Reduction and Elimination in Philosophy and the Sciences

Getting out from Inside: Why the Closure Principle cannot Support
External World Scepticism
Guido Melchior, Graz, Austria
The canonical version of the argument for external world
scepticism has the following structure:
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Premise1: If P does not know that she is not a
brain in a vat, then P does not have
knowledge of the external world.
Premise2: P does not know that she is not a brain
in a vat.
Conclusion: Therefore, P does not have knowledge
of the external world.
This version of the argument is presented by Brueckner
(1994 and 2004), Byrne (2004), Pritchard (2005) and others.
If “a” is any proposition about the external world and
“b” is the proposition that P is not a brain in a vat, then the
sceptical argument has the following structure:
Premise1: (¬K(b) → ¬K(a))/(K(a) → K(b))
Premise2: ¬K(b)
Conclusion: Therefore, ¬K(a)
This argument is logically valid. Therefore, any objection
against the argument has to be one against one of its two
premises. Subsequently, I will investigate how it can be
argued for and against each of the two premises.
Argumentations for premise1: The closure
principle and alternative arguments
Premise1 states that any knowledge of P about the external
world implies that P knows that she is not a brain in a
vat. Why should premise1 be true? Usually, in epistemological
discussions, the argumentations for premise1 are
grounded on one or the other version of the closure principle.
I will, firstly illustrate how the closure principle can be
used for arguing for premise1. Secondly, I will present an
alternative argumentation.
The closure principle
The closure principle is based on our epistemic intuition
that persons can gain new knowledge about facts through
inference from facts they already know. The closure principle
can occur in different forms. The simplest version is:
C: (K(a) ∧ (a → b)) → K(b)
According to this version, a person knows every proposition
which is entailed by a known proposition no matter if
the person has any knowledge about this entailment relation
itself. This is obviously an implausible account of
knowledge through inference. Hence, the more common
version is:
CP: (K(a) ∧ K(a → b)) → K(b)
This version expresses the idea that a person, who knows
a proposition a and knows that a implies another proposition
b, knows b through inference from a. This version
captures our intuition that a person can only gain knowledge
through inference if the person also knows the entailment
relation between the two propositions.
On the basis of the closure principle CP, it can be
argued for premise1 in the following way:
Argument1 for premise1:
CP: (K(a) ∧ K(a → b)) → K(b)
The proposition “P is a brain in a vat” and any
proposition which P believes about the external
world are contradictory.
P knows this contradiction.
Therefore, P infers that she is not a brain in vat, if P
has knowledge about the external world.
Therefore, P knows that she is not a brain in a vat, if
P has knowledge about the external world.
I think this argument captures the common philosophical
intuitions concerning premise1. The first premise of argument1
is the closure principle. One consequence of its
second premise is that the term “brain in a vat” has to refer
to persons, who not just have unjustified beliefs but who
have totally false beliefs about the external world. The third
premise implies that the person knows the contradiction
between propositions about the external world which she
believes and the proposition that she is a brain in a vat, i.e.
the person has to be epistemologically educated. Both
premises are philosophically acceptable. Argument1 explicates
how it can be argued for premise1 by using the closure
principle.
According to a common view in contemporary
epistemology premise1 is essentially based on the closure
principle. Therefore, a popular anti-sceptical strategy is to
attack premise1 of the sceptical argument by denying the
validity of the closure principle in the context of external
world scepticism. This strategy is famously chosen e.g. by
Dretske (1970) and Nozick (1981).
These philosophers regard the closure principle in
the sceptical context as too strong.
Alternative argumentations for premise1
Using the closure principle is the most popular but not the
only possible argumentation for premise1. Premise1 states
that P knows that she is not a brain in vat, if P has knowledge
of the external world. Premise1 is an implication of
the form K(a) → K(b). Inferences between a and b can be
drawn in two directions. According to this, any implication
of the form K(a) → K(b) can be interpreted in two ways:
If P knows a, then P infers b from a.
If P knows a, then P has inferred a from b.
In the first case, the direction of inference is from a to b, in
the second case it is from b to a. Both interpretations entail
the implication K(a) → K(b). According to the first version,
an inference is always drawn, according the second interpretation
an inference has necessarily to be made.
These two interpretations can be applied
analogously to premise1. Argument1 for premise1, which
is based on the closure principle, obviously corresponds to
the first interpretation. The argument for premise1, which