## 1. Kinds of certainty



There are various kinds of certainty (Russell 1948, p. 396). A belief
is *psychologically* certain when the subject who has it is
supremely convinced of its truth. Certainty in this sense is similar
to *incorrigibility*, which is the property a belief has of
being such that the subject is incapable of giving it up. But
psychological certainty is not the same thing as incorrigibility. A
belief can be certain in this sense without being incorrigible; this
may happen, for example, when the subject receives a very compelling
bit of counterevidence to the (previously) certain belief and gives it
up for that reason. Moreover, a belief can be incorrigible without
being psychologically certain. For example, a mother may be incapable
of giving up the belief that her son did not commit a gruesome murder,
and yet, compatible with that inextinguishable belief, she may be
tortured by doubt.



A second kind of certainty is *epistemic*. Roughly
characterized, a belief is certain in this sense when it has the
highest possible epistemic status. Epistemic certainty is often
accompanied by psychological certainty, but it need not be. It is
possible that a subject may have a belief that enjoys the highest
possible epistemic status and yet be unaware that it does. (More
generally, a subject's being certain that *p* does not
entail that she is certain that she is certain that *p*; on
this point, see Van Cleve 1979, and see Alston 1980 on level
confusions in epistemology.) In such a case, the subject may feel less
than the full confidence that her epistemic position warrants. I will
say more below about the analysis of epistemic certainty and its
relation to psychological certainty.



Some philosophers also make use of the notion of *moral*
certainty (see Markie 1986; James 2020). For example, in the Latin
version of Part IV of the *Principles of Philosophy*, Descartes
says that "some things are considered as morally certain, that
is, as having sufficient certainty for application to ordinary life,
even though they may be uncertain in relation to the absolute power of
God" (PW 1, pp. 289-90). Thus characterized, moral
certainty appears to be epistemic in nature, though it is a lesser
status than epistemic certainty (see Matthen 2014 for a
similar account of what he calls "empirical certainty"). In the
French version of this passage, however, Descartes says that
"moral certainty is certainty which is sufficient to regulate
our behaviour, or which measures up to the certainty we have on
matters relating to the conduct of life which we never normally doubt,
though we know that it is possible, absolutely speaking, that they may
be false" (PW 1, p. 289 n. 2). Understood in this way, it does
not appear to be a species of knowledge, given that a belief can be
morally certain and yet false (contra Markie 1986, p. 36). Rather, on
this view, for a belief to be morally certain is for it to be
subjectively rational to a high degree. In a similar way, Spinoza
distinguishes moral certainty from mathematical certainty and says
that the former should not be rejected when "it is confirmed by the
testimonies of so many prophets, is a source of great solace for those
whose capacity to reason is limited, is of great value to the state,
and may be believed unreservedly without danger or damage"
(*Tractatus Theologico-Politicus*, ch. 15; see James 2020, ch.
1). Moral certainty understood in this way is not merely a form of
psychological certainty, as someone who has the highest degree of
confidence in a particular claim might nevertheless do so for
manifestly irrational or frivolous reasons.



Although all three kinds of certainty are philosophically interesting,
it is epistemic certainty that has traditionally been of central
importance. In what follows, then, I shall focus mainly on this kind
of certainty.


## 2. Conceptions of certainty



There have been many different conceptions of certainty. Each of them
captures some central part of our intuitive understanding of
certainty, but, as we shall see, none of them is free from
problems.


### 2.1 Indubitability



Certainty is often explicated in terms of *indubitability*.
This has been done in a variety of ways (see, e.g., Goodman 1952;
Unger 1978, p. 328). One prominent account of certainty is suggested
by Descartes's presentation of his famous Archimedean point, the
*cogito* (I am thinking, therefore I exist). In the Second
Meditation, Descartes reviews the extensive doubts of the First
Meditation before saying that even if "there is a deceiver of
supreme power and cunning who is deliberately and constantly deceiving
me," still "he will never bring it about that I am nothing
so long as I am something" (PW 2, p. 17). Descartes then
concludes that the proposition that he himself exists is true whenever
he considers it. It is often thought that the *cogito* has a
unique epistemic status in virtue of its ability to resist even the
"hyperbolic" doubts raised in the First Meditation (see
Markie 1992 and Broughton 2002). However, even if Descartes took this
view of the certainty of the *cogito*, he did not accept the
general claim that certainty is grounded in indubitability. In the
Third Meditation, Descartes says that he is certain that he is a
thinking thing, and he explains the certainty of this "first
item of knowledge" (it is unclear whether he regards it as
distinct from the *cogito*) as resulting from the fact that it
is a clear and distinct perception (PW 2, p. 24). (Matters are
complicated, however, by the fact that Descartes also says in the
Third Meditation that certainty depends on knowing that God exists and
is not a deceiver.)



