following analysis of the meaning of the word interval in Wittgenstein’s Lec-
tures, Cambridge 1932–1935.
If we look at a river in which numbered logs are ®oating, we can de-
scribe events on land with reference to these, e.g., “When the 105th log
passed, I ate dinner.” Suppose the log makes a bang on passing me. We
can say these bangs are separated by equal, or unequal, intervals. We
could also say one set of bangs was twice as fast as another set. But
the equality or inequality of intervals so measured is entirely different
from that measured by a clock. The phrase “length of interval” has its
sense in virtue of the way we determine it, and differs according to the
method of measurement.^15 (13)Here, Wittgenstein’s investigation examines the curious shift in the meaning
of a single word—interval—depending on the context in which it occurs. The
“interval” measurable by the passage downstream of logs does not have
the same status as the “interval” measured by a clock. But the mystery of the
word has nothing to do with the speci¤c language in question: in French,
for example, we read, “Aussi les critères qui déterminent l’égalité des inter-
valles séparant le passage des rondins sont-ils différents de ceux qui déterminent
l’égalité des intervalles mesurés par une horloge.”^16 Whether interval, inter-
valle, or the German Abstand, the argument as to the possible meanings of
“interval” remains intact.
“But isn’t the same at least the same?” Wittgenstein’s question in the Philo-
sophical Investigations (§215) elicits the “useless proposition” that, yes, “A
thing is identical with itself.” Useless, because, as Wittgenstein has already ar-
gued earlier in the book (§61), we still have not come to a “general agreement
about the use of the expression ‘to have the same meaning’ or ‘to achieve the
same.’ For it can be asked in what cases we say: ‘These are merely two forms
of the same game.’ ” Or consider the following from the so-called Big Type-
script of the late thirties: “The man who said that one cannot step into the
same river twice said something wrong; one can step into the same river
twice.”^17 Literally this is the case: certainly, if Wittgenstein were walking
along the banks of the Thames, he could easily step into the same river twice.
But then Heraclitus, whose metaphorical aphorism Wittgenstein is calling
into question, could respond that the second time round, it would not be
quite the “same” river. Wittgenstein knows this, but he also knows that the
“same” in “same river” is not quite the same as the “same” of “I have the same
pain you have.” For how can I judge the intensity of your pain? How do I
know, for that matter, that you’re not just pretending to be in pain? What can
72 Chapter 4