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Concepts of Knowability
Conceptos de cognoscibilidad
Jan Heylen*; Felipe Morales Carbonell**
*Centre for Logic and Philosophy of Science, Institute of Philosophy,
KU Leuven, Belgium
jan.heylen@kuleuven.be
**Universidad de Chile, Chile
ef.em.carbonell@gmail.com
Abstract
Many philosophical discussions hinge on the concept of knowability. For example, there is a
blooming literature on the so-called paradox of knowability. How to understand this notion,
however? In this paper, we examine several approaches to the notion: the naive approach
to take knowability as the possibility to know, the counterfactual approach endorsed by
Edgington (1985) and Schlöder (2019) , approaches based on the notion of a capacity or
ability to know (Fara 2010, Humphreys 2011), and nally, approaches that make use of the
resources of dynamic epistemic logic (van Benthem 2004, Holliday 2017).
Keywords: knowability, counterfactual knowability, capacity to know, dynamic possibility
to know.
Resumen
Muchas discusiones losócas dependen del concepto de cognoscibilidad. Por ejemplo, hay
una oreciente literatura acerca de la así llamada paradoja de la cognoscibilidad. Sin embargo,
¿cómo hemos de entender la noción? En este paper, examinamos varios enfoques: el enfoque
naive de tomar a la cognoscibilidad como la posibilidad de conocer, el enfoque contrafáctico
defendido por Edgington (1985) y Schlöder (2019), enfoques basados en la noción de una
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capacidad o habilidad de saber (Fara 2010, Humphreys 2011), y nalmente, enfoques que
emplean los recursos de la lógica epistémica dinámica (van Benthem 2004, Holliday 2017).
Palabras clave: cognoscibilidad; cognoscibilidad contrafáctica; capacidad de conocer;
posibilidad dinámica de conocer.
1. Introduction
‘What can we know?’ is one of the main philosophical questions. It has two sides: rst, it
makes a question out of how we come to know whatever it is we know (in what ways we are
able to know), and second, it makes an issue of the limits of knowledge (in what ways we are
unable to know). Asking for the limits of knowledge entails asking what is knowable. e
history of philosophy is rife with dierent positions on the question of what is knowable:
• Everything is knowable (epistemic optimism).
• Some things are knowable and some things are not (epistemic moderatism).
• Nothing is knowable (epistemic pessimism).
How, though, should we understand the notion of knowability? In this paper, we examine
the problem of how to characterize the concept of knowability, and give an overview of
various directions taken in the literature about the problem, to then raise some concerns.
e structure of the paper is as follows: in section 2 we examine the traditional concept
of knowability in terms of there being a possibility to know, and raise the need for a factive
concept of knowability. Next, we branch out into three dierent types of conceptualization that
can handle this requirement: one that oers a counterfactual analysis (Edgington, Schlöder)
(section 3), one that oers an analysis in terms of capacities (Fara, Humphreys) (section 4),
and nally, one that makes use of the framework of dynamic logic (Van Benthem, Holliday)
(section 5). After we discuss the conceptual issues that arise from these perspectives, in section
6 we will summarize and consider the similarities shared by these three perspectives, which
point towards ways in which the discussion can be taken further.
2. Knowability as the possibility to know
e most common concept of knowability in the literature is that of there being a possible
state of the world (potentially counterfactual) in which someone knows that something is the
case .1
1 In this paper we are only concerned with ‘propositional’ knowability (‘it is knowable that φ’), not with objec-
tual knowability (‘x is knowable’).
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Naïve
φ is knowable i it is possible to know φ
To present things more formally, we will make use of the framework of possible world
semantics; we assume familiarity on part of the reader. Schematically, then, with k for the
knowability operator, ◇ for possibility and K for knowledge:
kφ ↔ ◇Kφ
e meaning of ◇ (possibility) and K (knowledge) are supposed to be given by the
ordinary semantic clauses:
• Kφ is true at world w i φ is true at all worlds that are epistemically accessible from w.
• ◇φ is true at world w i φ is true at least one world that is modally accessible from w.
Following this schema, the problem of characterizing the concept of knowability reduces
to the problem of fully characterizing these operators. To illustrate: Kripke raises the problem
in the context of a discussion of the concept of a priori knowability:
… And possible for whom? For God? For the Martians? Or just for people with minds
like ours? To make this all clear might [involve] a host of problems all of its own about
what sort of possibility is in question here. (Kripke, 1980, pp. 34-35)
e questions that arise naturally here are: How restrictive should we understand the
sense of possibility here? What are the adequate logical/modal conditions for an account of
knowledge?
An issue that came up fairly early (cf. Church, 2009; Fitch, 1963) with the Naive
conception of knowability is that, in the context of theories committed to the thesis that all
truths are knowable and under some fairly standard assumptions about the behaviour of the
◇ and K operators involved, it gives rise to what is now-called Fitch’s paradox. e paradox
states that, if all truths are possibly known, then every truth is in eect known. Epistemic
optimism, namely the position that all truths are knowable, then implies omniscience.
Many philosophers have tried to defend a version of epistemic optimism, but few would
want to defend omniscience. is has motivated many to look for alternative conceptions
of knowability that would avoid the paradox. Our goal here is to focus on the concept of
knowability, not on the knowability thesis that all truths are knowable, so we won’t dwell
on this point. ere are four strategies to deal with the paradox: biting the bullet, revising
the underlying logic(s), restricting the thesis and reformulating the thesis with help of other
concepts of knowability. In so far as the discussion that follows bears on the knowability
thesis, it only does so in the context of the reformulation strategy.2
2 is is why we don’t discuss any of the restriction strategies by Tenant (1997), Dummett (2001), Fischer
(2013) or Artemov & Protopopescu (2013). For an overview of the discussion on the knowability thesis, see
Brogaard & Salerno (2019).
