Content uploaded by Michael T. Stuart
Author content
All content in this area was uploaded by Michael T. Stuart on May 16, 2019
Content may be subject to copyright.
Content uploaded by Michael T. Stuart
Author content
All content in this area was uploaded by Michael T. Stuart on Dec 10, 2018
Content may be subject to copyright.
ORIGINAL PAPER
Norton and the Logic of Thought Experiments
Michael T. Stuart
1
Received: 5 August 2016 / Accepted: 16 August 2016 / Published online: 23 August 2016
ÓSpringer Science+Business Media Dordrecht 2016
Abstract John D. Norton defends an empiricist epistemology of thought experi-
ments, the central thesis of which is that thought experiments are nothing more than
arguments. Philosophers have attempted to provide counterexamples to this claim,
but they haven’t convinced Norton. I will point out a more fundamental reason for
reformulation that criticizes Norton’s claim that a thought experiment is a good one
when its underlying logical form possesses certain desirable properties. I argue that
by Norton’s empiricist standards, no thought experiment is ever justified in any deep
sense due to the properties of its logical form. Instead, empiricists should consider
again the merits of evaluating thought experiments more like laboratory experi-
ments, and less like arguments.
Keywords Empiricism Experimentalism John D. Norton Material theory of
induction Thought experiments
1 Introduction
Thought experiments seem to play a genuine role in scientific progress. However,
the precise nature of that role, and how thought experiments play it, remain unclear.
James R. Brown claims that some thought experiments, including Galileo’s falling
bodies thought experiment, can provide scientists with fallible a priori knowledge of
laws of nature through direct rational perception (1991, 2). John D. Norton attempts
to explain away the rationalist flavour of thought experiments by identifying them
with arguments. The epistemic import of a thought experiment comes in this case
from an inductive or deductive inference that only preserves or extends existing
&Michael T. Stuart
m.stuart@pitt.edu
1
Center for Philosophy of Science, University of Pittsburgh, Cathedral of Learning, Room 817Q,
Pittsburgh, PA 15213, USA
123
Axiomathes (2016) 26:451–466
DOI 10.1007/s10516-016-9306-2
empirical knowledge and does not require rational insight (Norton
1991,1996,2004a,b). Such a defense assumes that the justificatory force of those
preservations or extensions can also be reduced ultimately to experience. This latter
assumption, concerning the empirical foundations of logic, has received little or no
attention in the discussion of Norton’s view. Yet when we focus on it, serious
internal tensions appear.
In Sect. 2, I present Norton’s account of thought experiments, and show that the
justification of thought experiments by appeal to their logical form is in tension with
Norton’s own work on the nature and power of logic. In Sect. 3, I argue that when it
comes to identifying the source of their epistemic value, empiricists like Norton
should focus on the experimental aspect of thought experiments instead of their
logical aspects.
2 The Argument View
Norton is an empiricist who claims that thought experiments are nothing more than
arguments (1991,1996,2004a,b). It is an attractive view. After all, thought
experiments are presented to us in sentences, some of which are premises, and
they try to convince us of a conclusion, just like arguments. Nevertheless, most
philosophers in the literature reject it. Some argue that the best explanation for the
success of scientific thought experiments requires that we allow for the possibility
of a direct rational grasp of relations between universals (Brown
1986,1991,1992,2004), while others portray thought experiments as mental
models, fictions, exemplifications, or conditions for the possibility of empirical
experiments (see, e.g., Bishop 1999; Davies 2007; Gendler 2004; Gooding
1992,1994; Mis
ˇc
ˇevic
´2007; Nersessian 1991,1992,1993,2007; Elgin 2014;
Sorensen 1992; Bokulich 2001; Buzzoni 2008). Norton easily reconstructs all the
counterexamples the above authors present to his view. And in any case,
philosophers do admit that many thought experiments are nothing more than
arguments. In other words, the above writers disagree primarily with the scope of
Norton’s claim: that all thought experiments are arguments. Despite the relative
unpopularity of the view with philosophers in the literature on thought experiments,
it is still very popular with philosophers in general, and continues to deserve
discussion. Here are the relevant particulars of Norton’s account.
According to Norton, the only ‘‘non-miraculous’’ way to get new information
about the mind-independent world without empirical investigation is by performing
logical manipulations on existing knowledge. If thought experiments produce new
information about the world it is because they bring to light the hidden
consequences of and relations between facts that we already know. Thus, if we
wish to eliminate any appeal to ‘‘epistemic magic’’ (Norton 2004b, 45) we must
accept that thought experiments are arguments; the only empiricist-friendly way of
reasoning to new knowledge from old.
For this view to be substantial, we must be able to pinpoint what Norton means
by ‘‘argument.’’ Norton counts any inference that is licensed by a deductive,
inductive, abductive or informal logic as an argument (2004b, 64), and he allows
452 Axiomathes (2016) 26:451–466
123
diagrams to be steps in arguments (2004b, 58). He claims that we can be pretty sure
of the presence of an argument when a piece of reasoning is convincing (1996, 353),
and that the arguments underlying thought experiments will always be identifiable
(1991, 129) even though they may employ tacit premises (1996, 339) and tacit
inferences (1991, 142–3 note 2). Finally, the defining ‘‘mark’’ that tells us whether a
thought experiment or argument is justified is something completely internal; it is a
structural feature shared by other similarly successful inferences, something we get
by ‘‘merely reading its text’’ (2004a, 1143). Since Norton’s notion of argument is
tied to his notion of logic, it is important to mention that by logic Norton means any
systematization that respects the distinction between form and content. It need not
preserve truth, likelihood or even be formal (2004b, 53). Arguments are things that
are ‘‘governed’’ by such logics (2004a, 1140), and good arguments are those whose
forms are approved by their logic.
