"If 'a' and 'b' are rigid designators, it follows that 'a = b', if true, is a necessary truth."
(Kripke, Saul A. (1972): Naming and Necessity, 3)
"The reason is, I think, that we use 'gold' as a term for a certain kind of thing. Others have discovered this kind of thing and we have heard of it. We thus as part of a community of speakers have a certain connection between ourselves and a certain kind of thing. The kind of thing is thought to have certain identifying marks. Some of these marks may not really be true of gold. We might discover that we are wrong about them."
(Kripke, Saul A. (1972): Naming and Necessity, 118-119)
"So if this consideration is right, it tends to show that such statements representing scientific discoveries about what this stuff is are not contingent truths but necessary truths in the strictest possible sense. It's not just that it's a scientific law, but of course we can imagine a world in which it would fail. Any world in which we imagine a substance which does not have these properties is a world in which we imagine a substance which is not gold ... present scientific theory is such that it is part of the nature of gold as we have it to be an element with atomic number 79."
(Kripke, Saul A. (1972): Naming and Necessity, 125)
'In sum, the correspondence between a brain state and a mental state seems to have a certain obvious element of contingency. We have seen that identity is not a relation which can hold contingently between objects. Therefore, if the identity thesis were correct, the element of contingency would not lie in the relation between the mental and physical states.'
(Kripke, Saul A. (1972): Naming and Necessity, 154)
'All the cases of the necessary a posteriori advocated in the text have the special character attributed to mathematical statements: Philosophical analysis tells us that they cannot be contingently true, so any empirical knowledge of their truth is automatically empirical knowledge that they are necessary.'
(Kripke, Saul A. (1972): Naming and Necessity, 159)