Reduction and Elimination in Philosophy and the Sciences

Getting out from Inside: Why the Closure Principle cannot Support External World Scepticism — Guido Melchior
corresponds to the second interpretation of K(a) → K(b), is
the following:
Argument2 for premise1:
P can only have knowledge about the external world
if she infers it from knowledge that she is not a brain
in a vat.
Therefore, P knows that she is not a brain in a vat, if
P has knowledge about the external world.
To sum up, there are two possible argumentations for
premise1. The common one uses a version of the closure
principle for arguing that inferences from “e” to “¬BiV” can
always be drawn. According to the alternative argumentation,
the inference from “¬BiV” to “e” is a necessary condition
for K(¬BiV).
In a next step, I will show that premise2 of external
world scepticism can only be true if argument2 for
premise1 holds and if argument1, which is based on the
closure principle, is rejected.
Argumentations for premise2
I will now analyze possible argumentations for premise2,
which states that a person cannot know that she is not a
brain in a vat. If knowledge is justified, true belief, there are
obviously three possible reasons why P cannot know that
she is not a brain in a vat: the impossibility to believe it, the
impossibility that the belief is true and the impossibility that
the belief is justified. P can obviously believe that she is
not a brain in a vat and it is possible that this belief is true.
If knowledge is justified, true belief, the problematic aspect
for P’s knowledge that she is not a brain in a vat is justification.
Taking into account internalistic as well as
externalistic theories of justification, the obvious
candidates for methods of justification are evidence,
inference and externalistic justification. If it is possible that
P’s belief that she is not a brain in vat can either be
evident or externalistically justified, there is obviously no
specific problem of justification. Therefore, premise2 can
only be true, if P’s belief that she is not a brain in a vat
cannot be evident or externalistically justified. It is
philosophically plausible that this belief is neither evident
nor externalistically justified. Hence, it can be accepted
that premise2 is true if P’s belief that she is not a brain in
vat cannot be justified through inference.
Next, I will investigate why it should be impossible
that P’s belief that she is not a brain in vat is justified
through inference by focusing my attention on the following
challenge for sceptics: Why is it impossible for person to
justify that she is not a brain in vat by inferring it from
knowledge about the external world? Why is the following
argumentation inadequate?
The anti-sceptical argument:
K(e)
P infers “¬BiV” from “e”.
Therefore, K(¬BiV).
This argument is at least close to the anti-sceptical argumentation
proposed by Moore (1925 and 1939).
Example:
I know there is a computer in front of me.
Therefore, I am not a brain in a vat.
This anti-sceptical argument is an inference from K(e) to
K(¬BiV). It is based on the idea that a person can infer
from any knowledge of the external world that she is not a
brain in vat. The closure principle states: If K(a) and K(a →
b), then K(b). Hence, the anti-sceptical argument uses the
closure principle for arguing that a person can know that
she is not a brain in a vat. Why should this argumentation
line be wrong?
Generally speaking, there are three possible
reasons why an argument respectively an inference is not
a justification:
1. The argument is not preserving truth respectively
justification.
2. The premise of the argument is not justified.
3. Other reasons.
I will now investigate each of these three possible reasons:
1. The inference from a person’s belief about the
external world to the belief that she is not a brain in a vat is
truth-preserving. This follows from the fact, that premise1
can only be valid, if “brain in a vat” refers to persons with
totally false beliefs about the external world. If premise1 is
true, then the inference from a person’s belief of the
external world to the belief, that the person is not a brain in
a vat is truth preserving and, therefore, preserving
justification. Hence, in the context of defending external
world scepticism the first objection against the antisceptical
argument has to be rejected.
2. According to the second objection, the premise
of the anti-sceptical argument is false, i.e. P’s belief about
the external world is not justified. The conclusion of the
argument of external world scepticism is that P does have
knowledge respectively justified beliefs about the external
world. This is the same theory as the second objection to
the anti-sceptical argument. If it is assumed that the belief
about the external world is not justified in order to argue for
premise2 of the argument of external world scepticism this
sceptical argument itself becomes circular. Therefore, the
second objection against the anti-sceptical argument is not
adequate in the context of external world scepticism.
3. The first two objections against the anti-sceptical
argument are inadequate. Therefore, the anti-sceptical
argument only fails, if the inference is deficient for other
reasons. The only reason, why a truth-preserving inference
with justified premises is not a valid justification, is that the
inference leads into a vicious circle. This is the case for the
anti-sceptical argument, if a person can only justify beliefs
about the external world by inferring it from knowledge that
she is not a brain in a vat. This means that justification of
beliefs about the external world is only possible through
inference from “inside out”. Hence, premise2 is only true if
this internalistic condition for justifying beliefs about the
external world is fulfilled.
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