Identity of Indiscernibles

Core Idea

The Identity of Indiscernibles, attributed to Leibniz, states that no two distinct objects can share all their properties — if x and y have exactly the same properties, then x is y. The strong form includes only intrinsic, non-relational properties; the weak form includes relational and extrinsic properties as well. Max Black's famous thought experiment challenges the principle: imagine a universe containing nothing but two qualitatively identical iron spheres, the same in every intrinsic and relational respect. If such a universe is possible, two distinct objects share all properties, and the Identity of Indiscernibles is false. Defenders respond by denying the coherence of the scenario, invoking haecceities (primitive thisness), or arguing that the spheres differ in impure relational properties. The debate bears on whether individuation is grounded in qualities or in something beyond qualities.

How It's Best Learned

Read Leibniz's Discourse on Metaphysics section 9, then Black's 'The Identity of Indiscernibles' dialogue. Decide whether Black's two-sphere universe is genuinely possible or subtly incoherent, and trace what your answer commits you to about the nature of individuality.

Common Misconceptions

• The Identity of Indiscernibles is not the same as the Indiscernibility of Identicals (Leibniz's Law), which says identical things share all properties — this latter principle is uncontroversial.
• Rejecting the Identity of Indiscernibles does not require positing mysterious 'bare particulars'; one can hold that distinctness is primitive without invoking a propertyless substratum.

Explainer

You already understand the distinction between universals (properties and relations that can be shared by many particulars) and particulars (individual things). You also understand the substance/property structure: a substance is an individual that instantiates properties, but is not itself a property. This background sets up the Identity of Indiscernibles perfectly — it is a thesis about what makes *individuals* numerically distinct from one another.

There are two Leibnizian principles that are constantly confused. Leibniz's Law (the *Indiscernibility of Identicals*) says: if x and y are *identical* (numerically one thing), then they share all their properties. This is uncontroversial — how could one thing fail to have the very properties it has? The Identity of Indiscernibles runs in the opposite direction: if x and y share *all* their properties, then they are identical. This is the contentious claim. It says that qualitative sameness entails numerical sameness — that two distinct things must differ in at least one property. Formally, there can be no two distinct objects that are qualitatively perfect duplicates of each other.

The strength of the principle depends on which properties you include. The weak form counts relational and positional properties: two objects can be distinguished by their different spatial positions ("the sphere at coordinates A" vs. "the sphere at coordinates B"). The strong form restricts to intrinsic, non-relational properties only — and this is the version Max Black attacks. His thought experiment: imagine a symmetric universe containing only two qualitatively identical iron spheres, separated by some distance. Everything true of one sphere is true of the other: same radius, same mass, same composition. Even their relational properties seem symmetric — each is two meters from a sphere of the same kind. If this universe is coherent, two numerically distinct objects share every property, and the Identity of Indiscernibles (in the strong form) is false.

Haecceitism is one line of response: each object has a *primitive thisness* (haecceity) — a property of being *this very thing* — that is not reducible to any qualitative property. Sphere A has the property "being A" that Sphere B lacks. This preserves the Identity of Indiscernibles but at a cost: you must accept non-qualitative, purely identifying properties into your ontology. Critics find this unintelligible or viciously circular. An alternative response is to deny that Black's universe is genuinely conceivable — perhaps the description is subtly inconsistent. Another is to simply accept the conclusion: numerical distinctness is primitive and irreducible to any property, qualitative or otherwise. This position rejects the Identity of Indiscernibles without requiring bare particulars, treating individuality as a brute fact about the world's structure.