This is a very broad notion of argument. There are several reasons to worry about
it. First, it’s not clear what it means to be ‘‘governed’’ by a systematization whose
only feature is that it respects the distinction between form and content. Second, if
being an argument depends on the state of logic, and logic evolves, then Norton is
allowed to claim that the underlying argument of a thought experiment might only
be revealed by future logicians (2004b, 64). This makes the impressive coincidence
that thought experiments always happen to be reconstructible as arguments (Norton
1996, 339; 2004a, 1142) a good deal less impressive. This ‘‘coincidence’’ was
supposed to motivate us to believe that all thought experiments are arguments, but if
Norton’s claim includes the additional premise that all good reasoning will
eventually be formulated by future logicians, this means that there can be no true
counterexamples to his hypothesis until we have reached the end of logic. Or worse,
it defines all possible counterexamples away as instances of bad reasoning. Another
way to put this is that every inference we count as successful will necessarily be an
argument since we are assuming that logic will eventually get around to formalizing
all successful inference forms. I believe this is behind rejoinders like the following
from Brown: ‘‘Norton says that thought experiments are often disguised, not explicit
arguments. So the real claim is that they can be reconstructed along his empiricist
lines. Existence claims like this are devilishly difficult to defeat. I doubt that an
actual refutation could ever be delivered’’ (Brown 1992, 275).
These charges deserve consideration. For the purposes of this paper, however, I
will assume some non-trivial notion of argument can be specified so we can move
on to the more fundamental issue, which concerns the claim that we can justify
cognitive activities that produce epistemologically desirable changes in our overall
doxastic states by reference to the logical properties of those activities (or
propositional reconstructions of those activities). This obviates the need to discuss
arguments by focusing on the source of their justification: approved logical form.
Thus, whether the set of cognitive activities we call arguments and those we call
thought experiments are actually identical doesn’t matter for present purposes,
although it does for Norton’s account. I want to focus on the more fundamental
assumption that drives Norton’s view: that we can justify the output of thought
experiments by reference to the logical properties of the inferences that make up
those thought experiments.
Axiomathes (2016) 26:451–466 453
123
A natural way to begin an inquiry into empiricist accounts of logical justification
is by distinguishing deductive and inductive justification. I begin with deduction,
about which Norton writes: ‘‘Deductive inferences merely restate what we have
already presumed or learned. There is no mystery in what powers the inference and
permits the conclusion. We are just restating what we already have in the premises.
The warrant lies fully within the premises. If we know all winters are snowy, it
follows deductively that some winters are snowy’’ (Norton forthcoming, Chapter 2,
7–8).
2.1 Deductive Thought Experiments
Let’s take a case. Galileo invents a now-infamous thought experiment to criticize
the Aristotelian theory of motion according to which heavier bodies fall faster than
light ones. Here is Norton’s reconstruction (1996, 341–342):
1. Assumption for reductio proof: The speed of fall of bodies in a given medium is
proportionate to their weights.
2. From 1: If a large stone falls with 8 degrees of speed, a smaller stone half its
weight will fall with 4 degrees of speed.
3. Assumption: If a slower falling stone is connected to a faster falling stone, the
slower will retard the faster and the faster speed the slower.
4. From 3: If the two stones of 2 are connected, their composite will fall slower
than 8 degrees of speed.
5. Assumption: the composite of the two weights has greater weight than the
larger.
6. From 1 and 5: The composite will fall faster than 8 degrees.
7. Conclusions 4 and 6 contradict.
8. Therefore, we must reject Assumption 1.
9. Therefore, all stones fall alike.
Gendler (1998) provides excellent criticism of this reconstruction. But for the
sake of argument let’s assume that it is both historically faithful to Galileo and his
contemporaries, as well as logically valid. Why should we believe its conclusion?
Since the mark that tells us whether a thought experiment is justified ‘‘is just that the
thought experiment either uses an argument form licensed by a logic or can be
reconstructed as one’’ (2004b, 54; my emphasis), and since we’re assuming this
thought experiment can be reconstructed as a reductio ad absurdum, we should
conclude that it is a good thought experiment.
But validity is not soundness; we can still deny a premise in the reconstruction of
the thought experiment. This is an obvious point, but it means that Norton’s claim
that a thought experiment is justified ‘‘just’’ when it can be reconstructed as a good
(valid, cogent, etc.) argument is actually the claim that a thought experiment is
justified when it has true (or likely) premises and can be reconstructed as a good
argument. This means that reference to the logical features of a thought
experiment’s reconstruction is never going to provide all of a thought experiment’s
justification, even for Norton. And so in the remainder of this paper I will focus on
454 Axiomathes (2016) 26:451–466
123
the weaker claim that reference to the logical features of a thought experiment can
provide some of its justification. The new question is: do deductive thought
experiments provide some (any) justification for their conclusions that is not already
to be found in the premises and our background beliefs?
It is important that we look closely at what Norton says, since the quotation with
which I ended the last section claims that the warrant for a deductive conclusion
‘‘lies fully within the premises,’’ yet Norton claims that ‘‘the mark [of a good
thought experiment] is just that the thought experiment either uses an argument
form licensed by a logic or can be reconstructed as one’’ (2004b, 54). This latter
claim says that possessing a certain logical mark just is what justifies a thought
experiment. How do we navigate between these two claims? The natural thing to do
is deny this apparent dichotomy: what makes a deductive conclusion justified is
having true premises and instantiating an approved logical schema. Such an
interpretation goes against some of Norton’s more radical remarks. For example,
Norton writes that inferring with a logical license is justified because there is
‘‘something in the logic that evidently confers the power of a thought experiment to
justify its conclusion’’ (Norton 2004b, 54). Interpreting statements like these so that
logic confers only part of the total justification (to respect the point above
concerning soundness), we now want to know what it is about instantiating an
approved logical form that adds justification to an inference.
