unpublished note
A NOTE ON SKEPTICISM ABOUT
RULES
Summary:
The aim of this short note is to present a decisive
solution to the paradox proposed by Wittgenstein and Kripke concerning the
impossibility of learning a rule due do the infinite number of possible
interpretations of what is being teaching. The point was already noted by Craig DeLancey, and I am only calling attention to its importance. If the defended solution is correct, as it seems evident to me, then the paradox receives an easy solution, and the analysis of meaning is saved.
Key-Words:
Following a rule, Kripke,
Wittgenstein, paradox, meaning
One could say that
Wittgenstein (1984c, sec. 185 f.) formulated a skeptical riddle that endangers
the possibility of an ongoing common interpretation of rules and,
consequently, the idea that our language may work as a system of rules, and in
this way threatens the proper concept of meaning. A similar skeptical riddle
was imaginatively formulated by Saul Kripke (1982, Ch. 1). Answering this
riddle interests us here because if the argument were correct, it could imply
that it is a mistake to accept that there are verifiability rules responsible
for the cognitive meanings of sentences.
Wittgenstein introduced his riddle with the
following example. Let’s say that a person learns a rule to add 2 to natural
numbers. If you give him the number 6, he adds 2 and writes the number 8. If
you give him the number 73, he adds 2, writing the number 75... But imagine
that for the first time he is presented with a larger number, say the number
1,000, and that he then writes the number 2,004. If you ask why he did this, he
responds that she understood that he should add 2 up to the number 1,000, 4 up
to 2,000, 6 up to 3,000, etc. (1984, sec. 185). According to Kripke’s version,
a person learns the rule of addition, and it works well for additions with
numbers below 57. But when he performs additions with larger numbers, the
result is always 5. So for him 59 + 67 = 5… This occurs because she understood
‘plus’ as the rule ‘quus,’ according to which ‘x quus y = x + y
if {x, y} < 57, otherwise 5’ (1982: 9).
What these examples demonstrate is that a
rule can always be interpreted differently from the way it was intended, no
matter how many specifications we include in our instructions for using the
rule, since these instructions can also be differently interpreted. The
consequence is that we cannot be assured that everyone will follow our
rules in a similar way or that people will continue to coordinate their actions
based on them. And as meaning depends upon following rules, we cannot be
certain about the meanings of the expressions we use. How could we be certain,
in the exemplified cases, of the respective meanings of ‘add two’ and
‘plus’?
In my view, neither Wittgenstein nor Kripke
gives a satisfactory answer to the riddle. Both assume a Humean-kind skeptical
solution. Wittgenstein’s answer can be interpreted as saying that we follow
rules blindly, as a result of training in the conventions of our social
practices (1984 sec. 201, 202, 211, 219). Kripke’s answer is similar: following
a rule is justified not by truth-conditions derived from correct
interpretation, but by assertability conditions (1982: 74) based on the fact
that any other user in the same language community can assert that the rule
follower ‘passes the tests for rule following applied to any member of the
community’ (1982: 110). However, against both one could insist that the simple
fact that in our community we have so far openly coordinated our linguistic
activity according to rules does not imply that these coordinations need to
work this way, and does not even imply that they should continue to work this way, which shows that the
riddle remains basically unsolved.
For my part, I always thought that the
‘paradox’ had a more straightforward solution. A central point can be seen as
in some way suggested by Wittgenstein’s philosophy, namely, that we learn rules
in a similar way because we share a similar human nature modelled in our
form of life (Costa 1990: 64-66). This makes it easy for us to interpret
the rules we are taught in the same manner, and means that we must also be
naturally endowed with innate, internal corrective mechanisms able to reinforce
agreement.
I think, however, that if we follow this
path further, a decisive solution of the riddle can be found in Craig DeLancey
(2004). According to him, we are biologically predisposed to construct and
interpret statements in the most economical
way possible. Or, as we could also say, we are innately disposed to put in
practice the following principle of simplicity as a pragmatic maxim:
PS: We should interpret (and establish) a
semantic rule in the simplest way possible.
Because of this principle,
we prefer to maintain the interpretation of the rule ‘add 2’ in its usual form,
instead of complicating it with the further condition that we should add twice
two after each thousand. And because of the same principle, we prefer to
interpret the rule of addition as a ‘plus’ instead of a ‘quus’ addition, because with the ‘quus’
addition we would complicate the interpretation by adding the further condition
that any sum with numbers above 57 would give as a result the number 5. The
application of such a principle of simplicity allows us to harmonize our
interpretations of semantic rules, thus solving the riddle.
One might ask: what warrants the assumed
similarity of human nature or that we are innately equipped to develop such a
heuristic principle of simplicity? The obvious answer lies in the appeal to
Darwinian evolution. Over long periods of time, a process of natural selection
has harmonized our learning capacities, eliminating individuals with deviant,
less practical dispositions. Thus, within our human way of life the principle
of simplicity offers a plausible explanation of our capacity to share a
sufficiently similar understanding and meaning of semantic rules. If we add to
this the assumption that human nature and recurring patterns in the world will
not change in the future, we can be confident in the expectation that people
will not deviate from the semantic rules they have learned. Of course,
underlying this last assumption is Hume’s much more defiant criticism of
induction, which might remain a hidden source of uneasiness. But this is a
further issue that goes beyond our present concerns.
Summarizing: Our shared interpretation of
learned rules only seems puzzling if we insist on ignoring the implications of
the theory of evolution, which supports the principle of simplicity. By
ignoring considerations like these, we tend to ask ourselves (as Wittgenstein
and Kripke did) how it is possible that these rules are and continue to be
interpreted and applied in a similar manner by other human beings, losing
ourselves within a maze of philosophical perplexities. For a similar reason,
modern pre-Darwinian philosophers like Leibniz wondered that our minds are such
that we are able to understand each other, appealing to the Creator as
producing the necessary harmony among human souls. The puzzle about
understanding how to follow a rule arises from this same old perplexity.
REFERENCES:
DeLancey, C. (2004). ‘Meaning
Naturalism, Meaning Irrealism, and the Works of Language.’ Synthese 154 (2), 231-257.
Kripke, S. (1982). Wittgenstein on Rules and Private Language: An Elementary Exposition. Cambridge, MA: Harvard
University Press.
Wittgenstein, L. (1994). Philosophische Untersuchungen (Philosophical Investigations), Werkausgabe Band 1. Frankfurt: Suhrkamp.
