DOI: 10.1111/phin.12232
Philosophical Investigations 42:2 April 2019
ISSN 0190-0536
On Certainty: Wittgenstein and Einstein
Giovanni Mion, Istanbul Technical University
Abstract
The paper focuses on the role of relativistic ideas in Wittgenstein’s
philosophy. In particular, it focuses on On Certainty (1969), where in
(305), Wittgenstein explicitly invokes Einstein’s theory of relativity:
“Here once more there is needed a step like the one taken in relativity
theory.” The aim of the paper is to establish a connection between
Wittgenstein and Einstein that is both theoretically and exegetically
sound. In particular, the paper argues that Wittgenstein’s reaction to
scepticism closely resembles Einstein’s reaction to the ether.
I. Introduction
The connection between Wittgenstein and Einstein has been duly
explored. Quite recently, Carlo Penco (2010) and Martin Kusch (2011
and 2015) attempted to link several aspects of Wittgenstein’s philosophy
to Einstein’s special theory of relativity. Their methodologies diverge:
Penco takes a historical perspective, while Kusch is more interested in
theoretical problems. Yet, their conclusions are strikingly similar: both of
them argue that Einstein’s influence on Wittgenstein was genuine, and
that some of Einstein’s ideas can be profitably used in order to illuminate
Wittgenstein’s philosophy. Among other things, Kusch and Penco
engage the following issues: verificationism (Penco), holism (Penco),
rule-following (Penco and Kusch), scheme-content dualism (Kusch),
relativism and scepticism (Kusch).
Following their lead, I also wish to focus on the role of relativistic
ideas in Wittgenstein’s philosophy. However, in contrast to them, I will
only focus on On Certainty [OC], where, in (305), Wittgenstein explicitly invokes the theory of relativity: “Here once more there is needed a
step like the one taken in relativity theory.” My goal is to establish a
connection between Wittgenstein and Einstein that is both theoretically
and exegetically sound.
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II. Relativity in On Certainty
Notoriously, On Certainty was prompted by Moore’s rebuttal of scepticism in his “Proof on an External World”. When the sceptic claims that
we do not know about the existence of an external world, Moore replies
that he or she must be wrong, for we do know about the existence of
external things. According to him, their existence trivially follows from
the fact that we have hands:
I can prove now, for instance, that two human hands exist. How? By
holding up my two hands, and saying, as I make a certain gesture with
the right hand, ‘Here is one hand’, and adding, as I make a certain gesture with the left, ‘and here is another’. And if, by doing this, I have
proved ipso facto the existence of external things, you will all see that I
can also do it now in numbers of other ways: there is no need to multiply examples. (1939: 145–146)
However, according to Wittgenstein, Moore’s reply fails, for, among
other things, Moore does not to appreciate the role that propositions like
‘Here is one hand’ and ‘There are physical objects’ actually play “in the
system of our empirical judgements”:
137. Even if the most trustworthy of men assures me that he knows
things are thus and so, this by itself cannot satisfy me that he does
know. Only that he believes he knows. That is why Moore’s assurance
that he knows. . . does not interest us. The propositions, however,
which Moore retails as examples of such known truths are indeed
interesting. Not because anyone knows their truth, or believes he
knows them, but because they all have a similar role in the system of
our empirical judgements.
In particular, Moore seems to believe that the sceptic can be refuted by
empirical evidence, and that our knowledge about hands provides the
required evidence (OC 35).
In contrast to Moore, Wittgenstein claims that the sceptic fails to raise
any genuine challenge, for we cannot doubt everything at once (OC
115, 450), in the sense that a genuine doubt presupposes some more or
less explicit assumptions (OC 342, 509):
341. That is to say, the questions that we raise and our doubts depend on
the fact that some propositions are exempt from doubt, are as it were
like hinges on which those turn.
So, in contrast to Moore, Wittgenstein argues, among other things, that
truisms like ‘Here is one hand’ are not genuine empirical propositions, but
assumptions or postulates that are tacitly presupposed in all empirical inquiries (OC 136, 308). They belong to our frame of reference (OC 83).
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As I noted above, my goal is not to assess Moore’s reply to scepticism,
nor Wittgenstein’s reply to Moore, or his interpretation of Moore’s philosophy, for that matter. My goal is to attempt to shed some light on
Wittgenstein’s understanding of propositions such as ‘Here is one hand’
with the help of the special theory of relativity. This might seem bizarre.
Yet, as I am about to argue, the following entry in On Certainty points
straight to Einstein:
321. Isn’t what I am saying: any empirical proposition can be transformed into a postulate—and then becomes a norm of description.1
But then Wittgenstein continues:
But I am suspicious even of this. The sentence is too general. One
almost wants to say “any empirical proposition can, theoretically, be
transformed. . .” but what does “theoretically” mean here? It sounds all
too reminiscent of the Tractatus.