Ludwig Wittgenstein also seems to connect certainty with
indubitability. He says that "If you tried to doubt everything
you would not get as far as doubting anything. The game of doubting
itself presupposes certainty" (1969, SS115). What makes
possible doubting is "the fact that some propositions are exempt
from doubt, are as it were like hinges on which those turn"
(1969, SS341). Although Wittgenstein's view is sometimes
taken to be--or to provide the basis for--an epistemically
satisfying response to skepticism (see, e.g., Wright 2003 and 2004),
it is hard to see the kind of certainty he has characterized as being
epistemic, rather than merely psychological or moral, in nature (on
this point, see Pritchard 2005; Coliva 2010 and 2012). Thus, when
Wittgenstein says, "The difficulty is to realize the
groundlessness of our believing" (1969, SS166) it seems
clear that the so-called hinge propositions are ones that we are
psychologically incapable of calling into question. This is, of
course, compatible with their being false.



In general, every indubitability account of certainty will face a
dilemma: when the subject finds herself incapable of doubting one of
her beliefs, either she has good reasons for being incapable of
doubting it, or she does not. If she does not have good reasons for
being unable to doubt the belief, the type of certainty in question
can be only psychological, not epistemic, in nature. On the other
hand, if the subject does have good reasons for being unable to doubt
the belief, the belief may be epistemically certain. But, in this
case, what grounds the certainty of the belief will be the
subject's reasons for holding it, and not the fact that the
belief is indubitable.



A second problem for indubitability accounts of certainty is that, in
one sense, even beliefs that are epistemically certain can be
reasonably doubted. I shall say more about this in SS3 below.


### 2.2 Infallibility



According to a second conception, a subject's belief is certain
just in case it *could not have been mistaken*--i.e.,
false (see, e.g., Lewis 1929). Alternatively, the subject's
belief is certain when it is *guaranteed to be true*. This is
what Roderick Firth calls the "truth-evaluating" sense of
certainty (1967, pp. 7-8). As with knowing that *p*,
being certain that *p* entails that it is true that *p*.
Certainty is, however, significantly stronger than lesser forms of
knowledge (contra Mizrahi 2019, who conflates knowledge with certainty
on the grounds that knowledge is factive). In cases where the subject
knows without being certain that *p*, it is actually true that
*p*, though it could have been false. In that case, of course,
the subject would no longer know that *p*. But, where the
subject is certain that *p*, it does not merely turn out to be
true that *p*--in some sense it could not have been
otherwise.



The difficulty for this conception of certainty is specifying the
precise sense in which the belief could not have been false. What is
meant cannot be what is called metaphysical or broadly logical
impossibility. Although some of the paradigmatically certain beliefs
are necessarily true in this sense, many others are not. For example,
though I am certain of the truth of the *cogito*, it is not
necessarily true (in the metaphysical sense) that I exist. That is, it
is possible that I might not have existed. We might attempt to solve
this difficulty by saying that the belief is guaranteed to be true by
the subject's grounds for it (see, e.g., Audi 1998, pp.
218-9). But this opens up two further problems for this
conception of certainty. First, if the truth of the belief is
guaranteed by the subject's grounds for holding it, then it
looks as though the certainty of the belief ought to be attributed to
those grounds as well. That is to say, the belief would be certain,
not in virtue of the fact that it is guaranteed to be true, but rather
in virtue of its relation to the grounds that make that guarantee
possible. This would be so because the grounds would provide a deeper
explanation for the certainty of the belief than would the fact that
the belief is guaranteed to be true. Moreover, some further account of
the certainty of the grounds will still need to be provided.



