a proposition that asserts that something equals itself. Surely, this is true.
According to one influential interpretation, this should be the only logical
meaning of identity. It is known as Leibniz’s Law in reference to logician and
mathematician Gottfried Wilhelm Leibniz, who argued that any two expressions
conjoined by ‘=’ should be interchangeable in all contexts without altering the
truth-value of the statements in which they occur (salva veritate). While a
universal truth, Leibniz conceived of it also as an empirical law that holds for
everything. He asserted: ‘It is never true that two substances are entirely alike,
differing only in being two rather than one.’
Leibniz’s reasoning is often illustrated with a story that took place in the garden
of Princess Sophie at Herrenhausen (Figure 3). The princess wondered whether
in the abundant foliage two identical leaves could be found, which Leibniz
denied. He argued that each leaf had features, however minute, that set it apart
from all others, a unique identity.