哲学の門：大学院生研究論集

Thought Experiments as Objects of Comparison 1

The University of Tokyo, Kumpei YAMAMURO
1. Introduction

As Timothy Williamson points out (Williamson 2022, 181), themethod of thought experiments is the most conspicuous inanalytic philosophy. However, varied views exist on thought
experiments, and no consensus has been reached regarding whatthought experiments are and how they serve philosophicalinquiries. For example, James Robert Brown (1986, 1992, 2004,2011) claims that some thought experiments are Platonic 2 , andJohn

Norton(1991,

1996,

2004)

contends

thatthought

experiments can always be reconstructed as arguments; therefore,
they are arguments in disguise.
Moreover, with the emergence of experimental philosophy,
the importance of clarifying the nature and function of thought
experiments

cannotbeoveremphasized.

Experimental

philosophers have conducted empirical surveys to show thatpeople’s

intuitionsaresignificantly

affectedbyapparently

irrelevant factors, such as the subjects’ cultural background, theorder in which imaginary cases are presented, the environment inwhich the subjects’ intuitions are elicited, and so on (see, e.g.,Stich and Tobia 2017). Thus, experimental philosophy, albeit
controversially,
reliability

of

has

providedphilosophers’

muchevidence

intuitions.

The

to

doubt

the

plausibility

andrelevance of the challenges posed by experimental philosophy,
however, depend on the answer to the question: What is a thought
experiment? Suppose thought experiments are arguments in
disguise, as Norton argues. In that case, the fact that people’s
intuitions are biased in many ways does not pose any hurdle tothe plausibility of the method of thought experiments, just as theexistence of the belief bias is irrelevant to the validity of anargument.

However,ifthought

experiments

are

like

real

experiments, with the only difference being that they are
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conducted in the brain, then the challenges posed by experimental
philosophy can be critical because intuitions are then understoodin an analogous way to data in real experiments.
Against the backdrop of such metaphilosophical concerns,
I conceive of thought experiments as objects of comparison byarguing that Ludwig Wittgenstein’s language games are a revised
version of thought experiments. Wittgenstein’s later philosophy
contains many ingenious fictitious cases. However, the functionsof those imaginary scenarios are not well understood, leading
people to assume that Wittgenstein’s language games are thought
experiments despite his explicit denial. Nenad Miščević, forexample, asserts that Wittgenstein’s imaginary scenarios count as
thought experiments because they satisfy a standard definition ofthought

experiments.

misunderstanding,

I

begin

delineatingbyeliminating

Wittgenstein’s

such

a

thoughts

onlanguage games and thought experiments.
This paper is organized as follows. Section 2 examines
Miščević’s claim that Wittgenstein’s imaginary scenarios arethought experiments. Section 3 presents Wittgenstein’s thoughtson the concept of a thought experiment. Finally, Section 4 argues
that Wittgenstein’s method of language games is a revised versionof thought experiments. Before concluding the paper, I suggest
the advantage of the conception of thought experiments as objectsof comparison over the prevalent one.
2. Miščević on Wittgenstein’s Scenarios

At the beginning of his paper, Miščević quotes Wittgenstein on
thought experiments:
What Mach calls a thought experiment is of course not anexperiment

at

all.

At

bottomit

isagrammaticalinvestigation. (PR §1)
Then, Miščević presents a standard definition of thought239

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experiments and asserts that Wittgenstein’s scenarios are indeed
thought experiments because they satisfy the definition, despite
Wittgenstein’s denial. Miščević says:
Consider the definition of TE [= thought experiment] inStanford Encyclopedia (due to J.R. Brown and Y. Fehige):“Thought experiments are devices of the imagination used
to investigate the nature of things. Thought experimenting
often takes place when the method of variation is employed
in entertaining imaginative suppositions.” The Builders
scenario fits well; it is a device of the imagination used toinvestigate

thenatureoflinguistic

practicesandtointroduce the central idea of a language game. (Miščević
2017)
What he calls the “Builders scenario” here is a language gameWittgenstein