Reconstructing a thought experiment as an argument allows us to see whether it
is of an approved sort. But this act of checking a reconstruction against a list of
approved logical schemas is only justification by categorization, or justification by
proxy. Reconstructing a thought experiment as an instance of modus ponens is
nothing more than saying that it is relevantly similar to other inferences that we also
take to be justified. And this is not what we want from a normative theory. And
Norton seems to agree: ‘‘the mark [of a good thought experiment] must be
something that we can recognize in the thought experiment itself. It cannot merely
be that the thought experiment is found in an approved list; that would be an
external mark’’ (2004a, 1143; my emphasis). If resulting from the use of a
deductively valid schema is a fact that adds justification, we must find something
about that schema that justifies using it. The fact that such schemas help to
categorize inferences that we already recognize as justified is not enough. With this
we decide the logical Euthyphro problem: Logical forms are not good because
logicians say they are good. Logicians say they are good because they are good.
But what about a good logical form tells a logician that it is good? For an
empiricist, it cannot be that the good-making properties of abstract logical forms
exist and are ‘‘seen’’ in the rationalist’s sense. If instantiating an approved logical
form is going to add justificatory power, therefore, we need logical approval to be
more than what logicians happen to like, and less than direct perception of features
of abstract logical forms. Two empiricist strategies (taken from philosophy of
mathematics) might be useful here. An empiricist can portray logical form as real
only in the sense of 1) relations abstracted from experience or 2) as useful
tautologies.
Let’s begin with the first strategy, according to which logical form is abstracted
from experience (and logical approval attaches to features of those abstractions).
Axiomathes (2016) 26:451–466 455
123
Approval of logical form in this sense could not provide the ultimate justification for
inferences, precisely because such form arises as a representation of something non-
formal which must already be approved. For example, we discover that inferences
of a certain type are successful. Logicians abstract their logical form and approve of
it. But approval of the abstract reconstruction of good inferences is only justificatory
in so far as it is shorthand for approval of the inferences themselves (I take this to be
a form of the point made in Carroll 1895). Approval of logical form (where logical
form is thought of as a set of relations abstracted from experience) is again only
approval by proxy, and can therefore be justification only by proxy. Properties of
logical form thus conceived cannot serve as the ‘‘internal mark’’ of a good thought
experiment (or argument) at a fundamental level.
The other empiricist strategy listed above portrays logical form as a system of
conventional but useful tautological relations, ‘‘a convenient fiction that is very
helpful for purposes of calculation, and helpful too as providing a vocabulary with
which to express our scientific theories’’ (Bostock 2009, 226). This quotation
concerns empiricist accounts of mathematics, but the point translates. Tautological
systems like mathematics and logic are useful because they allow us to make
extremely subtle distinctions in our concepts, draw new inferences, display the
consequences of our commitments, point out contradictions, and so on. However,
when we conceive of mathematics and logic as conventional languages, we face the
problem that such languages only ever express and never justify truths about the
non-linguistic world.
In this sense, approved logical form would again be unable to provide any of the
ultimate justification for the conclusion of a thought experiment. Of course, the
same conclusion holds mutatis mutandis for empiricist accounts of mathematics. An
empiricist who claimed that our knowledge of a real-world system was justified in a
fundamental sense by that system’s instantiating a certain kind of approved
mathematical form would be estranging her own empiricism.
Returning to the question we asked above: despite his remarks to the contrary,
perhaps the best interpretation of Norton’s view would claim that instantiating
approved deductive logical form does not confer any additional justificatory power.
That is, no new justification is provided to a proposition by being the result of a
sound deduction. Norton’s account would therefore imply that we never gain new
knowledge from a thought experiment that is deductive. This is somewhat
surprising, however, given Norton’s deductive reconstructions of many of the most
powerful thought experiments in science, including the one above by Galileo,
Einstein’s magnet and conductor (1991, 135–136), Einstein’s elevator (1991,
136–138), Einstein’s two fluid bodies (1991, 138–139), Einstein’s falling bodies
thought experiment (1993, 6–8), Einstein’s spinning top (1993, 8–12), Einstein’s
stressed rod (1993, 12–15), Einstein’s radiation in a mirrored box (1991, 133–134;
1993, 15–19), Einstein’s lowering and raising a stressed rod (1993, 19–24),
Einstein’s moving rod and slot thought experiment in special relativity (2004a,
1145), Einstein’s rotating disk (2004b, 50–51), and Einstein’s clock in the box
(2004b, 63–64).
Either none of these thought experiments increase our knowledge, or despite their
deductive reconstructions by Norton, they are inductive. Norton admits that some of
456 Axiomathes (2016) 26:451–466
123
them do provide knowledge, since he grants it in the case of Einstein’s mirrored box
(1993, 17), Einstein’s rod and the slot (2014, 1148) and he allows in several places
that thought experiments can produce knowledge (2004a, 1140; 2004b, 44, 49–50)
justification (1991, 142; 1996, 339, 354; 2004a, 1143; 2004b, 53–54) and new
information about the empirical world (1991, 129; 1996, 333). So perhaps we
should conclude that despite their deductive-looking reconstructions, the logical
form that enables these thought experiments to produce new knowledge is actually
inductive. And we should then say in general that any thought experiment that
increases our knowledge is inductive.
