## 1. QBism

Quantum Bayesianism originated as a point of view on states and

probabilities in quantum theory developed by C.M. Caves, C.A. Fuchs,

and R. Schack (2002). In its more recent incarnation (Fuchs, Mermin,

& Schack 2014) its proponents have adopted the name QBism for

reasons discussed in

§1.1.

In deference to its contemporary proponents, this shorter

name is used. Fuchs, Mermin, and Schack 2014 is an elementary introduction to

QBism; Fuchs and Schack 2015 gives a more detailed summary of the

view; von Baeyer 2016 is a popular book-length introduction.

QBists maintain that rather than (either directly or indirectly)

representing a physical system, a quantum state represents the

epistemic state of the one who assigns it concerning that

agent’s possible future experiences. It does this by specifying

the agent’s coherent degree of belief (credence) in each of a

variety of alternative experiences that may result from a specific act

the agent may perform. To get an idea of the kinds of experience and

act the QBist has in mind it is helpful to think of the possible

outcomes of a quantum measurement on a physical system. But QBists

have proposed the extension of the view to encompass *every*

experience that may result from *any* action (Fuchs, Mermin,

and Schack 2014; Mermin 2017).

As quantum theory is usually presented, the Born Rule provides an

algorithm for generating probabilities for alternative outcomes of a

measurement of one or more observables on a quantum system. These

probabilities have traditionally been regarded as objective, in line

with the idea that the theory is irreducibly indeterministic.

By contrast, QBists hold a subjective Bayesian or personalist view of

quantum probabilities (see entry on

interpretations of probability).

Taking a quantum state merely to provide input to the Born Rule

specifying these probabilities, they regard quantum state assignments

as equally subjective. The quantum state assigned by an agent then

provides a convenient representation of an important part of his or

her own overall state of belief. So quantum theory as a whole is

“a users’ manual that any agent can pick up and use to

help make wiser decisions in this world of inherent uncertainty”

(Fuchs 2010, 8, Other Internet Resources).

QBists argue that from this point of view quantum theory faces no

conceptual problems associated with measurement or non-locality. While

QBism has implications for the nature of physical science, from this

point of view quantum theory has few if any *direct*

implications for the nature of physical reality.

### 1.1 History

Contemporary QBists (Mermin 2014: 422; Fuchs 2011) have sought

precedents among such authorities as Erwin Schrödinger, Niels

Bohr, Wolfgang Pauli, J.A. Wheeler, and William James. But what came

to be known as quantum Bayesianism and later QBism began as a

collaboration between Caves, Fuchs, and Schack at the turn of the

21^{st} century (Caves, Fuchs, and Schack 2002a,b). N. David

Mermin (2014) became a convert more recently and has proposed

extending the QBist vision of science to resolve at least one

long-standing conceptual issue raised by classical physics.

In conformity with standard terminology, on which the word

“Bayesian” does not carry a commitment to denying

objective probability, proponents of QBism no longer take the

“B” to refer simply to Bayesianism. Insisting that

probability has no physical existence even in a quantum world, they

follow Bruno de Finetti in identifying probability with coherent

degree of belief or credence. But according to Fuchs (2016, Other

Internet Resources) “B” should not be taken to abbreviate

“Brunism” since de Finetti would not have accepted all of

QBism’s metaphysics: so “QBism” is now best

understood simply as a stand-alone proper name for the view of quantum

theory described in what follows.

### 1.2 Probability

Applied to radioactive decay, the Born Rule of quantum theory is taken

successfully to predict such things as the half-life of the first

excited state of the hydrogen atom—that the probability that an

atom of hydrogen in this state will be found to have decayed to the

ground state after (1.1 times 10^{-9}) seconds (i.e., just over a

billionth of a second) is ½. This prediction has been

experimentally confirmed by measuring how the frequency with which

photons are emitted by a large number of hydrogen atoms in the decay

of this excited state decreases over time. Most physicists regard this

and other probabilities predicted by quantum theory as objective

physical features of the world, typically identifying the probability

of decay with the relative frequency of decay as measured in such an

experiment.

But there are strong reasons not to equate probability with any actual

relative frequency (see entry

interpretations of probability, §3.4).

Many philosophers, including Karl Popper (1967) and David Lewis

(1986), have taken Born probabilities instead to exemplify a

distinctive kind of objective property (propensity or chance,

respectively) that may be ascribed to actual or possible individual

events. Lewis took quantum indeterminism to be the last hold-out of

objective chance.

By contrast, QBists adopt a subjectivist or personalist interpretation

of probability, in quantum theory as elsewhere (see entry on

interpretations of probability, §3.3).

