas has turned out to be capable of providing a convincing explana

tion. I think the key to discovering its real source lies in taking to

heart the general lesson of the failure to establish a connection

between Brouwer and Wittgenstein's verificationism and calling into

question a fundamental assumption that has, thus far, gone unques

tioned. As we saw, the crucial mistake in that attempted explanation

lay in the assumption that Wittgenstein's conception of mathematics

underwent a complete transformation in 1929. Although there cer

tainly are important changes in Wittgenstein's view of mathematics, at

the most fundamental level the picture is not one of change, but of

complete continuity. The more general lesson of this discovery is that

we ought to be open to the possibility that even where there appears

to be dramatic change in Wittgenstein's views, beneath the apparent

change there may be deep continuity, and that what seems to be new

may not really be new at all. By now it is probably not too difficult to

guess what I am going to suggest is the correct explanation of the

source of Wittgenstein's verificationism. My claim will be that far from

representing the radical change they appear to, Wittgenstein's

verificationist ideas in fact stem directly from the Tractatus. My

method of trying to establish this will be to focus on the importance of

some key facts about Wittgenstein's interaction with the Vienna Circle

which were overlooked in our earlier discussion.

8. A SECOND LOOK AT THE VIENNA CIRCLE

Our earlier discussion of Wittgenstein's meetings with the Vienna

Circle left one important question unanswered. This was simply if

Wittgenstein did not, as I argued he cannot, learn his verificationism


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from the Vienna Circle, what was it that was of sufficient interest in

these discussions that provided him with the motivation to keep on

attending them? We can approach this question by asking another

obvious question. Why did these discussions ever start in the first

place? The initiative came from the Vienna Circle not from Witt

genstein. So what was it that they were so interested by in his ideas? I

think the answer to this question is that they thought that they had

found in the Tractatus an extraordinarily powerful and penetrating

crystallisation of the central tenets of views which they had arrived at

independently. They were eager to have discussions with Wittgenstein

because they felt certain that he had grasped far more clearly than

they yet had the full implications of these views. But what were these

views? It is hardly necessary to be reminded that Schlick and his circle

were all committed radical empiricists. And it was this philosophical

perspective of radical empiricism which they thought found expression

in Wittgenstein's Tractatus. But, as was pointed out earlier, one very

noticeable feature of the Tractatus is the absence of any explicit

reference to verificationism or any other sign of radical empiricism.

What is more, it has been apparently convincingly argued on the basis

of things that the Tractatus does say that we can rule out the

possibility that verificationism is implicit in the Tractatus at any level.

It was precisely for this reason that it was so important to discover

how Wittgenstein came to adopt verificationism since this appeared to

mark a radical change in his views at the most fundamental level.

But now remember what was argued in Section 2. We concluded

there that all the evidence is that between finishing the Tractatus in

1918 and his first encounter with the Vienna Circle in 1927 Witt

genstein's views did not change in any way. But this means that he

came to those discussions still holding exactly the views he had put

forward in the Tractatus. In other words when Wittgenstein first

encountered the Vienna Circle there must have been a direct con

frontation between the Tractatus as Wittgenstein himself understood it

and the Tractatus as the Vienna Circle understood it. And this clearly

provides us with an absolutely clearcut and decisive test of the

correctness or otherwise of the Vienna Circle's interpretation. It does

so because even where far less significant issues were concerned

Wittgenstein was most definitely not someone to take misrepresen

tations of his views lightly.27 So if the Vienna Circle's interpretation

had been half as far from the real intentions of the Tractatus as is

usually supposed, Wittgenstein's reaction would still have been one of


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outrage. And we can be certain that in that case he would not have

had the slightest interest in maintaining contact with these people who

had so badly misunderstood his ideas.

But of course Wittgenstein did nothing of the sort. Even if he was

not always the most forthcoming of participants in these discussions he

did come back and kept doing so. Far from being outraged he was

quite content to sit placidly by while the air was thick with talk of

verification, protocol sentences, sense-data, and so on, as the Vienna

Circle attempted to work out the details of the Tractatus. Evidently all

this was perfectly congenial to Wittgenstein. This can, I think, mean

only one thing. That far from being the travesty of the Tractatus it is

commonly taken to be, the Vienna Circle's interpretation contains a

very important element of truth. This must be so because by his mere

presence at their meetings Wittgenstein was clearly giving his tacit

approval to the general way in which the Vienna Circle wished to

interpret the Tractatus. And if this is right then we have finally found

the answer to our central question, although in the most unexpected of

places. The source of the radical verificationism which Wittgen

stein espoused so enthusiastically in the early Thirties lies in the

Tractatus.

