## 1. QBism



Because the term 'Bayesianism' may be understood in many
different ways, a variety of views of quantum theory could be
considered Quantum-Bayesian. QBism is a form of Quantum Bayesianism
that may be traced back to a point of view on states and probabilities
in quantum theory adopted 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
 SS1.1.
 In deference to its contemporary proponents, this shorter name is
used. Fuchs, Mermin, and Schack 2014, and DeBrota and Stacey (2019,
  Other Internet Resources)
 provide elementary introductions to QBism; Fuchs and Schack 2015, and
Fuchs and Stacey 2019 give more detailed summaries 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 Schrodinger, 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
21st century (Caves, Fuchs, and Schack 2002a,b), although
Caves no longer considers himself a QBist. N. David Mermin (2014,
2019) 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. Stacey (2019,
 Other Internet Resources)
 tracks changes from the Quantum-Bayesianism of 2002 to the QBism of
2019.



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 1/2. 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,
 SS3.4). 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,
 SS3.3). 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 Schrodinger equation specifying the time development of a
system's quantum state \(\psi\)

 
\[\tag{1}\label{ex1} H\psi = i\hslash \,{\partial \psi /\partial t} \]


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 synchronic constraint on an agent's credences concerning the
agent's experiences at different times, and not a diachronic
constraint on the system's properties at those times. 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 who assign the same quantum state to a system at a
time \(t\_1\) may consistently assign it different states at a time
\(t\_2\) because they apply the constraint supplied by the
Schrodinger 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]


 
\[\tag{2}\label{ex2} q(j) = \sum\_{i=1}^{d^2} [(d+1) p(i) -1/d].r(j\mathbin{|}i) \]


This equation is not just a revision of the law of total probability
it resembles, i.e.,

 
\[\tag{3}\label{ex3} q(j) =\sum\_{i=1}^{d^2} p (i).r(j \mathbin{|} i) \]


because \(p(i)\), \(r(j\mathbin{|}i)\) 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 \(r(j\mathbin{|}i)\) 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,
\(r(j\mathbin{|}i)\)) 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; DeBrota, Fuchs, Pienaar,
and Stacey, 2021) 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 Schrodinger 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,
 SS4).



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 Schrodinger 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 Schrodinger 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 Schrodinger 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 Schrodinger equation is a dynamical law
governing the evolution of an objective quantum state. For them it
merely provides a constraint on an agent's current 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, 2019) 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 (2019: 8) 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 **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 (2017a) 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 2017: 119)
> 
> 
> 



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 2019 draws related but possibly less radical
conclusions about science that (perhaps contrary to his intentions)
some might interpret as a kind of instrumentalism or even
phenomenalism:



> 
> 
> ...science in general, and quantum mechanics in particular, is a
> tool that *each* of us uses to organize and make sense of
> *our own* private experience. p.2
> 
> 
> 
> The fact is that my science has a subject (me) as well as an object
> (my world). Your science has a subject (you) as well as an object
> (your world). ... While each of us constructs a different world, the
> world of science is our joint construction of the vast body of
> phenomena that we try to infer, through language, to be common to our
> own individual worlds. Science arises out of our use of language to
> indicate to each other our individual experiences out of which we each
> construct our own individual worlds. p.5
> 
> 
> 


### 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 (followed by Brown 2019)
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 in *why it in fact
> does so*. (Timpson 2008: 600)
> 
> 
> 



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. QBists deny
this, assimilating a measurement outcome to an agent's personal
experience--including her experience of another agent's
verbal report of his outcome. QBists take a measurement outcome to be
personal to the agent whose action elicited it. This tenet is key both
to QBist denial that quantum phenomena involve any nonlocal influence
(Fuchs, Mermin and Schack 2014) and to the QBist (DeBrota, Fuchs and
Schack 2020) resolution of the paradox of Wigner's friend (see
the entry on
 Everett's relative-state formulation of quantum mechanics).
 But their notions of experience and agency are broad enough to
encompass personal experiences of agents other than individual,
conscious humans.



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,
 SS6.2.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** (Caves, Fuchs and Schack 2007). 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 providing an alternative notion
of objective probability in which this entailment fails (see entry on
 interpretations of probability,
 SS3.6). So QBist subjectivism about probability is not necessary
to block the EPR 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.


### 2.6 Should a QBist believe that an agent prepares a physically real state?



A QBist is convinced that an agent should take quantum mechanics as a
guide for setting her subjective degrees of belief about the outcomes
of future measurements. Myrvold (2020a,b) has used results of Pusey,
Barrett and Rudolph (2012) and Barrett, Cavalcanti, Lal, and Maroney
(2014) to argue that anyone with that conviction should also believe
that preparations with which she associates distinct pure quantum
states result in ontically distinct states of affairs, a conclusion
that QBists reject.



