Gottfried Wilhelm Leibniz Gottfried Wilhelm Leibniz writing at his desk

How many things are in a block of marble?

Gottfried Wilhelm Leibniz (1646–1716), a German philosopher and mathematician, wrote to the French scholar Antoine Arnauld about a question that a single object can raise. A block of marble lies before us. It can be lifted, weighed and set down again, and each operation deals with one piece. Is that experience sufficient grounds for calling it a single being in the strict philosophical sense?

Seeing a lake as one thing

Perhaps this block of marble is only a heap of infinitely many living bodies, or like a lake full of fish, although the eye can ordinarily distinguish these animals only in bodies that have partly decayed.

– Gottfried Wilhelm Leibniz, Brief an Antoine Arnauld vom 30. April 1687, 1846, p. 96–97.[1]

Leibniz gives visibility alone very little weight as evidence. A rainbow, too, can be seen perfectly clearly. The fact that marble is also solid and heavy does not settle the question for him. Hence the invitation to picture a lake. Standing on its bank, one can take in the surface at a glance. Beneath it fish are swimming, each with movements of its own. Nobody would suppose that these creatures together make one enormous fish just because the lake has one name.

What a name holds together

Leibniz goes on to describe a familiar operation of the mind. We perceive things in their relations and gather them under a name. This makes both reasoning and communication a great deal easier. Yet the very usefulness of the word can make it a misleading witness. “A block of marble” comes so easily to the lips that one might credit its grammatical singular with more than it can establish. Leibniz offers no examination of the rock under a magnifying glass. He needs the fish to bring out a question about unity which the solidity of the block cannot settle by itself.