This makes the Born Rule of quantum theory not a law of nature but an

empirically motivated norm of rationality a wise agent should follow

in addition to those whose violation would render the agent’s

degrees of belief incoherent. As usually formulated, the Born Rule

specifies probabilities for various possible measurement outcomes

given a quantum state: But QBists also adopt a subjectivist or

personalist interpretation of quantum states.

The Schrödinger equation specifying the time development of a

system’s quantum state (psi)

Hpsi = ihslash ,{partial psi /partial t}

]

is often thought of as the basic dynamical law of quantum mechanics,

where (H) (called the Hamiltonian operator) is said to represent the

system’s energy. Instead QBists take this equation as providing

a diachronic constraint on an agent’s credences, conformity to

which is required of a quantum user in the absence of new experience

such as that provided by awareness of the outcome of a measurement on

the system. But QBists also consider the Hamiltonian (along with all

other observables) within the purview of each individual agent rather

than objectively determined by the system’s properties. It

follows that equally rational agents assigning the same initial

quantum state may come to differ in their subsequent state assignments

because they apply the diachronic constraint supplied by the

Schrödinger equation in different ways.

In its usual formulation the Born Rule does not look like a normative

constraint on credences. QBists prefer to reformulate it purely as a

relation among (subjective) probabilities without reference to a

quantum state. In the form of Equation ((ref{ex2})) it relates

probabilities (q) of actual measurement outcomes (j) to

probabilities of outcomes of a hypothetical *fiducial*

measurement of a special kind called a

SIC.^{[2]}

q(j) = sum_{i=1}^{d^2} [(d+1) p(i) -1/d].r(jmathbin{|}i)

]

This equation is not just a revision of the law of total probability

it resembles, i.e.,

q(j) =sum_{i=1}^{d^2} p (i).r(j mathbin{|} i)

]

because (p(i)), (r(jmathbin{|}i)) in ((ref{ex2})) refer to a

hypothetical measurement, not the actual measurement.

In more detail, suppose an agent has degrees of belief (p(i)) that

the outcome of a SIC on a system would be the (i)^{th}, and

degree of belief (r(jmathbin{|}i)) in the (j)^{th}

outcome of an actual measurement (M) conditional on the

(i)^{th} outcome for the hypothetical SIC on that system.

Then QBists take Equation ((ref{ex2})), stating a condition on the

agent’s degree of belief (q(j)) that the outcome of (M) will

be the (j)^{th}, as their preferred formulation of the Born

Rule. In this expression (d) stands for the dimension of the

system’s Hilbert space (assumed to be a positive integer).

Their idea is that when the fiducial measurement is a SIC,

(r(jmathbin{|}i)) encodes the agent’s belief about the type

of measurement (M), while (p(i)) encodes his or her quantum state

for the system on which this measurement is performed. They maintain

that the Born Rule in this form is an empirically motivated addition

to probability theory—a normative requirement of quantum

Bayesian coherence (Fuchs and Schack 2013) that supplements the usual

coherence conditions on degrees of belief required to avoid a Dutch

book (a set of bets an agent is guaranteed to lose, come what

may).

It is common (at least in physical applications) to identify

probability 1 with objective certainty, at least for finite

probability spaces. Einstein, Podolsky, and Rosen (1935, EPR) made

this identification in the following sufficient condition for reality

with which they premised their famous argument for the incompleteness

of quantum mechanical description of physical reality:

If, without in any way disturbing a system, we can predict with

certainty (i.e., with probability equal to unity) the value of a

physical quantity, then there exists an element of physical reality

corresponding to this physical quantity. (EPR: 777)

QBists (Caves, Fuchs, and Schack 2007) reject this identification and

refute EPR’s argument that quantum description is incomplete by

denying this premise. Eschewing all objective physical probabilities,

they rather identify probability 1 with an agent’s subjective

certainty—full belief in a statement or event that an equally

well informed rational agent may believe to a lesser degree, or not at

all.

### 1.3 Measurement

Those who believe that a quantum state completely describes the system

to which it is assigned and that this state always evolves linearly

(e.g., according to the Schrödinger equation) face the notorious

quantum measurement problem: Application of quantum theory to the

interaction between a quantum system and a quantum measuring device

would almost always leave these in a state that describes the

measurement as having no outcome, contrary to the direct experience of

countless experimentalists (see entry on

philosophical issues in quantum theory, §4).

Some have followed Dirac (1930) and von Neumann (1932) in assuming

that a measurement is a physical process in which a quantum state

almost never evolves linearly but rather changes discontinuously and

stochastically into one of a variety of possible states, each of which

may describe its outcome. But attempts to state precisely when such a

process occurs and to verify its occurrence experimentally have been

unsuccessful, and many understand quantum theory as excluding its

occurrence.