The second problem is very similar to one that arises for philosophers
attempting to provide an account of fallibilistic knowledge (i.e.,
knowledge that is less than certain). According to the standard
account, the subject has fallibilistic knowledge that *p* when
she knows that *p* on the basis of some justification
*j*, and yet the subject's belief could have been false
while still held on the basis of *j* (see, e.g., BonJour 1985,
p. 26; Lehrer 1990, p. 45). Alternatively, the subject knows that
*p* on the basis of some justification *j*, but
*j* does not entail the truth that *p* (see, e.g., Cohen
1988, p. 91; Fogelin 1994, pp. 88-9; Jeshion 2000, pp.
334-5; Brown 2018, pp. 15-21). The problem with the
standard account, in either version, is that it does not allow for
fallibilistic knowledge of necessary truths. If it is necessarily true
that *p*, then the subject's belief that *p* could
not have been false, regardless of what her justification for it may
be like. And, if it is necessarily true that *p*, then
everything--including the subject's justification for her
belief--will entail or guarantee that *p*. Our attempt to
account for certainty encounters the opposite problem: it does not
allow for a subject to have a belief regarding a necessary truth that
does *not* count as certain. If the belief is necessarily true,
it cannot be false--even when the subject has come to hold the
belief for a very bad reason (say, as the result of guessing or
wishful thinking). And, given that the beliefs are necessarily true,
even these bad grounds for holding the belief will entail or guarantee
that it is true.



One way to solve the problem for the analysis of fallibilistic
knowledge is to focus, not on the entailment relation, but rather on
the probabilistic relation holding between the subject's
justification and the proposition believed (see Reed 2002 and 2013).
When the subject knows that *p* on the basis of justification
*j*, and *P*(*p*/*j*) is less than 1, the
subject's knowledge is fallibilistic. (Although epistemologists
will disagree about what the appropriate conception of probability is,
here is a crude example of how probability may figure in a
fallibilistic epistemology. A basic historical reliabilist will say
that a belief is justified just in case it has been produced by a
process that has yielded a preponderance of true beliefs. So, if the
process has yielded a true belief, say, 90% of the time, the
probability that the next belief will be true is 90%; this is so even
if the belief in question is necessarily true and has been logically
deduced from a set of beliefs, each of which is necessarily true.)
Adapting this solution to the problem for certainty, we can say that
the subject is certain that *p* when
*P*(*p*/*j*) = 1, where *j* is the
justification or grounds for the belief (see Van Cleve 1977 and Lewis
1952). However, in order for *j* to impart a probability of 1
to *p*, it must also be the case that *P*(*j*) =
1. That is to say, *j* must be certain for the subject before
it can make anything else certain. But, if we are to explain the
certainty that *p* by appeal to the certainty that *j*,
we fall into a vicious regress. The only way to stop it is to allow
that some beliefs may have an intrinsic probability of 1 (see Russell
1948, p. 396, and Van Cleve 1977). It is, however, difficult to see
how intrinsic probability of this sort is possible (barring, of
course, a subjectivist account of probability, which could, in any
case, capture only psychological certainty).



Timothy Williamson (2000, pp. 213-7) rejects the connection
between a belief having probability 1 and its being absolutely
certain. (On his view, one's evidence is identical with what one
knows, so what one knows will be evidence for itself. In a trivial
sense, then, everything one knows will have probability 1.) He argues
that the connection can be broken by denying that beliefs that have
probability 1 at a particular time will always thereafter remain at
that probability. Further evidence may be acquired that destroys the
knowledge in question; when that happens, it is no longer evidence,
let alone evidence for itself. Williamson finds this result congenial
because, he says, "it is hard to see
how *any* empirical proposition could have the
intertemporal and intersubjective certainty which the
conditionalization account demands of evidence" (p. 215). In breaking
the connection between certainty and probability 1, then, it is
important to keep in mind that Williamson has done so only for
absolute certainty (or certainty over time), but not for certainty at
a time. See
 section 3 below
 for more on the distinction between these two dimensions of
certainty.


### 2.3 Inimitability



According to a third conception of certainty, a subject's belief
that *p* is certain when it is
*inimitable*--i.e., justified in the highest degree (see,
e.g., Stanley 2008). This is what Firth calls the
"warrant-evaluating" sense of certainty (1967, pp.
8-12). Thus, Bertrand Russell says that "A proposition is
certain when it has the highest degree of credibility, either
intrinsically or as a result of argument" (1948, p. 396). There
are various ways to understand what it means for a belief to be
credible or justified in the highest degree. It could mean simply that
the belief in question is justified as highly as any belief the
subject happens to hold. But, in cases where the subject does not have
any beliefs that are highly justified, this will imply that even a
belief with relatively low justification is epistemically certain.
Perhaps we could say instead that a belief is justified to the highest
degree when it is justified as highly as any belief that
*anyone* happens to hold. But this, too, leaves open the
possibility that a belief with relatively low justification is
epistemically certain: if all the subjects in existence are in a
condition of universal ignorance, all of their beliefs--including
the best of them--will have only a low level of justification.
Perhaps, then, we should say that a belief is justified in the highest
degree when it has the highest level of justification
*possible*. But even this account is unsatisfactory. Suppose
that global skepticism is necessarily true: it is a necessary truth
that no subject is capable of having much justification for any of her
beliefs; although it may seem to us as though a significant degree of
justification is possible, this in fact is incorrect. It would then be
intuitively correct to say that every belief falls far short of
certainty, though this would not be permitted by the account of
certainty under consideration. We may of course doubt that skepticism
of this strong variety is correct; nevertheless, it should not be
simply ruled out as a matter of definition.