discusses

inthebeginningof

PhilosophicalInvestigations . Miščević claims that the Builders scenario counts
as a thought experiment because it satisfies the definition.
There are at least two problems with this claim. First,
Wittgenstein’s scenarios do not fit the definition. Second, Miščević
fails to grasp the point of Wittgenstein’s assertion that thought
experiments are not experiments; Wittgenstein is not saying that
his scenarios should not be called “thought experiments” but that
it is wrong to assume that thought experiments are pretty much
like real experiments, with the only difference being that theformer are conducted in the brain or the laboratory of the mind.
In the remainder of this section, I deal with the first point; that
is, I argue how Wittgenstein’s imaginary scenarios do not satisfy
the definition that Miščević quotes. To this end, let us have a lookat Wittgenstein’s thoughts on philosophy and language games.
Wittgenstein

statesthat“[p]hilosophy

just

puts

everything before us, and neither explains nor deduces anything”(PI §126); we can, therefore, conclude that Wittgenstein would not
employ language games to “investigate the nature of things.”
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Nevertheless, in the quote above, Miščević equates “the nature of
linguistic practices” with “the nature of things” so that thedefinitionofunderstanding

thoughtofexperiments

Philosophicalwill

resemble

Investigations .

Even

his
then,

Wittgenstein’s scenarios fail to fit the definition because he does
not attempt to investigate “the nature of linguistic practices” inthe first place. Wittgenstein maintains:
We want to establish an order in our knowledge of the useof language: an order for a particular purpose, one out ofmany possible orders, not the order. For this purpose weshall again and again emphasize distinctions which ourordinary forms of language easily make us overlook. (PI§132)
Wittgenstein does not try to establish the order to clarify thenature of linguistic practices. Instead, his language games aremeant to illuminate our language for a specific purpose . In thissense, the orders he tries to establish are in no way absolute; they
are relative to specific purposes. So what is the purpose for which
an order is established? Wittgenstein says:
All explanation must disappear, and description alone
must take its place. And this description gets its light —that is to say, its purpose — from the philosophical problems.
(PI §109)
The purpose is to solve (or dissolve) philosophical problems. It
is only insofar as it serves to solve philosophical problems that hetries to establish an order by means of language games. It is
mistaken to assume that he tries to discover the nature of
linguistic practices. Thus, Wittgenstein’s scenarios do not fit thedefinition.
One might argue that Wittgenstein’s fictitious cases canbe regarded as thought experiments if we adopt a less restrictive241

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definition of the term. However, this line of response would
trivialize Wittgenstein’s criticism. We need to understand therationale for his rejection.
3. Wittgenstein on Thought Experiments

Previously, I argued that Wittgenstein’s scenarios do not satisfy
the definition of a thought experiment that Miščević refers to.
Miščević seems to assume that terming Wittgenstein’s scenarios“thought experiments” or otherwise is a simple verbal matter.
That may be why he gives few arguments to endorse the claimthat Wittgenstein’s scenarios are thought experiments. However,this is not true, as I claim below.
First of all, let us look at what Wittgenstein says about
thought experiments.
What Mach calls a thought experiment is of course not anexperiment

at

all.

At

bottomit

isagrammaticalinvestigation. (PR §1)(Seemingly, I am performing ‘thought-experiments’. Well,they’re simply not experiments. Calculations would be muchcloser.) (LW I §519)
What is shown in these quotes is that Wittgenstein repudiates
the idea of thought experiments because he thinks they are notexperiments, and what we call thought experiments are muchcloser to “calculations” than to experiments. In other words,
Wittgenstein is not so much opposed to what we call thought
experiments being called “thought experiments” as he is opposedto them being considered experiments. Therefore, it is misguided
to bring up a definition of thought experiments and argue that
Wittgenstein’s scenarios can be called “thought experiments”
simply because they conform to it.
But what does he mean when he says that thought242

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experiments are not experiments but much closer to calculations?
To answer this question, we need to examine Wittgenstein’s
discussions

on

the

distinction

betweenexperiments

andcalculations.
AccordingtoWittgenstein,normativity

is

key

to

differentiating calculations and experiments. Suppose that we
make a calculation, say, 25 × 25, and get 625 one day and 624 thenext day. We would naturally suspect that we made a mistake, atleast in one of these calculations, which shows that we think that
there must be right and wrong answers when it comes tocalculations.