QBists avoid this problem by denying that a quantum state (even

incompletely) describes the system to which it assigned. Any user of

quantum theory assigns his or her personal quantum state on the basis

of available information, subject only to the normative constraints of

quantum Bayesian coherence. This state assignment need conform neither

to “the way that system really is”, nor to the state

assignments of other users. Quantum mechanics is a single user theory,

and any coincidence among states assigned by different users is just

that—coincidence. An agent may reassign a state on the basis of

newly acquired information, perhaps described as observation of the

outcome of a measurement. When this happens, the new state is often

not continuous with the old state. This represents no physical

discontinuity associated with measurement, but merely reflects the

agent’s updated epistemic state in the light of experience.

Nevertheless, in certain circumstances different users may be expected

to come to assign similar or even identical quantum states by updating

their prior credences to take account of common (though never

identical) experiences, some of which each may describe as experiences

of the outcomes of quantum measurements on systems. Because QBists

take the quantum state to have the role of representing an

agent’s epistemic state they may avail themselves of personalist

Bayesian arguments purporting to show the convergence of priors on

updating in the light of common information. Also, just as de Finetti

showed that a subjectivist agent’s credences may evolve as if

refining estimates of an unknown objective probability, QBists (Caves,

Fuchs, and Schack 2002b) have shown that the credences of a user of

quantum theory may evolve as if refining his or her assignment of an

unknown objective quantum state.

J.S. Bell (2004) argued forcefully that the word

“measurement” has no place in a formulation of quantum

mechanics with any pretension to physical precision. QBists frequently

use this word in formulating their view, but unlike Bohr and his

Copenhagen followers they do not think of a measurement as a purely

physical process, but as describing an agent’s action on the

world that results in a specific experience of it. They view quantum

theory not as offering descriptions of the world involving the

imprecise physical term “measurement”, but as an

intellectual tool for helping its users interact with the world to

predict, control, and understand their experiences of it. Fuchs (2010,

Other Internet Resources) and Mermin (2017) are quite explicit and

unapologetic that a thoroughgoing QBist presentation of quantum theory

would speak of agents, their actions and their experiences—all

primitive terms they take neither to require nor to admit of precise

physical specification.

### 1.4 Nonlocality

Bell’s arguments (2004) have convinced some physicists and many

philosophers that certain patterns of correlation among spatially

separated events correctly predicted by quantum theory manifest

non-local influences between some of these events (see entry on

action at a distance in quantum mechanics).

QBists use their view of measurement-as-experience to reject any such

non-local influences.

For a QBist, what science rests on are not objective reports of

localized physical events but the individual agent’s

experiences. Being present at a single location, at no time does an

individual agent experience spatially separated

events.^{[3]}

Correlations taken to manifest non-local influences supposedly

concern events in different places—say where Alice is and where

Bob is. But Alice can only experience events where she is, not at

Bob’s distant location. When she hears Bob’s report of

what he experienced at a distant location, this is an experience she

has where *she* is, not where Bob reports having had his

experience. So quantum theory is answerable to patterns of correlation

not among spatially separated physical events, but among Alice’s

(as also among Bob’s) spatially coincident experiences. QBists

argue that Alice, Bob, and any other agent can use quantum theory

successfully to account for her or his experiences with no appeal to

any physical states (hidden or otherwise) or non-local physical

influences.

### 1.5 Decoherence

Classical mechanics is generally taken to be reducible to quantum

mechanics, at least approximately in some appropriate limit. For

example, Newton’s second law of motion is sometimes said to be

derivable from the Schrödinger equation in the limit of large

mass. But to retrieve classical dynamics it is generally thought

necessary to supplement any such derivation with an account of why

ordinary macroscopic objects do not exhibit the interference behavior

characteristic of quantum superpositions.

Quantum models of environmental decoherence are commonly thought to

provide such an account (see entry on

the role of decoherence in quantum mechanics).

These typically involve the Schrödinger equation, this time

applied to a system in interaction with its quantum environment. The

application can show how interactions entangle the quantum states of

system and environment in a way that selects a “pointer

basis” in which the system’s reduced (mixed) state remains

very nearly diagonal indefinitely. Somehow a particular element of

this basis is supposed to be identifiable as the system’s

physical state, evolving in a way that approximates classical

dynamics.

If the Schrödinger equation were a dynamical law governing the

evolution of a physical quantum state this would provide a physical

foundation on which to base a reduction of classical dynamics to

quantum dynamics that appealed to quantum decoherence. But QBists

*deny* that the Schrödinger equation is a dynamical law

governing the evolution of an objective quantum state. For them it

merely provides a diachronic constraint on an agent’s epistemic

state. Fuchs (2010, Other Internet Resources) concluded that

decoherence has no role to play in the misguided program attempting to

reduce classical to quantum dynamics.