Once we turn to inductive thought experiments, however, the plot thickens.
2.2 Inductive Thought Experiments
Norton is explicit that his account is intended to capture inductive as well as
deductive thought experiments (Norton 2004b, 64; see also 49). However, it is not
clear that inductive inferences have logical form, and this is something emphasized
by Norton himself. In recent years Norton has developed a new theory of induction
(covering abduction, informal and probabilistic reasoning) according to which
inductive arguments do not admit of a distinction between form and content.
Norton’s new theory of inductive inference is called the ‘‘material theory of
induction’’ (Norton 2003,2005,2010,2011,2014, forthcoming), which is meant as
an alternative to formal theories of induction. Formal theories of induction attempt
to provide rules of inductive inference, whether in natural language or using a
formal calculus such as Bayesian probability theory. These attempts separate the
material of an inductive inference from its form, in order to isolate what is common
to the form of successful inductive inferences. According to formal theories of
induction, ‘‘valid inductive inferences are distinguished by their conformity to
universal templates. They may be simple, such as the template that licenses an
inference from some past A’s being B to the conclusion that all A’s are B. Or they
may be more complicated, such as the requirement that degrees of inductive support
conform to the probability calculus’’ (Norton 2014, 673).
The endeavour to find the approved logical schemas for good inferences is
precisely what Norton applauded earlier, and now rejects for induction: ‘‘If one
adopts a material theory of induction, one no longer separates factual content from
the rules of inductive inference. The problem of justifying some particular induction
is replaced by the straightforward task of justifying the facts that warrant it’’ (2014,
672).
If we stop separating the rules of inference from the ‘‘factual content’’ as Norton
recommends, then we eliminate the distinction between the form and the content of
inductive inferences. This means that according to Norton’s own definition of a
good argument, which requires ‘‘the familiar distinction between the form and
content’’ and instantiating ‘‘an argument form licensed by a logic’’ (2004b, 53),
inductive arguments are not arguments, and inductive thought experiments are not
either. A fortiori, inductive thought experiments will not be individuated or
evaluated based on their formal features, since they do not admit of a form/content
distinction that can be used by logic to identify good inferences.
Axiomathes (2016) 26:451–466 457
123
Norton argues that individual inductive inferences do follow local rules, so he
might try to escape this criticism by saying that the mark of a good inductive
thought experiment is to be found in the local logical form of the reconstructed
inductive argument. This won’t do, however, since the power of those local forms
must still ultimately derive from facts concerning the material invoked by the
inductive inference. It would be strange if Norton’s material theory of induction was
only material at the most general level, and fell back on formal inductive theories
everywhere else, since the heart of the material theory of induction is the claim that,
‘‘what separates the good from the bad inductive inferences are background facts,
the matter of the inference, as opposed to its form’’ (forthcoming, chapter one, page
4). The rule ‘‘fire causes smoke’’ locally justifies the inference from ‘‘there is
smoke’’ to ‘‘there is fire.’’ That is, ‘‘fire causes smoke’’ is a rule that is only
applicable to a certain (local) class of phenomena. Still, this rule is justified by and
inseparable from facts about smoke and fire, for Norton. We can appeal to the rule
that fire causes smoke as a justification for our alarm when seeing a great deal of
smoke, given that we find ourselves in a domain in which that rule applies (there are
flammable objects as well as oxygen and the possibility of sparks or heat). But when
we ask what justifies that rule, we cannot answer with reference to any of the purely
formal properties of our inference. Perhaps we could appeal to some formal
properties of fire or smoke themselves, but those formal properties are not what
justify our inference from smoke to fire. It’s the causal properties of fire and smoke
we learn through experience (and testimony) that do this, not formal ones. To
repeat, our experience with the material-causal relations is what justifies our ability
to make inductive inferences using them, not any logical-formal properties those
relations may have.
There is therefore a serious internal tension between Norton’s account of thought
experiments according to which thought experiments are filled with irrelevant but
picturesque details on the one hand, and his account of induction according to which
the particular details are crucially important for justification, on the other. Having
considered both deduction and induction, then, an empiricist like Norton cannot
consistently hold the following three claims: that thought experiments provide
knowledge, that thought experiments are justified by properties of their logical
forms, and that induction is material.
This is because if thought experiments provide knowledge, they are inductive.
And if inductions are justified by the properties of their logical forms, the material
theory of induction is mistaken. Next, if thought experiments provide knowledge
and the material theory of induction is correct, this contradicts the heart of Norton’s
argument view: that thought experiments receive their ultimate justification from
appeal to their logical-formal properties. Finally, if thought experiments are justified
by properties of their logical forms and the material theory of induction is correct,
then no thought experiment provides knowledge, and Norton claims in many places
that they do.
In sum, Norton must give up the claim that thought experiments provide
knowledge, or his account of thought experimental justification, or his material
theory of induction.
458 Axiomathes (2016) 26:451–466
123
With that I conclude my criticism of Norton’s view that thought experiments are
arguments. Since my criticisms have been specific to the combination of views held
by Norton, it would be instructive to consider whether another empiricist or
naturalist account of thought experiments can be created that explains their ultimate
source of justification in a way that is consistent with the empiricism of someone
like Norton.
If someone was tempted to go in this direction, they might start by going back to
the basic tenants of empiricism to decide which of the three claims to reject. The
fundamental source of justification for empiricists like Norton are facts about
experience. So perhaps it is facts about experience that justify inferences. And
indeed this is precisely what Norton is committed to with respect to his material
theory of induction. All an empiricist needs to do is extend the material theory of
inference to thought experiments, which, if we accept that they can provide new
knowledge when they are inductive, requires us to leave behind the commitment to
logical form as a justifying mark on the fundamental level.