Roderick Chisholm offers a variation on the above approach. According
to his first definition of certainty (where *h*, *S*,
and *t* are variables for propositions, subjects, and times,
respectively):



> 
> *h* is certain for *S* at *t* =df (i)
> Accepting *h* is more reasonable for *S* at *t*
> than withholding *h* (i.e., not accepting *h* and not
> accepting not-*h*) and (ii) there is no *i* such that
> accepting *i* is more reasonable for *S* at *t*
> than accepting *h*. (1976, p. 27)
> 



Clause (i) ensures that the subject has some measure of positive
justification for *h*--if she had no justification for it,
it would be more reasonable for her to withhold with respect to
*h*. Clause (ii) then says that those beliefs of the subject
are certain which are at the highest levels of justification for her.
However, this still leaves open the following possibility: *h*
is the most highly justified belief the subject has, but it is still
not very highly justified (e.g., it may not even be sufficiently
justified to count as knowledge).



Perhaps for this reason, Chisholm later offered a different definition
of certainty:



> 
> *p* is certain for *S* =df For every
> *q*, believing *p* is more justified for *S* than
> withholding *q*, and believing *p* is at least as
> justified for *S* as is believing *q*. (1989, p. 12)
> 



This definition still has the equivalent of clause (ii) above, and
therefore requires the belief that is certain for the subject be the
one that is most highly justified for her. But the second definition
appears to be more successful in requiring that *p* be
justified to a significant degree. Now, believing that *p* must
not only be more justified for the subject than withholding
*p*, it must also be more justified than withholding with
respect to any other proposition. There are many propositions that we
are capable of entertaining--e.g., the proposition that the
number of people alive at this precise moment is even--where
there is not the slightest reason for thinking them to be either true
or false (though, of course, they must be one or the other). In fact,
given the perfect lack of evidence with respect to propositions of
this sort, Chisholm's definition may set the standard for
certainty *too* high, for it is hard to see how there could be
any proposition one is *more* justified in believing than one
is in withholding belief regarding, say, the parity of the number of
people alive at this very moment.



It should be noted, however, that Chisholm's definition works
only by implicitly relying on what is a contingent feature of our
epistemic situation. It so happens that we find ourselves in a
position of total ignorance with respect to some propositions. But
that need not have been the case. We could have ended up in a world
where there is a moderate amount of evidence either for or against
every proposition. If one of a subject's beliefs then happened
to have slightly more justification than any of the others, it would
meet Chisholm's definition of certainty, though it might still
have what we would intuitively take to be a less than ideal level of
justification.



There is one further problem with both of Chisholm's
definitions. Because they both relativize certainty to a particular
subject, they make possible the following situation. Two subjects each
believe that *p*, and in each case the belief is justified to
degree *n*. For the first subject, the belief counts as certain
because none of her other beliefs have a higher level of
justification. But, for the second subject, the belief in question is
not certain because she does have another belief that is slightly more
justified. If certainty really is grounded in epistemic justification,
though, this should not be possible. If a given justification makes a
belief certain for one subject, it should do so for everyone.



There is another approach that Chisholm might take. According to
*particularism*, his favored method in epistemology, we should
use particular instances of knowledge and justification as our guide
in formulating an epistemology (Chisholm 1973 and 1989, pp.
6-7). (By contrast, *methodism* begins with criteria for
knowledge and justification and then attempts to ascertain whether, on
these criteria, we actually have any knowledge or justified beliefs.)
Adapting this approach to our present concern, the suggestion is that
we formulate an account of certainty in light of paradigmatic
instances of beliefs held with certainty. Thus, after giving the
second definition above, Chisholm says that the concept of certainty
is illustrated by propositions about what he calls
"self-presenting" mental states and by some logical and
metaphysical axioms (1989, p. 12).