Instead, QBists Fuchs and Schack (2012) have viewed decoherence as a

condition on an agent’s present assignment of a quantum state to

a system following one contemplated measurement, when making decisions

regarding the possible outcomes of a second measurement. As such, it

functions as a normative synchronic coherence condition that may be

seen as a consequence of van Fraassen’s (1984) Reflection

Principle. Instead of taking decoherence to select possible outcomes

of a physical measurement process, QBists take these to be just

whatever experiences may follow the agent’s action on the

world.

### 1.6 Generalizations of QBism

Mermin (2014) has proposed extending QBism’s view of the role

experience in science to what he calls CBism (Classical Bohrism).

According to Carnap, Einstein was seriously worried about the problem

of the Now

that the experience of the Now means something special for man,

something essentially different from the past and the future, but that

this important difference does not and cannot occur within physics.

(Carnap 1963: 37–38)

According to Mermin, Einstein had nothing to worry about because there

(is) a place in physics for the present moment. He takes the present

moment as something that is immediately experienced by each of us, and

so (from a CBist perspective) just the sort of thing that physics is

ultimately about. By contrast, he says

space-time is an abstraction that I construct to organize such

experiences. (Mermin 2014: 422–3)

According to Mermin, a common Now is an inference for each person from

his or her immediate experience: But that it is as fundamental a

feature of two perceiving subjects that when two people are together

at an event, if the event is Now for one of them, then it is Now for

both.

Unlike QBism, CBism is not a subjective or personalist view of states

and probabilities in physics. But both QBism and CBism depend on a

general view of science as an individual quest to organize one’s

past experiences and to anticipate one’s future experiences.

This is a view that has antecedents even in views expressed by

physicists generally thought of as realists, such as Einstein (1949:

673–4) and Bell, whom Mermin (2017: 83)

quotes as follows

I think we invent concepts, like “particle” or

“Professor Peierls”, to make the immediate sense of data

more intelligible. (J.S. Bell, letter to R.E. Peierls,

24-February-1983)

## 2. Objections and Replies

### 2.1 Solipsist?

A common reaction among those first hearing about QBism is to dismiss

it as a form of solipsism. Mermin (2017) replies as follows:

Facile charges of solipsism miss the point. My experience of you leads

me to hypothesize that you are a being very much like myself, with

your own private experience. This is as firm a belief as any I have. I

could not function without it. If asked to assign this hypothesis a

probability I would choose (p = 1).0. Although I have no direct

personal access to your own experience, an important component of my

private experience is the impact on me of your efforts to communicate,

in speech or writing, your verbal representations of your own

experience. Science is a collaborative human effort to find, through

our individual actions on the world and our verbal communications with

each other, a model for what is common to all of our privately

constructed external worlds. Conversations, conferences, research

papers, and books are an essential part of the scientific process. (84–85)

In his critical assessment of quantum Bayesianism, Timpson (2008)

offers a more detailed defense against the charge of solipsism.

But even if one accepts the existence of other people and their

experiences, adopting QBism does seem severely to restrict one’s

application of quantum theory to anticipations of one’s own

experiences, with no implications for those of anyone else.

### 2.2 Instrumentalist?

By portraying it as a tool for helping a user get by in an uncertain

world, QBism has been characterized as merely a form of

instrumentalism about quantum theory. But this is no reason to reject

the view absent arguments against such instrumentalism.

Instrumentalism is usually contrasted with realism as a view of

science (see entry on

scientific realism).

The contrast is often taken to depend on opposing views of the

content, aims, and epistemic reach of scientific theories. Crudely,

the realist takes theoretical statements to be either true or false of

the world, science to aim at theories that truly describe the world,

and theories of mature science to have given us increasingly reliable

and accurate knowledge even of things we can’t observe: While

the instrumentalist takes theoretical statements to be neither true

nor false of the world, science to aim only at theories that

accommodate and predict our observations, and theories even in mature

science to have given us increasingly reliable and accurate

predictions only of things we can observe.

QBism offers a more nuanced view, both of quantum theory as a theory

and of science in general. Fuchs (2016, Other Internet Resources)

adopted the slogan “participatory realism” for the view of

science he takes to emerge from QBism (if not also a variety of more

or less related views of quantum theory). For QBism a quantum state

assignment is true or false relative to the epistemic state of the

agent assigning it, insofar as it corresponds to that agent’s

partial beliefs concerning his or her future experiences (beliefs the

agent should have adopted in accordance with the Born Rule). But what

makes this quantum state assignment true or false is not the physical

world independent of the agent.

The QBist does not take quantum theory truly to describe the world:

but (s)he *does* take that to be the aim of science—an

aim to which quantum theory contributes only *indirectly*. For

example, the Born Rule in the form of Equation ((ref{ex2})).

is less agent-specific than any probability assignments themselves.

It’s a rule that any agent should pick up and use…. it

lives at the level of the impersonal. And because of that, the Born

Rule correlates with something that one might want to call real.