To see how this might go, let’s consider a simple example. We ask someone
whether square objects can fit through circular holes. This person cuts a square of
paper and drops it into our mug of coffee, annoyed by the absurdity of our question.
She has answered by direct reasoning. Alternatively, she could imagine cutting a
square of paper and dropping it into our coffee mug, infer that there is nothing to
prevent her from doing this, and provide the following report: ‘‘I could fit a square
object through a circular hole, and if I can do that, then there are at least some
square objects that fit through circular holes. So yes, square objects can fit through
circular holes.’’ Consider one final strategy, where the subject performs the same
mental actions as in the second case, but then also presents her reasoning in a
formally reconstructed manner.
In the first case, what made our subject’s action possible was the absence of any
physical law-like connection between the areas of everyday squares and the
diameters of everyday circles. This exact same fact is what justifies the argument
provided in the words of the second case, and the symbols of the third case. At least,
this is what an empiricist should claim.
The same is true of inductive thought experiments and arguments. Suppose we
could and did reconstruct all inductive thought experiments as arguments. Because
the same facts about experience are what justify thought experiments and
arguments, they will always enjoy exactly the same degree of justification. This
would satisfy both Norton’s ‘‘reconstruction’’ and ‘‘reliability’’ theses: that all
thought experiments are reconstructible as arguments and that all thought
experiments are equally justified as their reconstructed arguments (e.g., 1996, 339
and 2004b, 52 respectively). These are supposed to be surprising facts that warrant
the equation of thought experiments and arguments. However as we have seen, even
if both of these were true, we would still have no reason to believe that a given
thought experiment was justified by appeal to its reconstructed argument, or that it
was identical to its reconstructed argument.
In sum, if facts about experience are the ultimate ground for knowledge, and if
thought experiments sometimes produce new knowledge, then we should look at the
various ways we can generate new facts from old experience through thought.
Axiomathes (2016) 26:451–466 459
123
Perhaps the most epistemologically interesting and relevant of these is the running
and interpretation of experiments. So let us turn to thought experiments both as
interpretations of experiments, and as experiments themselves.
1
3 Material (As Opposed to Formal) Accounts of Thought Experiments
Experiments begin with a question concerning a system of interest, proceed through
a controlled intervention on or observation of that system (or a representation of that
system), and end with an interpretation of what transpired that hopefully addresses
our original question. To emerge with a high degree of confidence in the conclusion
of an experiment, we sometimes discuss our confidence in each of these stages: we
want to be confident that our question is the right one, that our representations are
accurate, that our manipulations target the right parts of the system, that our
observations are precise, and that our interpretations are free of bias.
If this is correct, then perhaps the ultimate justification of a thought experiment
that produces new knowledge lies with whatever makes experiments and their
interpretations reliable in general. Let’s start with five criteria for a good
experiment, drawn from the classic Franklin (1986).
1. The system to be investigated must be well-isolated, abstracting away irrelevant
features of the surrounding environment.
2. Experimental bias must be eliminated.
3. Sources of error must be understood and accounted for.
4. Instruments should be calibrated as well as possible.
5. We should have a theory of our instruments.
These criteria may be applied to thought experiments where we understand the
instrument of observation to be the mind, broadly construed. Here is an extremely
brief sketch of how this might go.
1. We can isolate the relevant features of interesting systems in our imaginations
through abstraction and idealization. Isolation of properties and processes in the
imagination is easier to do than the material equivalent, and this is likely one
reason thought experiments are so ubiquitous: they are economical when it
comes to this first requirement. There is a large and rapidly expanding literature
on how we perform these tasks (e.g., Giere 1988; Godfrey-Smith 2009; Laymon
1980; Matthews 2004; Portides 2011; Weisberg 2007).
2. We must eliminate experimental bias. In the case of thought experiments,
experimental bias is cognitive bias, and especially confirmation bias, which is a
fairly well-understood phenomenon. One way to keep confirmation bias in
check is by discussing thought experiments with others who do not share our
1
Several other philosophers have discussed the relationship between thought experiments and
experiments more generally, especially Buzzoni (2008), Gooding (1992,1994) and Sorensen (1992).
But none have tried to make this connection within the context of an empiricist account of thought
experiments. While I am not committed to empiricism, I think this is an important and interesting project,
and an extension of Nersessian’s ‘‘empiricism without logic’’ (Nersessian 2007).
460 Axiomathes (2016) 26:451–466
123
expectations, and this is partially what we see in classrooms, seminars,
conferences and journals, and confirmed as a desideratum by the growing
corpus in experimental philosophy. We have learned that as much as possible
we should present imaginary scenarios in different words, orders and using
different contents, to isolate for priming effects.
3. There are many sources of error in thought experiments, including inaccurate
representations of the target system and weak imaginations. These problems
must be appreciated, but they are not reasons to be skeptical about thought
experiments in general. Laboratory experiments can also fail when their
representations are inaccurate, or when their instruments have powers of
resolution that are too weak to yield a single conclusion on interpretation. One
might object that laboratory experiments have better ways of checking their
representations for accuracy, but if this is true it seems to be a matter of degree,
as coherence is our main check in both cases: laboratory experiments require
coherence between theories, experience and across experimental repetition.
Thought experiments require coherence with all of our knowledge, including
that which derives from experience, as well as coherence across repetition by
dissenting scientists (Popper 1935, 464–480). This is not to say that coherence
guarantees success, merely that the method for error checking is relevantly
similar in both cases.