His argument depends on results proved within the ontological models
framework of Harrigan and Spekkens (2010). Myrvold defends this
framework as merely codifying a form of reasoning implicit in much of
science and daily life which there is no good reason to reject when
applied in the quantum domain. One reasons that an action on a
physical system affects what one will experience later only via the
physical transmission of that action's effect from the system to
events one later experiences. If so, then the action of preparing a
system's quantum state must affect some physical property of the
system reflected in what the framework calls its ontic state.



In response, QBists insist that quantum states have no ontic hold on
the world and that the QBist notion of quantum indeterminism is a far
more radical variety than anything proposed in the quantum debate
before because it says that nature does what it wants, without a
mechanism underneath (Fuchs 2017b, p. 272; 2018, p. 19). The QBist
Schack rejects Myrvold's form of reasoning in the quantum domain
as follows (Schack 2018).



> 
> 
> There are no laws that determine objective probabilities for
> measurement outcomes. The world does not evolve according to a
> mechanism.
> 
> 
> 


### 2.7 Other Objections and Replies



Other objections to QBism may be found in Brown (2019) and Zwirn
(forthcoming).



According to Brown (2019, p. 75) "...a variant of
Berkeleyan idealism suffuses QBism." QBists insist on the
existence of a real world in which agents and their experiences are
embedded, along with rocks, trees and everything else in the usual
world of common experience. But they deny that quantum mechanics
itself describes this world, while hoping eventually to infer more
about it from our successful use of quantum mechanics to anticipate
each of our experiences when acting on it. Brown objects to the
currently ineffable character of the world for a QBist, contrasting
this unfavorably with the way a realist about a quantum state can use
it to describe the physical world and explain how it gives rise to our
experiences by affecting our brains.



Brown also objects to the QBists' understanding of the
Schrodinger equation, assuming they consider this to track
changes not in the physical state of a quantum system but in what an
agent believes she is likely to experience were she to act on it. But
QBists understand this equation as a normative constraint on an
agent's belief state at a single time, not as a constraint on
how that state evolves (see
 SS1.2).



Brown further questions QBist entitlement to divide up the external
world, either into subsystems or spatiotemporally, complaining that
"That part of QBism which relates to 'a theory of
stimulation and response' between the agent and the world is not
grounded in known physics." (2019, p. 81)



Barzegar (2020) has replied to Brown's objections. His reply
includes a defense of a claim by Fuchs (2017, p. 118) that Brown
(2019) sought to refute--the claim that QBism is pursuing
Einstein's (1949) program of "the real".



Following a largely sympathetic sketch of QBism, Zwirn (forthcoming,
SS10) highlights ways in which some of its key notions remain
unclear. Regarding quantum mechanics as an extension of subjective
probability theory, QBists (DeBrota and Stacey (2019), see
 Other Internet Resources)
 reject the demand to provide a reductive definition of the notion of
an agent. Zwirn presses this demand because in this context the agent
is not merely a passive witness: "It is the interaction between
an agent and the external world that creates a result. Without agent,
there is no result."



Zwirn (forthcoming) also challenges QBists to clarify their key
concepts of *world* and *experience*: "QBism
endorses the existence of an external world independent of any agent,
but it is not clear if the external world is unique and shared by all
agents or if each agent has her own external world."



Zwirn believes that his own view of Convivial Solipsism (Zwirn 2016,
2020) improves on QBism because it provides clear answers to these
challenging questions. In his view an agent is something whose
conscious experiences are produced by a common external physical
world, but organized into that agent's personal external
world.


## 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 Hoffding, 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 Bachtold



Bachtold (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.



Bachtold (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 (2012a,b, 2017a,b, 2020) 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 may be said to correctly represent
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 predict and explain. 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 inferentialist pragmatism. While not endorsing
any pragmatist identification of truth with "what works",
in its deflationary approach to truth and representation it follows
the contemporary pragmatist Huw Price (2003, 2011). Healey (2020)
argues for a conception of realism according to which this pragmatist
approach is realist rather than anti-realist.


#### 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
 SS5). 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 inferentialist pragmatism 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
 SS1.6),
 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.