(Fuchs 2016, 6, Other Internet Resources)

Fuchs thinks one thing quantum theory has taught us about the world is

that it is much richer than we may have thought: as agents using

quantum theory to make wise decisions we are not just placing bets on

an unknown but timelessly existing future but actively

*creating* that future reality: “reality is more than any

third-person perspective can capture”. That is the sense in

which he takes QBism to support a strong participatory realism, about

the world in and on which we act and about how science should describe

it.

By contrast, Mermin (2017) draws related but possibly less radical

conclusions about science that (perhaps contrary to his intentions)

some might interpret as instrumentalist:

…science is a user’s manual. Its purpose is to help each

of us make sense of our private experience induced in us by the world

outside of us.Science is about the interface between the experience of any

particular person and the subset of the world that is external to that

particular user. (88)

### 2.3 Is QBist Quantum Theory Explanatory?

Realists often appeal to scientific explanation when arguing against

instrumentalists. Quantum theory is generally acknowledged to provide

us with a wide variety of successful explanations of phenomena we

can’t explain without it. Timpson objects that QBists cannot

account for its explanatory success.

… think of the question of why some solids conduct and some

insulate; why yet others are in between, while they all contain

electrons, sometimes in quite similar densities…. Ultimately we

are not interested in agents’ expectation that matter structured

like sodium would conduct; we are interested inwhy it in fact. (Timpson 2008: 600)

does so

QBists face two problems here. In their view a user of quantum theory

can’t appeal to a description of objective, physical quantum

states in explaining the phenomena; and quantum theory’s Born

rule outputs subjective probabilities for each user independently that

bear not on what is objectively likely to happen but only on what

(s)he should expect to experience, given her prior beliefs and

experiences.

Fuchs and Schack (2015) reply that explanations offered by quantum

theory have a similar character to explanations offered by probability

theory and give examples. This does not address the first problem. But

QBists could rationalize biting that bullet by pointing to

long-standing problems of measurement and non-locality faced by

interpretations that take quantum states to be physically real that

don’t arise in their view. To respond to the second problem they

could try to develop a subjectivist view of scientific explanation as

ultimately a matter of making an economical and effective unity out of

all an agent’s beliefs and expectations.

### 2.4 Is the Born Rule a New Bayesian Norm?

Bacciagaluppi (2014) has raised an objection against the claim that

the Born rule as formulated in Equation ((ref{ex2})) states an

empirically motivated normative addition to Bayesian coherence

conditions. His basic objection is that QBism assumes the probability

(q(j)) of an actual measurement outcome (as also the probability

(p(j)) of a hypothetical measurement outcome) is independent of the

procedure by which this measurement is performed. That this is so

follows from the usual formulation of the Born Rule relating Born

probabilities of measurement outcomes to quantum state assignments.

But QBism cannot justify the procedure-independence of (q(j)) and

(p(j)) in this way because it considers the Born Rule in the form of

Equation ((ref{ex2})) to be primitive, and so incapable of

empirical support from the relation between quantum states and

outcomes of laboratory procedures.

There are also technical problems with Equation ((ref{ex2})), which

assumes the existence of SICs in the relevant Hilbert space. But

infinite as well as finite-dimensional Hilbert spaces are used in

quantum theory, and SICs have not (yet) been shown to exist in every

finite

dimension.^{[4]}

Informationally-complete (but not necessarily symmetric) POVMs do

exist in all finite dimensional spaces. Fuchs and Schack (2015) give a

schematic alternative to Equation ((ref{ex2})) that does not

require symmetry of an informationally-complete POVM representing a

hypothetical fiducial measurement.

### 2.5 Is QBism too Subjective?

The QBist approach to quantum theory is often criticized as too

subjective in its treatment of quantum states, measurement outcomes,

and probabilities.

Many people assume a wave-function or state vector represents a

physical quantum state. On this assumption a quantum state is

ontic—a fundamental element of reality obeying the quantum

dynamics that underlies classical dynamical laws. Bacciagaluppi (2014)

urges QBists to accept this approach to dynamics even while

maintaining a subjectivist or pragmatist interpretation of

probability. But doing so would undercut the QBist account of

discontinuous change of quantum state on measurement as simply

corresponding to epistemic updating.

Most people take it for granted that a competently performed quantum

measurement procedure has a unique, objective outcome. But QBists deny

this, assimilating a measurement outcome to an individual

agent’s personal experience—including her experience of

another agent’s verbal report of his outcome. By rejecting the

objective authority of observation reports QBists challenge what many

have considered a presupposition of the scientific method. This

rejection also threatens to undercut the standard personalist argument

(see entry on

Bayesian epistemology, §6.2.F)

that the opinions of agents with very different prior degrees of

belief will converge after they have accumulated sufficient common

evidence.