4. Our imaginations must be calibrated. And they are, through years of practice
with hypothetical reasoning. In all skilled positions from electrician to tennis
player, we will have considered abstract cases almost every day as part of our
education and work. This is not to say that thought experiments are always
justified when they are performed by someone who has spent years working in
the subject area of the thought experiment. For example, the recent objections
against the use of philosophical imagination might be more worrying than the
same objection applied to the use of thought experiments in other fields like
engineering or mathematics (Thagard 2014, and see Buzzoni, forthcoming).
Still, we care about philosophical intuitions. Here are two reasons for optimism.
First, there are methods for resolving conflict. This is again the same as in the
case of laboratory experiments. If two well-calibrated experiments provide
robust and conflicting outcomes, the reaction is either to make a theoretical
change or perform more experiments. If the theoretical change is not ad hoc, it
will have empirical consequences that can be tested. It is therefore ultimately to
experience that we make recourse. Second, intuitions in philosophy and science
work in similar ways—mostly as hypotheses. In this case, they do not bear
evidential weight, and in fact they can be quite mistaken and still lead
eventually to epistemologically warranted outcomes (Buzzoni, forthcoming,
also argues that scientific and philosophical thought experiments will be
evaluated in the same way, despite their different ‘‘directions of fit’’ to the
world. For more discussion on philosophical reasoning as experimental see
Stuart 2015).
5. To have a theory of our instrument we need a theory of inference-making. Much
work in this direction has been carried out in psychology, sociology,
phenomenology, philosophy of mind, neuroscience, and more broadly speaking,
Axiomathes (2016) 26:451–466 461
123
the arts and humanities. It would be difficult to deny that these projects have
provided any insights into how we make (good) inferences. Studies in logic,
informal reasoning, and work on cognitive biases alone represent important
strides in the last century.
In sum, whether thought experiments are reconstructed as arguments or not,
applying the norms of laboratory practice seems prima facie to be a good way to
evaluate their level of justification for an empiricist. And there are myriad resources
from which to build such an account, not least including cognitive science, which
recognizes and explains how to avoid some of the pitfalls of using imaginary
scenarios in certain contexts.
I leave the full explication of such an account for future work. For now, I want to
deal with two objections concerning the differences between thought experiments
and laboratory experiments. The first claims that thought experiments cannot
intervene on extra-mental systems, which is one of the most important features of a
laboratory experiment. Here are two replies to such an objection.
Intervention—while important—is not a necessary condition for experimenta-
tion. There are many examples in science where an experiment does not intervene.
A classic example concerns peppered moth camouflage (Kettlewell
1955,1956,1958). There were several colourings of peppered moths in England,
and it appeared that the darker (and rarer) forms were becoming more common in
areas downwind of factories responsible for industrial pollution that darkened the
trees and killed much of the lichen cover. To see if the spread of the melanic gene
was due to the inability of predators to spot the darker moths against the darkened
trees, Henry Kettlewell collected moths of different colours and placed them on
different coloured tree barks in a laboratory setting. Predators were then brought
into see which moths were preyed upon. Kettlewell found a significant advantage
for the darker moths when darkened tree bark was used: they were more than twice
as likely as the paler moths to avoid predation. This was well-prepared observation
of natural processes, not intervention. Nevertheless, it has all the trappings of a
controlled experiment, and it established a historically important result.
Another example is Pasteur’s famous set of experiments in which he showed that
spontaneous generation (of insects, rats, etc.) does not occur when soiled rags or
dead flesh are kept away from circulating air. He established this result simply by
watching rags and meat kept under limited air circulation (see Conant 1953). Again,
we shouldn’t describe Pasteur’s experiments as interventions, because we wouldn’t
be able to say on what he intervened. The life cycles of hypothetical houseflies that
might have lived if their progenitors had been able to lay eggs on a particular piece
of meat hardly forms a system on which we could intervene. Like Kettlewell, what
Pasteur did was create a new and different system, one in which there were no
housefly eggs, and observed it, finding that a state without houseflies begets no
houseflies.
The second response to the charge that thought experiments cannot intervene is
to affirm that thought experiments can intervene, by making an analogy to other
homomorphic representations (like material models). When a scientist aims to learn
about a given natural system, she primarily does her intervening on idealized
462 Axiomathes (2016) 26:451–466
123
versions of these systems. We can map the strengths of different representational
relations on a continuum that runs from direct material reasoning (like putting
square objects through circular openings), to scientific field experiment, laboratory
experiment, material modelling, computer simulation, thought experiment, all the
way to reasoning with representations that have almost nothing in common with
what they represent (like the dots and dashes of Morse code, or binary
representations in a computer). When we consider this continuum, we notice that
direct intervention is an ideal that typically goes unachieved. Almost always, we
intervene on abstracted and idealized versions of natural systems, not on the systems
themselves. And thought experimental scenarios in science are abstracted or
idealized versions of natural systems. It is true that we cannot be sure that a
mentally represented system will react as a natural system would, but this problem
is only gradually more severe than it is for material models, computer simulations
and laboratory experiments. In all these cases, we hope that our representations of
natural systems preserve enough of the relevant structure of the natural systems that
something new can be learned from them. This hope is grounded in the quality of
our assumptions, confidence in our background theory, and understanding of our
instruments.