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ere is a more general issue with the Naive concept of knowability: it is not factive, that
is, there are (actual) falsehoods that are known in counterfactual states of the world, where
they are not false. For example: one of the authors has only one sister, but he could have had
two, so if he had counted his sisters, he would have known (in that scenario) that he has
two sisters.3 In many cases we worry about what is knowable about the actual state of the
world, not about what is knowable in purely counterfactual scenarios. To address this point,
we require a factive concept of knowability, so that in the relevant sense of ‘knowable’, only
actual truths are knowable. For a factive concept of knowability, the following will hold:
Factivity
kφ → φ
Brogaard & Salerno (2006) rehearse the following dialogue to stress the point that non-
factive conceptions of knowability are problematic:
A: We could be discovered.
B: Discovered doing what?
A: Someone might discover that we are having an aair.
B: But we are not having an aair!
A: I didn’t say that we were.
Clearly, we don’t normally worry about what could merely happen, and by extension,
about what could merely be possibly known.4 Even if non-factive conceptions of knowability
are admissible for some purposes, it would pay o to have a factive notion available.5
Nowadays there are alternative conceptualizations of knowability that restrict its range
to (f)actual truths: having the counterfactual possibility to know that something is actually
true (Edgington, 1985); actually having the capacity to know that something is actually true
(Fara, 2010); having the potential to know (Fuhrmann, 2014); having the ability to know
3 ere are other reasons to be careful about the factivity of possible knowledge. Heylen (2013, p. 96) notes the
following consequence. First, suppose that theorems of arithmetic are possibly known. Second, assume a weak
introspection principle: if one knows an arithmetical theorem, then it is possible that one knows that one knows
that theorem. ird, assume some modal logic (i.e., the monotonicity rule for the diamond operator and modal
axiom scheme 4 for the diamond operator). Fourth, suppose that possible knowledge is factive. en if follows
that theorems of arithmetic are known. Williamson (1992, p. 67) shows that the factivity of possible knowl-
edge, in combination with the knowability of truth, and under the same modal assumptions as above entails
a modal collapse: possibility entails truth. Heylen (2020b) mentions that the factivity of possible knowledge
together with modal axiom scheme 5 entails that whatever is possibly known is also necessarily true.
4 Cf. Sinhababu’s (2008) argument that perhaps we are allowed to worry about merely counterfactual aairs.
5 It has been suggested that φ is knowable if and only if ♦Kφ, ♦ ranges only over accessible worlds in which
the non-epistemic facts are the same (Williamson, 1992; Tennant, 2009). For a critical discussion, see Heylen
(2021).
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(Spencer, 2017); becoming known to be previously true after a hypothetical future of updates
(Holliday, 2017). We will examine several of these in the following sections.
3. e counterfactual approach
In this section we will discuss the counterfactual approach to knowability. is approach
nds its contemporary roots in the work of Edgington (section 3.1) and it has recently been
developed further by Schlöder (section 3.2).
3.1 Edgington and counterfactual knowability
An early attempt to construe a factive conception of knowability is pursued by Edgington
(1985). According to her, knowability could be characterized in terms of what could be
known to be actually the case. Schematically:
aK
φ is knowable i it is possible to know that φ is actually the case.
kφ ↔ ◇KAφ
We assume that the meaning of the A (actuality) operator obeys the following semantic
clause, which is traditional:
• Aφ is true at w i φ is true at the actual world, w0.6
is eectively makes only actual truths knowable. Suppose that there is some φ that is
not actually true, and which therefore cannot be actually true, and in turn, cannot be known
to be actually true. en, φ is unknowable, because it cannot be the case that it is known to
be actually true in any world, because it isn’t actually true in any world. It might be worth
noticing that this also rules out knowability of contingently false statements about the actual
past. For example: I didn’t have breakfast this morning. So it is false at any world that I
actually had breakfast this morning. It is unknowable in this sense, then, that I had breakfast
this morning. Again, this is in contrast with non-factive conceptions of knowability like
Naive. It could happen that I had breakfast; if I had, I could have known it.
Edgington points out that this concept of knowability can avoid Fitch’s paradox. However,
Rabinowicz & Segerberg (1994) show that the problem comes back with a vengeance: from
the formulation of the knowability thesis using aK, we get Aφ→ KAφ. Indeed, if φ is true
at the actual world, then it is true at all worlds that Aφ, and all worlds that are epistemically
accessible worlds from a given world are among those, so KAφ is true at that given world.
However, they also show that the issue can be circumvented using a dierent two-dimensional
6 In natural language there are some senses of ‘actually’ that do not follow these semantics. Edgington herself
admits her use of ‘actually’ is a theoretical construct. Cf. Stephanou (2001).
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semantics. e basic idea is that formulas have to be evaluated not with respect to a single
world but to pairs of worlds:7
• ◇φ is true at the pair of worlds (w, v) i there is at least one world w’ that is modally
accessible from w and φ is true at the pair (w’, v).
• Aφ is true at the pair of worlds (w, v) i φ is true at the pair of worlds (v, v).
• Kφ is true at the pair of worlds (w, v) i φ is true at all the pairs of worlds (w’, v’) that
are epistemically accessible from (w, v).
We leave it to the reader to check that this indeed solves the problem.
