Reduction and Elimination in Philosophy and the Sciences
Reduction and Elimination in Philosophy and the Sciences
Reduction and Elimination in Philosophy and the Sciences
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Gett<strong>in</strong>g out from Inside: Why <strong>the</strong> Closure Pr<strong>in</strong>ciple cannot Support<br />
External World Scepticism<br />
Guido Melchior, Graz, Austria<br />
The canonical version of <strong>the</strong> argument for external world<br />
scepticism has <strong>the</strong> follow<strong>in</strong>g structure:<br />
218<br />
Premise1: If P does not know that she is not a<br />
bra<strong>in</strong> <strong>in</strong> a vat, <strong>the</strong>n P does not have<br />
knowledge of <strong>the</strong> external world.<br />
Premise2: P does not know that she is not a bra<strong>in</strong><br />
<strong>in</strong> a vat.<br />
Conclusion: Therefore, P does not have knowledge<br />
of <strong>the</strong> external world.<br />
This version of <strong>the</strong> argument is presented by Brueckner<br />
(1994 <strong>and</strong> 2004), Byrne (2004), Pritchard (2005) <strong>and</strong> o<strong>the</strong>rs.<br />
If “a” is any proposition about <strong>the</strong> external world <strong>and</strong><br />
“b” is <strong>the</strong> proposition that P is not a bra<strong>in</strong> <strong>in</strong> a vat, <strong>the</strong>n <strong>the</strong><br />
sceptical argument has <strong>the</strong> follow<strong>in</strong>g structure:<br />
Premise1: (¬K(b) → ¬K(a))/(K(a) → K(b))<br />
Premise2: ¬K(b)<br />
Conclusion: Therefore, ¬K(a)<br />
This argument is logically valid. Therefore, any objection<br />
aga<strong>in</strong>st <strong>the</strong> argument has to be one aga<strong>in</strong>st one of its two<br />
premises. Subsequently, I will <strong>in</strong>vestigate how it can be<br />
argued for <strong>and</strong> aga<strong>in</strong>st each of <strong>the</strong> two premises.<br />
Argumentations for premise1: The closure<br />
pr<strong>in</strong>ciple <strong>and</strong> alternative arguments<br />
Premise1 states that any knowledge of P about <strong>the</strong> external<br />
world implies that P knows that she is not a bra<strong>in</strong> <strong>in</strong> a<br />
vat. Why should premise1 be true? Usually, <strong>in</strong> epistemological<br />
discussions, <strong>the</strong> argumentations for premise1 are<br />
grounded on one or <strong>the</strong> o<strong>the</strong>r version of <strong>the</strong> closure pr<strong>in</strong>ciple.<br />
I will, firstly illustrate how <strong>the</strong> closure pr<strong>in</strong>ciple can be<br />
used for argu<strong>in</strong>g for premise1. Secondly, I will present an<br />
alternative argumentation.<br />
The closure pr<strong>in</strong>ciple<br />
The closure pr<strong>in</strong>ciple is based on our epistemic <strong>in</strong>tuition<br />
that persons can ga<strong>in</strong> new knowledge about facts through<br />
<strong>in</strong>ference from facts <strong>the</strong>y already know. The closure pr<strong>in</strong>ciple<br />
can occur <strong>in</strong> different forms. The simplest version is:<br />
C: (K(a) ∧ (a → b)) → K(b)<br />
Accord<strong>in</strong>g to this version, a person knows every proposition<br />
which is entailed by a known proposition no matter if<br />
<strong>the</strong> person has any knowledge about this entailment relation<br />
itself. This is obviously an implausible account of<br />
knowledge through <strong>in</strong>ference. Hence, <strong>the</strong> more common<br />
version is:<br />
CP: (K(a) ∧ K(a → b)) → K(b)<br />
This version expresses <strong>the</strong> idea that a person, who knows<br />
a proposition a <strong>and</strong> knows that a implies ano<strong>the</strong>r proposition<br />
b, knows b through <strong>in</strong>ference from a. This version<br />
captures our <strong>in</strong>tuition that a person can only ga<strong>in</strong> knowledge<br />
through <strong>in</strong>ference if <strong>the</strong> person also knows <strong>the</strong> entailment<br />
relation between <strong>the</strong> two propositions.<br />
On <strong>the</strong> basis of <strong>the</strong> closure pr<strong>in</strong>ciple CP, it can be<br />
argued for premise1 <strong>in</strong> <strong>the</strong> follow<strong>in</strong>g way:<br />