Even if this does answer our central question, however, we still have

to answer the question with which this section began. What was it that

held Wittgenstein's attention in the Vienna Circle discussions? And in

answering this we can also deal with a further question which is raised

by our central conclusion. Even if the source of Wittgenstein's

verificationism is in the Tractatus there is still one very obvious

difference between the verificationism of the Tractatus and the

verificationism of the early Thirties. It is simply that in the Tractatus it

was only implicit, whereas after 1929 it became very explicit. Why was

this? Although this change is a great deal less dramatic than the one

which was initially supposed to have occurred between 1918 and

1929, it is still a genuine change and some explanation is required of

why it happened. I think that the way to explain this change is to

realise that although the Tractatus is tacitly committed to some form

of verificationism, it is not committed to any particular detailed

formulation of verificationism. As so often in the Tractatus Witt

genstein is operating at a very high level of generality. It seems likely

that he may have had a number of different possible candidates in

mind for the specific way his general commitment to verificationism

might be worked out, but he had not come to any decision between


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them since it was not crucial for him to do so because he knew (or

thought he knew) on a priori grounds that some candidate must fit the

bill. Finding out which it was was simply a matter of detail that Witt

genstein was not particularly interested in. This is surely the reason

why we do not find any detailed explicit verificationist pronounce

ments in the Tractatus itself. However once he had been confronted

with the Vienna Circle's determined efforts to work out a fully explicit

answer to the question of what precise form verificationism should

take Wittgenstein did gradually become more concerned with these

questions of detail himself. And in doing so he now did commit

himself to a specific formulation of verificationism. It was his parti

cipation in this gradual process of trying to arrive at a satisfactory

detailed and explicit formulation of verificationism which was what

held Wittgenstein's attention in the Vienna Circle discussions, and it

was for the same reason that by 1929 he formulated his verificationism

absolutely explicitly. Yet because much of this was already relatively

familiar to Wittgenstein and because this was also a relatively gradual

process this claim is not inconsistent with his relatively low level

of interest in the proceedings.

Let me now conclude by making clear what I think has been

established and what not, and indicate some further questions raised

by my conclusions.

9. RECONSIDERING THE TRACTATUS'

First of all let me emphasize what I am not claiming. I am not

proposing simply to revive the Vienna Circle interpretation of the

Tractatus in its entirety. Undoubtedly the Vienna Circle's inter

pretation did badly misrepresent the Tractatus on many issues, the

nature of philosophy, the nature of mathematics and logic, ethics, to

give only a few examples. It has undoubtedly been one of the major

achievements of recent work on the Tractatus to make this very clear

and to show how much there is in the Tractatus that stems from Frege,

Hertz, Schopenhauer and elsewhere, and has nothing to do with the

Vienna Circle or radical empiricism. It was precisely all these aspects

of the Tractatus which the Vienna Circle were completely blind to.

However now that this lesson has been thoroughly learned, and also

now that some of the texts from Wittgenstein's crucial middle period

are available, we can perhaps take a second look at the Vienna


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Circle's interpretation and realise that while this interpretation is

certainly not the whole truth about the Tractatus, it is not wholly

mistaken either, and on one point of some importance it does contain

a genuine insight. So although the Vienna Circle's interpretation is not

without its shortcomings it is certainly an exaggeration to claim that

this interpretation fails 'not from any minor defect but because it

comes from entirely the wrong philosophical tradition'.28 The reply

to this must surely be that this interpretation is far from being the

complete failure suggested since there is every sign that Wittgenstein

felt perfectly at home in this supposedly alien philosophical tradition.

In one sense this conclusion about the source of Wittgenstein's

verificationism raises many more questions than it answers. For those

who reject the Vienna Circle's reading do so on the basis of what look

like very persuasive arguments which are based on what Wittgenstein

says in the Tractatus. Whereas my claim that we must trace the source

of Wittgenstein's verificationism back to the Tractatus is not based on

what he actually says in the Tractatus. While I do not think that this

makes my argument any less conclusive, clearly if I am right then it

must be possible to demonstrate the existence of Wittgenstein's tacit

verificationism directly on the basis of what he says in the Tractatus.

