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Does the claim that knowledge is not closed under known entailment
provide a reasonable response to external world skepticism?
The claim that knowledge is closed under known entailment asserts that one
must know to be false everything which one knows is an alternative to p. If you know
that p, and you know that p logically entails not-q, then you have to know, or at least
have the potential to also know not-q. The closure principle is based on the
observation that there is a strong connection between knowing something and
knowing its implications; so in principle one can extend ones knowledge by
deduction. The skeptic employs the closure principle to argue that because one cannot
deny skeptical alternatives such as existing only as a brain in a vat manipulated into
believing that one is having certain kinds of sense experience, one can also not know
that they are standing up. The broader skeptical position is to question how it is
possible to gain knowledge using a source of belief unless knowledge is first shown to
be trustworthy; specifically, external world skepticism is the doubt about whether we
can have knowledge of the external world. This threatens to demonstrate that we
can't even hold justified beliefs about the external world, which would imply that it's
no more reasonable to believe that one is standing up than it is to believe in existing
as a brain in a vat. Skepticism in its extreme form is an untenable position if we are to
exist functionally in the world, however it is useful to guide reflection about how our
knowledge might be extended to the implications of what we know.
Some have attempted to argue that the closure principle is not a valid
argument as there are things we know to be implied by what we know, that we do not
know to be true. In these cases the defeat of skepticism is supposedly provided by a
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denial of closure. Dretkse demonstrates some cases where the closure principle fails
and argues for a relevant alternatives theory instead. Nozick too argues that under the
correct analysis of knowledge, closure fails. These attempts to demonstrate that
knowledge is not closed under known entailment potentially provide a response to
external world skepticism, given that the closure principle can support this view.
Dretske argues that traditional skeptical arguments exploit precisely those
consequences of a proposition to which the epistemic operators, such as ‘S has reason
to believe that…’, do not penetrate. To say that one knows that the church is empty, is
not to say that one knows it is a church1. Although a statement may entail certain
presuppositions, these suppositions are not operated on by the epistemic operator, and
the epistemic operators do not penetrate them. To say that there is reason to believe
that the church is empty, is not to say that this reason applies to the fact it is a church,
and so one would not have to know all the consequences that follow from its being a
church.
Dretske constructs a scenario in which one is visiting the zebra enclosure at
the zoo, and claims that you can know that the animal in the enclosure is a zebra on
the basis of evidence, but this evidence does not enable you to know that the animal
isn’t a mule cleverly-disguised by the zoo authorities. So Dretske agrees with the
skeptic that one cannot know that this alternative hypothesis is false, but he does not
agree that it follows one cannot know the animals in the enclosure to be zebras.
Dretske asserts that on his account the contrast consequence that the animals may in
fact be cleverly diguised mules is not penetrated by the epistemic operator in ‘I know
1
F. Dretske, Epistemic Operators, in Epistemology: An Anthology ed. by E. Sosa, J. Kim, J. Fantl, and
M. McGrath p.240
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that those animals are zebras’. Ones reasons for believing and jusitifying they have
knowledge of p, don’t necessarily penetrate to q, even if they know that p is entailed
by q.2 Vogel articulates Dretske’s point; that your belief that the animals are zebras is
visual evidence, but this same evidence doesn’t lend support to knowledge that they
are not cleverly disguised mules as the visual experience would be the same. So
although you know the truth of the proposition that “Those animals are zebras”, you
do not know it’s logical consequence.3 The skeptic introduces a broader more unusual
set of alternatives to exhibit the consequences of what we know, that we may not
know or have reason to believe, but this does not prove there is no reason to believe
our original knowledge claim; in this example, that we know the animals to be zebras.
For Dretske, to know is to know something in opposition to a range of relevant
alternatives, and according to his relevant alternatives theory, one can fail to know the
falsity of skeptical alternatives if they do not relevantly pertain to the object of
knowledge. So Dretske denies closure because on his view, the epistemic operator
does not always penetrate from p to q. In this way he responds to external world
skepticism as although it seems intuitive that the falsity of the skeptical alternatives is
implicit in our ordinary knowledge claims, our reasons for believing our ordinary
knowledge claims do not penetrate the skeptical hypotheses as they are not relevant
alternatives.
Nozick also presents an attempt to challenge the closure principle by correctly
analysing knowledge, but in a different way to Dretske. Nozick proposes that we must
admit our compulsion to be drawn by the skeptical argument and not reject it too
2
F. Dretske, Epistemic Operators, in Epistemology: An Anthology, p.242
J. Vogel, Are there counter-examples to the closure principle?, in Epistemology: An Anthology ed. by
E. Sosa, J. Kim, J. Fantl, and M. McGrath p.291
3
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glibly thereby refusing to acknowledge the power of its position. 4 His goal is not to
refute the skeptic, but to explain how knowledge is possible even if what the skeptic
says is potentially true. His task is to formulate necessary and jointly sufficient
conditions for knowledge that go beyond; 1) ‘p is true’ and 2) ‘S believes that p’. He
considers condition 3) If p weren’t true, S wouldn’t believe that p, because the truth of
the fact of p is partially causally responsible for S holding that belief and belief should
somehow vary with the truth of what is believed; and condition 4) If p were true, then
S would believe that p, which specifies how belief shouldn’t vary when the truth of
what is believed does not vary.5 So according to Nozick, knowledge is sensitive to
truth and to know is to have a belief that tracks the truth.
Nozick questions how the skeptical possibilities, such as being a brain in a vat
on Alpha Centauri count against knowledge of p; and it appears the skeptic challenges
Nozick’s third condition of knowledge, that if p were false S wouldn’t believe that p.
