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Single Idea 17044

[filed under theme 9. Objects / F. Identity among Objects / 5. Self-Identity ]

Full Idea

Some philosophers have thought that a relation, being essentially two-termed, cannot hold between a thing and itself. This position is plainly absurd ('he is his own worst enemy'). Identity is nothing but the smallest reflexive relation.

Gist of Idea

A relation can clearly be reflexive, and identity is the smallest reflexive relation

Source

Saul A. Kripke (Naming and Necessity notes and addenda [1972], note 50)

Book Ref

Kripke,Saul: 'Naming and Necessity' [Blackwell 1980], p.109

A Reaction

I have no idea what 'smallest' means here. I can't be 'to the left of myself', so not all of my relations can be reflexive. I just don't understand what it means to say something is 'identical with itself'. You've got the thing - what have you added?

The 14 ideas from 'Naming and Necessity notes and addenda'

17059 Unicorns are vague, so no actual or possible creature could count as a unicorn [Kripke]
17058 What many people consider merely physically necessary I consider completely necessary [Kripke]
4970 What is often held to be mere physical necessity is actually metaphysical necessity [Kripke]
9221 The best known objection to counterparts is Kripke's, that Humphrey doesn't care if his counterpart wins [Kripke, by Sider]
4950 Possible worlds are useful in set theory, but can be very misleading elsewhere [Kripke]
17000 We might fix identities for small particulars, but it is utopian to hope for such things [Kripke]
16999 A vague identity may seem intransitive, and we might want to talk of 'counterparts' [Kripke]
17003 Kaplan's 'Dthat' is a useful operator for transforming a description into a rigid designation [Kripke]
4956 A description may fix a reference even when it is not true of its object [Kripke]
17032 Even if Gödel didn't produce his theorems, he's still called 'Gödel' [Kripke]
17044 A relation can clearly be reflexive, and identity is the smallest reflexive relation [Kripke]
11868 A different piece of wood could have been used for that table; constitution isn't identity [Wiggins on Kripke]
17052 The a priori analytic truths involving fixing of reference are contingent [Kripke]
4969 I regard the mind-body problem as wide open, and extremely confusing [Kripke]