#### 4.3.3 Objections and Replies



Jansson (2020) challenges the claim of Healey's pragmatist
approach to offer objective explanations of phenomena, while
acknowledging the attractions of a position that seeks to occupy the
middle ground between explanation seeking realism and prediction
focused instrumentalism. She concludes (2020: 165) that



> 
> 
> Many explanations according to this approach to quantum theory seem to
> at least partially black-box crucial information about the physical
> ground for the appropriate assignment of quantum states or
> applications of the Born rule. ...neither quantum states nor the
> Born rule can act as initial explanatory input. While this is a
> serious cost, it is not clear that a pragmatist approach to quantum
> theory has to resist this conclusion.
> 
> 
> 



One taking Healey's pragmatist approach to quantum theory could
reply as follows (see Healey 2020, SS7.7). The primary target of
an explanatory application of quantum theory is not a collection of
events but a probabilistic phenomenon they manifest. A probabilistic
phenomenon is a probabilistic data model of a statistical regularity.
One explains the phenomenon by demonstrating how the probabilities of
the model are a consequence of the Born rule, as applied to events
that manifest the regularity. Since the *explanandum* is not
itself a physical condition, it is inappropriate to demand a physical
*explanans* (such as a physically real quantum state). But the
demonstration is explanatory only if each event manifesting the
regularity itself depended on whatever physical conditions obtained,
including whatever conditions backed assignment of the quantum state
input to the Born rule. One can have good evidence for such backing
conditions while unable to specify exactly what they are. The more
complete the description of the physical conditions on which each
event manifesting the regularity depended, the better the explanation
of the probabilistic phenomenon they manifest.



Lewis (2020) raises concerns about Healey's application of
inferentialist pragmatism to the content of claims in quantum theory
and its applications. His first worry concerns the distinction between
the prescriptive content of quantum claims (about the quantum state,
for example) and descriptive non-quantum claims about magnitudes like
position and energy.



But, as he notes, a claim's having a distinctive prescriptive
function does not show that it has no representational content. A
pragmatist could reply that a quantum state represents something other
than an "element of physical reality" while functioning to
prescribe credences about such elements: Healey (2017a) suggests that
a quantum state represents probabilistic relations between them.



Lewis's second worry is that Healey's position fails to
adequately take into account the role of conditional or counterfactual
inferences in conferring content both on quantum, and on non-quantum
magnitude, claims. Through its prescriptive role in applications of
the Born rule, Lewis maintains, a claim about a quantum state or a
magnitude implies many counterfactual probabilistic claims about
magnitudes. For an inferentialist then, quantum claims and magnitude
claims derive content from the corresponding inferences.



On Healey's (2017, pp. 208-210) pragmatist approach, a
claim assigning a quantum state does derive much of its content from
inferences involving counterfactuals. The inference is to a
counterfactual whose antecedent is (or supervenes on) a claim about
magnitudes, and whose consequent specifies a probability as great as
**1** for a different magnitude claim that is meaningful
in these counterfactual circumstances. Healey could argue that the
magnitude claims Lewis considers do not derive content from his
corresponding counterfactuals, on the grounds that they do not
materially imply those counterfactuals and so in quantum theory an
inference from the claim to the counterfactual is not reliable.
According to Healey's inferentialist pragmatism, only reliable
material inferences confer content. Magnitude claims about the
trajectory of a molecule might be meaningful and true according to an
alternative theory such as
 Bohmian mechanics.
 But in Healey's pragmatist view (2012b, pp. 1547-8), even
an imprecise claim about the location and velocity of a molecule is
true only in a situation that can be modeled by decoherence of a kind
that would block the inference to the counterfactual.



Lewis's final worry is that this application of inferentialist
pragmatism renders the content of a claim highly sensitive to the
physical environment of the system concerned. He correctly notes that,
on this pragmatist approach, quantum theory requires acknowledgement
of radical changes to physical concepts that do not flow from other
applications of pragmatism.



One taking Healey's pragmatist approach might respond to this
worry by noting that these conceptual changes are a straightforward
consequence of the application of inferentialist pragmatism to quantum
theory. For an inferentialist pragmatist, a material inference can
contribute to the content of a claim only if it is reliable, but in
the quantum domain physical inferences of a sort we all make in
everyday life fail dramatically. The sensitivity of physical concepts
to a system's physical environment is arguably the natural
result of reconfiguring our physical concepts to restore the
reliability of inferences involving them.


## 5. Related Views



The view that a quantum state describes physical reality is sometimes
called \(\psi\)-ontic, by contrast with a \(\psi\)-epistemic view that
it represents an agent's incomplete information about an
underlying physical state. When Harrigan and Spekkens (2010)
originally defined these terms they applied them only to what they
called ontic models of quantum theory. But others have since used them
more broadly to classify alternative views of quantum states outside
of the ontological models framework. QBists and pragmatists are not
the only ones to adopt a view that is neither \(\psi\)-ontic nor
\(\psi\)-epistemic in these broader 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) follow Schrodinger
(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 1/2 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 (2018) 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, such an
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.