The Debt Einstein Owes Leibnitz

The Identity of Indiscernibles from google AI:

The Identity of Indiscernibles (II) is a metaphysical principle stating that if two entities share all their properties, they are actually the same entity. Coined as part of Leibniz’s Law, it dictates that numerical difference (being two separate things) requires some qualitative difference (a different property). 

Key Concepts and Context:

• Definition: If for every property 
  
  F, an object x has F 
  if and only if 
  
  y has F,
   then x and y are identical (x = y).
• Leibniz's View: It argues that there cannot be two distinct things that are absolutely identical in every respect (e.g., two identical spheres).
• Counter-arguments: Critics like Max Black proposed scenarios where two identical items could exist in different locations, challenging the idea that spatial location is an intrinsic property that makes them distinct.
• Indiscernibility of Identicals (II vs. IdI): This is a closely related but distinct, less controversial principle stating that if two things are identical, they share all properties. 

Key Aspects of the Principle:

• Properties Defined: The principle often includes all properties, including spatial and temporal ones.
• Ontological Status: It is considered an ontological principle, rather than a rule of natural science.
• Alternatives: Some philosophers argue that objects can be numerically distinct even if they share all their qualities (a view often referred to as "individual haecceity" or, as in the case of Max Black's, a challenge to the principle). 

Why it Matters:

• It impacts discussions on the nature of space and time.
• It influences theories on substance, individuality, and whether two items can ever be "exactly" alike.