FOLLOWING A RULE: WAISMANN’S VARIANT
Mathieu Marion
Université du Québec à Montréal(Joint paper with Mitsuhiro Okada, Keio University)
In this paper, we wish to reconstruct a variant of Wittgenstein’s ‘rule-following
argument’ in Wittgenstein 2009, §§ 143-242 on the basis of passages in Waismann
1997, 119-124 and Waismann 2011, §§ 10-11. Although this variant is inextricably
linked with Wittgenstein’s own argument, our aim is not to propose a reading of thelatter, but only discuss elements of it as it becomes necessary for our reconstruction.
We thus begin with brief remarks concerning Waismann’s collaboration withWittgenstein, out of which Principles of Linguistic Philosophy came out, in order toestablish the claim that, although Waismann can be read as having interpreted
Wittgenstein more or less accurately, he also can be read by the same token as having
devised an independent argument.
To establish the originality of Waismann’s variant, it is useful to go back to
Saul Kripke’s controversial argument (Kripke 1982), which is based on the case at(Wittgenstein 2009, §§ 143 & 185) of the pupil, who, upon having been asked to follow
the rule ‘+2’, goes on adding ‘+4’ after 1000:

2 4 6 … 996 998 1000 1004 1008 …

Although the example involves explicitly two persons, the teacher and her pupil, thisappears to be inessential and Kripke focused away from this, discussing ‘rule
following’ form the viewpoint of the first person: his characterization of scepticism
concerning ‘rule following’ was thus oriented towards one’s own inability to justify
which rule one follows, on the basis of past intentions, dispositions, etc.
By way of contrast, Waismann’s variation is based on a closely related
example introduced in the Brown Book as language game # 62 (Wittgenstein 1969,112), and recurring at (Wittgenstein 2009, §§ 151 & 179), which we call the ‘guessing
game’. It involves two persons, with, say, Smith writing down on the blackboard theinitial segment of a series:

1 4 9 16

And Jones trying to guess which rule Smith has been following. Let us suppose thatthe game goes on the following way: having observed Smith, Jones deduces that hemust have been working the first values of the function y = x2 but, upon being asked
if that is the case, Smith replies: “No, I have been computing the first values of therule y = x/50 x (24 + 35x2 – 10x3 + x4) !”At this stage, it is important to notice that the ‘guessing game’ is not an inessential
variant of the case of the deviant pupil on which Kripke based his interpretation.
Here, the second-person standpoint cannot be so dismissed.
Indeed, as Waismann points out, this shows “how unfounded it would be tosuppose that we can discover the reason for a man’s action by observation”(Waismann 2010, § 10). An important mathematical fact that underlies this point: it

is nearly impossible for Jones to discover which function Smith was computing by
mere observation because any such initial segment, whatever its length, is in fact
the initial segment of an infinite number of mathematical functions. The point
Waismann was making is that one must distinguish between reasons (here: grounds)
and causes: “So, we must distinguish between ground and cause, for we learn of bothin different ways. The cause for his writing down certain figures may lie in the factthat he was taught so in school and that this teaching has created a disposition, e.g.,left definite traces in his nervous system and his brain; the ground for his procedureis the rule which he states when asked for the ground.” (Waismann 2010, § 10)
Taking our lead from this, we will explore the role of the distinction between reasonsand causes in Waismann’s texts as well as in Wittgenstein’s The Blue Book
(Wittgenstein 1969, 11-15), and in his rule-following argument. In a nutshell, thepoint of the ‘guessing game’ is only to show that Jones can only come up with‘hypotheses’ that are causal in nature, while Smith’s admission that he followed agiven function counts as giving a reason justifying his actions: if further whyquestions are then raised about Smith’s calculations, the ‘chain of reasons’ will
eventually have to come to an end, and philosophical entanglement will only occur
when one continues asking questions after that point, forcing one to answer withcausal explanations.
To show to relevance of Waismann’s variant, we will focus in the last part ofour talk on parallels with Lewis Carroll’s paradox of inference (Carroll 1895) in thecase of ‘basic rule-following’ such as merely applying Modus Ponens, and on thecurrent discussion about ‘blind reasoning’, in the wake of Crispin Wright’s reply(Wright 2007) to Boghossian 2003. The point will be to show that Waismann’s
discussion of rule-following provides us with ideas that can be used to handle suchcases of ‘basic rule-following’, while avoiding some of the difficulties raised in thesepapers, including the infinite regress in the ‘chain of reasons’ involved in the paradoxof inference.
REFERENCES: Boghossian, P., 2003, ‘Blind Reasoning’, Proceedings of the
Aristotelian Society, Supplementary Volumes, vol. 77, 225-293.
Carroll, L., 1895, ‘What the Tortoise said to Achilles’, Mind, n. s., vol. 4, 278-280.
Kripke, S., 1982, Wittgenstein on Rules and Private Language, Harvard UP.
Waismann, F., 1997, The rinciples of Linguistic Philosophy, 2nd ed., Basingstokes &London, MacMillan.
Waismann, F., 2011, ‘Causality’, in B. F. McGuinness (ed.), Friedrich Waismann.
Causality and Logical Positivism, Dordrecht, Springer, 2011, 91-184.
Wittgenstein, L., 1969, The Blue and Brown Books, 2nded., Oxford, Blackwell.

Wittgenstein, L., 2009, Philosophical Investigations, revised 4th ed., Oxford, WileyBlackwell.
Wright, C., 2007, Rule-Following without Reasons: Wittgenstein’s Quietism and theConstitutive Question’, Ratio, n. s., vol. 20, 481-502.