In

other

words,

normativity

isintrinsic

tocalculations. At the same time, when we conduct experiments, weare concerned with what results we will obtain, not what the right
results are 3 . So if the conditions of an experiment are fulfilled,“then we must accept whatever comes, as the result” (RFM 336).
Obviously, this is not how we use calculations. Thus, treating
calculations as experiments leads to a bizarre consequence:[I]f a calculation is an experiment then the proposition
that it yields such and such a result is after all the
proposition that under such conditions this kind of sign
makes its appearance. And if under these conditions one
result appears at one time and another at another, we haveno right to say “there’s something wrong here” or “bothcalculations cannot be all right”, but we should have to say:this calculation does not always yield the same result ( whyneed not be known). (ibid.)
In most cases 4 , when making calculations we do not want toknow how the subject will behave or what number a specificindividual will arrive at in such and such conditions, which iswhere Wittgenstein thinks the distinction between experiments
and calculations lies. If a calculation is an experiment, and theconditions are fulfilled, we have no right to say that the result isright or wrong. As Wittgenstein says: “The conditions of the243

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experiment don’t include the result” (LFM 97).
However, when it comes to thought experiments, people
freely say certain results or intuitive judgments are wrong or
unreliable.

For

example,some

proponentsofexperimental

philosophy criticize the use of thought experiments and intuitions
therein, and some philosophers who defend the method claim thatlaypeople’s intuitions are unreliable because they lack expertise
(see,

e.g.,

philosophers

Williamson
have2022).

offeredMeanwhile,

empirical

experimental

evidence

that

even

professional philosophers are not immune to various cognitive
biases (see, e.g., Schwitzgebel and Cushman 2012) and argue thatphilosophers do not possess the kind of expertise they claim. In
summary, people seem to be arguing about the right and wrong
results of thought experiments. If thought experiments areexperiments, then how can they be made sense of?
One way to make sense of them is to assume thatphilosophers are discussing the conditions of experiments when
they seem to be arguing about the right and wrong results. Those
who say some results are wrong and others are right must be
taken as saying that certain conditions are not fulfilled.
But what are the conditions? They may be, for instance,such that the intuitions must be elicited from professional
philosophers, or every detail of the thought experiment must be
fully understood. If thought experiments include such conditions,people may be able to contend that some results are unreliablebecause the conditions are not fulfilled. For instance, those who
say that experimental philosophers’ challenges are irrelevant
because they carried out surveys on the wrong subjects can beunderstood as complaining about the inadequacy with which
experimental philosophers conducted the experiment.
Here, the problems are that (1) philosophers do not admit
the divergence of intuitions even if the conditions are fulfilled,and (2) the meaning of the condition that every detail of thethought experiment must be fully understood is not clear. I
discuss each of these below.
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First, I have suggested above that the conditions ofthought experiments may include one that the subjects should bephilosophers. However, a homogeneous group of philosophers canalso report divergence in intuitive judgments (e.g., Stich andTobia 2017). In other words, even if the condition that the subjects
should be philosophers is fulfilled, they would not cease talking
about the right and wrong results, which shows that thought
experiments are not treated as experiments. Philosophers think
thought experiments allow for right and wrong results.
Second, some people might stipulate that subjects ofthought experiments should understand the scenario well so thatthe results converge. In this case, however, normativity is built
into the conditions of the experiment. As normativity is what
differentiates experiments and calculations, this response must
fail. Since the conditions of the experiment don’t include theresult, the criterion for understanding well should not be includedin the conditions.
Therefore, it is unlikely that philosophers treat thought
experiments as experiments. Philosophers discuss right andwrong results, but as we have seen above, it is difficult tointerpret them as addressing the conditions of the experiment.
Even if we call them “thought experiments,” we do not treat themas such; we assume that the results are included in the conditions.
What we call “thought experiments” are not experiments.
Then, how are we to understand Wittgenstein’s imaginary
cases? In the next section, I will argue that Wittgenstein’s
language games are a revised version of thought experiments,that is, thought experiments used not as experiments but asobjects of comparison.