A lingering problem is that this notion of knowability, by appealing to possible knowledge
of actual truth, seems to require trans-world de re knowledge of actuality. Suppose, for
example, that actually there is a true among the roots of an oak tree. In some possible world
w, trues are found among the roots with the help of a true hog. at there is a true
among the roots of the tree is known at w, but this is not knowledge about what is the case
at w0. How could one know about the actual world in other worlds? e point is pressed by
Williamson (1987, 2000) and Rabinowicz & Segerberg (1994).
Edgington’s initial answer was to observe that the actuality operator works in relation to
situations, not complete worlds. Schematically:8
αK
Where α characterizes the actual situation:
kφ ↔ ◇K(α→ φ)
e idea is as follows. Suppose that at some possible world w one knows that if α, then φ.
en one knows that φ is true at all the α-worlds, which includes the actual world.9 But this
also falls prey to triviality objections (Williamson; 1987, 2000; Fara 2010; Heylen 2020b).
Williamson (1987) points out that, if α Is any correct description of the actual world and if
φ Is true at the actual world, then α ∧ φ is also a correct description of the actual world. But
K((α ∧ φ) → φ) is just knowledge of a logical truth. So, possibly knowing a trivial logical
truth is then sucient for the knowability of φ, even when φ supposedly is an empirical truth.
A major drawback of αK is that α needs to be as complete a description of the actual world as
is feasible, because that will shrink the set of worlds that satisfy the description to the smallest
set that is feasible, with the singleton consisting of just the actual world as the ideal. A more
promising approach consists in using a counterfactual, which selects the α-worlds that are
closest to the given world, where α may be a very unspecic description (e.g., it rained last
7 See also Heylen (2016).
8 The schemes αK and αK’ are based on Schlöder (2019).
9 Note that since α is an incomplete description, there are multiple ways to complete it.
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night). In other words, the closeness relation compensates for the lack of specicity of the
description. e proposed conceptualization of knowability is the following:
αK’
Where α characterizes the actual situation:
kφ ↔ ◇K(α□→ φ)
e semantical clause for □→ is the following:
• φ □→ ψ is true at a world w i all φ-worlds that are closest to w are also ψ-worlds.
It turns out that the counterfactual-based version is not immune to trivialization worries
(cf. Williamson, 1987; Fara, 2010; Schlöder, 2019; Heylen, 2020b). For any ψ that is true
at the actual world and for any given world w, the closest α-worlds also have to be the closest
(α ∧ ψ)-worlds, since otherwise a non-actual world in which (α ∧ ¬ψ) is true is closer to w,
which would undermine factivity. By assumption, φ is true at the actual world. Hence, the
closest α-worlds to any given world w are also the closest (α ∧ ψ)-worlds. erefore, α
□→ φ is necessarily equivalent to (α ∧ ψ) □→ φ, which is just a logical truth.
3.2 e counterfactual approach revisited: Schlöder
Schlöder (2019) proposes a new analysis of counterfactual knowability that is meant to
avoid the triviality objections:
ARTK
φ is knowable either if it is known that φ or there is a way i to enquire whether φ that
isn’t actually successfully pursued but that, if it were to be successfully pursued, would
impart the knowledge that φ would be true even if i wasn’t successfully pursued. Using
sp(i) to indicate that i is successfully pursued we get the schema:
kφ ↔ Kφ v ∃i∈Inq(¬sp(i) & (sp(i)□ → K(¬sp(i)□ → φ)))
is elaborates on Edgington’s idea that we can have counterfactual knowledge of actual
truths (in this case, that truths would have remained stable if we hadn’t successfully pursued
some lines of inquiry).
Schlöder’s account is free from the triviality worries noted earlier because the knowledge of
a counterfactual is not directly within the scope of a possibility operator but it is embedded
within another counterfactual. e counterfactual ¬sp(i)□ → φ has to be true at all the
closest sp(i)-worlds (relative to the actual world), but it is left open that it could be false (and,
therefore, not logically true) outside the set of the closest sp(i)-worlds (relative to the actual
world).
Factivity is enforced by stipulating that the following symmetry principle holds: if v is
among the closest-to-w worlds at which sp(i) is true, then w is among the closest-to-v worlds
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at which sp(i) is false. It is important to note that while this is a factive notion of knowability,
it makes no use of the actuality operator, which dispenses with some of the worries that
plagued Edgington’s analysis. Yet, the symmetry problem that is appealed to is not without
critics.
Heylen (2020b) points out that some lines of inquiries consist of multiple steps and that
fact can be used to criticize the symmetry principle:
Suppose that in the actual world the line of inquiry was not successfully pursued
because something went amiss before even the rst step could be executed. Before
you are walking into the kitchen, one of your children is crying and you go and check
on the child instead. Now consider a possible world w in which you have successfully
pursued the line of inquiry. Arguably, the worlds that are closest to w in which the
line of inquiry has not been successfully pursued do not include the actual world but
rather the worlds in which something went amiss before the line of inquiry could be
completed. For instance, consider a world in which you did walk into the kitchen, you
did open the cupboard, and you did look at the objects in front of you, but you did not
yet rummage through the cupboard to look at the objects hidden behind other objects,
because in this world you hear the music of an ice cream van and you decide to abort
your search for cookies and buy an ice cream instead.
To solve this problem it was suggested by Heylen (2020b) to reformulate the symmetry
principle to take multiple-steps procedures into account. e key idea is the following: if w is
among the closest-to-v worlds where the n-th step of the line of inquiry has been successfully
executed, then v is among the closest-to-w worlds where an earlier step m has not been
successfully executed. We will not go into further details here, but do note that it is important
to take the internal structure of lines of inquiries into account.
