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Full Idea
It is clear from (x)□(x=x) and Leibniz's Law that identity is an 'internal' relation: (x)(y)(x=y ⊃ □x=y). What pairs (w,y) could be counterexamples? Not pairs of distinct objects, …nor an object and itself.
Gist of Idea
With the necessity of self-identity plus Leibniz's Law, identity has to be an 'internal' relation
Source
Saul A. Kripke (Naming and Necessity preface [1980], p.03)
Book Ref
Kripke,Saul: 'Naming and Necessity' [Blackwell 1980], p.3
A Reaction
I take 'internal' to mean that the necessity of identity is intrinsic to the item(s), and not imposed by some other force.
| 16981 | With the necessity of self-identity plus Leibniz's Law, identity has to be an 'internal' relation [Kripke] |
| 4942 | The indiscernibility of identicals is as self-evident as the law of contradiction [Kripke] |
| 16982 | A man has two names if the historical chains are different - even if they are the same! [Kripke] |
| 9385 | The very act of designating of an object with properties gives knowledge of a contingent truth [Kripke] |
| 4943 | Instead of talking about possible worlds, we can always say "It is possible that.." [Kripke] |
| 16983 | Probability with dice uses possible worlds, abstractions which fictionally simplify things [Kripke] |
| 16985 | Possible worlds allowed the application of set-theoretic models to modal logic [Kripke] |
| 16984 | I don't think possible worlds reductively reveal the natures of modal operators etc. [Kripke] |