(321) presupposes a conceptual distinction between empirical propositions and norms of descriptions. This distinction is reminiscent of the
traditional distinction between necessary truths and empirical truths. For
example, in Language, Truth and Logic, Ayer writes that
[t]he best way to substantiate our assertion that the truths of formal
logic and pure mathematics are necessarily true is to examine cases
in which they might seem to be confuted. It might easily happen,
for example, that when I came to count what I had taken to be
five pairs of objects, I found that they amounted only to nine. And
if I wished to mislead people I might say that on this occasion
twice five was not ten. But in that case I should not be using the
complex sign ‘2 9 5 = 10’ in the way in which is it ordinarily used.
I should be taking it not as the expression of a purely mathematical
proposition, but as the expression of an empirical generalization, to
the effect that whenever I counted what appeared to me to be five
pairs of objects I discovered that they were ten in number. This
generalization may very well be false. But if it proved false in a
given case, one would not say that the mathematical proposition
‘2 9 5 = 10’ had been confuted. One would say that I was wrong
in supposing that there were five pairs of objects to start with, or
that one of the objects had been taken away while I was counting,
or that two of them had coalesced, or that I had counted wrongly.
One would adopt as an explanation whatever empirical hypothesis
fitted in best with the accredited facts. The one explanation which
would in no circumstances he adopted is that ten is not always the
product of two and five. (1936: 75–76)
1. (321) is dated 12.3.51, and it succeeds almost immediately (305), which is dated
10.3.51. There is no entry in 11.3.51.
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As Wittgenstein continues:
380. I might go on: “Nothing in the world will convince me of the
opposite!” For me this fact is at the bottom of all knowledge. I shall
give up other things but not this.
According to Wittgenstein, we would never conclude that ten is not
always the product of two and five, precisely because in our community
‘2 9 5 = 10’ is treated as a “norm of description”, as opposed to a mere
empirical proposition.
Yet, in On Certainty, by switching from the concept of necessary truth
to the concept of norm of description, Wittgenstein introduces some
revolutionary elements:
(I) He claims that theoretically, all empirical propositions can function as a
norm of description.
(II) He maintains that at least some propositions can be profitably reinterpreted as norms of description. (And, conversely, that some norms
of description can turn into empirical propositions: OC 96).2
(I) and (II) ought to be clearly distinguished, otherwise we would fail to
appreciate that the target of Wittgenstein’s dissatisfaction in (305) is (I). In
particular, when Wittgenstein writes that the sentence “any empirical proposition can be transformed into a postulate – and then becomes a norm of
description” is too general, he wishes to straightforwardly reject his Tractatus-like oversimplification: “It sounds all too reminiscent of the Tractatus.”3
In the Tractatus (1921), Wittgenstein maintained that all propositions are
pictures of reality (4.01), and that all complex propositions are truth-functions of elementary propositions (5, 5.3). Moreover, he also maintained
that it must be theoretically possible to analyse any complex proposition into
its hidden elementary constituents: names that signify objects which are
simple (2.02, 3.201–3.22, 4.22–4.221). Yet, he was unable to deliver any
actual analysis. Even worse, he was unable to provide an example of an
elementary proposition, name, or simple object. According to Malcolm’s
testimony, he believed that these were mere empirical issues:
2. Accordingly, Antony Kenny writes: “There can also, we may note, be change in the
other direction—as is shown by the proposition ‘no man has ever been on the moon’
which Wittgenstein notoriously gave as an example of something that stands fast for us. ‘If
we are thinking within our system, then it is certain that no one has ever been on the
moon. Not merely is nothing of the sort ever seriously reported to us by reasonable people, but our whole system of physics forbids us to believe it’ (OC 208). Nowadays, of
course, it is a matter of straightforward empirical inquiry to ascertain how many men have
been on the moon.” (2008: 151)
3. In The Blue Book (1958: 18), Wittgenstein argues that the craving for generality is
one of the sources of metaphysics.
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One anecdote should be recorded. I asked Wittgenstein whether, when
he wrote the Tractatus, he had ever decided upon anything as an example of a ‘simple object’. His reply was that at that time his thought had
been that he was a logician; and that it was not his business, as a logician, to try to decide whether this thing or that was a simple thing or a
complex thing, that being a purely empirical matter! It was clear that he
regarded his former opinion as absurd. (1958: 70)
So, by the time he wrote On Certainty, Wittgenstein believed that
there was nothing that all propositions had in common (1953: §65) and
that in philosophy, nothing was hidden (1953: §91–92, §126–129).
Accordingly, he rejected any philosophical practice which assumed that
some things must be theoretically possible.
On the other hand, even if not all empirical propositions can be readily transformed into norms, some of them definitely enjoy such a status:
167. It is clear that our empirical propositions do not all have the same
status, since one can lay down such a proposition and turn it from an
empirical proposition into a norm of description.