They challenge this principle by asserting situations in which if p were false, S would
still believe p, in order to conclude that it is not possible to have knowledge of p.
However, Nozick states that although his account of knowledge agrees with the
skeptic in this way, it appears that it places no formidable barriers before my not
knowing that I am typing an essay; for it is true that I am, I believe that I am, if I
weren’t I wouldn’t believe I was and if I were, I would believe it. In this way, we
track the truth of p. This account does not lead to any general skepticism, and yet we
still cannot shake the skeptic’s assertion that I do not know that I am not a brain in a
vat, since had I been a brain in a vat so deceived, I would still believe in my existence
4
5
R. Nozick, Philosophical Explanations, (Cambridge MA: Harvard University Press, 1981), p.262
R. Nozick, Philosophical Explanations, pp.172-85
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as an embodied human being. So, there are cases in which one tracks the truth of p,
tracks the truth of ‘p entails q’, but fails to track the truth of q.6
Nozick turns to inspect the closure principle which the skeptic assumes in
order to argue that since S does not know q, assuming that since he does know that p
entails q, it follows that he does not know p. For if he did know that p, he would also
know that q. Nozick’s analysis of knowledge has shown that I can know that I’m
typing, I can know that if I’m typing then I’m not a brain-in-a-vat, but I can’t know
I’m not a brain-in-a-vat, and so the closure principle fails. Nozick’s conclusion that
knowledge is not closed under known entailment responds to external world
skepticism by acknowledging the strength of the skeptical argument but undermining
its conclusion that because we cannot know the falsity of the alternatives they present
we also cannot have everyday knowledge, by an appeal to truth-tracking and a
developed analysis of knowledge.
According to the skeptic, if I don’t know now that I’m not dreaming, it
follows that I don’t know that I’m standing up, even if I both actually am and think
that I am. But Moore argues in ‘Philosophical Papers’ that this is a consideration
which cuts both ways and asserts that he can just as well argue since I do know that
I’m standing up, then I do know that I’m not dreaming, unless his opponent can give
better reasons for asserting that I don’t know that I’m not dreaming. He proceeds to
discuss sensory experience as evidence in favour of the proposition that I am standing
up. If a man is only dreaming that he is standing up, then it follows that he has not at
6
R. Nozick, Philosophical Explanations, p. 267
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that time the evidence of his senses in favour of that proposition. 7 It follows from
Moore’s argument that the closure principle can equally be employed to argue that
since I know that I am writing an essay at the moment, I must know that I exist,
because this entails that I know that I exist. It appears to be arbitrary whether one
utilises this line of argument as modus ponens or a modus tollens.
Moore’s argument equally relies on the closure principle but he turns it on its
head; if indeed Nozick and Dretske are convincing that closure fails, Moore’s
argument collapses but his emphasis on our embodied sense-experience remains
important, and his claim that we can have knowledge of many things which entail the
falsity of the skeptical hypotheses remains true. Our unique embodied awareness as
humans of our experience of the world is difficult to deny and the benefits of relying
on this source of knowledge allow for engagement with the world and others as we
perceive them; outweighing the implications if we concede to the skeptic’s argument.
It is desirable to make a choice in the same vein as Pascal’s wager, to trust in our
experience of ourselves and the world as existing, in order to participate in a fully
conscious integrated engagement with our life. For Hume, our belief in the existence
of an external world is unjustifiable but both natural and unavoidable, and it is this
acceptance of the power of the skeptical alternatives combined with a clarity about
our lived experience of the world that is vital if we are to progress in the justification
of our commonly held knowledge claims.
“The greatest subverter of... the excessive principles of skepticism is action,
and employment, and the occupation of common life. These principles may flourish
and triumph in the schools; where it is, indeed, difficult, if not impossible, to refute
7
G. E. Moore, Philosophical Papers, (New York: Collier Books, 1962), pp.241-243
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them. But…by the presence of the real objects, which actuate our passions and
sentiments… they vanish like smoke, and leave the most determined skeptic in the
same condition as other mortals.”8
So the skeptical argument remains unresolved because in response to the
Moorean view of common sense, the skeptic is able to respond with the assertion that
if we were indeed a brain in a vat, then we would still be of this belief. As long as we
accept the closure principle, whether we affirm or deny skepticism, we cannot
maintain that we both know common sense propositions, and that we do not know the
falsity of skeptical propositions, and we must feel compelled to do so, because while
we cannot deny the skeptic’s argument, it is vital that we can preserve knowledge of
our own experience. Nozick and Dretske provide a reasonable response to skepticism
given that they establish a means to both hold that skeptical arguments cannot be
disproved and maintain justification of our everday beliefs, through a denial of the
claim that knowledge is closed under known entailment. They acknowledge the
compulsion of the skeptical arguments, and correctly ascertain that they cannot be
disproved as we cannot track the truth of their falsity; for if it were true, our
experience would still lead us to deny it.
8
David Hume, An Enquiry Concerning Human Understanding, Section XII, Part II, Early Modern
Texts, 2004 <http://www.earlymoderntexts.com/pdfbits/he1.pdf>
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Bibliography
Epistemology: An Anthology ed. by E. Sosa, J. Kim, J. Fantl, and M. McGrath,
(Blackwell Publishing, 2008)
G. E. Moore, Philosophical Papers, (New York: Collier Books, 1962),
R. Nozick, Philosophical Explanations, (Cambridge MA: Harvard University Press,
1981),
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