Although this particularist approach probably is the way in which most
philosophers think of certainty, it faces several difficulties. One is
that the epistemology of the *a priori* is far from clear.
Given that we do not, apparently, causally interact with necessary
truths, it is hard to see how our minds can have access to them. A
second difficulty has to do with knowledge of our own mental
states--sometimes referred to as knowledge *by
acquaintance*. According to the "speckled hen"
problem, there are aspects of our mental states, such as the rich
detail of one's present visual experience, that we are not
capable of knowing--e.g., if one is looking at a speckled hen,
there will be a determinate number of speckles in one's visual
experience, which one will not be able to know just in virtue of
having the experience (Ayer 1940, Chisholm 1989, Fumerton 2005). But
those aspects we cannot know merely by being conscious of them are
part of our conscious experience in just the same way as those aspects
we *are* supposed to be able to know; the difficulty is
specifying a principled difference between the two. Much more could be
said about the first two problems, but they lie beyond the scope of
this article. A third difficulty is that, at least *prima
facie*, knowledge of one's mental states seems to be of a
fairly different kind from knowledge of necessary truths. It is not
clear, at the outset, that we are warranted in taking them to be
paradigmatic instances of a genuine epistemological kind.


### 2.4 Indefeasibility



According to a fourth conception of certainty, defended by Peter
Klein, a belief "is absolutely certain just in case it is
*subjectively* and *objectively* immune to doubt"
(1992, p. 63; see also Miller 1978). He explicates this in the
following way:



> 
> *p* is absolutely certain for *S* if and only if (1)
> *p* is warranted for *S* and (2) *S* is warranted
> in denying every proposition, *g*, such that if *g* is
> added to *S*'s beliefs, the warrant for *p* is
> reduced (even if only very slightly) and (3) there is no true
> proposition, *d*, such that if *d* is added to
> *S*'s true beliefs the warrant for *p* is reduced
> (even if only very slightly). (1992, p. 63)
> 



Klein says that the second condition is what makes the belief
subjectively immune to doubt, presumably because it is the beliefs and
experiences that constitute *S*'s subjective perspective
that render her warranted in denying all propositions that would
reduce the warrant for *p*. However, *S*'s belief
system might contain false beliefs that could warrant her in denying
every *g* relevant to *p*--even, in some cases,
where the *g* in question is itself true--and so her
belief that *p* might meet condition (2) and yet still be
false. Condition (3) is meant to prevent this situation; if *p*
is false, the true belief that ~*p* can be added to
*S*'s belief system, thereby reducing the warrant
*S* has for *p*. In requiring both (2) and (3), then,
the account focuses on beliefs where the subject's subjective
situation is in a sense properly aligned with an objective structure
of reasons (for a similar view, see Pollock 1986).



There are two major difficulties facing a view of this sort. First, it
is not clear how one belief is supposed to reduce the warrant for
another. Suppose that I correctly believe that I have a headache and
that my belief is, in an intuitive sense, absolutely certain. The
first condition of Klein's account is satisfied: the belief is
warranted in virtue of my experiencing the headache. But is the second
condition also satisfied? That is, would I be warranted in denying,
say, the proposition that I do not in fact have a headache? If this
were to be a belief added to my belief system, I would of course have
contradictory beliefs. Would that entail that the warrant for both
beliefs should be diminished? If the answer is yes, then my belief
that I have a headache is not absolutely certain. Moreover, it is hard
to see how *any* belief could then be absolutely certain, given
that we can always add to our belief systems the contradictory of any
of our beliefs. If the answer is no, however, there should be some
explanation for why the proposition that I do not have a headache can
be denied. Presumably, the explanation would have something to do with
my experiencing the headache. But then what explains the certainty of
the belief is the fact that it is grounded in the experience; the
belief's being subjectively immune to doubt is merely a
consequence of its certainty, and not the explanation for it. This
would mean that the focus of the view has shifted from subjective
immunity to doubt to some sort of special warrant. How there could be
such a special warrant, though, would need an account. To see the
point more clearly, notice that subjective immunity to doubt will be
possible only in cases where the subject's belief is
(intuitively) absolutely certain. For any belief *b* that is
less than certain, the following belief could be added to the
subject's belief system: the warrant for *b* could be
misleading. That belief would reduce the subject's warrant for
*b* (even if only slightly) were it to be added to her belief
system, but it is not a proposition the subject can deny without being
absolutely certain that *b* is true. The upshot, then, is that
subjective immunity to doubt is not well-suited to playing a role in
an account of certainty. Instead, it looks as though our understanding
of subjective immunity to doubt depends on a prior grasp of what
certainty is.