QBists consider a subjective view of quantum probability a core

commitment of the view, even when that probability is 1. But Stairs

(2011) and others have argued that QBist strategies for resolving

conceptual problems associated with non-locality may be co-opted by a

qualified objectivist about quantum probabilities.

QBists identify probability 1 with an individual agent’s

subjective certainty, in contrast to the objective certainty EPR took

to entail the existence of a physical quantity whose value could be

predicted with probability 1. Stairs (2011) referred to developments

of David Lewis’s (1986: Appendix C) best systems analysis as

offering an alternative notion of objective probability in which this

entailment fails (see entry on

interpretations of probability, §3.6).

Adopting this alternative blocks the inference to an element of

reality (or beable, to use Bell’s term) grounding the objective

certainty of Bob’s distant measurement outcome on his component

of a non-separable system following Alice’s measurement on her

component, thereby undercutting Bell’s proof that quantum theory

is not locally causal.

## 3. QBism and Pragmatism

Most QBists are physicists rather than philosophers. But Fuchs locates

QBism in the tradition of classical American pragmatism (see entry on

pragmatism).

While quoting Peirce and referring to Dewey, Fuchs (2011; 2016, Other

Internet Resources)

acknowledges especially the influence of William James’s ideas

of pure experience and an open and pluralistic universe in which

“new being comes in local spots and patches which add themselves

or stay away at random, independently of the rest” (2016, 9,

Other Internet Resources).

Mermin’s CBist introduction of the “Now” into

physics and Fuchs’s choice of title for his 2014 (Other Internet

Resources) both show

affinity with James’s reaction against what he called the

block-universe (see entry

being and becoming in modern physics).

Moreover, they both credit the influence on QBism of Niels Bohr. Bohr

himself never acknowledged pragmatist influences on his view of

quantum theory. But in a late interview^{[5]} he expressed enthusiasm

for James’s conception of consciousness, and he was almost

certainly acquainted with some of James’s ideas by the Danish

philosopher Høffding, a friend and admirer of James.

## 4. Pragmatist Views

Pragmatists agree with QBists that quantum theory should not be

thought to offer a description or representation of physical reality:

in particular, to ascribe a quantum state is not to describe physical

reality. But they deny that this makes the theory in any way

subjective. It is objective not because it faithfully mirrors the

physical world, but because every individual’s use of the theory

is subject to objective standards supported by the common knowledge

and goals of the scientific community. So an individual’s

assignment of a quantum state may be correct (or incorrect) even

though no quantum state is an element of physical reality; Born

probabilities are similarly objective; and measurement is a physical

process with a unique objective outcome, albeit

epistemically-characterized.

### 4.1 Stapp

In attempting to clarify the Copenhagen interpretation of quantum

theory, Stapp called it pragmatic and used James’s views on

truth and experience to provide an appropriate philosophical

background for the Copenhagen interpretation “which is

fundamentally a shift to a philosophic perspective resembling that of

William James” (1972: 1105).

The significance of this viewpoint for science is its negation of the

idea that the aim of science is to construct a mental or mathematical

image of the world itself. According to the pragmatic view, the proper

goal of science is to augment and order our experience. (Stapp 1972:

1104)

He follows Bohr (1958), Landau and Lifshitz (1977), and others in

insisting on the objective character of quantum measurements, taking

“our experience” not as individual and subjective but as

constituted by physical events, on whose correct description in the

everyday language of the laboratory we can (and must) all agree if

physical science is to continue its progress.

### 4.2 Bächtold

Bächtold (2008a,b) takes an approach to quantum theory he calls

pragmatist. Quoting C.S. Peirce’s pragmatic maxim, he offers

what he calls pragmatic definitions of terms used by researchers in

microphysics, including “preparation”,

“measurement”, “observable”, and

“microscopic system”. His “pragmatist”

approach to interpreting a theory is to isolate the pragmatic

functions to be fulfilled by successful research activity in

microphysics, and then to show that quantum theory alone fulfills

these functions.

While acknowledging that his interpretation has an instrumentalist

flavor, in his 2008a he distinguishes it from the instrumentalism of

Peres (1995) and others, who all (allegedly) claim some metaphysical

ideas but seek to remove the expression “microscopic

system” from the vocabulary used by quantum physicists. By

contrast, his “pragmatic definition” of that expression

licenses this usage, taking “quantum system” to refer to a

specified set of preparations.

Bächtold (2008b: chapter 2) elaborates on his pragmatist

conception of knowledge, appealing to a variety of philosophical

progenitors, including Peirce, James, Carnap, Wittgenstein, Putnam,

and Kant. But his overall approach to quantum theory has strong

affinities with operationalist approaches to the theory.

