The Logicians
One of the schools of Mohism that has received some attention is the
Logicians school, which was interested in resolving logical puzzles. Not much survives from the writings of this school, since problems of
logic were deemed trivial by most subsequent Chinese philosophers. Historians such as
Joseph Needham have seen this group as developing a precursor
philosophy of science that was never fully developed, but others[
who?] believe that recognizing the Logicians as proto-scientists reveals too much of a modern bias.
Mathematics
The Mohist canon of the
Mo Jing described various aspects of many fields associated with physical science, and provided a small wealth of information on
mathematics as well. It provided an 'atomic' definition of the geometric point, stating that a line is separated into parts, and the part which has no remaining parts (i.e. cannot be divided into smaller parts) and thus the extreme end of a line is a point.
[7] Much like
Euclid's first and third definitions and
Plato's 'beginning of a line', the
Mo Jing stated that "a point may stand at the end (of a line) or at its beginning like a head-presentation in childbirth. (As to its invisibility) there is nothing similar to it."
[8] Similar to the
atomists of
Democritus, the
Mo Jing stated that a point is the smallest unit, and cannot be cut in half, since 'nothing' cannot be halved.
[8] It stated that two lines of equal length will always finish at the same place,
[8] while providing definitions for the
comparison of lengths and for
parallels,
[9] along with principles of space and bounded space.
[9] It also described the fact that planes without the quality of thickness cannot be piled up since they cannot mutually touch.
[10] The book provided definitions for circumference, diameter, and radius, along with the definition of volume.
[11]
Siege engineers
One consequence of Mohist understanding of mathematics and the physical sciences combined with their skills as
artisans was that they became the pre-eminent siege engineers of pre Qin unification China, capable of both reducing defences and holding cities. In keeping with their belief in furthering peace, small
cadres of mohist
siege engineers would offer their services to city states at risk of being swallowed up by larger neighbors. On occasion the knowledge that Mohists were helping to prepare a city's defences was enough to dissuade attack.