The Identity of Indiscernibles Current Status and Mathematical Provability

The Identity of Indiscernibles: Current Status and Mathematical Provability

As you correctly point out, the identity of indiscernibles (IoI) is a much more controversial principle than its converse, the indiscernibility of identicals. While the latter is widely accepted as a logical truth, the IoI has been subject to various criticisms and debates.

Here's a summary of the current state of the debate:

Arguments against IoI:

Definition of "property": Critics argue that the IoI hinges on a clear and comprehensive definition of "property," which is difficult to provide. What counts as a property for the purposes of this principle? Are there properties beyond those expressible in our current language or conceptual framework?
Possible worlds and counterexamples: Some philosophers, like Max Black, have constructed thought experiments involving possible worlds with perfectly symmetrical objects that seem to violate the IoI. These thought experiments challenge the claim that sharing all properties necessitates identity.
Quantum mechanics: The existence of indistinguishable particles in quantum mechanics also appears to contradict the IoI. However, some argue that these particles are not truly identical due to their differing quantum states.

Arguments for IoI:

Intuitive appeal: The IoI has a strong intuitive appeal. It seems to align with our basic understanding of identity and individuality. If two things are truly indistinguishable in every way, how can they be different entities?
Theoretical implications: Proponents argue that the IoI has important theoretical implications for various philosophical issues, such as the nature of space and time, the existence of individuals, and the possibility of certain metaphysical theories.

Mathematical Provability:

It is important to note that the IoI cannot be proven or disproven within pure mathematics. This is because the concept of "property" and the notion of "sharing all properties" are not purely mathematical concepts. They involve metaphysical and philosophical assumptions about the nature of reality and the kinds of properties that exist.

Therefore, the debate about the IoI remains primarily a philosophical one, with arguments and counterarguments based on different conceptions of identity, possibility, and the nature of reality.

Current Status:

There is no definitive consensus on the truth or falsity of the IoI. Some philosophers accept it as a fundamental principle, while others reject it or remain agnostic. The debate continues, with ongoing discussions about the definition of "property," the interpretation of thought experiments, and the implications of quantum mechanics.

It is important to engage with the arguments on both sides and consider the various interpretations and implications of the IoI before reaching a personal conclusion on its validity.

Seealso

Summary of "Identity of Indiscernibles" from Wikipedia

This Wikipedia page discusses the identity of indiscernibles (IoI), a philosophical principle stating that two objects are identical if they share all the same properties. This means that no two distinct things can be exactly alike.

The principle is closely associated with the philosopher Gottfried Wilhelm Leibniz, though there are different interpretations of his intended meaning and the principle's logical strength.

The page delves into the following key points:

Distinguishing Identity and Indiscernibility:

Both concepts are related to "sameness," but identity refers to numerical sameness (being one and the same object), while indiscernibility refers to qualitative sameness (sharing all properties).
Two principles link these concepts:
Indiscernibility of identicals: If two objects are identical, they must share all the same properties. This is widely accepted as a logical truth.
Identity of indiscernibles: If two objects share all the same properties, they must be identical. This is the more controversial principle.

Conceptions of Properties:

The strength of the IoI depends on how "property" is defined.
Pure vs. impure properties: Impure properties involve reference to a specific substance (e.g., "being the wife of Socrates"), while pure properties do not (e.g., "being a wife"). Discernibility is usually defined using only pure properties to avoid triviality.
Intrinsic vs. extrinsic properties: Intrinsic properties belong to an object independently of other objects (e.g., "having a mass of 60 kg"), while extrinsic properties depend on relations to other objects (e.g., "being an aunt"). The scope of the IoI can vary depending on whether extrinsic properties are considered.

Critiques of the IoI:

Symmetric universe: Max Black challenged the IoI with a thought experiment involving a symmetrical universe with two identical spheres. He argued that even relational properties wouldn't distinguish them, seemingly contradicting the IoI.
Quantum mechanics: The existence of indistinguishable particles in quantum mechanics also raises questions about the IoI. However, some argue that these particles are not truly identical due to their differing quantum states.

Arguments for the IoI:

Intuition: The principle aligns with our intuitive understanding of identity and individuality.
Theoretical implications: Proponents argue that the IoI has important implications for understanding various philosophical issues like the nature of space and time and the existence of individuals.

Mathematical Provability:

The IoI cannot be proven or disproven within pure mathematics because the concepts of "property" and "sharing all properties" involve metaphysical and philosophical assumptions that go beyond the scope of mathematics.

Current Status:

There is no definitive consensus on the IoI's truth or falsity. The debate continues, with ongoing discussions about the definition of "property," interpretations of thought experiments, and the implications of quantum mechanics.

The page concludes by emphasizing the importance of engaging with the arguments on both sides and considering various interpretations before reaching a conclusion about the validity of the identity of indiscernibles.