Pii Quotes

“From a philosophical point of view, Leibniz's most interesting argument was that absolute space conflicted with what he called the principle of the identity of indiscernibles (PII). PII says that if two objects are indiscernible, then they are identical, i.e. they are really one and the same object. What does it mean to call two objects indiscernible? It means that no difference at all can be found between them--they have exactly the same attributes. So if PII is true, then any two genuinely distinct objects must differ in at least one of their attributes--otherwise they would be one, not two. PII is intuitively quite compelling. It certainly is not easy to find an example of two distinct objects that share all their attributes. Even two mass-produced factory goods will normally differ in innumerable ways, even if the differences cannot be detected with the naked eye.

Leibniz asks us to imagine two different universes, both containing exactly the same objects. In Universe One, each object occupies a particular location in absolute space.In Universe Two, each object has been shifted to a different location in absolute space, two miles to the east (for example). There would be no way of telling these two universes apart. For we cannot observe the position of an object in absolute space, as Newton himself admitted. All we can observe are the positions of objects relative to each other, and these would remain unchanged--for all objects are shifted by the same amount. No observations or experiments could ever reveal whether we lived in universe One or Two.”
― Samir Okasha, Philosophy of Science: A Very Short Introduction