Principium identitatis indiscernibilium

Principium identitatis indiscernibilium ( Latin , often abbreviated as pii ) denotes the “sentence of the identity of the indistinguishable”.

This theorem on logical identity states that two real objects, if they are not one and the same, must differ from one another in at least one observable property ( quality ). There are no two qualitatively absolutely identical, but really different things in real reality. For a more detailed representation see Identity (Logic) .

Even Cicero reported that this principle of the Stoics has been known. Even Seneca took it. This principle can also be found in Athanasius . In the Middle Ages Nikolaus von Kues , in the Renaissance Giordano Bruno , Giovanni Pico della Mirandola and Nicolas Malebranche knew about it . In Leibniz one finds the statement that there would never be exactly the same things, otherwise one could not distinguish between individuals. The monads are all qualitatively different with him inside her. There are no substances that are perfectly alike. Even Christian Wolff discussed this principle.

With Immanuel Kant there is a restriction on metaphysical inferences that could be derived from the principle. In his view, the local relationship plays a major role. Even if several things coincide as internally, they are not identical if they can be found in different places. In the Critique of Pure Reason , he explains:

“The principle of the indistinguishable was actually based on the presupposition: that if a certain distinction is not to be found in the concept of a thing, then it is not to be found in the things themselves; consequently all things are completely the same (numero eadem), which do not already differ from one another in terms of their concept (in terms of quality or quantity). ” (A 281 / B 337) - This would only apply if the“ things ”were not mere Appearances would be.

For him, “internal” and “external” are only considered “reflection concepts”. Even without Leibniz's monadology, the multiplicity and numerical difference - “would already be indicated by space itself, as the condition of external appearance. Because a part of the space, whether it may be completely similar and identical to another, is outside of it, and precisely because of this a part that is different from the former. ” ( Critique of pure reason A 264 / B 320) ... “ The difference the place makes the multiplicity and differentiation of objects, as phenomena, without further conditions, not in itself possible, but also necessary ” (A 272 / B 328).

The scope of the theorem pii has been questioned since the 1950s because it was discovered in 1927 in atomic physics that the electrons of an atom must be viewed as absolutely indistinguishable, but that there are more than one of them. For the physical content of this discovery, see indistinguishable particles . Many theorists of science (such as Erwin Schrödinger , Henry Margenau , Steven French , Peter Mittelstaedt ) consider pii to be refuted by this discovery. Others (such as Bas van Fraassen , Frederik Archibald Muller, among others ) consider pii , with more precise specifications, to be valid, at least as far as quantum mechanics is concerned, which only knows states with a fixed number of particles. For the area of ​​quantum field theory, in which the number of particles can vary, because all types of particles are viewed as quantum excitations of a corresponding field (such as the photon as a quantum of the electromagnetic wave), a more detailed analysis is still pending; the discussion continues.

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This article is essentially based on the article of the same name from Rudolf Eisler's dictionary of philosophical terms from 1904.

1. ↑ Cicero, Acad. III, 17, 18, 26
2. ↑ Seneca, Epist. 113, 13, cf. Cicero, Acad. II, 26, 85
3. ↑ Nicalaus Cusanuswerk, De docta ignorantia II, 11
4. ↑ Malebranche, De la recherche de la vérité, III, 2, 10
5. ^ Leibniz, Nouveaux Essais sur L'entendement humain II, ch. 27, § 1, 3
6. ↑ Leibniz, Monadologie, 9
7. ↑ Wolff , Cosmologia generalis, § 195f.
8. ↑ The identity of Indiscernibles entry in Edward N. Zalta (ed.): Stanford Encyclopedia of Philosophy .
9. ^ Identity and Individuality in Quantum Theory Entry in Edward N. Zalta (Ed.): Stanford Encyclopedia of Philosophy .