Argument1 for premise1:<br />
CP: (K(a) ∧ K(a → b)) → K(b)<br />
The proposition “P is a bra<strong>in</strong> <strong>in</strong> a vat” <strong>and</strong> any<br />
proposition which P believes about <strong>the</strong> external<br />
world are contradictory.<br />
P knows this contradiction.<br />
Therefore, P <strong>in</strong>fers that she is not a bra<strong>in</strong> <strong>in</strong> vat, if P<br />
has knowledge about <strong>the</strong> external world.<br />
Therefore, P knows that she is not a bra<strong>in</strong> <strong>in</strong> a vat, if<br />
P has knowledge about <strong>the</strong> external world.<br />
I th<strong>in</strong>k this argument captures <strong>the</strong> common philosophical<br />
<strong>in</strong>tuitions concern<strong>in</strong>g premise1. The first premise of argument1<br />
is <strong>the</strong> closure pr<strong>in</strong>ciple. One consequence of its<br />
second premise is that <strong>the</strong> term “bra<strong>in</strong> <strong>in</strong> a vat” has to refer<br />
to persons, who not just have unjustified beliefs but who<br />
have totally false beliefs about <strong>the</strong> external world. The third<br />
premise implies that <strong>the</strong> person knows <strong>the</strong> contradiction<br />
between propositions about <strong>the</strong> external world which she<br />
believes <strong>and</strong> <strong>the</strong> proposition that she is a bra<strong>in</strong> <strong>in</strong> a vat, i.e.<br />
<strong>the</strong> person has to be epistemologically educated. Both<br />
premises are philosophically acceptable. Argument1 explicates<br />
how it can be argued for premise1 by us<strong>in</strong>g <strong>the</strong> closure<br />
pr<strong>in</strong>ciple.<br />
Accord<strong>in</strong>g to a common view <strong>in</strong> contemporary<br />
epistemology premise1 is essentially based on <strong>the</strong> closure<br />
pr<strong>in</strong>ciple. Therefore, a popular anti-sceptical strategy is to<br />
attack premise1 of <strong>the</strong> sceptical argument by deny<strong>in</strong>g <strong>the</strong><br />
validity of <strong>the</strong> closure pr<strong>in</strong>ciple <strong>in</strong> <strong>the</strong> context of external<br />
world scepticism. This strategy is famously chosen e.g. by<br />
Dretske (1970) <strong>and</strong> Nozick (1981).<br />
These philosophers regard <strong>the</strong> closure pr<strong>in</strong>ciple <strong>in</strong><br />
<strong>the</strong> sceptical context as too strong.<br />
Alternative argumentations for premise1<br />
Us<strong>in</strong>g <strong>the</strong> closure pr<strong>in</strong>ciple is <strong>the</strong> most popular but not <strong>the</strong><br />
only possible argumentation for premise1. Premise1 states<br />
that P knows that she is not a bra<strong>in</strong> <strong>in</strong> vat, if P has knowledge<br />
of <strong>the</strong> external world. Premise1 is an implication of<br />
<strong>the</strong> form K(a) → K(b). Inferences between a <strong>and</strong> b can be<br />
drawn <strong>in</strong> two directions. Accord<strong>in</strong>g to this, any implication<br />
of <strong>the</strong> form K(a) → K(b) can be <strong>in</strong>terpreted <strong>in</strong> two ways:<br />
If P knows a, <strong>the</strong>n P <strong>in</strong>fers b from a.<br />
If P knows a, <strong>the</strong>n P has <strong>in</strong>ferred a from b.<br />
In <strong>the</strong> first case, <strong>the</strong> direction of <strong>in</strong>ference is from a to b, <strong>in</strong><br />
<strong>the</strong> second case it is from b to a. Both <strong>in</strong>terpretations entail<br />
<strong>the</strong> implication K(a) → K(b). Accord<strong>in</strong>g to <strong>the</strong> first version,<br />
an <strong>in</strong>ference is always drawn, accord<strong>in</strong>g <strong>the</strong> second <strong>in</strong>terpretation<br />
an <strong>in</strong>ference has necessarily to be made.<br />
These two <strong>in</strong>terpretations can be applied<br />
analogously to premise1. Argument1 for premise1, which<br />
is based on <strong>the</strong> closure pr<strong>in</strong>ciple, obviously corresponds to<br />
<strong>the</strong> first <strong>in</strong>terpretation. The argument for premise1, which