Another problem has been pointed out by Williamson (2000, 298) in a discussion of
Edgington’s work:
For example, let p be the proposition that there is a pebble at spatiotemporal location
xyzt, and s be a situation in which p is true but unknown because the conditions for
intelligent life emerge only long after t (the time of xyzt). Let s* be a situation as close
as possible to s in which p is known. Cosmic history follows vastly divergent paths in
s and s*. In the closest possible situation to s* in which p is unknown, it is unknown
simply because no one chances to travel near xyzt; such situations are far closer to s*
than to s in cosmic history.
Once more, it seems important to think about what possible lines of inquiries are. A
minimal condition is that, for any possible line of inquiry, there is a possible world in which
that line of inquiry is successfully pursued. (Otherwise it trivializes Schlöder’s concept of
knowability.) However, that leaves open whether it is successfully pursued by a possible agent
or by an actual agent. If the latter, then there is a way to resist Williamson’s counterexample.
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Part of any putative line of inquiry into whether there is a pebble at coordinates xyzt is for an
agent to pursue this line of inquiry to travel to xyzt, or to a point on a line of sight ending at
xyzt. But it is impossible for any agent in the actual world to travel to xyzt or to a point on a
line of sight ending at xyzt, because any actual agent exists only at times much later than t.
(In addition, it is assumed that time travel within the same world is not feasible for agents.)
So, there is no possible world in which a line of inquiry into the presence of a pebble at xyzt
succeeds. erefore, it is not a counterexample to the symmetry principle, which applies to
worlds at which a line of inquiry has been successfully pursued. If possible lines of inquiries
being successfully pursued is compatible with them being successfully pursued by possible
agents, then Williamson’s counterexample remains a serious challenge. To save factivity by
appeal to symmetry from Williamson’s counterexample, it suces to restrict possible lines
of inquiries to one that are possibly successfully pursued by actual agents. As we will see in
the next section, in the analysis of knowability as the capacity to know, there is an explicit
restriction to actual agents.
e counterfactual approach to knowability that was put on the contemporary research
agenda by Edgington suered rst from a host of triviality problems. Recently, it was
reinvigorated by Schlöder. It turns out that to ensure that Schlöder’s counterfactual concept
of knowability is factive it is important to think about the internal structure and the
individuation of lines of inquiries.
4. e capacity and the ability to know
A dierent line of thought about knowability makes a more direct use of the fact that
knowability is a kind of ability. A somewhat natural approach towards abilities is to account
for them in terms of items such as capacities, potentials or dispositions more generally. e
idea is that one is able to do something if doing it is within one’s capacities, or if there is a
potential for one to do it, or if one is disposed to do it (given some triggering conditions). In
turn, capacities, potentials and dispositions can be accounted for in various dierent ways (for
an overview, see Choi & Fara, 2018). One theoretical possibility is that these items should
be understood in terms of counterfactuals. In that case an analysis of knowability in terms of
capacities would end up with some of the problems we have already raised for counterfactual
approaches. Consequently, it is more interesting to consider if we can gain anything by
rejecting the reduction of these items to counterfactuals. An approach of this kind is taken
by Vetter (2015), who argues that dispositions are sui generis precisely in this way. Indeed,
for Vetter objective modality is metaphysically dependent on what she calls potentialities. In
a framework that takes dispositions as primitives, ability concepts are not analyzed in terms
of counterfactuals, but rather in terms of the available dispositional primitives (cf. Vetter &
Jaster, 2016) for a critical overview of some recent views of this sort).
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is kind of approach to the concept of knowability is developed explicitly by Fara
(2010), who proposes to use the notion of a capacity as his conceptually primitive notion. For
knowability, he proposes the following analysis:
Capacity to know
φ is knowable if actually there is an x who has the capacity to know that actually φ.
kφ ↔ A∃x(CxKxAφ)10
e idea is that somebody has the capacity to know something if the agent possesses
the appropriate epistemic faculties, exercised or not, that would yield knowledge in the
appropriate circumstances. In Fara’s words:
... one has the capacity to perform some feat provided one’s internal constitution does
not rule out the performance of that feat ... (2010, p. 68)
Interestingly, Fara distinguishes between the ability to know and the capacity to know:
while the former typically is manifested in successes (in coming to know), the second can fail.
According to him, for someone to have an ability, they must at least satisfy the condition that
if they were to try, they would succeed. Consequently, the concept of capacity is (in Fara’s
reconstruction) relatively more fundamental than that of ability.
Fara takes the feature of capacities that they can fail to be manifested even further. In his
conception, while typically abilities are possibilities to do something, capacities need not
correspond to possibilities.11 is gives a conceptual solution to Lewis (1976) grandfather
paradox scenario: people can have the capacity to kill their own grandfather without there
being a possibility where they indeed kill them (even if they tried). So Fara raises the possibility
of having the capacity to do something impossible: the capacity to know something that is not
possibly known, for example. Spencer (2017) also oers a notion of ability that is compatible
with impossibility: according to him, one can be able to do the impossible.12
10 e Cx-operator (‘x has the capacity to …’) is an unary operator that can only meaningfully combine with
an expression that expresses a verb in an innitive clause (i.c. know). e Kx-operator (‘x knows that …’) is
an unary operator that expresses a sentence (clause), not merely a verb. So, it would seem that both operators
cannot be meaningfully combined. Fara (2010, p. 70, fn. 25) is aware of this issue and he proposes to read the
formula CxKxAφ as ‘x has the capacity to know that Aφ’.