4. Thought Experiments as Objects of Comparison

Earlier,I

illustrated

Wittgenstein’s

claim

that

thought

experiments are not experiments but closer to calculations. This
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section deals with the positive characterization of what we call“thought experiments.” I first present Wittgenstein’s conceptionof language games as objects of comparison. Then, I argue thatthought experiments should be taken as objects of comparison.
Finally, I outline a possible significance of the revised conceptionof thought experiments.
Imaginary scenarios are ubiquitous in Wittgenstein’s later
writings, and some people call them “thought experiments” justbecause they are fictitious. However, as we saw in the previous
section, he is against the idea of thought experiments . What are
the fictitious language games in his writings, if not thought
experiments? How are they supposed to function? Wittgenstein
explains the method of language games as follows:
Our clear and simple language-games are not preliminary
studies for a future regimentation of language—as it were,first approximations, ignoring friction and air resistance.
Rather, the language-games stand there as objects ofcomparison which, through similarities and dissimilarities,
are meant to throw light on features of our language. (PI§130)
Although Wittgenstein criticizes the conception of imaginary
scenarios as thought experiments, he recognizes the importanceof constructing fiction in philosophy (cf. CV 74e). In this quote,
he offers a positive characterization of language games as objectsof comparison 5 . Wittgenstein’s language games are a revised
version of thought experiments. That is, not only does he reject
the conception of imaginary scenarios as thought experiments, but
he proposes a viable way of using fictitious cases in philosophy.
The fact that he refers to what is called a thought experiment as
a grammatical investigation seems to endorse this claim (cf. PR
§1),

for

“grammaticalinvestigation”

isanothernameforWittgenstein’s later philosophy.
How does the conception of thought experiments as objects
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of comparison connect with the claim that thought experiments
are much closer to calculations? To answer this question, let us
look at Wittgenstein’s remarks about calculations.
If it is a calculation, we adopt it as a calculation—that is,
we make a rule of it. We make the description of it thedescription of a norm —we say, “This is what we are going tocompare things with.” (LFM 98)
Wittgensteinstraightforwardlyconnects

calculations

withobjects of comparison or standards of comparison.
Additionally, a mundane example can easily be offeredbecause we always use calculations as objects of comparison in
everyday life 6 . If you put two things in a bag and then add three
but find only four items in the bag, you would suspect that you
miscounted them or failed to put a thing into the bag. Here, thecalculation “2 + 3 = 5” serves as an object of comparison or aparadigm. You compare it with reality and assume you made a
mistake. Note, however, that calculations do not apply to all
experiences. If you add two drops to three drops of water, you will
get one instead of five. So, it is crucial to remember that they are,after all, objects of comparison. Calculations or objects ofcomparison are not, as it were, responsible for reality; they are
not preconceptions “to which reality must correspond” (PI §131).
Therefore,

itisconsistent

to

think

Wittgenstein’s

language games are a revised version of thought experiments withhis claim that thought experiments are more like calculations
than experiments. As I argued above, calculations can also serve
as objects of comparison. Additionally, what Wittgenstein says
about the method of language games applies to calculations. He
says a language game is not a preconception to which reality mustcorrespond. Similarly, we can say that a calculation is not a
preconception to which reality must correspond (recall theexample of drops of water). Both language games and calculations
are adopted because they are useful for some purposes.
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What is wrong with the conception of thought experiments
as experiments? Wittgenstein says that “we can avoid unfairness
or vacuity in our assertions only by presenting the model as what
it is, as an object of comparison” (PI §131), but he doesn’t provide
further clarifications. So, I offer a possible consequence of taking
fictitious scenarios as experiments, although the paper does notallow for a detailed discussion.
Oneobviousdrawback

is

shown

in

the

current

metaphilosophical debates on the reliability of philosophicalintuitions. My contention is that it is the conception of thought
experiments as experiments that gives rise to the challenges ofnegative experimental philosophy. An easy way to see the point is
to consider the fact that we do not cast doubt on the reliability of
intuitions when we calculate, say, 2 + 3 = 5 7 . It is irrelevant tothe validity of calculations that we are prone to various biases orthat calculations don’t hold for some sorts of objects. Likewise, we
don’t take someone’s answering “2 + 3 = 6” as a counterexample
for a mathematical theory. If we make it perspicuous that thought
experiments are not experiments, such doubts should evaporate.
One might argue that thought experiments are very much
unlike calculations in that we have a variety of “intuitions” about
an imaginary case while we have the answer to a given
calculation; hence, it must be wrong to understand thought
experiments as something close to calculations. My claim is thatitisbecausewemistakenly