The second difficulty has to do with condition (3), which is supposed
to secure objective immunity to doubt. Although it is undeniable that
a subject for whom condition (3) is satisfied would be in a desirable
situation, it does not seem to be attributable to her in the right
sort of way--and, especially, not in the way that we expect
certainty to be attributable to the person who is certain. To see
this, suppose that my warrant for the belief that *p* is only
moderately good. Nevertheless, my guardian angel protects my belief by
making sure that any proposition such that, if it were true, would
(when added to my belief system) reduce my warrant for *p*, is
false. That is, my guardian angel makes sure that all potential
defeaters for my belief are removed. Suppose, for example, that I see
from a great distance what looks like a hawk. My guardian angel
immediately annihilates all non-hawk flying objects in the area; the
potential defeater, that there are flying objects indistinguishable
from a hawk in the vicinity, has thus been rendered false. Although
this would make my belief that *p* objectively immune to doubt,
insofar as (3) is satisfied, it does not seem as though it would carry
my belief any closer to certainty. The fact that the warrant for my
belief is only moderately good renders irrelevant the work my guardian
angel does in the world outsid of my beliefs. (Nor would the situation
be helped if we stipulated that condition (2) is also satisfied. Given
that my belief system could contain many false beliefs that might
warrant me in rejecting all potential defeaters, my belief might be
both subjectively and objectively immune to doubt--and yet still
have a relatively low degree of warrant.)



It may be that one of the four conceptions of certainty discussed
above could be improved so as to answer all objections. But, until
that happens, it is safe to say that there is at present no completely
satisfactory conception of certainty.


## 3. Two dimensions of certainty



Typically, epistemologists are concerned with the conditions under
which a subject may know or be certain that *p* at a particular
moment. Interestingly, however, somewhat different issues arise for
certainty over time. As this was a primary concern for Descartes, who
tells us in the First Meditation that he wants to establish something
"in the sciences that was stable and likely to last," we
can best see how those issues arise in the context of
Descartes's epistemology (PW 2, p. 12).



In the Second Set of Objections, Mersenne poses the following problem:
although Descartes has argued that our ability to know anything
depends on our first knowing that God exists and is not a deceiver, it
seems clear that an atheist mathematician can have the same sort of
mathematical knowledge as a theist. In response, Descartes allows that
the atheist does have a clear awareness (*cognitio*) of simple
mathematical truths, but he denies that this clear awareness is
"true knowledge [*scientia*]" (PW 2, p. 101). At
first glance, it seems that Descartes draws the distinction between
*cognitio* and *scientia* precisely so he can deny
certainty to the atheist mathematician. But there is good reason to
think that this is not what he has in mind.



To see this, notice that, if Descartes does not allow the atheist to
be able to acquire knowledge through clear and distinct perception, he
will fall into the so-called Cartesian Circle. This problem, first
identified by Arnauld in the Fourth Set of Objections, arises if
Descartes holds both of the following claims: (i) I can know that my
clear and distinct perceptions are true only if I first know that a
non-deceiving God exists, and (ii) I can know that a non-deceiving God
exists only if I first know that my clear and distinct perceptions are
true. Because knowing one thing is a precondition for knowing the
other, and *vice versa*, I cannot know either of them. In fact,
however, it does not look as though Descartes does fall into the
circle. Although it is pretty clear that he is committed to
(1)--in the Third Meditation, he says that, "if I do not
know [whether there is a non-deceiving God], it seems that I can never
be quite certain about anything else" (PW 2, p. 25)--there
is no reason to take him to be committed to (ii). Descartes is willing
to permit the meditator to use clear and distinct perceptions before
knowing that they are generally true. The clearest example, of course,
is the *cogito*; the meditator first comes to know that he
exists as a thinking thing and only later comes to know that his
knowledge of the *cogito* is grounded in its clarity and
distinctness. The same, then, can be said for the meditator's
knowledge--grounded in some clearly and distinctly perceived
causal principles--that God exists. In using those principles,
the meditator does not first need to have the general knowledge that
clear and distinct perceptions are true (see Van Cleve 1979).