11 Similarly, Fuhrman (2014) talks about knowability as potential knowledge, and rejects that knowability
entails possible knowledge and that possible knowledge entails knowability. In (Heylen, 2020a) it was shown
that, for all models based on Fuhrmann’s so-called ‘hyperrelational’ frames that make a certain the closure of
potential knowledge under conjunction introduction frame-valid and that are not ‘innitary’ in a certain sense,
there are Kripke-style models based on bi-relational frames that are elementarily equivalent to the former. What
this means conceptually is that, under those conditions, potential knowledge behaves as possible knowledge.
12 Nguyen (2018) oers various arguments against Spencer; it is an open question if these arguments apply to
Fara.
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At this point it might be worth raising some more general issues about the individuation
of capacities, abilities, and dispositions.
e rst thing to notice is that capacities, abilities and dispositions can be context-
sensitive: something or someone can have certain capacities or abilities restricted to certain
circumstances only. Consider this scenario:
Wanderer
Odysseus had been travelling at sea for many years, looking for a way back home. He
was unable to nd rest in Polyphemus island, where he lost many men. Neither could
he in Circe’s island. Even when he came back home he was restless, because of the
pretenders that were trying to take over his household. Once he disposed of them with
the help of his son, he was able to rest at last.
Odysseus’ abilities seem to change as his circumstances change. Alternatively, we could
say that they remain constant, but are masked as his circumstances change. Using Fara’s
distinction between capacities and abilities, we could say that Odysseus has the capacity to be
at rest all throughout, even though at times it was impossible for him to be at rest, and thus,
lacked the ability to be at rest. Capacities in Fara’s sense are less sensitive to the circumstances
than abilities; they are more about their subject (the individual who has them) than about the
integrated system of the subject and its environment.
Transposing to the case of knowability, we should raise the question whether knowability
is a property of (potential) epistemic agents, of the environment in which epistemic agents
could be, or of the (potential) systems which integrate agents and environment. is gives
three dierent ways in which the concept of knowability can be developed in a framework
of this sort. We can thus pick apart dierent senses of ‘capacity’ in the characterization that
we gave above. Whether any of these concepts would be more adequate, is an open question.
For example, we could argue that the relation between the subject and the environment must
always be taken into consideration.13 We could ask what makes an individual able to know
something across various changing environments. Or we could ask what in the environment
makes it possible for individuals in the environment to know or ignore truths that are in some
sense available in these environments. In principle, one could take a pluralist stance and argue
that all three types of concept can be useful in dierent contexts.
Two types of factors involved in the constitution of the capacities and abilities of agents
like us are worth some special attention: the technological and social circumstances. We are
able to do certain things only because we have tools to do them. For example, measuring
the pressure of a bike tire requires a special gauge. We are also able to do certain things only
because we live alongside other people. ese things often go hand in hand: the authors of
13 For example, somebody could argue that epistemic abilities are relational because epistemic concepts have
anti-individualistic satisfaction conditions. Cf. Brandom (1995).
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this paper were able to write this paper on their computers only because other people designed
and manufactured those computers. is already puts some pressure on the distinction
between capacities and abilities: we may be capable of certain things only because somebody
has certain abilities, for example. Furthermore, abilities might require knowing how to do
certain things. In this case, this know-how could also be relative to the use of technology or
to social interaction. ere is a sense in which merely having the tools to do something is not
sucient to be able to do it: one might also need to know how to use them. Can Odysseus
sail his ship without a skilled crew? No, unless he also knows how to do the things the crew
knows how to do. e same goes for the necessity of social skills (including communication
skills): even if every member of Odysseus crew knew what to do and how to do it, could
they sail the ship if they didn’t also have the means to coordinate, or even evaluate the other
crew members actions?14 ese points are obviously important in the context of knowability,
where often methods of detection require specialized skill and coordination from various
researchers (think, for example, of the experiments at CERN). An issue closely related to
this has to do with the connection between having an ability, capacity or disposition to do
something, and there being a counterfactual situation in which that thing is satised; in the
cases where we deal with actions, we worry about the possibility of counterfactual successes.
In Fara’s conception, on the assumption that it is possible to try to know, the ability to know
entails the possibility to know. Remember that for Fara, abilities to do something entail that
if one tried to do it, one would succeed in doing it. us, if it is possible to try to do it, it
is possible that one succeeds. is gives a necessary condition for having an ability, but also
indirectly for having a capacity that depends on an ability (see above).
We can ask if that is also a sucient condition. Suppose that there are possible worlds in
which somebody lifts a 10 ton rock without mechanical assistance. Let’s suppose that the
person in question actually can barely lift 20 kg. It seems then that this person would have
to be very dierent from the way they actually are in order to be like in the possible world
where they lift 10 tons without assistance. So perhaps that world is too distant from the actual
world for us to say that the person has the ability to lift it, even if it is possible. Maybe we
would say that they have the ability if there is a good proportion of worlds where they lift it
versus worlds where they don’t. Some authors say that in those cases one has more than the
ability: one has a competence.15 e same can be said in the case of knowability: the possibility
(for somebody) of counterfactual knowledge might not be sucient for something to be
knowable (for that person).
14 A crew can collectively navigate without any of the members of the crew being in a position to know all the
required steps. For a description of the distributed cognitive processes involved in the navigation of a modern
ship, see Hutchins (1995).
15 Cf. Sosa (2010) for a discussion on the epistemological importance of the notion of competence, and Morales
(2018, s. 4) for a critical overview of dierent accounts of competence.
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e second point to raise has to do with the possibility of iterated capacities/dispositions.