In addition it needs to be shown precisely where the arguments which

appear to show that there is no place within the framework of the

Tractatus for verificationism go wrong. It seems like no easy task to

do either of these things, and I shall not attempt to do either here. But

I do not think it will prove any easier to find a convincing alternative

explanation of the source of Wittgenstein's verificationism or to show

where my own argument goes wrong.

I suggested earlier that finding an answer to the question of the

origins of Wittgenstein's verification might well have far-reaching

consequences and involve radical revisions of widely accepted views

about Wittgenstein's ideas beyond the brief period of his explicit

verificationism. This much seems certain, that if my argument is

correct then this suggestion has very definitely been borne out.

NOTES

1 These remarks come, respectively, from Philosophical Remarks, Basil Blackwell,

Oxford, 1975, pp. 174, 200; and from Ludwig Wittgenstein and the Vienna Circle, Basil

Blackwell, Oxford, 1979, pp. 47, 53, 79.


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288 MICHAEL WRIGLEY

2 Desmond Lee (ed.): 1980, Wittgenstein's Lectures: Cambridge, 1930-1932, Basil

Blackwell, Oxford, p. 66.

3 He once said, 'I used at one time to say that, in order to get clear how a certain

sentence is used, it was a good idea to ask oneself: How would one try to verify such an

assertion? _But some people have turned this suggestion about asking for the

verification into a dogma - as if I'd been advancing a theory about meaning', Gasking

and Jackson: 1978, 'Wittgenstein as a Teacher', in K. T. Fann (ed.), Ludwig Witt

genstein: The Man and His Philosophy, Harvester, Brighton, p. 54. Notice that even

here what Wittgenstein was objecting to was not so much the idea that meaning was in

some way connected with verification as the idea that this provided the basis for a theory

of meaning. Of course it is not clear that he was even justified in complaining about this.

Certainly it's hard on reading the texts of the early Thirties to escape the impression

that, in one sense at least of 'theory', that was exactly what Wittgenstein was doing.

4 Cf. Ramsey's description of these meetings in the letter to his mother written while he

was still in Austria, in Wittgenstein, Letters to C. K. Ogden, Basil Blackwell and

Routledge and Kegan Paul, Oxford and London, 1973, p. 78.

5 So G. E. Moore reports, 'Wittgenstein's Lectures, 1930-1933', Philosophical Papers,

Allen and Unwin, London, 1959, pp. 248-49.

6 Letter to Keynes, 4th July 1924, in Wittgenstein's Letters to Russell, Keynes and

Moore, Basil Blackwell, Oxford, 1974, p. 116.

7 As he remarked later, 'When I was building the house for my sister in Vienna I was so

completely exhausted at the end of each day that all I could do was go to a flick every

night', Drury: 1984, 'Conversations with Wittgenstein', in Rhees (ed.), Recollections of

Wittgenstein, Oxford University Press, London, p. 106.

8 Wittgenstein never attended the official meetings of the Vienna Circle, but met some

members of the Circle separately. Cf. McGuinness' introduction to Wittgenstein and the

Vienna Circle.

9 Feigl: 1980, 'The Wiener Kreis in America', in R. S. Cohen (ed.), Inquiries and

Provocations: Selected Writings, 1929-1974, D. Reidel, Dordrecht, p. 63.

10 Cf. McGuinness' introduction to Wittgenstein and the Vienna Circle, p. 15, and Feigl

op. cit.

11 Feigl op. cit., p. 64.

12 Cf. Hallett: 1977, A Companion to Wittgenstein's Philosophical Investigations',

Cornell University Press, Ithaca, p. 762.

13 Indeed Wittgenstein seems to go even further and takes Frege himself to task for

lapsing into psychologism, commenting, 'it is remarkable that a thinker as rigorous as

Frege appealed to self-evidence as a criterion of a logical proposition', Tractatus

6.1271.

14 As we know from von Wright's report in 'Ludwig Wittgenstein: A Biographical

Sketch' Wittgenstein, Basil Blackwell, Oxford, 1982, p. 18. Although von Wright goes

on to say that Wittgenstein abandoned some of his earliest Schopenhauerian views as a

result of the influence of Frege, it has been argued very convincingly that the ideas of

the Tractatus still incorporate substantial Schopenhauerian elements. Cf. Hacker: 1972,

Insight and Illusion, Clarendon Press, Oxford, pp. 58fF.

