Reduction and Elimination in Philosophy and the Sciences

Scepticism, Wittgenstein's Hinge Propositions,
and Common Ground
Erik Stei, Mainz, Germany
1. Introduction
Traditionally, systematic scepticism states that knowing a
contingent proposition p, e. g., that I have hands, entails
that I know the denial of a sceptical hypothesis (sh), e. g.,
that I am a brain in a vat. Because sh is usually formulated
in a way that apparently makes it impossible for me to
know its denial on basis of my evidence, it seems as if I do
not know p. More formally, the sceptical argument looks
like this 1 :
334
(1) a. K(S, p) → K(S, ¬sh)
b. ¬K(S, ¬sh)
c. ¬K(S, p)
The notorious Moorean response is to make the sceptical
modus tollens a modus ponens by affirming the antecedent
of (1a) in the second step of the inference, concluding
K(S, ¬sh). Effectively, if we want to maintain epistemic
closure, (1b) seems to be the crucial step. However, which
premise we assume—K(S, p) or ¬K(S, ¬sh)—certainly
needs some further justification. The problem is that in an
epistemology classroom the sceptic’s story sounds just as
plausible as our ordinary knowledge-claims, which seems
to leave us in an epistemically underdetermined situation.
However, I follow Williams’s (2003) conjecture that
the justification of either of the two propositions depends
(at least in part) on the question which other propositions
we (tacitly) accept in a given context. It is Wittgenstein’s
notion of hinge propositions that underpins this thought.
2. Hinge propositions
The metaphor of hinges (HP) goes back to a famous paragraph
in On Certainty, in which it is employed to illustrate
the necessity of accepting certain propositions in order to
make sense of doubting others:
“That is to say, the questions that we raise and our
doubts depend on the fact that some propositions
are exempt from doubt, are as it were like hinges on
which those turn.”
(Wittgenstein 1984: 186 – § 341) 2
Thus if “I make an experiment I do not doubt the existence
of the apparatus before my eyes. I have plenty of doubts,
but not that” (Wittgenstein 1984: 185). This, however, does
not mean that there is a rigid set of self-evident propositions,
i. e., Wittgenstein does not advocate a strictly foundationalist
conception of justification. This is quite obvious
in the following paragraph:
1 Where knowledge is symbolized by a two-place relation K, taking an epistemic
subject S and a proposition (p or sh) as arguments. I will disregard time
in this paper.
2 Translation of Wittgenstein quotes by Denis Paul and G. E. M. Anscombe,
as found on http://budni.by.ru/oncertainty.html on March, 20th, 2008
“But it isn’t that the situation is like this: We just can’t
investigate everything, and for that reason we are
forced to rest content with assumption. If I want the
door to turn, the hinges must stay put.”
(Wittgenstein 1984: 187 – § 343)
Now, how could these ideas help us with respect to the
sceptical problem? A first rough answer is that i) which
proposition we are justified in assuming as our second
premise (1b) depends on certain HP and that ii) these HP
in turn depend on the inquiry we are interested in. Thus,
Wittgenstein’s remarks seem to support the idea that a
given knowledge claim might vary in truth value, depending
on which HP we accept in a conversational context or
in certain circumstances of evaluation. 3 If this is correct,
then using the notion of HP might strengthen the thesis
that knowledge claims are sensitive to contextual factors in
a wider sense.
3. Sceptical Presuppositions
Before going on, let me briefly sketch another important
feature of this view. One dubious point often made in favour
of the sceptic is the Cartesian claim that scepticism
operates in some kind of neutral context and does not rely
on any axioms or assumptions. If this were true then the
sceptic would in fact be in a privileged position. However,
Williams 2007 offers many arguments for the point that this
claim is in fact a platitude, arguing that scepticism does
indeed depend on certain assumptions or HP. Many philosophers
from quite a diverse range of positions seem to
share at least the spirit of this view. From a methodological
point of view, Timothy Williamson highlights that “the sceptic
relies uncritically on rules of dialectical engagement
(…), without questioning their appropriateness to the radical
questions which scepticism raises” (Williamson 2000:
188). Another point, addressed by Barry Stroud (Stroud
2000), could be the (traditional) philosopher’s wish to give
a completely general account of knowledge. However,
even if this general kind of knowledge is not available to us
it does not follow that we cannot have any more specific
kind of knowledge. Still another presupposition of the
sceptic is that our perceptions are independent of how the
world really is and that the meanings we assign to words
and propositions are in our heads only. It is due to this
internalist worry that scepticism seems so convincing, but
that is no reason for accepting it. There is of course much
more to be said on this topic, but let me adhere without
further argument, relying on Wittgenstein, that there must
be something the sceptic takes for granted in order to
make sense of her worries in the first place.
Obviously, this analysis only transfers the problem
of underdeterminacy to a meta-level. To see this, let us
grant for the moment that according to the above picture
the justification for assuming, say, (1b) is that it can be
derived from a set of HP operative in a given context. We
3 I am deliberately vague on the mechanisms yielding the truth-value of
knowledge claims as I do not want to enter the debate between Contextualism
and Subject Sensitive Invariantism. What is important here, however, is that
both views hold that a given knowledge claim can vary in truth-value.