In his response to Fara (2010), Paul Humphreys (2011) elaborates on the point as follows:
ere is a sense of ‘capability’ for which it is true that if an agent has, for example, the
technological capability to construct an instrument that would provide evidence for a
true sentence p, and the existence of that instrument would endow the agent with the
epistemic capability to know that p, then the agent has the capability to know that p.
ere is another sense of ‘capability’ in which collapsing the successive capability claims
is illegitimate. (p. 550)
Does, then, having the capacity to have the capacity to do something entail having the
capacity to do it? Can we come from our capacities in distant possible worlds to the capacities
we actually have in close worlds? How far is too far in this sense? Again, we will have a variety
of concepts of knowability depending on the conditions we impose on iterated capacities.
is goes back to our earlier point about the dependencies of capacities on technological
and social circumstances. e features of circumstances make the capacity to have certain
capacities available. For example, you might want to know the pressure of your bike’s tire.
Typically, you will need some instrument to measure the pressure. So you might lack the
capacity unless you had the required instrument, which in turn would make certain capacities
available. Further, you might lack the capacity even if you had the instrument, if you didn’t
know how to use it.16 ese problems of iteration put further pressure on the distinction
between capacities and abilities.
e third point has to do with the fact we have just noticed that capacities and abilities
can stand in various types of relations to each other. In the cases we just mentioned, some
capacities might be dependent on abilities. ere can be other hierarchies of capacities and
abilities. For example, whoever has the capacity to chop down 20 trees has the capacity to
chop down 19, and 18, and so on. Someone has the (more general) capacity to chop down
trees and bring them to market might also have some of those capacities. In both cases the
less general abilities compose the more general ones. Abilities can stand to each other in the
relation that in order to be able to do something specic, you must have a more general
ability, without it being possible to decompose the more general ability in more specic
ones. For example, someone could argue that to understand a word in one circumstance it is
necessary to be able to understand it in a vast array of circumstances.
e case of knowledge gives a dierent example of what we are discussing, more relevant
to our concerns here: in order for one to know p, according to reliabilists, one’s method of
forming the belief that p must be reliable, so that it would give the right result in a wide range
16 is is another point of contact with the literature on know-how. Indeed, the structure of the worry that hav-
ing the capacity requires other capacities, which in turn might require other capacities, is at the base of a classic
regress argument against intellectualism by Ryle (1949). Cf. also Carroll (1895).
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of counterfactual cases. Methods of belief formation can also be more or less general. For
example, one can form a belief based on (in order of decreasing generality):
1. directly looking at something,
2. directly looking at something in broad daylight,
3. directly looking at something in broad daylight and at a short distance,
4. directly looking at something in broad daylight and at a short distance from the
front of my house,
5. on Friday 27 December at 12:07 directly looking at something in broad daylight
and at a short distance from the front of my house.
Each of these methods of forming beliefs comes with dierent levels of reliability. e
so-called Generality problem is to determine which of these belief forming methods is the
relevant one. On the one hand what is to be avoided is that the individuation of belief
forming methods is so ne-grained that they are tied to single beliefs, which are true or false,
so that the reliability of a belief forming process reduces to the truth of the single belief that
is formed. On the other hand it is also to be avoided that the individuation of belief forming
methods is so coarse-grained that they are bound to result in false beliefs in a fairly wide range
of circumstances. For example, directly looking at something in dim light or at something
that is far away can easily result in false beliefs.
If knowability is analysed in terms of capacities or abilities and given that capacities and
abilities can be more or less general,17 then the question is what the relevant capacities and
abilities are, where they can be neither too ne-grained nor too coarse-grained.18
e capacity/ability approach to knowability may seem prima facie promising: it gives
a framework to make a series of distinctions and connections that are dicult to evaluate
from other perspectives. However, this apparent strength is also its weakness, since in order
to make good on the promise several signicant diculties concerning the individuation of
capacities and abilities should be dealt with rst. In this sense, Fara’s proposal (and similar
ones) is under-specied. We have seen this in that the distinction between capacities and
abilities that it deploys is unstable. is general problem puts pressure on the purported
autonomy of the capacity/ability framework from, for example, counterfactual approaches.
17 Cf. Mele (2003).
18 e Generality problem is usually described in terms of processes, but this is not necessary. In the virtue
reliabilism camp (like in Sosa, 2010), which emphasizes competences and abilities, some processes are also
considered as competences or abilities. For a more extensive treatment of the Generality problem, see Conee &
Feldman (1998), who raise it as a general problem against reliabilism, and Bishop (2010), who argues that the
Generality problem aects all plausible epistemologies, both reliabilist and non-reliabilist.
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5. e dynamic approach
A dierent conceptual framework for understanding knowability comes from the dynamic
logic camp. Van Benthem (2004), Balbiani et al. (2008) and Van Ditmarsch et al. (2011)
have proposed to analyze ‘φ is knowable’ is ‘after the public announcement of some formula
ψ’ (with certain restrictions on ψ to avoid circularity), it is known that φ. (We will not go into
the formal details.) For reference, here is the proposal:
Dk
φ is knowable i after the public announcement of some formula ψ (with certain
restrictions on ψ to avoid circularity), written <!>, it is known that φ.
kφ ↔ <!>Kφ
e semantical clause for public announcements is the following (Van Benthem & Liu,
2007; Balbiani et al. 2008):19
• <!ψ> φ is true in the model M at the world w i (1) ψ is true in the model M at
the world w and (2) φ is true at w in the model M| ψ, where M| ψ is identical to M,
except that the epistemic accessibility relation R| ψ of M| ψ is dened as follows: <v,u>
belongs to R| ψ i (i) <v,u> belongs to R (the epistemic accessibility relation of M) and
(ii) ψ is true at v i ψ is true at u.