### 4.3 Healey

In recent work, Healey (2012, forthcoming a,b) has also taken what he

calls a pragmatist approach to quantum theory. He contrasts this with

interpretations that attempt to say what the world would (or could) be

like if quantum theory were true of it. On his approach quantum states

are objective, though a true quantum state assignment does not

describe or represent the condition or behavior of a physical system.

But quantum states are relational: Different agents may correctly and

consistently assign different quantum states to the same system in the

same circumstances—not because these represent their subjective

personal beliefs but because each agent has access to different

objective information backing these (superficially conflicting) state

assignments. Each such assignment correctly represents objective

probabilistic relations between its backing conditions and claims

about values of magnitudes.

On this approach, quantum theory is not about agents or their states

of belief: and nor does it (directly) describe the physical world. It

is a source of objectively good advice about *how* to describe

the world and what to believe about it as so described. This advice is

tailored to meet the needs of physically situated, and hence

informationally-deprived, agents like us. It is good because the

physical world manifests regular statistical patterns the right Born

probabilities help a situated agent to track. But the advice is

available even with no agents in a position to benefit from it: there

are quantum states and Born probabilities in possible worlds with no

agents.

Born probabilities are neither credences nor frequencies. They are

objective because they are authoritative. Setting credences equal to

Born probabilities derived from the correct quantum state for one in

that physical situation is a wise epistemic policy for any agent in a

world like ours. Born probabilities are equally objective even when

they differ more radically from Lewis’s (1986) chances because

they are based on more (physically) limited information.

Healey’s approach is pragmatist in several respects. It

prioritizes use over representation in its general approach to quantum

theory; its account of probability and causation is pragmatist, in

quantum theory and elsewhere; and it rests on a theory of content that

Brandom (2000) calls pragmatist inferentialism. While not endorsing

any pragmatist identification of truth with “what works”,

in its minimalism about truth and representation it follows the

contemporary pragmatist Huw Price (2003, 2011).

#### 4.3.1 Contrasts with QBism

Independently of similar suggestions by Bacciagaluppi (2014) and

Stairs (2011), Healey co-opts some QBist strategies for dissolving the

measurement problem and removing worries about non-locality, while

rejecting the accompanying subjectivism about quantum states, Born

probabilities, and measurement outcomes.

While QBists take quantum state assignments to be subject only to the

demand that an agent’s degrees of belief be coherent and conform

to Equation ((ref{ex2})), Healey takes these to be answerable to

the statistics of objective events, including (but not restricted to)

outcomes of quantum measurements. This makes the objective existence

of quantum states independent of that of agents even though their main

function is as a source of good advice to any agents there happen to

be. And it makes quantum states relative, not to the epistemic

situation of actual agents, but to the physical situation of actual

and merely hypothetical agents.

While QBists follow de Finetti in taking all probabilities to be

credences of actual agents, Healey’s pragmatist takes

probabilities to exist independently of the existence of agents but

not to be physical propensities or frequencies, nor even to supervene

on Lewis’s Humean mosaic (see entry on

David Lewis §5).

There are probabilities insofar as probability statements are

objectively true, which they may be when sensitive to though not

determined by physical facts.

There is no measurement problem since reassignment of quantum state on

measurement is not a physical process but corresponds to

relativization of that state to a different physical situation from

which additional information has become physically accessible to a

hypothetical agent so situated.

There is no instantaneous action at a distance in a quantum world,

despite the probabilistic counterfactual dependencies between

space-like separated events such as (macroscopic) outcomes of

measurements confirming violation of Bell inequalities. On a

pragmatist approach, these dependencies admit no conceptual

possibility of intervention on one outcome that would alter (any

relevant probability of) the other. So there is no instantaneous

non-local influence, in conformity to Einstein’s principle of

local action.

#### 4.3.2 Decoherence and Content

On Healey’s pragmatist approach, an application of the Born rule

directly specifies probabilities for claims about the values of

physical magnitudes (dynamical variables of classical physics as well

as new variables such as strangeness and color): it does not

explicitly specify probabilities for measurement outcomes. But the

Born rule is legitimately applied only to claims with sufficiently

well-defined content. The content of a claim about the value of a

physical magnitude on a system depends on how the system interacts

with its environment. Quantum theory may be used to model such

interaction. Only if a system’s quantum state is then stably

decohered in some basis (see entry on

the role of decoherence in quantum mechanics)

do claims about the value of the associated “pointer

magnitude” acquire a sufficiently well-defined content to

license application of the Born rule to them. Because of this

restriction on its legitimate application, the Born rule may be

consistently applied to claims of this form (not just to claims about

the outcomes of measurements) without running afoul of no-go results

such as that of Kochen and Specker (see entry on

the Kochen-Specker theorem).