But how do we intervene on a representation? To intervene experimentally is to
interrupt or otherwise tamper with the time-evolution of a process. When done
properly, we are able to gauge counterfactually how the trajectory of the process
compares pre- and post-intervention using a control. There are several authors who
point out the dynamic aspects of thought experiments (Mis
ˇc
ˇevic
´1992, 220;
Nersessian 2007, 143, and forthcoming). According to an interpretation of thought
experiments which portrays them as dynamic, we can take the control case to be the
evolution of the system according to the rules and constraints we build into the
scenario without an intervention. The rules and constraints that determine the time-
evolution of a system come partially from representational conventions, partially
from background knowledge. Just as with all systems of representation, there are
conventions governing acceptable sets of outcomes for imagined scenarios. The
constraints in a scientific thought experiment will often be more flexible than the
constraints on say, Euler circles or Venn diagrams, but this is not to say they don’t
exist. Looking at the way we reason with fiction might reveal some general types of
constraint (Ichikawa and Jarvis 2009), and common sense tells us that particular
scenario types will have specific rules that vary with the content (for example,
Sherlock Holmes can only do what a human can do). Given that there are rules and
constraints that we use to imagine the evolution of a system, there will be
interventions we can perform on the control case by altering the initial conditions or
the constraints themselves, and then ‘‘seeing’’ how it plays out (see Nersessian,
forthcoming). And this is exactly what we find in cognitive science studies of how
students create and interact with thought experiments in the classroom (Ko
¨sem and
O
¨zdemir 2014).
Finally, we might worry that the imagined results of a thought experiment thus
conceived will be hopelessly indeterminate compared to a laboratory experiment
since we can imagine any outcomes to a given scenario that we want, and real-world
systems only evolve in only one way. But this is not necessarily true. Real-world
Axiomathes (2016) 26:451–466 463
123
systems often have as many or more degrees of freedom than a thought experiment
does—consider all the possible outcomes of a social or psychological experiment,
for instance. And we have greater control over the constraints involved in a thought
experiment, which we can tighten as we see fit. In any case, the real concern is
whether the constraints we place in our imaginations for a given scenario reliably
track the constraints present in a system of interest, to some degree. The answer to
this question will depend on the system, the quality of our imagined scenario, and
our training; it cannot be determined in advance.
4 Conclusion
Norton argues that thought experiments are arguments. According to Norton,
arguments are inferences governed by logic, and their conclusions are justified by
logic. For an empiricist, logical justification must boil down to empirical
justification. According to Norton, deduction merely rearranges what we already
know, but it does not provide any new justification. And according to Norton’s
account of induction, inductive inferences are justified because of the real-world
relations between the material of the premises of the argument, and not their logical
properties.
Therefore, deductive thought experiments say nothing new, and inductive
thought experiments are not justified by appeal to logic. If new knowledge results
from a thought experiment, which Norton allows, then Norton’s account is
incapable of explaining it by reference to features of logical form. This is
problematic because it is a desideratum of any epistemological account of thought
experiments that it provide some explanation of the source of thought experimental
justification.
That said, we are not about to stop representing thought experiments logically as
arguments; doing so is a helpful clarificatory exercise that provides a quick means of
separating good from bad inferences. But for a complete epistemology of thought
experiments, we need more than handy heuristics. We must identify the fount of
justification, and for an empiricist, reference to logical form will not do. This
seemingly minor point is crucial when applied to the literature on thought
experiments, because with it, we remove a fundamental component of Norton’s
account, which has been very influential in the literature.
Empiricists may still claim that thought experiments are regular inferences that
are justified when that particular sort of inference is justified, but they will need a
story about how those inferences themselves are justified, and it will not proceed by
appeal to logical schemas if we accept the material theory of induction. In light of
this problem, I have suggested an alternative source for a thought experiment’s
justification: experimental interaction and interpretation, whose epistemic evalua-
tion would follow similar criteria as in other sorts of experiments and interpreta-
tions. This might be a preferable direction for empiricists in the ongoing discussion
of the epistemology of thought experiments, although it is equally open to
naturalists and rationalists as well.
464 Axiomathes (2016) 26:451–466
123
Acknowledgments I’d like to thank John D. Norton, Nancy Nersessian, Yiftach Fehige, James R.
Brown, Marco Buzzoni, Joseph Berkovitz, Catherine Elgin, So
¨ren Ha
¨ggqvist, Elke Brendel, Geordie
McComb and an anonymous referee for comments and discussion, as well as audiences at the University
of Toronto, Bonn and Pittsburgh. This research was supported by an Ontario Graduate Research
scholarship, the Germany/Europe fund from the University of Toronto, and a postdoctoral fellowship at
the Center for Philosophy of Science at the University of Pittsburgh.
References
Bishop M (1999) Why thought experiments are not arguments. Philos Sci 66:534–541
Bokulich A (2001) Rethinking thought experiments. Perspect Sci 9:285–307
Bostock D (2009) Empiricism in the philosophy of mathematics. In: Irvine A (ed) Handbook of the
philosophy of science: philosophy of mathematics. Elsevier B.V, Amsterdam, pp 157–229
Brown J (1986) Thought experiments since the scientific revolution. Int Stud Philos Sci 1:1–15
Brown J (1991)[2011] The laboratory of the mind: thought experiments in the natural sciences.