15 For example, 'when the intuitionists speak of the basic intuition - is this a


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psychological process? If so, how does it come into mathematics?', Philosophical

Grammar, Basil Blackwell, Oxford, 1974, p. 322.

16 Cf. Dummett: 1977, Elements of Intuitionism, Clarendon Press, Oxford; and, espe

cially, 'The Philosophical Basis of Intuitionist Logic', Truth and Other Enigmas,

Duckworth, London, 1978.

17 Although two points are worth making briefly. One obvious question, whose im

portance was stressed to me by Peter Eggenberger, is whether Dummett's interpretation

can do justice to the evident transcendental dimension of Brouwer's thought. At a

different level questions can be raised whether the kind of picture of mathematics which

follows from the theory of meaning which Dummett claims is implicit in Brouwer

actually tallies with the views which Brouwer put forward. In particular, it can be

questioned whether Dummett's theory of meaning really has the revisionary con

sequences with respect to mathematics which are such a notorious part of Brouwer's

ideas. Cf. Crispin Wright: 1981, 'Dummett and Revisionism' in Philosophical Quarterly,

where it is forcefully argued that Dummett's account of meaning does not have any such

revisionary consequences. If this is right then Dummett's claim to have extracted the

true core of Brouwer's intuitionism is clearly called into question.

18 Although the key idea behind this perspective on Wittgenstein is due to Dummett, he

has not been much concerned with working out any detailed interpretation of Witt

genstein himself. The most detailed presentation of such an interpretation is to be found

in the early work of Baker and Hacker, e.g., Hacker Insight and Illusion, and Baker and

Hacker 'Critical Notice of Wittgenstein's Philosophical Grammar', Mind, April 1976.

(Although I should stress that Baker and Hacker have long since vigorously rejected

such a reading of Wittgenstein. Cf. Scepticism, Rules and Language, Basil Blackwell,

Oxford, 1984, pp. 46-47.) Similar ideas have been put forward in John Richardson:

1976, The Grammar of Justification, Sussex University Press, London, and in Crispin

Wright: 1980, Wittgenstein on the Foundations of Mathematics, Duckworth, London.

19 Dummett has discussed this aspect of his ideas most fully in 'What is a Theory of

Meaning? (II)', in Evans and McDowell (eds.), Truth and Meaning, Clarendon Press,

Oxford, 1976. Cf. also Crispin Wright 'Truth-Conditions and Criteria', Proceedings of

the Aristotelian Society, Suppl. Vol. 1976.

20 Philosophical Grammar, p. 290.



23 In fact it is an oversimplification to say that Hubert completely rejected the idea that

mathematical sentences had a meaning. For a certain very restricted class of sentences

he did allow that they had descriptive content.

24 In 'Mathematics in the Tractatus' (to appear) I have tried to show that it is possible to

piece together enough of the extremely compressed account of mathematics given in

the Tractatus to see that this claim about the relation between a mathematical sentence

and its proof is implicit in that account.

25 Cf. 'Mathematics in the Tractatus' for arguments that, contrary to what is often

claimed, Wittgenstein did not reject the completed infinite in the Tractatus.

26 I have discussed how exactly Brouwer did influence Wittgenstein in more detail in

'Wittgenstein and Brouwer' (to appear).

27 As both Russell and Waismann, among others, found. Cf. Kenneth Blackwell: 1981,


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290 MICHAEL WRIGLEY

'The Early Wittgenstein and the Middle Russell', in I. Block (ed.), Perspectives on the

Philosophy of Wittgenstein, Basil Blackwell, Oxford, p. 27n, and Gordon Baker: 1979,

'Verehrung und Verkehrung: Wittgenstein and Waismann', in Luckhardt (ed.), Wit

genstein: Sources and Perspectives, Cornell University Press, Ithaca, New York, pp.

267 68.

28 James Griffin: 1964, Wittgenstein's Logical Atomism, Clarendon Press, Oxford, p.

150.

Departamento de Filosof?a (IFCH)

Universidade Estadual de Campinas

CP? 117

13100 Campinas, S.P.

Brazil

20116622

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