What endows a claim (e.g., about the value of a magnitude) with

content is the web of inferences in which it is located. Such a claim

has a well-defined content if many reliable inferences link it to

other claims with well-defined content. It is the nature of a

system’s interaction with its environment that determines which

inferences to and from a magnitude claim about it are reliable.

Quantum decoherence and pragmatist inferentialism work together here

to make objective sense of the Born rule with no need to mention

measurement: Though of course at some stage all actual measurements do

involve interactions with an environment well modeled by quantum

decoherence.

Contra to Mermin’s view (see

§1.6),

concepts are not invented by each of us to make his or her experience

more intelligible. They acquire content from the social practice of

linguistic communication about a physical world that perception

represents (to humans as well as organisms with no capacity for

language) as independently existing.

## 5. Related Views

The view that a quantum state describes physical reality is often

called (psi)-ontic, by contrast with a (psi)-epistemic view that

it represents an agent’s incomplete information about an

underlying ontic state (Harrigan and Speckens 2010). QBists and

pragmatists are not the only ones to adopt a view that is neither

(psi)-ontic nor (psi)-epistemic in these senses. Other views

share the pragmatist thought that quantum states aren’t a

function of any agent’s actual epistemic state because quantum

state assignments are required to conform to objective standards of

correctness. This section covers two such views.

### 5.1 Friederich

Friederich (2011, 2015) favors what he calls a therapeutic approach to

interpreting quantum theory, taking his cue from the later philosophy

of Ludwig Wittgenstein. This approach grounds the objectivity of

quantum state assignments in the implicit constitutive rules governing

this practice. Those rules determine the state an agent has to assign

depending on her knowledge of the values of observables, perhaps

obtained by consulting the outcome of their measurement on the system.

Friederich agrees with Healey that differently situated agents may

therefore have to assign different states to the same system in the

same circumstances insofar as their situations permit some to consult

outcomes inaccessible to others, and makes the point by saying a

system is not (in) whichever quantum state it is assigned.

Friederich treats quantum probabilities as rational quasi-Lewisian

constraints on credence and, together with his relational account of

quantum states, this enables him to refute the claim that Bell’s

theorem demonstrates instantaneous action at a distance. He uses (what

he calls) his epistemic conception of quantum states to dissolve the

measurement problem by denying that an entangled superposition of

system and apparatus quantum states is incompatible with the

occurrence of a definite, unique outcome. Like Healey, he appeals to

decoherence in picking out the particular observable(s) a suitable

interaction may be considered to measure.

So far Friederich’s therapeutic approach parallels

Healey’s pragmatist approach (though there are significant

differences of detail, especially as regards their treatments of

probability and causation). But Friederich rejects Healey’s

inferentialist account of the content of claims about the values of

physical magnitudes, taking restrictions on legitimate applications of

the Born Rule to follow directly from the constitutive rules governing

its use rather than from the need to apply it only to magnitude claims

with well-defined content. And Friederich seriously explores the

possibility that a set of magnitude claims collectively assigning a

precise value to *all* dynamical variables may be not only

meaningful but true together. His idea is that the constitutive rules

governing the Born Rule may forbid any attempt to apply the rule in a

way that would imply the existence of a non-contextual probability

distribution over their possible values, thus avoiding conflict with

no-go theorems like that of Kochen and Specker.

### 5.2 Brukner and Zeilinger

Brukner and Zeilinger (2003; Zeilinger 2005; Brukner 2017) follow

Schrödinger (1935) and many others in viewing a quantum state as

a catalogue of our knowledge about a system. Their view is not

(psi)-epistemic because it denies that the system *has* an

ontic state about which we may learn by observing it. Instead, a

system is characterized by its information content. An elementary

system contains information sufficient to answer one question. For a

spin ½ system, a question about spin component in any direction

may be answered by a suitable observation. But the answer cannot

typically be understood as revealing the pre-existing value of

spin-component in that direction, and answering this question by

observation randomizes the answer to any future question about

spin-component in different directions. So the catalog of knowledge

takes the form of a probability distribution over possible answers to

all meaningful question about a quantum system that contains only one

entry with probability 1 that might be considered a property that

would be revealed if observed.

Brukner (2017) has recently used an extension of Wigner’s friend paradox (Wigner 1962) to argue that even the answers to such questions given by observation cannot be regarded as reflecting objective properties of the devices

supposedly recording them. If sound, this argument provides a reason

to modify this view of quantum states to make it closer to that of

QBists.

## 6. Conclusion

A variety of QBist and pragmatist views of quantum theory have been

proposed since quantum theory assumed close to its present form. In

recent years this has been an active area of research especially by

philosophically aware physicists working in quantum foundations.

Philosophers have tended to dismiss such approaches, objecting to

their instrumentalism and/or anti-realism. But there is much to learn

from responses to such objections and good *philosophical*

reasons to take these views more seriously.

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