In particular, a genuine solution to the puzzles raised by the sceptic
requires us to reinterpret Moorean propositions like ‘Here is one hand’
as norms of descriptions. This is a radical departure from Moore’s perspective: Moore takes his claims to empirically refute the sceptic; while
Wittgenstein takes Moore’s truisms to refute the sceptic because they
are norms of description that need to be presupposed or postulated in
order to meaningfully raise this or that specific doubt. In short, what
Moore takes to be an empirical truth is, for Wittgenstein, in reality a
postulate.
We are now ready to appreciate the role that relativity plays in
Wittgenstein’s thinking. In a vacuum, light travels at approximately
300,000 km/s. Its speed is noteworthy, but the startling fact is that the
speed of light is the same in every frame of reference, and this seems to
conflict with the principle of Newtonian relativity. So, in order to
accommodate the speed of light, Lorentz invoked the presence of an
immaterial substance: the ether, for which no independent empirical evidence was even possible. In short, for Lorentz, the ether wind caused a
contraction along the direction of motion of the apparatus that was used
to measure the speed of light, and such a contraction in turn explained
why the speed of light appeared to be always constant. Yet, since any
ruler that we might use to detect the contraction in question would also
be affected, such a contraction cannot otherwise be tested.
For Einstein, the contraction invoked by Lorenz was not the mechanical
result of an immaterial ether, but the logical consequence of the fact that
the speed of light is actually constant. So, in contrast to Lorentz, Einstein
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rejected the ether, and he explicitly decided to take the fixity of the speed
of light as a postulate of his theory (together with Newtonian Relativity).
Accordingly, he inferred, among other things, that the spatial distance
between two points on a rigid body depended upon the motion of the
frame of reference. As Cassirer wrote in his Einstein’s Theory of Relativity:
The conflict between the principle of the constancy of the propagation of light and the principle of relativity of mechanics became the
“paraclete of thought”—the real awakener of the theory of relativity.
But how did physical thought go about overcoming this conflict,
since it was bound to the outcome of observation as such, since it
could neither set aside the facts expressed in the principle of the constant velocity of light in a vacuum, nor those expressed in the principle of relativity of mechanics? If we look back on the historical
development of the theory of relativity, we recognize that the latter
has followed here a counsel which was once given by Goethe. “The
greatest art in theoretical and practical life,” wrote Goethe to Zelter,
“consists in changing the problem into a postulate; that way one succeeds.” In fact, this was the course which Einstein followed in his
fundamental essay: Zur Elektrodynamik bewegter Systeme of the year
1905. (1921: 370–371)
In short, according to Cassirer, Einstein, implicitly following Goethe’s
advice, managed to accommodate the absoluteness of the speed of light
within a relativistic framework by changing its status from a mere empirical datum into a postulate of his theory.
The connection between Wittgenstein and Einstein should now be
clear, and what Cassirer wrote about Einstein’s solution to the conflict
between Newtonian relativity and the speed of light might be the link
between the two. Be that as it may, the analogies between Einstein’s
disagreement with Lorentz and Wittgenstein’s disagreement with Moore
are striking, and they alone can justify what Wittgenstein writes in
(305):
- Neither the ether nor the sceptical hypothesis can be grounded in any
empirical evidence: the ether, for Einstein, and the sceptical hypothesis,
for Wittgenstein, are the result of an idle theoretical commitment.
- Lorentz and Moore take an empirical approach: for Lorentz, the speed
of light is a mere empirical datum. For Moore, propositions like
‘There are physical objects’ are straightforwardly empirical.
- Both Einstein and Wittgenstein seek a solution to their problems by
elevating mere empirical data to the role of a priori postulates. So, for
Einstein, the fixity of the speed of light becomes an assumption of his
theory of relativity; while, for Wittgenstein, mere empirical propositions such as ‘There are physical objects’ became assumptions that are
generally presupposed in all empirical inquiries.
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Finally, the presence of Goethe might also be a significant clue.
Goethe’s influence on Wittgenstein is well known,4 and in On Certainty
(402), Wittgenstein invokes him as well: “Im Anfang war die Tat” (“In
the beginning was the deed”), meaning that our epistemic practices cannot be grounded by rational justification, but only understood in connection with the way we naturally behave (OC 204, 359). Like the
speed of light in the special theory of relativity, our epistemic practices
“must be taught us as a foundation” (OC 449).
III. Conclusion
As I wrote in the introduction, the connection between Wittgenstein
and Einstein has been duly explored. Yet, the specific connection
between OC (305) and OC (321) has gone unnoticed. However, if my
reading is correct, by invoking the theory of relativity, Wittgenstein
wishes to align his move against Moore with Einstein’s move against
Lorentz. In short, by implicitly following Goethe’s methodological
advice, both Wittgenstein and Einstein try to find a solution to their
problems by changing them into postulates.
Department of Humanities and Social Sciences
Istanbul Technical University
34469 Maslak – Istanbul
Turkey
gmion22@gmail.com
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