32 karine chemla
for an end, but their texts were also read as conveying other meanings. Th e
‘techniques’ read in the proofs do not have the same nature in diff erent con-
texts. However, what is important to note here is that in all these cases the
epistemological value of the proof cannot be exhausted by the question of
determining whether it duly establishes the statement to be proved.
According to the fi rst hypothesis too, the reader looked for something
general in a proof – a method, the use of which could extend beyond the
limits of a proposition. Th e fact that, as Saito showed, some techniques of
somewhat general validity were actually composed indicates the possible
outcome of such a search. A straightforward interpretation of the text of
each proof taken separately would miss this feature of the practice of proof.
Th e virtue of the techniques thereby identifi ed was their potential useful-
ness in other contexts: if we follow this interpretation, a certain fruitfulness
was recognized in it. Th ese concerns indicate epistemological values that
actors may have attached to proofs and that too narrow a focus on certainty
could hide from our view.
Th e preceding remarks illustrate what kind of benefi ts could be derived
from re-examining standard texts with wider expectations in mind. Th ey
also bring to light an issue that will prove essential in what follows. Th e
way in which actors have read proofs or have written them down, the
motivation driving the composition of explicit proofs, cannot be taken for
granted. As I have indicated, reading meanings into proofs is apparently
a widely shared practice. However, this does not mean that practitioners
belonging to diff erent scholarly cultures read the meanings in texts in the
same way or that the texts intended the meanings to be read in the same
way. Whether one accepts only the fi rst hypothesis or both hypotheses as
formulated, the perception of the various dimensions of the Greek texts to
which I have just alluded requires an unusual and specifi c reading of the
text. If one admits the second hypothesis, texts of proofs were to be read as
paradigms. Interestingly enough, as we saw in Section ii of this introduc-
tion, the diagrams in Greek texts seem to have required the same kind of
reading, at least if we agree on the fact that the original fi gures resembled
those in the manuscripts and not those which Heiberg drew. Interpretation
of the sources appears more generally to be a delicate procedure, on which
our ability to perceive the various dimensions of the proofs examined will
depend. As I shall argue below, this problem is intrinsic to our endeavour:
it is, in my view, tied to the fact that shaping a practice of proof has always
involved designing a kind of text to work out and deliver the proofs. Th e
task of interpreting the texts thus cannot be separated from the job of
describing the practice of proof to which they adhere.