takethought

experiments

asexperiments that it seems we cannot discern “reliable intuitions.”
In philosophical thought experiments, people’s intuitions count asevidence for or against philosophical claims. We think ourintuitions need to be reliable enough to count as evidence, which
in turn leads to experimental philosophical endeavors 8 . Thus, at
the root of current philosophical debates about the reliability of
intuitions

lies

the

conceptionofthought

experiments

asexperiments.
Note that I am not saying that experimental philosophy isentirely futile. Studies on the Knobe effect demonstrate the248

哲学の門：大学院生研究論集

significance of experimental philosophy (see, e.g., Knobe 2003;
2010).

My

claim

is

that

by

construing

so-calledthought

experiments as objects of comparison, one can avoid the challenge
posed by experimental philosophy as it stems from the conceptionof thought experiments as experiments 9 . However, this is just an
outline. To delve deeper, we have to look at Wittgenstein’s
philosophy of mathematics, especially his view on the status ofmathematical propositions. Due to the lack of space, the task
should be tackled in future work.

5. Concluding Remarks

Wittgenstein denies that thought experiments are experiments,
accentuatingthedistinction

betweenexperiments

andcalculations. According to him, what we call thought experiments
are not experiments at all, but closer to calculations. Therefore,
Wittgenstein’s language games should not be considered thought
experiments. They are objects of comparison that “throw light onfeatures of our language” (PI §130).
I suggested a connection between experimental philosophy
and the conception of thought experiments as experiments.
However, due to the lack of space, I could only touch upon apossible connection. Future work is needed to show that thealternative conception of thought experiments as objects ofcomparison avoids the challenge of experimental philosophy, andthat the conception continues to serves philosophical inquiries.

Notes

1.

This paper is sponsored by Japan Society for the

Promotion of Science (22J20062).

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哲学の門：大学院生研究論集

2.

“A Platonic thought experiment is a single thought

experiment which destroys an old or existing theory andsimultaneously generates a new one; it is a priori in that it
is not based on new empirical evidence, nor is it merely
logically derived from old data; and it is an advance in thatthe resulting theory is better than the predecessor theory.”(Brown 2011: 99)
3.

There might be cases where we are inclined to saythat certain results of an experiment are wrong (e.g., resultsthat seem to indicate that neutrinos travel faster than light).
However, even in such cases, it is not the results that we say
are wrong but the conditions of the experiment.
4.

Wittgenstein says that the act of calculating canfunction as an experiment in some cases. For example, if the
purpose

is

to

see

whetherastudent

has

masteredmultiplication or whether chalk will stand the strain, theact of calculating can count as an experiment (cf. RFM: 380;
LFM: 93).
5.

For the elucidation of how language games such as

the Builders scenario are used as objects of comparison, see
Kuusela 2019: Section 5.2.
6.

It is obvious that calculations are not, in most cases,“meant to throw light on features of our language” (PI §130),but it does not follow that calculations are not objects ofcomparison. It is just that they are not the objects ofcomparison with our language.
7.

I do not mean that we cannot cast doubt on thevalidity. Of course, this point is related to the so-called rulefollowing

considerations,butI

cannot

deal

with

the

connection here.
8.

“If intuitions generated in response to thought250

哲学の門：大学院生研究論集

experiments are supposed to be able to be used as reasonsto accept or reject some philosophical claim, then we should
be interested in studying the nature of the relevant
intuitions. Experimental philosophy takes up this challenge,
applying the methods of experimental psychology to thestudy of the nature of intuitions generated in response tothought-experiments.” (Alexander and Weinberg 2007).
9.

If thought experiments could be interpreted asarguments as Norton tries to do, the problem of thereliability of intuition might be avoided. However, several
problems exist with this claim. See, for example, Häggqvist
2009.

(3,795 words)

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