• <!> φ is true in the model M at the world w i there is a formula ψ (with certain
restrictions to avoid circularity) such that <!ψ> φ is true in the model M at the world w.
However, this notion of knowability is not factive, since φ is interpreted after the public
announcement has taken place. In other words, after the announcement it is known that φ is
true or φ is false, but not that φ was true or φ was false. Some formulas can be known to be true
(false) after an announcement even though they were false (true) before the announcement.
Take, for example, a situation in which it is unknown that there is an odd number of books
in Williamson’s oce. After the (true) announcement that there is an odd number of books
in his oce, it is known that there is an odd number of books in his oce and, moreover, it is
known that it is known that there is an odd number of books in his oce.20 So, what is known
after the announcement is false before the announcement. It thus comes not as a surprise that
Van Ditmarsch et al. (2011, p. 93) conclude that ‘[t]his restricts the philosophical relevance
of interpreting ‘knowable’ as ‘known after an announcement’.
Holliday (2017)’s important contribution is to describe a framework in which something
along the following lines can be expressed: after the public announcement of some formula ψ
(again with certain restrictions on ψ to avoid circularity), it will in some hypothetical future
19 is is the so-called ‘link-cutting’ version of public announcement logic.
20 It is provable that <!ψ> K…Kφ follows from <!ψ> Kφ.
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be known that φ was true before that public announcement took place. For reference, here is
the core idea:
FDk
φ is knowable i after the public announcement of some formula ψ (again with certain
restrictions on ψ to avoid circularity), it will in some hypothetical future be known that
φ was true before that public announcement took place.
kφ ↔ <!>KYφ
We will not go into all the details of Holliday’s proposal, but the basic idea is roughly as
follows:
• <!ψ> φ is true at a world w and a time t i (1) ψ is true at world w and time t, (2) the
epistemic accessibility relation at time t+1 (which may be part of a hypothetical rather
than actual future)21 is dened by cutting links as before, and (3) φ is true at world w
and time t+1.
• Y φ is true at a world w and a time t i φ is true at world w and time t-1.22
Clearly, this concept of knowability is factive: if at a world w and a time t+1 it is known
that φ was the case before the public announcement that resulted in the epistemic state at
time t+1, then φ is true at a world w and time t.
What is striking about this concept of knowability is that it allows self-fullling
announcements (Holliday, 2017, section 4.2). For example, it could be announced that next
you will know that the number of books in Williamson’s oce on 19 December 2019 is odd.
Suppose that it indeed (eternally) true that the number of books in Williamson’s oce on 19
December 2019 is odd. en the announcement that next you will know that the number
of books in Williamson’s oce on 19 December 2019 will (in some hypothetical future) lead
to the knowledge that the number of books in Williamson’s oce on 19 December 2019 is
odd. Let us also suppose that between the moment right before the announcement and the
(hypothetical) moment right after the announcement no other epistemically relevant action
pertaining to the subject matter is taken. It would then seem to be that the announcement
itself is the source of the knowledge. is raises a vexing question:
[Y]ou could plausibly reason as follows: I have been told something that entails p
by an authoritative source I trust, so p is true. Perhaps you could thereby acquire
not only belief but also knowledge of p. Compare this with the case, used in science
ction stories, of an agent who encounters a machine that can predict the future, and
21 In the actual future there may be a dierent public announcement resulting in a dierent epistemic accessi-
bility relation at t+1.
22 If there is an initial time t0, then the right-hand side of the equivalence should be: φ is true at the initial time
t0 or φ is true at time t-1.
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the machine predicts for her that she will come to know some important proposition
(tenselessly formulated, let us suppose). Does the agent thereby come to know the
proposition? (Holliday, 2017, section 4.2)
To put the issue in sharper focus, let us consider another case. At xyzt there is an earth
worm, with xyz the spatial coordinates of a remote location in the Amazon rain forest and
with t the time coordinate. at there is an earth worm at xyzt t is an eternal truth. Given
the remoteness of xyz, no human beings were suciently close to xyzt to discover that there
is an earth worm at xyzt. (Time t can be set before any human exploration of the Amazon
rain forest took place or even before there were any humans.) Rodrigo lives in Chile in the
early 21th century. If anybody has ever told Rodrigo that next he will know that p (e.g., a
particular person is not to be trusted), it was always in cases in which Rodrigo discovered
whether p via independent means (e.g., Rodrigo is put in a position in which that particular
person can betray his trust). Let us use t’ for the current date in the lifetime of Rodrigo.
In a hypothetical future Rodrigo hears the announcement that next he will know that
there is an earth worm at xyzt. “Next” here means: at time t’+1. Where is this announcement
coming from? In the actual history (up to and including t’) nobody has the means to
determine that there is an earth worm at xyzt. However, at the hypothetical future t’+1 there
is supposed to be an authoritative source regarding the presence of an earth worm at a remote
location in the Amazon rainforest before it was explored by humans. Are we to imagine the
sudden appearance of an oracle or a semi-divine message? On what basis could Rodrigo deem
the announcement trustworthy? Even if he were to get into contact with an oracle and even
if he starts to trust the oracle, his trust is presumably based on checking its proclamations
or their implications by independent means and/or perhaps by studying the principles by
which the oracle operates. In this scenario Rodrigo has no means to check independently of
the oracle whether there is an earth worm at xyzt. More importantly even, assuming that this
authoritative source is indeed new, there is no time between t’ and t’+1 to start trusting the
source on any basis that would lead to epistemic updates.
e dynamic approach to knowability in its original form, championed especially by van
Benthem, faces the problem that it turns knowability into a non-factive notion. Holliday has
shown that a dynamic approach can also yield a factive notion of knowability. Unfortunately,
his version is confronted with the puzzling phenomenon of self-fullling announcements.