Still, some philosophers might object that the meditator has no
business using principles that he does not know to be true. Descartes
would not be sympathetic to this objection. As he says in his
conversation with Burman, so long as the meditator is using the causal
principles, "he is actually paying attention to them. And for as
long as he does pay attention to them, he is certain that he is not
being deceived, and he is compelled to give his assent to them"
(PW 3, p. 334; see also PW 2, pp. 25, 48; see also Cottingham 1986, p.
67). So, the doubt that Descartes raises with respect to clear and
distinct perceptions does not extend to the moments at which one is
actually enjoying them. Rather, it is a doubt that, *in
general*, clear and distinct perception may not be a reliable
source of beliefs (Kenny 1968, p. 194). When Descartes introduces the
evil demon hypothesis in the First Meditation, it is meant to
encapsulate his ignorance of his own origin--and, in particular,
ignorance of the construction of his own mind. Without knowing that a
non-deceiving God exists, it is possible for the meditator that his
mind works in such a way that it falls into error even when it is
contemplating the simplest questions. This doubt is chased away when
he actually *does* contemplate such a question, but it can
easily return at a later time when his thoughts are turned elsewhere.
This is the sense in which the atheist mathematician's
*cognitio*, or clear awareness, is imperfect. Although it is
certain at the time the atheist has the perception, it can always be
rendered doubtful at another time. The theist has *no*
advantage over the atheist at the time each enjoys a clear and
distinct perception. Rather, the theist's advantage lies in the
fact that, armed with the certainty that a non-deceiving God exists,
she will *always* remain free from doubt (Descartes PW 2, p.
48; see also Kenny 1968, p. 193; Reed 2012). Consequently, she will be
able to construct her scientific theories without ever falling prey to
worries about whether her work has value, and--perhaps even more
importantly--she will be in a position to definitively put an end
to theoretical disagreements with others. (The Stoics make a similar
distinction; see Cicero *On Academic Scepticism*, p. 84.)



Given this account of Descartes's epistemology, we can now see
that both *cognitio* and *scientia* are varieties of,
not only knowledge, but certainty as well. This is an important point
to note, for it means that certainty cannot be straightforwardly
characterized in terms of indubitability. For a belief known with
certainty to be immune to doubt--not merely at a moment but
absolutely--it must be embedded in a coherent system of beliefs,
all of which are known with certainty (for a similar account of
Descartes's epistemology, see Sosa 1997, though Sosa takes
*cognitio* to be a lower grade of knowledge than
*scientia*; also, see Loeb 1992 on the importance of stability
for Descartes's epistemology). *Scientia*, or systematic
certainty, represents an admirable, but probably unattainable, goal.
If humans are capable of certainty at all, it is surely of the sort
that is capable of mixing with doubts.


## 4. Applications of certainty



Edward Craig (1990) has argued that we can better understand the
concept of knowledge by examining the purpose or purposes it serves.
In a similar way, perhaps, the concept of certainty can be rendered
clearer by looking at the ways in which philosophers have tried to put
certainty to use. Most fundamentally, certainties provide us with
inputs to inference that are stable and secure. If they are immune to
doubt, they can put an end to the demand for reasons that feature in
the Pyrrhonist's argument for general skepticism (see Sextus
Empiricus, *Outlines of Scepticism*; Sosa 1997; Sienkiewicz
2019). If they have probability 1, they can simplify reasoning by
allowing the reasoner to treat them as simply given, without having to
attend to the risk of error for each individual premise or the
accumulation of error as uncertain premises are combined. If they are
indefeasible, they can allow us to reject any potential
counterevidence as misleading.



Some philosophers have argued that certainty is the norm of assertion:
one can assert that *p* just in case one is certain
that *p* (Stanley 2008; Peterson 2019; Beddor 2020b).
The norm is often defended by adapting Moore's paradox to certainty
(Moore 1942). According to the original form of the paradox, there is
something infelicitous about assertions like, "It's raining, but I
don't believe it is." Defenders of the certainty norm of assertion
argue that assertions like, "Dogs bark, but I'm not certain that they
do," are just as odd (Stanley 2008, p. 47). The explanation
of this infelicity is then provided by the fact that
certainty is the norm of assertion. When the speaker asserts, "Dogs
bark," but then goes on to deny being certain of that claim, she has
undermined her own assertion, contradicting in practice what she has
just said.