Routledge, London
Brown J (1992) Why empiricism won’t work. Proc Philos Sci Assoc 2:271–279
Brown J (2004) Why thought experiments do transcend empiricism. In: Hitchcock C (ed) Contemporary
debates in the philosophy of science. Blackwell, Malden, pp 23–43
Buzzoni M (2008) Thought experiment in the natural sciences. Ko
¨nigshausen & Neumann, Wu
¨rzburg
Buzzoni M (forthcoming) Thought experiments in philosophy. Topoi
Carroll L (1895) What the tortoise said to achilles. Mind 4:278–280
Conant J (ed) (1953) Pasteur’s and Tyndall’s study of spontaneous generation. Harvard University Press,
Cambridge
Davies D (2007) Thought experiments and fictional narratives. Croat J Philos 7:29–45
Elgin C (2014) Fiction as thought experiment. Perspect Sci 22:221–241
Franklin A (1986) The neglect of experiment. Cambridge University Press, Cambridge
Gendler T-S (1998) Galileo and the indispensability of scientific thought experiment. Br J Philos Sci
49:397–424
Gendler T-S (2004) Thought experiments rethought—and reperceived. Philos Sci 71:1152–1163
Giere RN (1988) Explaining science: a cognitive approach. The University of Chicago Press, Chicago
Godfrey-Smith P (2009) Models and fictions in science. Philos Stud 143:101–116
Gooding D (1992) What is experimental about thought experiments? PSA: Proc Bienn Meet Philos Sci
Assoc 2:280–290
Gooding D (1994) Imaginary science. Br J Philos Sci 45:1029–1045
Ichikawa J, Jarvis B (2009) Thought-experiment intuitions and truth in fiction. Philos Stud 142:221–246
Kettlewell HB (1955) Selection experiments on industrial melanism in the Lepidoptera. Heredity
9:323–342
Kettlewell HB (1956) Further selection experiments on industrial melanism in the Lepidoptera. Heredity
10:287–301
Kettlewell HB (1958) A survey of the frequencies of Biston betularia (L.) (Lep.) and its melanic forms in
Great Britain. Heredity 12:51–72
Ko
¨sem S¸, O
¨zdemir O
¨(2014) The nature and function of thought experiments in solving conceptual
problems. Sci Educ 23:865–895
Laymon R (1980) Idealisation, explanation, and confirmation. In: Asquith PD, Giere RN (eds) PSA 1982,
vol 1. Philosophy of Science Association, East Lansing, pp 336–350
Matthews RM (2004) Idealisation and Galileo’s pendulum discoveries: historical, philosophical and
pedagogical considerations. Sci Educ 13:689–715
Mis
ˇc
ˇevic
´N (1992) Mental models and thought experiments. Int Stud Philos Sci 6:215–226
Mis
ˇc
ˇevic
´N (2007) Modelling intuitions and thought experiments. Croat J Philos 7:181–214
Nersessian N (1991) Why do thought experiments work? Proc Cogn Sci Soc 13:430–438
Nersessian N (1992) How do scientists think? Capturing the dynamics of conceptual change in science.
In: Giere RN (ed) Cognitive models of science. University of Minnesota Press, Minneapolis,
pp 3–44
Nersessian N (1993) In the Theoretician’s laboratory: thought experimenting as mental modeling. Proc
Philos Sci Assoc 2:291–301
Axiomathes (2016) 26:451–466 465
123
Nersessian N (2007) Thought experiments as mental modelling: empiricism without logic. Croat J Philos
7:125–161
Nersessian N (forthcoming) Cognitive science, mental modelling, and thought experiments. In: Stuart
et al. (eds) The routledge companion to thought experiments. Routledge, London
Norton J (1991) Thought experiments in Einstein’s work. In: Horowitz T, Massey G (eds) Thought
experiments in science and philosophy. Rowman & Littlefield, Lanham, pp 129–148
Norton J (1993) Einstein and Nordstrom: some lesser-known thought experiments in gravitation. In:
Earman J, Janssen M, Norton JD (eds) The attraction of gravitation: new studies in the history of
general relativity. Birkhauser, Boston, pp 3–28
Norton J (1996) Are thought experiments just what you thought? Can J Philos 26:333–366
Norton J (2003) A material theory of induction. Philos Sci 70:647–670
Norton J (2004a) On thought experiments: is there more to the argument? Philos Sci 71:1139–1151
Norton J (2004b) Why thought experiments do not transcend empiricism. In: Hitchcock C (ed)
Contemporary debates in the philosophy of science. Wiley-Blackwell, Somerset, pp 44–66
Norton J (2005) A little survey of induction. In: Achinstein P (ed) Scientific evidence: philosophical
theories and applications. Johns Hopkins University Press, Baltimore, pp 9–34
Norton J (2010) There are no universal rules for induction. Philos Sci 77:765–777
Norton J (2011) History of science and the material theory of induction: Einstein’s Quanta, Mercury’s
Perihelion. Eur J Philos Sci 1:3–27
Norton J (2014) A material dissolution of the problem of induction. Synthese 191:671–690
Norton J (Forthcoming) The material theory of induction. http://www.pitt.edu/*jdnorton/homepage/cv.
html#material_theory
Popper K (1935)[2005] The logic of scientific discovery. Routledge, London
Portides D (2011) Seeking representations of phenomena: phenomenological models. Stud Hist Philos Sci
Part A 42:334–341
Sorensen R (1992) Thought experiments. Oxford University Press, Oxford
Stuart M (2015) Philosophical conceptual analysis as an experimental method. In: Gamerschlag T,
Gerland D, Osswald R, Petersen W (eds) Meaning, frames and conceptual representation.
Du
¨sseldorf University Press, Du
¨sseldorf, pp 267–292
Thagard P (2014) Thought experiments considered harmful. Perspect Sci 22:288–305
Weisberg M (2007) Three kinds of idealization. J Philos 104(12):639–659
466 Axiomathes (2016) 26:451–466
123
A preview of this full-text is provided by Springer Nature.
Content available from Axiomathes
This content is subject to copyright. Terms and conditions apply.
