Mathematical, Psychological, and Philosophical (?) Experiments for
Wittgenstein
Masaharu Mizumoto
Japan Advanced Institute of Science and Technology
Wittgenstein famously criticized the idea of “experiment” in mathematics. But
even outside of mathematics, he was also critical about experimental method inpsychology. Then one may naturally expect that the same criticism applies toexperimental philosophy. But what was wrong with experiment for him? After
discussing such issues, I will then take up what I call Wittgenstein’s “first-personexperiment”, which is neither thought-experiment nor mere introspection, andexamine, in the context of X-Phi, its relevance and implication to empirical science.
1) No Experiments in Mathematics:

Wittgenstein rejected any notion of experiment in mathematics, in his 1939
lectures and Remarks on the Foundations of Mathematics. He was not trying tosecure the notion of “apriority” like logical positivists, but trying to emphasize thenormative role mathematics plays in empirical science and our form of life.
However, it is often thought that the use of computers in mathematics made such a
conception of mathematics obsolete. I defended the idea elsewhere (Mizumotoforthcoming), but here I mention in this connection the relevance of X-Phi even tomathematics: There is indeed a place where folk intuition is relevant even inmathematics. That is where the status of Church-Turing Thesis is debated.
2) Psychological Experiments and Conceptual Confusions:
The critical attitude against experimental psychology expressed in the very lastpassages of Philosophical Investigations is famous (there the phrase “psychologyas a young science” is taken from Köhler). One may then expect that he would be
all the more critical about the idea of philosophers’ doing experiment. In fact, whatis often regarded as one of the major achievements in X-Phi, the discovery of“Knobe effect”, seems not really new from the traditional experimental psychology.
With some data of my own, I shall show that the Knobe effect can be explained byFundamental Attribution Error (together with people’s practical considerations),
which has been well-known to psychologists. But even apart from this particularobjection, most contemporary X-Phi research shares with experimental psychology
the very assumption that Wittgenstein was attacking (as conceptual confusion)
when he was criticizing the latter. Namely, that they are trying to reveal hidden
mental processes, or “how the mind works”. At least this subfield of X-Phi istherefore no less conceptually confused for Wittgenstein than experimental
psychology. Though I rather wish to remain neutral on this issue, I will explain
why the experimental approach in this context is misleading or even pernicious

according to Wittgenstein, demonstrating the point by using the data of Machery etal. (2004), which allegedly shows the cultural divergence of “semantic intuitions”.
3) Experiment and Thought-Experiment:
As we know, Wittgenstein presented many interesting thought-experiments.
Contemporary philosophers often think, however, thought-experiments are forconceptual analysis. Wittgenstein does speak of analyzing a concept (PI 383).
However, given his notion of family resemblance, one may naturally think that hemust have been very critical about conceptual analysis. In fact, there is an
important difference between conceptual analysis done by Wittgenstein and that ofcontemporary analytic philosophy. But I will argue that, if we distinguish
Wittgenstein’s “elucidatory” analysis and contemporary “progressive” analysis, wewill find not only that the latter need not be criticized by Wittgenstein, but alsothat neither types of conceptual analysis is in conflict with experimental
philosophy, unless we assume Platonistic conception of concepts, which was ofcourse Wittgenstein’s target of criticism in the early part of PhilosophicalInvestigations.
But

Wittgenstein’sconsiderations

containnot

only

ordinary

thought-experiments, but also actual instructions to do specific things, like “trythis” or “try to do this” (PI 33, 303, 330, 332, 420, p. 176, etc.). This kind of“experiment” is neither thought-experiment nor introspection. It is aimed to showwhether the reader can actually do a particular thing, letting him or her to realize“what it is like” to do it. It then suggests another important variant of experimentin philosophy, what might be called the “first-person experiment”, and makes us
reconsider

thenaïve

disjunctionofX-Phi(asusuallyconceived)orarmchair-philosophy. In fact, as I will show using my own brand of experiments(Mizumotoetal.

2001),

whichiscloselyrelatedtoWittgenstein’s

thought-experiment, that there is even an a posteriori version of such experiments(though “a priori experiment” may sound contradictory, this use can be justified).
Now even though I do think this kind of experiment to be still scientific in a broad
sense, providing no quantitative data it may not count as scientific experiment in
the narrower sense. But I will argue, using various examples, that even if it is nottaken as scientific, it can still be scientifically significant. If that is correct, we may
say that, even though it is now justified for philosophers to go experimental (due tothe flourishing results of X-Phi today), that does not necessarily mean they must
thereby go “scientific” in the narrow sense. That would otherwise limit not only thepotential of philosophy, but also the scientific development, if the purpose ofscience is not the accumulation of “scientific data” itself, but the understanding of
the world based upon it (and if scientific theories are to be evaluated on the basis ofcontribution to the latter).