Williamson (2000) and Turri (2016) reject the certainty norm of
assertion. Although a certainty version of Moore's paradox does
sound infelicitous, it doesn't sound quite so bad as a knowledge
version. Moreover, the oddity of the certainty version can be
explained by the fact that there is generally "a reluctance to allow
the contextually set standards for knowledge and certainty to diverge"
(Williamson 2000, p. 254). That is, the standards for what counts as
knowledge and as certainty typically match one another. Nevertheless,
in some contexts we can pull them apart. When that happens, Williamson
suggests that we assess assertions in accordance with the knowledge
norm. Turri (2016) reports empirical results confirming that this is
in fact the way ordinary speakers assess assertions.



Some philosophers have also argued that certainty is the norm of
practical reasoning: one can rely on *p* in relevant
practical reasoning just in case one is certain
that *p* (Beddor 2020a). The argument for the
certainty norm depends on two premises. First, if one is genuinely
relying on the premise that *p*, one is psychologically
certain that *p*. If one has a lower credence with respect
to whether *p*, one is not in fact relying
on *p* but instead on the proposition that it is
likely that *p*. Second, the epistemic norm for psychological
certainty is epistemic certainty. To be psychologically certain with
respect to a proposition for which one does not have epistemic
certainty is to violate Hume's dictum that "A wise man...proportions
his belief to the evidence" (Hume 1748 [2007]).



Although the second premise of the argument seems reasonable enough,
the first premise is overly rigorous. In many cases, the chance of a
premise being false is negligible, though not quite zero. We
might well rely on it simply because it isn't worth the effort to
formulate a more precise premise. For example, in choosing a path to
walk home on a day when I am in no particular hurry, I might rely on
the thought that the path I'm on is as good as any other--and I don't
bother to calculate the possibility that I'm wrong. Even in cases
where I am, in fact, trying to be more careful, I'll often have to
rely on an uncertain belief at some point. Suppose I'm trying to
decide whether to rely on the proposition
that *p* but come to see that it is uncertain. So, I
pull back to the claim that it is likely that *p*. But I
may not be certain that it's likely that *p*. If so, I can
either pull back even further--to the proposition that it is likely
that it is likely that *p*--or I can simply rely, albeit
tentatively, on the proposition that *p*. In almost every
case, the latter is the more natural course of action to take.



A common objection to both the claim that certainty is the norm of
assertion and the claim that certainty is the norm of practical action
is that certainty is scarce (see Unger 1975). If so, this will mean
that we rarely make proper assertions or behave in a practically
rational way. Defenders of these norms typically respond by offering a
contextualist account of certainty (Stanley 2008, p. 54; Beddor 2020a,
p. 722). On such a view, the epistemic standards governing
attributions of certainty can vary from one context to another.
(Variations in conversational context will yield a contextualist view
of the sort DeRose 1995 defends for knowledge attributions;
variations in practical context will yield a subjective-sensitive or
interest-relative view like those Hawthorne 2004 and Stanley 2005
defend with respect to knowledge.) So, what is certain in one context
may fail to be in another, if the relevant standards have risen in the
latter context. Although some contexts will have relatively stringent
standards for what counts as certain, others may have standards that
are relatively lax. In the latter contexts, then, attaining certainty
shouldn't be overly challenging.



The debate regarding contextualism is too enormous to enter into here.
Still, it is worth asking whether certainty that is protected by the
contextualist strategy really should count as genuine certainty. After
all, the idea was that a belief one knew with certainty to be correct
was one that made one immune from doubt *full stop*, and
not just immune from doubt in the present circumstances. It was
supposed to be a belief that one could rely on without hesitation in
drawing inferences, evaluating new evidence, and answering questions
and challenges from others. Contextually protected certainty is
capable of nothing quite so stable and secure. In fact, it looks more
like the epistemic version of moral certainty--good enough for most
purposes, but not as good as it might be (see Matthen 2014
and Locke 2015 for views that more explicitly eschew the label of
"epistemic certainty" in fleshing out this kind of epistemic
status).



Philosophers who defend fallibilism about knowledge will be untroubled
by this outcome (see Hetherington 2001; Reed 2013; Brown 2018). Others
may lament the fading of certainty as an epistemic ideal while arguing
that its abandonment is nevertheless better than going down to
epistemic defeat (Pasnau 2017). A hardy few may continue to press
ahead, like Descartes, in the attempt to "scale the heights of human
knowledge" (PW 1, p. 11; Klein 1981).