6. Conclusion
e scope of what is knowable is and has been a major point of discussion among
philosophers. Epistemic optimists think that all truths are knowable, epistemic moderates
think that some truths are knowable and some are not, epistemic pessimists think that no
truths are knowable. All these position presuppose that we have a good understanding of the
concept of knowability.
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As we have discussed throughout this paper, giving an analysis of the concept of
knowability raises various technical and philosophical diculties. Because of the importance
of the concept, it is important to get things right, in the sense of capturing adequately the
features that would allow the concept to serve its functions. For the reasons we mentioned in
section 2, it is important to develop a factive concept of knowability.
e nowadays standard concept of knowability is the following: for something to be
knowable is for that something to be possibly known. However, this concept of knowability
is not factive. We have seen that, broadly speaking, there are three alternative approaches to
the analysis of the concept of knowability:
a) a counterfactual approach, rst proposed by Edgington (1985) and recently revisited
by Schlöder (2019),
b) an approach making use of the notions of capacity and ability, exemplied by Fara
(2010),
c) an application of the framework of dynamic logic, exemplied by Holliday (2017).
We have seen how all these approaches can oer prima facie workable factive concepts of
knowability. However, as we have also pointed out, each of these approaches faces diculties.
e counterfactual approach to knowability has faced for a long time the diculty of
providing a counterfactual analysis of knowability that is factive on the one hand and non-
trivial on the other hand. (A trivial concept of knowability is one that, for instances, makes
only logical truths knowable.) Schlöder’s recent contribution is a counterfactual analysis of
knowability that is non-trivial. is analysis crucially involves lines of inquiries, which if they
were successfully pursued, would result in the knowledge that, if they were not successfully
pursued, that what is knowable would be true. However, we have seen that the factivity of his
notion of knowability can be challenged. We have concluded that it is vital to reect on the
internal structure and the individuation of lines of inquiries.
e capacity approach to knowability says that for something to be knowable is to for an
actual agent having the capacity to know that that something is actually true. According to
Fara, a key dierence with the counterfactual approach is that capacities are not analyzed in
terms of counterfactuals but in terms of performances that are not ruled out by the internal
constitution of the agents. Whether that is a real or imagined distinction is something
we discussed. Capacities depend to some extent on circumstances, including social and
technological contexts, where the agents need to be able to communicate and collaborate
with other agents and where they need to be able to use the technological tools. If abilities
are analyzed counterfactually, as Fara does (but Spencer does not), then there is again a
counterfactual component in the analysis of knowability. Here as well we need to think
further about what capacities and abilities are.
One diculty that both the counterfactual approach and the capacity/ability approach to
knowability face is the Generality problem. is problem was raised for the capacity/ability
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approach but, as we will now argue, also applies to the counterfactual approach, at least in
Schlöder’s version. We can think of lines of inquiry as procedures that lead to knowledge,
where these procedures can be described in more or less general terms. Each of those more or
less generally described procedures may be more or less reliable. e diculty consists then
in picking the right grain of individuation of lines of inquiries.23
Finally, we have discussed the dynamic approach to knowability. Regrettably, the idea
in its form due to van Benthem results in a non-factive concept of knowability. Holliday
has recognized this problem and built on the work of van Benthem and others to develop
a dynamic analysis of knowability that is factive. Roughly, the idea is that for something to
be knowable, it has to be the case that, after some public announcement, it will in some
hypothetical future be known that that something was true before that public announcement
took place. However, Holliday’s approach has as a mystifying consequence that self-fulling
announcements can take place: if something is (eternally) true, then the announcement that
next it will be known results in the knowledge that it is true.
Where the counterfactual approach and the capacities/abilities approach are confronted
with questions about, for example, the grain of individuation of lines of inquiries and
capacities/abilities, the dynamic approach has in a sense a deeper problem: the public
announcements come out of nowhere. e update machinery has a black box at its core. e
dynamic approach to the concept of knowability could prot from replacing the black box
by, for instance, successfully pursued lines of inquiries.
Our work here was to oer a critical overview of the conceptual frameworks that we
currently have in the literature. We hope this will oer some insight into how we can
develop better solutions in the future. Ultimately, we hope that this will also lead to a better
understanding of the limits of what is knowable.
Acknowledgements
Previous versions of this paper have been presented at the XX Jornadas Rolando Chuaqui
Kettlun (Santiago de Chile, 27-30 August 2019), the Universität zu Köln (Köln - online, 16
June 2021) and the Knowability and the Limits of Knowledge workshop (MeLo Seminar –
online, 2-3 September 2021). We would like to thank the audiences at those talks for their
questions and comments. Furthermore, we would also like to thank Lorenz Demey, Sybren
Heyndels, Lars Arthur Tump and Kristine Grigoryan for their feedback. Research for this
paper was funded by the Fund for Scientic Research – Flanders (project grant G088219N).
23 From the perspective of our discussion of the structure of lines of inquiry, Lyons (2019) is also interesting.
Lyons’ proposed solution to the Generality problem is that cognitive processes should be individuated in terms
of certain types algorithms and parameters for those algorithms; it is natural to see certain lines of inquiry as
implementations of algorithms.
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